Physics
A ball moves on a tabletop. The ball has initial x & y coordinates (1.8m, 3.6m). The ball moves 10m/s at 53.1° above the x-axis for 4s. What are the x & y coordinates of the ball's final position?
(25.8m, 35.6m)
Latent heat
heat absorbed or radiated during a change of phase at a constant temperature and pressure.
Friction is ______.
not a conservative force. It always acts to resist the motion of one object sliding on another. Microscopically, friction arises from many minute temporary bonds between the contact point of the two surfaces.
3 moles of an ideal gas are compressed isothermally at 20°C. During this compression, 1850 J of work is done on the gas. What is the change of entropy of the gas?
-6.31 J/K
To move between celsius and kelvin we just have to add or subtract:
273.15
Power is expressed in
Watts (W)
The Gibbs free energy of a pure substance _________ as the temperature is raised.
decreases
If we sum the two works, we always get ______.
negative quantity - the force is opposite to the motion. There must be another force pushing the object. The friction always acts perpendicular to the direction of the motion: if there is no displacement, there is no friction.
If the displacement is going in the opposite direction of the axis, the displacement would be ...
negative.
If the thermodynamic process goes towards the origin, Q & ΔT are ______
negative.
1. Isolated System
no exchange of energy or matter (no exchange with the surroundings). The universe is an isolated system, because it comprises everything.
If vector F is perpendicular to vector s, then...
no work is done (angle=90°; cos90°=0).
Explain the different processes in the cycle: Point B - C
2) Then we remove the heat reservoir so the temperature can change and the system still has energy to increase the volume. As a result volume is going through an adiabatic expansion, which means that we isolate the system.
Find the magnitude of the Resultant Vector D=C-B-A. sol.
2.24
A coastal breeze pushes your sailboat at constant velocity for 8 min. After checking your instruments, you determine you've been pushed 650 m west and 800 m south. What was the magnitude & direction of your average velocity?
2.24 m/s; 50.9° south of west
Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm3 at 30°C with a pressure of 1 × 105 Pa, calculate how many hydrogen atoms (particles) there are in the sample.
2.39 × 10^22 https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/ideal-gas-law
We used Q = mcΔT for solids & liquids, but ______.
we use a different equation for gases (not given the m = mass for gases).
The magnitude of the friction depends on the...
weight exerted on the surface, while the direction depends on the direction of the motion. The kinetic friction force is a little less than the static friction force and, therefore, the coefficient of the kinetic friction is always smaller than the coefficient of the static friction.
A gas in a cylinder held at a constant pressure 1.80×105 Pa expands from a volume of 1.2 m3 to 1.6 m3. The internal energy of the gas decreases from 4.40×105 J to 3×105 J. How much heat was transferred to the gas?
-6.8 × 10^4 J
The position-time graph for a ball on a track is shown below.(a) What is the ball's velocity at 4s? (b) At what time(s) is the ball approximately travelling at -10m/s? (c) From t = 3 to 7s, what is the sign of the acceleration?
(a) +5 m/s; (b) t=7 s; (c) negative
Fourier's Law
(aka law of heat conduction) The transfer of heat moves through matter from higher temperatures to lower temperatures in order to equalize differences.
A balloon contains 3900cm3 of a gas at a pressure of 101 kPa and a temperature of -9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.
0.0044 m3 https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/ideal-gas-law
What is a capacitor?
1. A capacitor is a device that stores electrical energy. It is a passive electronic component with two terminals (eg. could be a membrane of an axon -- membrane behaves as a capacitor, eg. axons will change if they have myelin sheeth or not - changes the capacitance). 2. A capacitor consists of two conductors separated by a vacuum or a dielectric. Examples of dielectric media are glass, air, paper, plastic, and ceramic. 3. The conductors hold equal and opposite charges on their facing surfaces and the dielectric develops an electric field.
To clarify the reactions inside the Carnot cycle we need to talk about the adiabatic processes in thermodynamics =
1. Adiabatic processes are a type of thermodynamic process that occurs without transferring heat or mass to the environment. 2. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. -> NO HEAT FLOW.
Ways to transfer energy: What is Radiation?
1. All objects give off energy in the form of radiation, as electromagnetic waves - infrared, visible light, ultraviolet - which, unlike conduction and convection, can transport heat through a vacuum. 2. Objects that are hot enough will glow - first red, then yellow, white, and blue. Objects at body temperature radiate in the infrared and can be seen with night vision binoculars.
Thermal expansion
1. As we were saying regarding thermometers, some of them exploit thermal expansion. But what is it? 2. An increase in the size of a substance (density & change in sire or volume as temperature changes) when the temperature is increased. 3. The expansion of matter, when it is heated. If the matter is in an enclosed container = it can not expand (volume is fixed), but pressure increases. 4. The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a given system as its temperature changes. The most visible example is the expansion of hot air: when air is heated, it expands and becomes less dense than the surrounding air, which then exerts an (upward) force on the hot air and makes steam and smoke rise, hot air balloons float, and so forth. 5. Thermal expansion of long continuous sections of rail tracks is the driving force for rail buckling. This phenomenon resulted in 190 train derailments during 1998-2002 in the US alone. So not many years ago. 6. Metal tracks can expand a little bit, but even the slightest expansion can become a problem when the rail tracks are fixed, since it can cause buckling. The strategy used to avoid accidents is inserting segments and hollow spaces, in order to allow a certain degree of freedom in the expansion. Also in concrete bridges they use these segments that allow the expansion of the two concrete blocks.
How can the law of universal gravitation be written using the gravity field?
1. Earth attracts any mass that is around it (gravity field). 2. The law of universal gravitation can be written considering the Earth as m1 (ME=6 x 1024 kg). The distance r between the centre of the Earth and a generic mass m2 is equal to the Earth radius (RE=6.4 x 106 m). 3. Since the gravitational constant G, the Earth mass ME and Earth radius RE are constant, where g is called gravitational acceleration and is a constant too.
What is the acceleration of a linear motion with constant velocity?
1. For this type of motion, the acceleration is always 0 (since v is constant). 2. If we plot the velocity as a function of time, the graph shows a straight line (constant velocity). If we plot the acceleration as the function of time, this will be constant and equal to zero.
What happens in this graphy?
1. Here we can see all the motion in one picture. X = 0 is the equilibrium position of the spring 2. In t = 0, the mass is pulled up to x = +A. Then, I release the mass, which is under the action of the restoring force (which pulls the mass towards the equilibrium position). The acceleration of the mass can be found by dividing the force with the mass. So we have an acceleration motion until it reaches the equilibrium point in t = ¼ T. 3. Then, the motion becomes decelerating: the force is acting in the opposite direction. The mass reaches the point with zero velocity in t = ½ T, where the spring is completely compressed. 4. Then, the restoring force will repeat the same exact curve with the same dynamic. This process can go forever. Of course, if we pull the mass up to x = +A, the compression will reach x = -A. As much as we pull, as much as we compress the spring. 5. T is 1/ω = the period is the inverse of the frequency. The longer the period, the slower the motion = the frequency is slow. If the spring moves fast, we have a high frequency but a short period. 6. The velocity is t = 0 is zero. When we release the mass, the acceleration is maximum in x = +A because the force is maximal. The elastic force decreases because it is proportional to the distance from the equilibrium point: in x = 0, the force is equal to zero. In x = 0, the mass reaches the maximum velocity because it was accelerated. Then, the velocity decreases again until we reach v = 0 in x = +A. It is a continuous balance between velocity and acceleration.
What type of lever is the elbow joint?
1. In the first configuration the arm is extended. The fulcrum is located where the elbow is. Then, there is the force exerted by the muscles to keep the book fixed in hand and the resistive force, which is exerted by the object kept balanced (it's the weight of the book). 2. This is a Class 3 lever, where the gain is always negative.
[For objects that are not spherical, there can be a slightly different effect; however, we can assume that they will occupy the space of a sphere, so they will have an equivalent radius; thus, the same formula can be applied.]
1. Larger objects will have a large sedimentation velocity 2. Large viscosity will result to a lower sedimentation velocity (eg. An iron sphere in a medium of honey will have a much lower speed than if it is in a medium of water) 3. In order to fall, the object must be heavier than the medium. What is important to remember is that if we drop an object that is heavier than water in water, it will not fall neglecting friction forces (like an object falling in air with an accelerated motion would), but rather with an acceleration equal to 0. This is because the two forces (weight and friction) will balance each other. The object will therefore fall with constant velocity(a=0). If we put a particle in a liquid, the part where it will be accelerated is extremely small, almost impossible to detect, so we would just see an object falling with constant velocity. We will see that in air, instead, there is a part where the motion is accelerated and a part where the object reaches a stable velocity.
What are the different types of motion?
1. Linear motion with constant velocity 2. Linear motion with constant acceleration 3. Motion in 2 Dimensions 4. Uniform Circular Motion
Conditions for equilibrium:
1. Material point 2. Rigid body
Formulae with DoF (degrees of freedom):
1. Molecular degrees of freedom refer to the number of ways a molecule in the gas phase may move, rotate, or vibrate in space. 2. The number of degrees of freedom of each type possessed by a molecule depends on both the number of atoms in the molecule and the geometry of the molecule. 3. The number of degrees of freedom a molecule possesses plays a role in estimating the values of various thermodynamic variables; these molecular degrees of freedom essentially describe how a molecule is able to contain and distribute its energy.
If we compare them, we obtain a graph similar to the one velocity/acceleration:
1. The elastic potential depends on the distance with respect to the equilibrium point. The elastic potential is maximum at both ends because we have the maximum distance from the equilibrium point and we have stored the maximum energy in the spring. 2. Then, the elastic potential decreases as the mass goes back to the initial position. 3. The velocity is zero at both ends, but then the mass is accelerated while it goes back to the initial position and so the maximum velocity is in x = 0 (as a consequence also the kinetic energy is maximum in that point). 4. We obtain two parabolic distributions and they depend quadratically with x. The sum of the two defines the total mechanical energy, which is constant. Again, it is a transfer between elastic potential energy and kinetic energy. Without friction (in a conservative field), this motion would go on forever.
What is an electric dipole moment?
1. The electric dipole moment is the product between the charges in the dipole and the distance between them. 2. It has the direction of the line connecting the two charges. 3. It has the versus of the negative to the positive charge.
Conditions for equilibrium of a rigid body?
1. The first condition is that the net force should be equal to 0. This is the condition related to the translation motion. It means that if we have forces that balance each other acting on a sphere at rest, then it will stay at rest in terms of motion in space. This condition is called translational equilibrium. 2. We can also add an additional condition for the equilibrium. This object (that is an extended object) does not move in space, but it can still rotate around some axes. The condition for the equilibrium is therefore that the sum of the torques (so all the forces that generate torques with respect to a generic point) must be equal to 0. This condition is necessary for the rotational equilibrium.
Ways to transfer energy: What is convection?
1. The process that transfers energy by the movement of large numbers of particles in the same direction within a liquid or gas. 2. Cycle in Nature 3. Boiling water and heating a room Particles with lower densities move up (warmer) and particles with a higher density move down (colder). Hence, this cycle is driven by the difference in density and the gravitational force. Unlike conduction, which is the heat transfer by 2 objects physically touching = usually in solid objects.
KINDS OF THERMOMETERS
1. There are several kinds of thermometers, which exploit different properties of the substances. 2. The most common ones contain a substance that increases its volume as temperature rises. 3. This concept will be clearer when we will talk about thermal expansion in a few pages. 4. Examples of this kind of thermometer are the alcohol and mercury ones. Other properties used in thermometers include electrical resistance, color, and the emission of infrared radiation.
Phase Changes
1. There is no temperature change during a phase change, thus there is no change in the kinetic energy of the particles in the material. 2. The energy released comes from the potential energy stored in the bonds between the particles. Q (energy measured in joules (J)) = mass * latent heat --> unit is J/kg = Jkg^-1 ** we can have latent heat of fusion or latent heat of vaporization.
How do we find the centre of mass?
1. We define a generic point O (which could be the origin of a Cartesian reference system) 2. We consider small elementary volumes of this object, each of which will have a generic mass mi 3. We also consider the distance of each element with respect to the generic point O, (ri) So the center of mass or center of gravity, (called B in this case, for barycenter), is the point that has a distance with respect to this point O, which is defined in the following way:
Elastic Force
1. We have a spring which has a definite length at rest (without applying forces); we attach a mass to the spring and then we consider the stretching of the spring in only one direction (unidirectional motion). We also define an axis X, which is the direction of the stretching and compression of the spring. 2. Zero is the spring at rest without stretching. 3. The spring is defined by a constant k, which depends on the properties of the spring
Looking at the position-time graph, where: 1. is the object moving forwards? 2. is the object moving backwards? 3. is the object at rest? 4. is the object's acceleration positive? 5. is the object's acceleration negative?
1. is the object moving forwards? A, C, G 2. is the object moving backwards? E 3. is the object at rest? B, D, F 4. is the object's acceleration positive? F, G 5. is the object's acceleration negative? C, D
The Carnot cycle is composed of four defined processes:
1. isothermal expansion 2. adiabatic expansion 3. isothermal compression 4. adiabatic compression.
4 types of motion
1. linear motion with constant velocity: graph 1) distance is directly proportional to time graph 2) velocity is constant over time graph 3) acceleration is equal to 0 2. linear motion with constant acceleration: graph 1) distances is quadratically proportional to time graph 2) velocity is directly proportional to time graph 3) acceleration is constant over time 3. parabolic motion: linear motion with constant acceleration on the x axis and linear motion with constant acceleration on the y axis 4. uniform circular motion: an object moves in a circular path at a velocity constant in magnitude and continuously changing in direction
In the case of a lever there are 2 forces acting:
1. the force we apply, the motion force 2. the other is the resistive force, which is used to catch an object or break something. The torques exerted by these 2 forces are acting in opposite directions (clockwise and counter-clockwise) and the sum of them must be 0.
But as the velocity of the falling particle is increasing, the friction will also increase, reaching a point where it will completely balance the weight. When we reach this condition:
1. the friction is equal to the weight, so the net force will be 0, as weight and drag force balance each other. 2. if the net force is 0, the acceleration will also be 0, so the velocity is constant. We start with a linear motion with constant acceleration; then, as soon as the friction force is equal to the weight, the two balance each other, the acceleration stops and the particle starts falling with constant velocity. In liquids the friction is proportional to v, whereas in gases the friction is proportional to v squared.
What are the SUVAT equations?
1. v = u + at 2. s = t(u+v)/2 3. s = ut + (at^2)/2 4. v^2 = u^2 + 2as (useful when you don't know the time). 5. s = vt - (at^2)/2
A football at rest is kicked by a football kicker. The ball is in contact with the kicker's foot for 0.050s, during which it experiences an acceleration a = 340 m/s2. The ball is launched at an angle of 40° above the ground (x-axis). Calculate the horizontal and vertical components of the launch velocity.
13 m/s horizontal; 10.9 m/s vertical
A container filled with 2 mol of an ideal, monoatomic gas is has a total internal energy equal to the kinetic energy of a 0.008kg bullet travelling at 700 m/s. What is the temperature of the gas in Kelvin?
78.6 K https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/internal-energy-gases
Calculate the dot product between A = (6.6 i - 3.4 j - 6.4 k ) and B = (8.6 i + 2.6 j - 5.8 k).
84.98
A Carnot engine with an efficiency of 70% is cooled by water at 10°C. What temperature must the hot reservoir be maintained at?
943.3 K
What is a fictitious force?
A fictitious force (or inertial force) is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference.
The vector A represented is by the pair of components Ax = -77 cm, Ay = 36 cm. (a) Find the magnitude of vector A. (b) Find the absolute angle of this vector.
A = 85 cm @ 154.9°
Example: Problem
A Carnot heat engine, operating between 850 K and 300 K, delivers a work output of 1200 J at every cycle. Calculate the entropy change of the heat reservoir.
Model system: ideal gas
An example of a model closed system is an ideal gas confined in a cylinder. The boundary is made by the cylinder and the piston walls. An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. Looking at the image, one quantity can be the number of particles N, while V is the volume occupied by the gas, which is by construction in this case A h, in which A is the area of the piston and h is the height of the piston. So, for example, if we push down the piston the volume will be smaller because we are reducing h, so we can control the volume of the gas. Then we also have another quantity which is the pressure of the gas p, that is the force exerted by all the molecules of the gas on the walls of the cylinder. This pressure must be equal at equilibrium to the force F divided by the area A, and so by pushing we can change not only the volume but also the pressure of the gas. As the last variable we have the temperature T of the gas, which completes the set of variables in the system. It's also important to say that the number of particles N will be a constant because we're using a closed system.
What are isobaric and isovolumetric processes?
An isobaric process (a) occurs at constant pressure; an isovolumetric one (b) at constant volume
What are the ideal gases and their formulas?
And considering the ideal gas inside this cylinder (like in the picture), we may deduce a few formulas:
What is the centre of mass?
Another definition that is important when we consider extended objects (the mass is distributed all over the object) is the definition of center of mass (CM) or center of gravity (CG).
3 mol of a monoatomic gas undergo the process shown in the image. Calculate the ΔE(int) (= internal energy).
As seen from the image (it's an isovolumetric process, because it is a straight, vertical line).
Larger entropy ususally means more disorder, because they have a higher possible number of microstates (but this is not always true).
As the temperature of a solid increases, entropy increases, because they are still fixed in one position, but the more they move = more energy = move faster. Liquid allows molecules to have more freedom, explore a higher number of microstates. From the liquid to the gas there is a big jump in entropy. Molecules can explore all microstates available. 'disorder' means that the particles have more freedom.
What is Gibbs free energy?
energy available to do work; 𝐺 = 𝑈 − 𝑇S + 𝑝V. G, H, S are state functions, T is constant.
A = (4.0 m)i + (3.0 m)j and B = (−13.0 m)i + (7.0 m)j. You add them together to produce another vector C. (a) Express this new vector C in unit-vector notation. (b) What are the magnitude and direction of C?
C = -(9 m) i + (10 m) j = 13.5 m @ 48° above the -x-axis
What is a cyclic thermodynamic process?
Cyclic process: System completes a series of steps, return to its initial state.
What are elastic collisions?
During elastic collisions, both the total linear momentum and the kinetic energy of the particle are conserved.
What are inelastic collisions?
During inelastic collisions, the total linear momentum is conserved, whereas the kinetic energy is not conserved.
1st process: isothermal expansion
During isothermal expansion temperature is constant and so there is no change in its internal energy so Ua→b = 0. This means that QH - Wa→b = 0 so Wa→b = QH
For a generic isothermal process:
For a reversible isothermal process the entropy has to be equal to Q/T. For an irreversible isothermal process, the entropy has to be bigger than Q/T.
2. Linear motion with constant acceleration
For example, something that falls (free fall), by the constant acceleration of gravity. Velocity increases linearly with time. The distance increases quadratically with time (graphically it is a parabola). Acceleration is constant. If we know acceleration and velocity, we can predict the distance traveled (formula on the right).
If we consider gravity acting on this object, for example, the effect of gravity will be the weight of this object times distance of this center of gravity, which can be calculated in this case by multiplying the weight times the distance, either in terms of total weight or of masses:
It is important because if we know the center of mass of an extended object, we can assume that all the mass is concentrated at the center of gravity.
Temperature
Kelvin (K)
What is kinetic friction?
Kinetic friction. When the box is moving, there is a kinetic friction which acts in the opposite direction with respect to the force we apply. The force necessary to keep the object sliding at constant velocity is given by. *** Kinetic friction is usually smaller than static friction.
What is Kirchhoff's 2nd law?
Kirchhoff's 2nd law: The directed sum of the potential differences (voltages = V) around any closed loop = 0. Δ𝑉2 - Δ𝑉3 - Δ𝑉4 = 0.
What is a heat engine?
Machine that converts heat into useful work (eg. a car engine). W = Q(heat) - Q(waste)
If work is done on the system, its sign is:
POSITIVE
The work may be...
POSITIVE or NEGATIVE depending on whether the work is done on or by the system.
Ideal Gas Law
PV=nRT
These thermodynamic processes can either be:
REVERSIBLE or IRREVERSIBLE: 1. A reversible process is a process whose direction can be reversed to return the system to its original state. Throughout the entire reversible process, the system is in thermodynamic equilibrium with its surroundings (e.g. the Carnot cycle) 2. an irreversible process is one in which the system and its surroundings cannot return together to exactly the states that they were in.
Kinematics Equations:
Remember: for constant velocity (a=0), the only equation you can use is v = Δx/Δt → x = xi + vt. If a is not 0, you will need to use the 4 Kinematics Equations. To use these equations, acceleration must be constant.
What are reversible and irreversible processes?
Reversible process: a process such that variables can be reversed and the system would follow the same path back, with no change in system or surroundings. The system is always very close to equilibrium. vs. Irreversible process: unidirectional process: once it happens, it cannot be reversed spontaneously.
How do you find the direction of vector products?
Right-Hand-Rule
Velocity is
The displacement an object travels per unit of time.
Speed is
The distance an object travels per unit of time.
second law of thermodynamics: the carnot cycle
The efficiency = work done (W) / how much heat is absorbed (QH) → (heat absorbed <QH> - heat released <QL>) / heat absorbed <QH> = 1 - (temperature of cold source <QH>- temperature of hot source <QL>)
Different emissivity depending on material:
The emissivity (e), which is a number between 0 and 1 that indicates how effective a radiator the object is (depends on the what the object is, eg. gold vs. copper vs. lead); a perfect radiator would have an emissivity of 1. This behavior is contained in the: Stefan-Boltzmann Law for Radiated Power, P.
Formulae with molar heat capacity
The molar heat capacity, intended as the energy needed to raise the temperature of one mole of substance by one degree, can be applied on gases as well in the following way::
What is the Carnot cycle?
The most efficient possible (idealised) heat engine, involving two isothermal processes and two adiabatic processes -- produce the most amount of net work.
Temperature: 'microscopic view'
The picture with the red and blue dots is actually an interactive, where the particles (dots) were moving. Shows the average kinetic energy (average velocity) = temperature. If the temperature increases, the average velocity (kinetic energy) of the gaseous particles increases. The kinetic energy and temperature are proportional.
The conditions for equilibrium are as follows:
The product between the motion force (Fm) and motion arm (bm) is equal to the product between the resistive force (Fr) and resistive arm (br).
What is Kirchhoff's 1st law?
The total current entering a junction = the total current leaving it For any point in an electrical circuit, the sum of currents into that point is equal to the sum of currents out of that point. I(1) = I(2) + I(3) = I(1) = the sum of the 2 currents going out. I(1) - I(2) - I(3) = 0. Kirchhoff's first law: The algebraic sum of currents in an electrical network meeting at a node = 0. Sum of currents (positive when goes into the node and negative when goes out) = 0. 2 goes in and when goes out, eg. I(1) and I(2) goes in. I(3) goes out. = I(1) + I(2) - I(3) = 0. I(1) + I(2) = I(3).
Quiz: The second law of thermodynamics states that
The total entropy of a system plus its surroundings may never decrease.
Vector math you need:
To pay attention to direction.
What is the electric field between parallel plates?
Total charge / Area = Surface Charge density. The larger the total charge = larger density. Why are the charges uniformly distributed on the plates? Because they would repel eachother -- spontaneous uniform distribution, because they always repel eachother.
You'll need to do vector math without using grids/squares:
Vectors have magnitude (length), direction (angle θ) and components (legs).
Which of the following quantities are constant during projectile motion?
Vertical acceleration & horizontal velocity
What is an electric field?
a region around a charged object where the object's electric force is exerted on other charged objects
Dimensional analysis
can not subtract or add, but multiply or divide between separate units.
Luminous intensity
candela (cd)
Thermodynamic processes take place thanks to...
changes in the thermodynamic state variables (pressure, volume, temperature, mass and internal energy); n closed systems we only have changes within the first three variables (as, logically, matter can't be exchanged with the surroundings).
The velocity for a fixed arch is constant in magnitude but:
changing in direction, so there is an acceleration, called centripetal acceleration (centripetal because the acceleration is towards the center -- ):
If there are 2 isolated objects, so no other forces are acting on these 2 objects, for the linear acceleration there's the:
conservation of linear momentum. The same applies in the case of rotational motion: if there are 2 isolated objects and the net torque of the system is equal to 0, then the angular momentum will be conserved (angular momentum will be constant).
Gravitational force is a ______.
conservative force.
What is Q in an isobaric process?
constant pressure (use Cp)
What is Q in an isothermal process?
constant temperature, Q = W §
Weight is always...
constant,
Instead, if we have a sphere that is falling in a liquid medium, this friction force ______.
depends on the velocity. This is also known as drag force.
In the previous case (solid-solid interface) the drag force _____.
didn't depend on the velocity. 1. It was the case of an object sliding on a solid surface (1), and moving in one direction; in that case the force just depends on the normal force (so on the mass and the gravitational acceleration, but not on the velocity). 2. As we said, if we have an inclined plane (2), the normal force is the projection of the weight along the parallel line (the one containing N).
Some measurements also have ______.
direction.
As we previously said, temperature is
directly proportional to the average kinetic energy. Kinetic energy is defined as follows:
How do you calculate an electric field of a dipole (N/C)?
eg. magnet
Another type of force is the _______.
elastic force, which is for example the one exerted by a spring (also considered as a conservative force).
In thermodynamics, entropy measures how randomly a system's ________ is spread out.
energy
CAD trauma is characterized by various signs and symptoms, including these radiographic features:
fractures, dislocations, kyphotic angulation, reduced and reversed sagittal cervical curves, and soft-tissues injuries. In addition, vertigo, neck and shoulder pain, upper extremity paresthesia, tinnitus, impaired cognitive function, and visual disturbances have been reported after CAD traumas.
In the case of a rigid body fixed to a point, which is called _____ we have a _______.
fulcrum (or pivot point), we have a necessary and sufficient condition that states that the sum of the torques need to be 0.
A thermometer measures
its own temperature. It is through the concepts of thermal equilibrium that we can say that a thermometer measures the temperature of something else. Because when it reaches thermal equilibrium with the object that we want to measure, they will have the same temperature.
A body is in motion when...
its position, with respect to a fixed reference system (we need a frame of reference. Normally a cartesian x,y,z coordinate system. This is where the "observer" is positioned), changes with time.
The amount of energy radiated by an object due to its temperature is proportional to
its surface area and to the fourth (!) power of its temperature.
Work is expressed in ______.
joules (J=N m=(kg m2)/s2).
Mass
kilogram (kg)
Heat absorbed or released as the result of a phase change is called
latent heat.
When we take measurements, you always get the ______.
magnitude (size of measurement).
If we instead plot how the velocity changes in time, we can define the ________, which is the change of velocity over a certain time interval.
mean acceleration; can be calculated for each interval.
Amount of substance
mole (mol)
Ideal Gas Law =
n = number of moles N = number of particles
If we have a monoatomic gas, there is
only movement of translation in x, y and z, so f=3.
As we compress the spring, the force is acting in the _____.
opposite direction. The spring starts oscillating.
All thermodynamic processes that occur with an ideal gas can be expressed by a generic equation:
p * Vk = constant
The internal energy of an ideal gas can be defined and used for describing...
particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment. It describes molecular kinetic energies at a particular temperature. (Few particles have zero or very high energy, most particles have around average).
What is a thermodynamic system?
portion of the universe that we are interested in observing. We define something as a system, everything else is the surroundings and is the universe. 3 different types of systems: 1. Isolated System 2. Closed System 3. Open System
Position-time graphs shown an object's ______ in the y-axis vs. ______ in the x-axis.
position; time.
Charges exist in ____.
positive and negative nature.
Speed is always ...
positive or 0, cannot be negative.
You drop a ball from rest from a 100m-tall building. Calculate the ball's velocity right before hitting the gorund.
positive velocity does not make sense here, because the ball is moving downwards.
If the thermodynamic process goes away from origin, Q & ΔT are ______
positive.
Charges of the same sign ______ eachother.
repel
Distance is
scalar; he length of a path between two points
Time
second (s)
A thermodynamic process always sees a change in the thermodynamic variables, all starting from an ____ and concluding in ______.
starting from an initial state (A), concluding in a final state (B).
Dissipative forces are...
the ones in which the work done to go from a point to another point depends on the path - it means that if we go from a position (A) to another (B) and then we go back to the initial position, the work is not zero and therefore the variation of the kinetic energy is not zero.
Average Kinetic Energy depends ONLY on the __________ of the gas, not the _________ of gas.
temperature; TYPE
This torque tends to allign the object parallel to ____.
the E (and this is minimizing the potential energy of the system).
The expansion of a gas is a consequence from
the absorption of heat.
What is drift velocity?
the average velocity of an electron in the direction of current
Coulomb's law is
the corrispective of the gravitational law in the electromagnetic field.
The linear velocity (or tangential velocity) would be:
the distance traveled along the arc in a Δt. Δs is the radius times the angle variation (in fact, if we have to consider the distance around the entire circle, Δθ would be 2𝜋, and 2𝜋r equals to the circumference)
Another lever that can be found in the human body is: ______.
the elbow joint.
The amount of energy radiated also depends on
the emissivity (e), which is a number between 0 and 1 that indicates how effective a radiator the object is (depends on the what the object is, eg. gold vs. copper vs. lead); a perfect radiator would have an emissivity of 1. This behavior is contained in the: Stefan-Boltzmann Law for Radiated Power, P.
What is an electric force?
the force of attraction or repulsion between electrically charged objects
When we consider biomechanics it means that we want to understand which are:
the forces (in general, the forces act in three dimensions, but we can assume that in most cases the forces are acting on a plane), the torques and the conditions of equilibrium that are involved in a human body (or a part of it).
Kinematics is the branch of physics that describes:
the motion of bodies, and it is part of the mechanics together with the statics and the dynamics (investigating the mechanisms and the forces ruling the motion under equilibrium or non equilibrium).
For a polyatomic gas we can take into account
the movement of translation and the movement of rotation along three axes, so f=6.
If we have a diatomic gas we can take into account
the movement of translation and the movement of rotation along two axes, so f=5.
Acceleration can be described by...
the ratio between the variation in velocity and the variation of time. If a=∆v/∆t=0, then ∆v=0, therefore v is constant. This is how the first Newton's law can be derived from the second.
The smaller the distance between the particles =
the smaller the dipole and the smaller the electric field.
The total work of this cycle should =
the sum of all work done in each stage.
velocity =
vector
Displacement is
vector; the shortest path taken between 2 points.
Measurements with direction are _______
vectors; eg. It would make sense to ask which direction force would go.
The work can be substituted as the product between the force and the displacement; displacement over time interval is the:
velocity, so the power can also be represented as the product between force and velocity.
The gravitational force was first described by Isaac Newton in the 17th century. In 1687 he elaborated the law of universal gravitation:
where a force F of attraction acts between two different masses m1 and m2, located at a distance r. F is directly proportional to the product of m1 and m2, and it is inversely proportional to the squared distance between the two masses. G is the gravitational constant.
A theoretical heat engine in space could operate between the Sun's 5500°C surface and the -270.3°C temperature of intergalactic space. What would be its maximum theoretical efficiency?
99.95%
Friction is a _______ force.
dissipative force; it always acts in the opposite direction of the force: if we have an object going from A to B, the friction force would be from B to A. As a consequence, the work done by the friction force (force x displacement) is always negative.
Elastic force is also conservative and we can define an:
elastic potential; because it is an energy, it should be equal to force (F) x displacement (S). We previously said that the F = kx. As a consequence, Uelast = F x s = (kx) x (x) The ½ comes from the fact that the force is not constant as we pull but it changes with the distance.
The FIRST LAW OF THERMODYNAMICS, also known as the law of conservation of energy states that:
energy can't be created nor destroyed in an isolated system (=it is constant); energy can only be transferred or changed from one form to another. Basically it is just the law of conservation of energy applied to thermal systems.
Thermodynamics relies on...
equilibrium states, because every time we want to do a measurement the system shall start from an equilibrium position, so all the variables are measured in an equilibrium state, it's hard to get information when the system is changing.
The Carnot cycle is an ideal process, which means:
everything is reversible and quasistatic, so we can calculate the efficiency of the engine, which usually is the amount of work that can be done by giving a certain amount of heat, and it can be expressed in this way. e = (Th - Tl) / Th Th is the highest temperature, when we have isothermal expansion. Tl is the temperature of the isothermal compression.
the ISOLATED system can't
exchange any form of energy or matter with the surroundings.
the OPEN system can
exchange energy (under any form) and matter with the surroundings.
the CLOSED system can
exchange energy with the surroundings but not matter
3. Open System
exchange of energy & matter (more seen in Chemistry).
2. Closed System
exchange of energy (lossing or gaining energy from the surroundings), but not matter (no exchange of matter with the surroundings).
Let's say a skater is rotating with her arms stretched. When the arms are closed the spinning takes place ____.
faster since the angular velocity increases. This is because, considering the conservation of angular momentum, the two momenta (initial and final) must be equal.
What is entropy?
first law of thermodynamics formula: △U=Q-W (change in internal energy = heat - work) Q = △U + W (heat = change in internal energy + work)
Therefore, motion is always ______.
relative. If we are on a train, our reference system is the train. If we are not walking, we are not moving relatively to the train (our frame of reference). A person outside of the train, even if he's not moving, he's moving from our point of view, considering the train as the frame of reference.
All motion is _______
relative; the laws of physics are the same in any inertial frame of motion. Motion is relative with respect to a particular system.
We can also have reversible processes, in which the variables can be reversed with no modification in the system, so it would follow the same path back. If a system performed a quasistatic process, even if we go very slowly this doesn't mean that the process will be:
reversible. For example, if we go from liquid to gas, we can't go back even if we manage to do the process in a slowly quasistatic way, so a quasistatic process is not necessarily reversible. We can also have irreversible processes, which are unidirectional, so they cannot be reversed without changing the surroundings.
In diatomic gases, as well as translational, they also have...
rotational kinetic energy as the molecules can rotate in 2 axes (x & y). This means for each diatomic molecule, the 3 translation directions contribute 1/2 KT each per molecule and the 2 rotational axes contribute 1/2KT each. 5 degrees in total Therefore there is 5/2KT. U = 5/2nRT
Beginning from a signpost, you run 60m to the right, then 60m back. The entire trip takes 24 seconds. What is your speed and velocity for the whole trip?
s=5 m/s v=0 m/s
The work done by a force F, along the displacement, is the _____ product...
scalar product of the force F and the displacement S (F is a vector, represented by the blue arrow). ***α is the angle between the two vectors F and S.
Measurements without direction are _______
scalars; eg. It would not make sense to ask, which direction does mass/time/temperature go.
In liquids v is known as:
sedimentation velocity when we have the drag force equal to the weight. In a liquid medium there is Archimedes' force (the force exerted on an object that is in a liquid; because the pressure of the liquid is higher at a lower density, it's an upward force, given by the mass of liquid in a volume that is equivalent to the one occupied by this object). The weight in a liquid is therefore not just mg but it's (m-m')g, where m' is the equivalent mass occupied by the liquid. It's a reduced gravity that relates to the density, being equal to the density of the particle(p)minus the density of the liquid(ρ'). 1. If the two have the same density, the object will stay there without falling. 2. If the density of the particle is higher, then the object is falling through the liquid 3. If the density of the particle is lower than the one of the liquid, then the object is rising up
Example of the Centre of Mass:
Example: we consider a bar connected to two masses m1 and m2(in the picture above); the weight of the bar is negligible, so if we assume that the two masses are connected by an invisibly thin wire, we can calculate the center of mass of this bar. If we use the previous definition, the center of mass will be given by the sum of mass 1 times its distance from the center of mass plus m2 times its distance from the center of mass; all of it is divided by the total mass, which the sum of the two masses (m1+m2). If we put the origin of the reference system at the center of mass, we can see that the distance r1 is negative (so -r1); we can also see that the distance between the origin of the system and the center of mass will be 0 (they are the same point). In this way we can know where the center of mass is located along this bar: it is at the distance where r1 divided by r2 is equal to m2 divided by m1, so the larger is m2, the closer is the center of mass with respect to this point. We know that the center of mass will be shifted towards the heavier weight in the object.
You have a block of ice at 0°C. Heat is added to the ice, causing an increase in entropy of 120J/K. How much ice melts into water in this process?
0.098 kg
Solution:
0.24kg
There are 2 ways to connect capacitors:
1. Capacitors in series 2. Capacitors in parallel
What are levers?
1. Forces acting on a rigid body can generate some torques inducing rotation in that specific body. 2. Therefore, we need to make sure that the net force acting on the body is equal to 0 as well as the sum of all torques.
What is the first law of thermodynamics?
1. The First Law of Thermodynamics states that energy is always conserved, it cannot be created or destroyed. 2. In essence, energy can be converted from one form into another. 3. The First Law of Thermodynamics is a just the law of conservation of energy applied to thermal systems.
Why is Gibbs energy so important in biology?
1. The Gibbs free energy is of the greatest importance in chemistry and in the field of bioenergetics, the study of energy utilization in biology. 2. Most processes in chemistry and biology occur at constant temperature and pressure, and so to decide whether they are spontaneous and able to produce non-expansion work we need to consider the Gibbs free energy.
What is the most stable phase and how does it correspond to the amount of Gibbs free energy?
1. The most stable phase corresponds to the lowest Gibbs free energy; thus, the solid is most stable at low temperatures, then the liquid, and finally the gas. 2. If the gas line falls more steeply, it might intersect the solid line before the liquid line does, in which case the liquid is never the stable phase and the solid sublimes directly to a vapor phase.
Ways to transfer energy: What is conduction?
1. The process that moves energy from one object to another when they are touching physically. 2. Conductors: materials that transfer energy easily. 3. Insulators: materials that do not transfer energy easily.
What are levers in the human body?
1. There are various muscles in the neck which are responsible for providing a force that raises and keeps the human head in an horizontal position. 3. So, the whole human head acts as a lever. 4. The pivot point is the fulcrum, the point around which the head rotates. 5. Then, Fm (motion force) is the force exerted by neck muscles to keep the head straight and Fr (resistive force) is the weight of the head. 6. We assume that the point of application of the gravitational force is at the center of mass of the head. 7. Since the fulcrum is located in the middle of the two forces, this is a Class 1 lever The mechanical gain < 1 because bm is smaller than br.
Thermometers and temperature scales:
1. Thermometers measure temperature according to well defined scales of measurement. 2. The three most common temperature scales are Fahrenheit, Celsius, and Kelvin. 3. Temperature scales are created by identifying two reproducible temperatures. 4. The freezing and boiling temperatures of water at standard atmospheric pressure are commonly used.
4 main types of forces exist:
These first two act macroscopically: 1. gravitational force 2. electromagnetic force: related to interaction between particles; it is always greater than the gravitational force; it is the main force studied in chemistry. It may come as friction force These two act at nuclear level: 1. strong force: holds together the protons and neutrons of an atomic nucleus 2. weak force: governs the decay of a nuclear atom
What are heat engines?
a machine that transforms heat into mechanical energy, or work. 1. The high temperature reservoir transfers an amount of heat QH to the engine, where part of it is transformed into work W and the rest, QL, is exhausted to the lower temperature reservoir. ***Note that all three of these quantities are positive. 2. This is the base of some heat engines, it means that for example we can use water by heating it in order to heat up a steam that will move a piston, releasing energy by doing this work. 2. Then the water will link to a condenser, where the gas will do some work, always releasing energy. 3. These types of heat engines are always mechanisms that operate between a high temperature and a lower temperature, so we have two systems where the temperature is constant. 4. One at a higher temperature from which the system gets heat and the other one at a lower temperature in which this system releases some heat, so the difference between these two energies gives the total amount of work.
An inertial frame of reference is one in which...
a motion of a particle not subject to forces, is in a straight line at constant speed (the particle in an inertial frame of reference is fixed or it is moving with linear motion with constant velocity).
The Carnot cycle is an idealized model of a thermodynamic system for a heat engine which is a perfect example of:
a reversible thermodynamic process.
An object (a molecule) with an electric dipole moment, when placed in an external electric field is subject to:
a torque; effect of the torque is to rotate.
A force field is...
a vector field that describes a force acting on a particle at various positions in space.
How much heat energy is needed to increase the temperature of 5 mol of an ideal diatomic gas by from 273K to 300K if the a) pressure is held constant; b) the volume is held constant?
a) 3928 J b) 2806 J https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/heat-capacities
PROBLEM: A sled of 20 kg of mass, initially at rest, slides on a plane inclined 30° compared to the ground. Considering that the speed of the sled at the end of the inclined plane is 10 m/s and the coefficient of kinetic friction is 0.1, calculate: a) the work done by the weight force b) the initial height from the horizontal plane c) the work done by the friction force
a) the work done by the weight force = 81N b) the initial height from the horizontal plane = 6.17m
If we pull the mass and then we release the mass, it will _____.
accelerate in the direction of the elastic force. The force can be considered as the product between mass and acceleration: ma(x) = -kx
Work done by a gas in adiabatic expansion is the same work done on a gas during (= heat absorbed and heat released = equal and opposite to eachother = how much heat is absorbed - how much heat is released is the same):
adiabatic compression.
But as the velocity of the falling particle is increasing, the friction will...
also increase, reaching a point where it will completely balance the weight. When we reach this condition,
If we substitute this acceleration in the previous equation, we get the ______.
angular frequency
What is work (w)?
any energy transfer that isn't heat. Work is done when a force acts upon a body and moves it. Force times distance of displacement. W = F x s W = p*(V2 - V1)
A non-inertial frame of reference is one which is...
accelerating or rotating relative to an inertial frame of reference. 1. Let's consider one person A still on a platform, looking at person B walking on a train (towards its locomotive), which is moving too. Person A represents a fixed frame and, from their point of view, person B is walking on the train with relative velocity (vR). Also, for person A, the train itself has velocity vT, since the train is the translating frame reference. 2. From their perspective, person B feels like it is not the train to move, but it is the platform with person A, and the platform seems to move with absolute velocity v0=vR+vT.
If I pull the mass in the direction of positive x, there is a force which ______.
acts in the opposite direction because it is trying to restore the initial equilibrium length. The more you pull a spring, the stronger is the force = the longer is the distance from the equilibrium point, the stronger is the elastic force. Indeed, the force is: F = -kx
If vector F is parallel to vector s, then the work is...
the greatest that could be done (angle=180°; cos180°=1; 1=greatest value of cosine).
A student throws a set of keys vertically upward to her sorority sister who is in a window 14.00 m above. The second student catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (+sol part a)
(a) v0y=16.7 m/s
A rock is thrown vertically upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. The rock doesn't hit the building on its way back down and lands in the street below. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street? (+sol part a)
(a) vy = 36.6 m/s downward;
ideal gas vs. real gas
*Ideal gas* is a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory. *Real gas* does not behave completely according to the assumptions of the kinetic-molecular theory.
How much heat must be removed from 0.7 kg of water at 23°C to cool it to 0°C and completely freeze it?
- 3.01 × 105 J https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/changes-in-phase-latent-heat
A gas with an initial volume of 0.2 m3 is heated at constant volume, and the pressure increases from 2×10^5 Pa to 5×10^5. Then, it compresses at constant pressure until it reaches a final volume of 0.12 m3. Draw the two processes in the PV diagram below and find the total work done by the gas.
- 4 × 10^4 J
An ideal gas is taken through the four processes shown below. The changes in internal energy for three of these processes are as follows:ΔEAB = +82 J; ΔEBC = +15 J; ΔEDA = -56 J. Find the change in internal energy for the process from C to D.
- 41 J
A ball of lead at a temperature of 333K has a volume of 50.000cm3. By how much does the ball shrink when you decrease the temperature to 303K? The coefficient of linear expansion for lead is 2.9x10-5.
-0.13cm3
Ideal Gas = A simplified, "perfect" gas that satisfies the following conditions:
1) The gas has a low density, i.e. particles very spread out (low pressure, high temperature). 2) There are no forces between the gas particles. 3) Particles have zero size, so we can treat them as points. 4) Particles move in straight lines and collide elastically (energy is conserved).
Explain the different processes in the cycle: Point A - B
1) This process is explained in the picture above, we start from a point A where the system will expand, so the piston of the cylinder is going up and volume will increase, while pressure is going down by keeping the temperature constant, so we have an isothermal expansion.
Charges of the opposite sign ______ eachother.
attract
What is a normal force?
1, If we have a solid surface and a mass on top of it, the mass is in equilibrium (not moving). 2. There is the gravitational force which acts on the mass, but it doesn't move in a vertical direction because there is the solid boundary. 3. The net force should be zero because otherwise we should have some motion: we have the gravitational force, but also a second force which acts in the opposite direction = Normal force or reaction of the surface. 4. It is the force exerted by the solid boundary on the mass. Again, it is the third principle: if the mass is exerting a force on the boundary due to the weight, the solid surface exerts a force with equal magnitude but in the opposite direction with respect to the mass.
3. Motion in 2 Dimensions Essentially, we have a combination of two motions:
1. Along the x-axis, there is no acceleration and so the motion is linear with constant velocity. This constant velocity will be equal to the horizontal component of v0, the v0x. 2. Along the y-axis, there is linear motion with constant acceleration (a negative acceleration). Overall, this is parabolic motion.
What is the adiabatic process?
1. An adiabatic process is one where there is no heat flow into or out of the system. 2. In this type of process, we thermally insulate the system, so we put something that isolates the cylinder with the surroundings, as a result there will be no exchange of heat even if the gas temperature will change and this is called adiabatic process. 3. In this mechanism if we increase volume, pressure will go down but it'll go down more than in the case of an isothermal process.
A coordinate system needs:
1. An axis - cartesian plane 2. An origin - the starting point 3. A scale - representing the units of measurement 4. A direction - the direction a point is going on the axis
If we look for a velocity over a time interval, we can define an _____ for this interval.
average (mean) velocity; the mean velocity can change when we look at another time interval.
What is the isothermal process?
1. An isothermal process is one where the temperature does not change. 2. We can have different processes depending on variables that remain constant or change. 3. The first process that we consider is called isothermal, that is a process where the temperature is fixed. 4. We can do that by basically placing this cylinder, with a gas and a piston, in a heat reservoir so in a place where the temperature of the gas will be constant. In this way the temperature of the gas will never change, which means that in order to keep temperature constant we need a continuous exchange of heat. 5. For this case we can plot the process as pressure p over volume V, so p V = cost because in the ideal gas law the number of moles n is constant, R is a constant and temperature T is constant. 6. So, pressure times volume is constant, it means that if we increase volume, pressure goes down and vice-versa, so this is the inverse relationship which characterizes isothermal processes.
3. Motion in 2 Dimensions
1. Another case is a motion in 2 dimensions, for example, say we throw an object from the origin (O), it follows a curve-like trajectory with an initial speed v0 with a horizontal and a vertical component (v0x and v0y respectively). 2. Since it is two dimensional, we can define a reference system of x,y plane (x is the horizontal direction and y is the vertical direction). Then we know that all along this motion, there will be an action of something on the object that will force it to decelerate (this can be gravitational acceleration).
What is a system boundary?
1. As we can see, a system is the sample taken into consideration for the analysis; this system is outlined within limits, also called "system boundary". 2. Outside this boundary we have the surroundings, with which the system may or may not be in relation with; finally, beyond the surroundings, we have the universe, defined as the totality of matter and energy.
Now it is important to consider the mass of the person, the gravitational acceleration and the other parameters. The projected area is important because the larger it is, the stronger is the interaction with the air molecules during the fall, so the smaller will be the terminal velocity. Indeed, when the parachute is open, its effect is to increase dramatically the projected area, in order to decrease the terminal velocity. Normally, the terminal speed of the skydiver belly-to-earth (facing down) in a free fall position is about 54m/s, (so around 200km/h). With a parachute, since the area covered by the parachute is around 20m and the projected area is around 400m2, the terminal velocity can drop to around 5-6m/s, a velocity that allows the skydiver to reach the ground without dying. To sum up, it is important to remember that:
1. At first there is no friction, so we have a linear motion with constant acceleration in which velocity increases 2. Then as the velocity increases, friction forces will also increase 3. At some point the velocity that is critical will be reached (terminal velocity for gases, sedimentation velocity for liquids). When we consider solid objects sliding on one another the friction is independent from the velocity, so this condition will never be reached and the motion will always be accelerated.
How does a combination of all these processes (isothermal and adiabatic, isobaric and isovolumetric) form the thermodynamic cycle?
1. At the end we can also combined many of these processes, so as in the picture, we can create a path, first we start from the point A and then we move following an isothermal process to a point B, but we keep changing all the variables in order to switch also between different processes such as the isovolumetric and isobaric mechanism; by doing this at the end we can also manage to go back to the initial point. 2. When we start from a state and then we return to this state after making a series of changes, then we call this a thermodynamic cycle. 3. To create this cycle of course we need to do something on the system, so for example first in the isothermal process we need to put the container in contact with a thermal reservoir, then we need to maintain the pressure constant (isobaric) and also the volume has to be maintained constant by forcing the piston to stay in a certain position. 4. So we're definitely doing something on the system in order to maintain this cycle, but also on the other hand we can use this to do some work.
Thermometers and temperature scales
1. Because many physical properties depend on temperature, the variety of thermometers is remarkable. 2. For example, volume increases with temperature for most substances. This property is the basis for the common alcohol thermometer and the original mercury thermometers. 3. Other properties used to measure temperature include electrical resistance, color, and the emission of infrared radiation.
Specific heat
1. But the ability of an object to absorb heat depends also on its quantity. The heat capacity of an object depends on its mass. A quantity which is proper only of the material is the specific heat. It is essentially the heat capacity divided by the mass of the object. 2. So, starting from the previous definition it is possible to define heat capacity as the product of specific heat and mass of a certain object. 3. C= c m. 4. On the other hand, specific heat is specific for the material. 5. Specific heat also depends on pressure. That is why the following table shows values measured at atmospheric pressure. 6. Water's value is quite high. It means that for a given heat there will be a lower increment of temperature. Or that if we want to raise the temperature of our system, we need to provide a lot of heat. This has some important biological consequences, also in the human body, composed in great proportion of water.
What are the classes of levers?
1. Class 1 Levers 2. Class 2 Levers 3. Class 3 Levers
Types of levers:
1. Class 1 levers 2. Class 2 levers 3. Class 3 levers
Classes of Levers: 1. Class 1 Levers 2. Class 2 Levers 3. Class 3 Levers What are Class 1 Levers?
1. Class 1 levers: the fulcrum is in between the motion arm and the resistive arm. 2. In such cases the mechanical gain (G) can be greater/lesser than 1 depending on the ratio between the arms. 3. An example of this is a plier.
Classes of Levers: 1. Class 1 Levers 2. Class 2 Levers 3. Class 3 Levers What are Class 2 Levers?
1. Class 2 levers: by construction they have a resistive arm which is smaller than the motion arm. 2. Hence, the mechanical gain (G) is destined to be greater than 1. 3. An example of this is a nutcracker.
Classes of Levers: 1. Class 1 Levers 2. Class 2 Levers 3. Class 3 Levers What are Class 3 Levers?
1. Class 3 levers: by construction they have a resistive arm which is bigger than the motion arm. 2. Hence, the mechanical gain is destined to be smaller than 1. 3. An example of this is a tweezer. Whenever a force is applied at the center of the tweezer that force is magnified for more precision.
What are the different mechanisms of heat transfer?
1. Conduction: transfer of energy from one place to another by contact. 2. Convection: heat transfer in a fluid in which hot fluid rises and cold fluid sinks, setting up a cycle (convection is a faster way to transfer heat from the bottom of the pan to the top of the pan). 3. Radiation: The transfer of energy by electromagnetic waves.
How does the cycle of convection work?
1. Cooler denser air sinks and flows under the warmer air (less dense) to push the warmer air upward. 2. As the warmer air rises it cools and becomes denser. 3. This cooling and movement of warmer air upward creates the cycle of convection.
Let's look at the forces acting on the hip joint, specifically the force acting on the point where the femur is connected to the acetabulum, when a person is standing in equilibrium on one leg. We know the following information (some of them, such as the different angles, are known from the anatomy):
1. F = traction force generated by the adductor muscles. Its module it's unknown and it's what we are going to find. 2. Wf = weight of the leg (which is 1/7th the weight of the body). It's acting on the center of mass of the leg. 3. N = reaction of the floor acting on the leg. It's acting on the foot. 4. R = force acting on the head of the femur by the entire body. It is unknown, and it's what we are going to find.
For R and F, we don't know both their vertical and horizontal components.
1. First of all we need to consider the forces acting on the horizontal plane; these have to respect the condition of equilibrium. 2. Then we need to do the same thing for the vertical plane. 3. Then we calculate the sum of the torques in respect to the point that we are considering. It's recommended to choose the point where most of the forces will give 0 torque (in this case is the head of the femur). Pay attention to the direction in which the torque is applied (clockwise = "+"; counter-clockwise = "-"). Also in this case condition of equilibrium have to be respected.
Example of linear momentum:
1. For example, if one billiard ball A (with mass m1 and constant velocity v1) hits a second billiard ball B (with mass m2) initially at rest (v2=0), after the collision ball 2. A stops (v1'=0) and ball B begins to roll with constant velocity v2' (we neglect friction). 3. The system's linear momentum before collision is the following: p(tot)=m1v1+m2v2 4. Since ball B is initially at rest, before collision p(tot)=m1v1 5. p' (tot) = m1v1' + m2v2'---> m2v2' (v1' is 0, ball 1 stops after interaction) 6. The system's linear momentum after collision is the following: p(tot)'=m1v1'+m2v2' 7. Since ball A stops its motion after the collision, p(tot)'=m2v2' 8. According to the law of conservation of linear momentum, ptot=ptot' 9. So, m1v1=m2v2'. Therefore, v2'=(m1v1)/m2. If m1=m2, then v1=v2'.
What is Mechanical Gain?
1. From the equation for the conditions for equilibrium equation we can also define a new term named "Mechanical Gain". 2. The mechanical gain is essentially the ratio between resistive force and mechanical force. 3. This ratio is also equal to the opposite ratio of the motion arm (the arm that undergoes motion) and the resistive arm.
In the picture above we can clearly distinguish four different steps in the cycle, now let's describe them in detail:
1. ISOTHERMAL EXPANSION, the gas is subjected to a heat reservoir -> it expands its volume and lowers its pressure (=the system absorbs heat and does work). 2. ADIABATIC EXPANSION, (Q=0, so no heat exchange with the surroundings) the gas still has some residual energy left to push the pistol up -> it expands its volume a little while the pressure and temperature lower their value. We do work on the system. 3. ISOTHERMAL COMPRESSION, the gas is put in contact with a cold reservoir and the lower temperature reached in the adiabatic expansion now remains constant -> the volume lowers while the pressure increases. We are giving heat to the surroundings. 4. ADIABATIC COMPRESSION, (Q=0, so no heat exchange with the surroundings) the gas restores its initial condition (at the beginning of the cycle) and reaches equilibrium -> the volume decreases while pressure and temperature increase.
The unit of measurement of the torque is equal to the unit of force multiplied by the unit of a distance. A force times a length normally gives a joule, but in this case we are not considering the energy, we just express it as the product of newtons and meters. If a force F is acting on the object, it will induce a rotation. By definition:
1. If a force causes a counter-clockwise rotation, the torque (t) is a positive term. 2. If a force causes a clockwise rotation, the torque (t) is a negative term.
The magnitude is given by the lever arm times the magnitude of the force. For a torque it is important the force but also the point O. We always say the torque of the force with respect to the point O; if we change point O we will have a different force(torque).
1. If point O lies on the line of action, then the torque is equal to 0. This is because the leaver arm (distance between the point and the line of action) is 0, so the whole product(force times leaver arm) will be equal to 0. In this case the vector r is parallel to the vector F. The vector product of two vectors that are parallel is always 0, so we don't have rotation. 2. Torque is positive when the force is applied to a point of the object that is at some distance with another reference point.
Conservation of mechanical energy: Example (sleigh)
1. If we assume there is no friction and the only force acting is gravity, which is a conservative force, we can find the height H from which the sleigh starts with initial velocity equals to zero and with final velocity equals to 10 m/s. 2. We use the conservation of mechanical energy: the mechanical energy EM at the starting point is equal to the mechanical energy EM at the final point: (1/2)*m*v^2 + mgh = (1/2)*m*v(f)^2 + m*g*0 3. The mechanical energy at the starting point is the kinetic energy + potential energy: With Vo = zero -- (1/2)*m*v(0)^2 + mgh 4. The mechanical energy at the end of the plane is: (1/2)*m*v(f)^2 + mgh VF is the velocity at the end of the plane and H = 0 (because we reached the ground). 5. VF is the velocity at the end of the plane and H = 0 (because we reached the ground). Writing all the equation together, we get: mgh = (1/2)*m*v(f)^2 Because: 1. Initial mechanical energy = kinetic energy + potential energy. BUT kinetic energy is equal to zero (because Vo = zero). 2. Final mechanical energy = kinetic energy + potential energy. BUT potential energy is equal to zero (because we reached the ground). In this case we have a complete transfer between the potential energy at the beginning and the kinetic energy at the end. Then, we simplify the mass + we consider Vf = 10 m/s and we get: h = (v(f))^2/(2g) = 5.1m By using the mechanical energy, we are not focusing on the particular motion, but just on the initial and final state. This sleigh could have started with an initial velocity different from zero: in this case, the initial kinetic energy would have been different from zero. This is possible if we consider only the action of conservative forces like gravity.
Why does the equation change for the second configuration of the arm (see the image)?
1. In the second configuration the arm is flexed. Therefore, the distance between the fulcrum and muscles is smaller hence bm decreases; br does not change in this case because the distance between the book and the hand remains the same. 2. Since bm is different in the two images (bm(a) ≠ bm(b)), we need to draft a different equation for both the cases. 3. Since, the ratio of the equation is higher than one, we can deduce that the amount of power required to keep a book balanced is higher when the arm is straight than when it is flexed. That's because as soon as bm decreases, Fm decreases simultaneously.
What is an example of motion of a solid object through a gas at a high speed?
1. In this case there is a person jumping first without a parachute; at the beginning there is a small velocity, then as he falls the velocity is increasing. 2. At first the friction force is negligible, but at some point it becomes important.
Image representing a thermodynamic system:
1. In this image we can see a way to represent a thermodynamic system. 2. We have many variables but let's assume that we have only three variables changing (pressure, volume and temperature) and then we plot these quantities in a three-dimensional graph. 3. On one axis we have pressure, and on the others two we have temperature and volume. 4. The state A is characterized by some values of the three variables, it's the initial state, if we do something such as add heat at the system, there will be another equilibrium state at point B, with different values of pressure, temperature and volume than A. 5. So, if we go from A to B in a way that any small step is again in equilibrium state, we say that the process is reversible, that means we can go back to the initial state following the same path.
Biomechanics: Hip Joint - Injury Case If a person has an injury on one leg, this person will use a cane in order to walk. The cane can be used in 2 ways:
1. Ipsilateral = using a cane on the same side as the injury. 2. Contralateral = using a cane on the opposite side to the injury. Calculating the same way as before we find that with the ipsilateral cane the normal force exerted on the foot by the floor is reduced to 5/6th of the original weight of the person. However, through a contralateral cane, the point of application of the same normal force has shifted.
How is the friction force calculated?
1. It is given by the friction coefficient (k) times the normal force(N), which is the force that is acting perpendicularly to the plane that we are considering. 2. Therefore, there is an opposite and equal force that the plane is exerting on this object. In the case of a horizontal plane for example, if the weight is sitting on its surface, the normal force we consider is mg. If we have an inclined plane (it's not horizontal, so it has some angle with respect to the horizontal plane), instead of mg there will be the component of the weight that is perpendicular to the inclined plane. 4. u(k) : coefficient of kinetic friction. It depends on the types of surfaces, in the solid-solid interfaces interaction. We can have other friction forces if we consider another... so also in this case we have to say that , in general, is just a value that depends on the interactions between the two surfaces and is not dependent on the velocity, so if we have an object that is sliding the force is just opposing with this value. It doesn't depend on how fast this object is sliding.
What is the equation for the centre of mass?
1. It's the sum of the generic mass times the vector r(distance). It is therefore mass1 times vector r1 (distance between m1 and O), plus mass2 times vector r2, and so on, for the almost infinite number of masses in. which we divide the mass of this object. This sum is then divided by the total mass (M). 2. It will be the sum of all these elementary masses multiplied by the distance with respect to this point, divided by the total mass. 3. This formula is true of any object and any reference system that we consider. It is a generic definition of center of mass, and it is a vector with respect to a generic point O that we can choose. If we choose that it corresponds to the center of mass, then r is 0.
Kelvin vs. Clausius vs. Carnot
1. Kelvin's definition: "There exists no thermodynamic cycle whose sole effect is to extract heat from a system and to convert it entirely into work. (The system releases some heat)". This means that we cannot design a heat engine that absorbs heat and converts all the heat into work, some heat will always be lost. 2. Clausius's definition: "No process exists in which the sole effect is that heat flows from a reservoir at a given temperature to a reservoir at a higher temperature". Work must be done on the system to transfer heat from a hot source to a cold one. Heat cannot spontaneously flow from colder source to hotter source. 3. Carnot's logical conclusion: "The most efficient heat engine operating between two reservoirs at temperatures T1 and T2 is the Carnot cycle".
What are real gases?
1. Non-hypothetical gases whose molecules occupy space and have interaction. 2. The Ideal Gas equation works well enough for most gases at ordinary pressure, as long as the temperature is reasonably high.
What type of capacitors are there?
1. Parallel-plate capacitor 2. Cylindrical Capacitor 3. Spherical Capacitor
What are pulleys?
1. Pulleys are another type of lever system; they consist of a rotating wheel with a rope that goes around it in its groove. 2. Force is applied on one end and its impact balances a force applied on the other end of the rope.
There are 2 ways to connect resistors:
1. Resistors in series 2. Resistors in parallel
There are 2 types of pulleys:
1. Single fixed pulleys: the gain is 1, so if we push down by 100N we can exert a force that is 100N to keep in balance a mass. 2. Single movable pulleys: the pulley can slide along a rope, so the condition of equilibrium is such that the force that must be applied, being the system fixed at one point, is half of the weight. The gain is therefore 2 in this case.
Classes of Pulleys: 1. Single fixed pulleys 2. Single moveable pulleys What are single moveable pulleys?
1. Single moveable pulleys: in this case, since the pulley is moveable, it can slide along the rope. 2. One force is applied at the center of the wheel; one end of the rope is fixed while on the other one a force is applied. 3. On the fixed side the force is given by the tension of the rope.
Heat transfer and thermal equilibrium
1. So, after considering these last quantities, we can go back to the concept of thermal equilibrium at a deeper grade of analysis. 2. Ex: We have one object with a certain temperature T1, mass m1 and specific heat c1. We put it in contact with another object that has a temperature T2 (T2<T1), a mass m2 and a specific heat c2, (c1 different from c2 and m1 different from m2). Heat will flow from the warmer to the cooler object, and after a while they will reach the same intermediate temperature T3 at the thermal equilibrium. If we know the initial temperature and the masses and specific heats of the two objects, it is possible to determine the value of this final temperature. 3. We start from the assumption that at thermal equilibrium the heat given by one object will be exactly equal to the heat absorbed by the other object. So, we can put these parameters in an equation (highlighted in yellow). 4. Regarding the object with higher temperature, it will have a negative variation of temperature as it transfers heat to the other. In order to avoid the negative sign in the equation, we define its variation of temperature as the difference between the initial and the final (not the final minus the initial, as every variation usually requires).
There are two types of friction force:
1. Static friction. 2. Kinetic Friction.
What do the Kelvin and Clausius observations conclude?
1. The Kelvin and Clausius observations are, respectively, that a cold sink is essential to the operation of a heat engine and that heat does not flow spontaneously from a cooler to a hotter body. 2. The Clausius and Kelvin statements are entirely equivalent. This equivalence can be demonstrated by showing that the violation of either statement will result in a violation of the other one.
What is cervical acceleration/deceleration (CAD) trauma?
1. The cervical acceleration/deceleration (CAD) trauma, whiplash, has traditionally been described in association with cervical spine movements in the sagittal plane after a motor vehicle collision. 2. The head weighs approximately 12 to 15 pounds and is at the end of a long, flexible lever arm, which acts like a whip in the presence of rapid acceleration and deceleration. 3. The hyperflexion experienced by the cervical spine may be further exaggerated by the shoulder harness seat belt. Because this device prohibits the chest from coming forward, it facilitates a more forceful whipping of the head and neck.
Heat - definitions
1. The concept of heat is strictly connected with the one of temperature. 2. There are different definitions of heat. It is typically defined as the energy transfer between objects triggered by temperature difference. 3. When we place two objects in contact, energy, in the form of heat, will flow between them. The exchange decreases over time until it stops completely when the two objects reach thermal equilibrium. 4. This exchange only occurs if the two objects are not thermally isolated.
In the case of a gas medium, friction forces are proportional to the velocity squared (so if the velocity is small, they are negligible, whereas if it is large, they will become important) and opposite to the direction of motion. In this case there is a different friction coefficient, also called drag equation, which takes into account:
1. The density of the medium (p), 2. A coefficient that depends on the shape of the falling object (C(d)) 3. The projected area (not to the radius like in the liquid) of the falling object (A)
The Clausius and Kelvin statements are entirely equivalent. This equivalence can be demonstrated by showing that the violation of either statement will result in a violation of the other one.
1. The diagram on the left depicts the fact that the failure of the kelvin statement implies the failure of the Clausius statement. 2. The diagram on the right depicts the fact that the failure of the Clausius stamen implies the failure of the Kelvin statement.
Microscopic description of Entropy: How many arrangements can we have (arrangements of the particles -- snapshots of molecules in 2 separate chambers connected) what are all the possible configurations?
1. The first configuration is that all the particles stay in one chamber or they all go to the other chamber = single arrangement (1). 2. The second arrangement is that 3 are one one side and 1 is in the other = 4 for each colour. 3. The third arrangement is to have 2 on each side (6 possible different arrangements = most probable).
We now consider a force acting on this object, that has an extension (it's not just a point); because of this, the force can act at different points of this object. We consider:
1. The force F, having a certain direction and magnitude, that is acting on a point 2. A, the point on which F is acting. 3. O, a fixed generic point taken as a reference 4. r, a vector connecting O and A The torque (t) is a vector of the force F with respect to the point O, and it is the vector product of vector r and the force F applied on this object.
Internal energy of an ideal gas
1. The internal energy of a gas is the sum of all kinetic energy (translational, rotational and vibrational) for all molecules in the gas. 2. The general equation for the internal energy of a gas is U = f/2 nRT where f is the degrees of freedom. 3. In total (for what we need to know) there are 6 degrees of freedom; 3 for translation in x ,y and z directions and another 3 for rotation in x, y and z axes. 4. Each degree of freedom contributes 1/2KT (same as nR) per molecule.
What is the moment of inertia?
1. The moment of inertia is a geometrical factor; its value depends on the mass but also on the geometry of the object (essentially the extension of the object with respect to the rotation). 2. We need to consider on which axis the rotation happens. 3. The heavier the object is the larger the moment of inertia is and so smaller the rotation is. The extension of the object is important because the larger the object is, the more torque is needed to put the object in rotation.
Why do we use pistons as model systems?
1. Thermodynamic was mainly developed in the 18th century at the beginning of the industrial revolution so the main examples come from pistons, and how we can use gasses in order to change temperature, create heat and produce work. 2. A very simple model can be a closed cylinder, where the top surface of the cylinder is moveable and connected to a piston and inside this cylinder, we have a gas which occupies the whole volume. 3. The first approximation is that inside we have an ideal gas that is composed of many randomly moving point particles that are independent from each other.
What is the harmonic motion?
1. This is the harmonic motion created by pulling and releasing the spring, which then starts oscillating. 2. The harmonic motion is a periodic motion: after defining time, the mass will go back to the same position. 3. The spring constant and the mass define how fast the harmonic motion is.
Actual definition:
1. Two objects are in thermal equilibrium if they are in close contact that allows either to gain energy from the other, but nevertheless, no net energy is transferred between them. If two objects remain in contact for a long time, they typically come to equilibrium. In other words, two objects in thermal equilibrium do not exchange energy. 2. When the two objects are in contact there is still a little exchange of energy but it is not net, since there is some continuous absorption and emission. 3. If thermometer A is in thermal equilibrium with object B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C. Therefore, the reading on A stays the same when A is moved over to contact C.
Calculate the force exerted by the neck muscles to keep the head balanced knowing that the resistive forced of the head is 80N and the distance between the fulcrum and the center of mass of the head is around 8cm and the distance between the fulcrum and neck muscles (knowing the anatomy of the head we can say that it's roughly 2 cm:
1. We assume that the resistive force of the head is 80N (this is the general weight of the head). Thus, br is the distance between the fulcrum and the center of mass of the head (knowing the anatomy of the head we can say that it's close to 8 cm) and bm is the distance between the fulcrum and neck muscles (knowing the anatomy of the head we can say that it's roughly 2 cm). In order to find out the force exerted by the neck muscles to keep the head balanced, so Fm, we can apply the formula of the equilibrium condition. 2. Hence, the force exerted by the neck muscles is around 320N (this force doesn't balance only the weight of the head but also the torque of it). 3. This is an approximation; in order to be more precise we should also consider the angle of the force.
How do we calculate the erythrocyte sedimentation rate?
1. We can assume that r is the equivalent hydrodynamic radius, roughly 3.5 microns. 2. We know the density () of a red blood cell, which is roughly 1.1g/cm3, 3. We know the density (ρ') of the liquid medium (plasma in this case), which is roughly 1.02 g/cm3, 4. We know the viscosity of the blood(n), which is 0.01 poise (Pascals per seconds) So if we put these values in the previous formula, v(s) = (2(ρ-p')gr / 9η) , we can get the sedimentation speed, which is in the order of 7mm per hour. Essentially, if we look at the meniscus of this blood, we will see that in one hour if has fallen by roughly 1 cm, or 7mm. This is a measurement of this value (ESR), that is useful to diagnose diseases such as multiple myeloma, various autoimmune diseases, lupus, inflammatory bowel disease and chronic kidney diseases. In some cases, the ESR can exceed 100mm/h (an order of magnitude larger than the normal sedimentation speed), so it can be easily seen if there is a pathological condition. That value is because of the fact that in such pathological conditions red blood cells will cluster; by clustering, they will be larger and fall with a higher speed (because sedimentation speed is proportional to r squared).
What is an example of the conditions for equilibrium of a rigid body?
1. We have a bar that is pulled in two different directions by two forces (F1 and F2), which are equal in magnitude. The net force acting on the object will be F1-F2, both acting in the vertical direction and equal but opposite in magnitude. So F=F1+-F2=0. the object is not moving in space, so it will not translate. We cannot say that this object is in equilibrium, because we should also consider the torques generated by these two forces with respect to the middle point O. 2. The torque generated by the force F1 is F1 times the lever arm(b1) with respect to the point O. The motion is counterclockwise so the torque will be positive. The torque generated by the second force (F2) is given by F2 times the distance between the force and the point O, which is b2. Also in this case the motion is counterclockwise (it has the same direction as the motion of the first torque); being both torques positive, the net torque is not 0. The resulting motion of this is a rotation along this point O. The two forces, pulling in opposite directions, have a net force equal to 0 but they have a positive total torque, so a positive total momentum, which will generate a rotation, so it will not be in equilibrium with respect to the rotation. On the other hand if we consider a different bar(green one), all the points that we could take as reference lie on the same line of action, so b1 and b2 will necessarily be 0; the two torques are always 0.
What is the torque?
1. We move to forces acting on an extended object. 2. We'll first consider what is known as a rigid body (an extended object that is rigid, so we can assume that deformations are equal to 0, or so small that they can be neglected). 3. If we have forces acting on this object, they will not deform it (or the deformation will be so small that it can be neglected). This also means that the distance between any two given points of this object will remain constant. 4. It is considered as a continuous distribution of mass, meaning that the extended object will have a mass that is continuous through it.
Motion of a solid object through a liquid: Now, if we are in a liquid medium and the sphere is falling, we'll see that the force will be different and, more importantly, we'll have a friction force (drag force) that is proportional to the velocity at which this particle is falling:
1. When the particle starts with velocity=0, friction is also =0. 2. Then it starts accelerating, so the velocity will be small but different from 0, so the friction will also be small and different from 0. 3. As the particle accelerates, the velocity will increase proportionally to acceleration; acceleration will also increase 4. As acceleration increases, the friction force will increase, as well.
The Carnot Cycle steps:
1. a to b: Isothermal Expansion (absorbing heat from the hot reservoir). 2. b to c: Adiabatic Expansion (no heat transfer). 3. c to d: Isothermal Compression (heat is flowing out to the colder reservoir). 4. d to a: Adiabatic Compression (no heat transfer).
Examples of fictitious forces are:
1. acceleration-deceleration forces 2. centrifugal force (F(CF)=m(𝜔^2)R) 3. Coriolis force (vortical forces in the atmosphere are formed due to the rotation of the Earth)
How do you calculate the drag force for the motion of a solid object through a liquid?
1. v is a vector, representing sedimentation, which is the velocity at which this particle is falling in the liquid medium. 2. There is a minus sign because [the force] it's going in the opposite direction to the velocity; the force is proportional to the velocity through a coefficient called drag coefficient (fs), which in the case of a sphere has a precise value; this value is defined by what is known as Stoke's law and this value is 6 times the radius of the sphere (r) times the viscosity of the medium (n). 3. We consider a sphere that is falling without friction in a medium: with the action of gravity (Fg=mg) the sphere will have a motion that is accelerated. It's falling starting, for example, with velocity=0; velocity will then increase with constant acceleration, given by the gravitational acceleration.
rigid bodies vs. real bodies
1. we considered the dynamics and actions of forces acting on rigid bodies, which cannot deform or the deformations are negligible. 2. Real bodies have some elasticity as they can be deformed to a certain extent. Therefore if we have a body and apply a force there will be a small or large variation of the volume.
expansion work (pressure-volume work)
1. when pressure is constant, calculating work done is very simple. 2. Work done = force x distance = (pressure x area) x distance = pV 3. From a to b: W(a -> b) = pV = p(V2 - V1) 4. The reverse reaction requires the same work so W(a -> b) = -W(b -> a). 1. when pressure and volume changes, to calculate the work done you need to work out the area underneath the graph which can be done 2 ways; 2. The more accurate one is finding the integral of the pΔV graph and working out exactly the area under the graph. The integral of pΔV = nRT(ln)( Vb/Va) 3. The less accurate way is defining small segments/intervals and assume the pressure and volume is constant at specific segments, multiply them together, and then add them up to find the total area. Wa -> b = p1v1 + p2v2 + p3v3......... **taking the integral (area below the curve) of the function in the graph.
While following a treasure map, you start at an old oak tree. You first walk 85 m at 30.0° west of north, then walk 92 m at 67.0° north of east. You reach the treasure 2 minutes later. Calculate the magnitude of your average velocity for the entire trip.
1.32 m/s
Certain rifles can fire a bullet with a speed of 970 m/s just as it leaves the muzzle (this speed is called the muzzle velocity). The muzzle is 71.0 cm long and the bullet is accelerated uniformly from rest within it. For how long (in ms) is the bullet in the muzzle?
1.44 ms
While following a treasure map, you start at an old oak tree. You first walk 85 m at 30.0° west of north, then walk 92 m at 67.0° north of east. You reach the treasure 2 minutes later. Calculate your average speed for the entire trip.
1.5 m/s
What is the elementary charge?
1.6 x 10^-19 C
A survey drone has just completed a scan at x,y coordinates (57m, 8m) at t=0. It needs to return to a lab located at (-115, 72) m. If its initial velocity is 16m/s in the +y-direction, and it has only 18s of battery life remaining, what constant acceleration (magnitude and direction) does it need to reach the lab?
1.8 m/s2; 51.8° below -x axis
1Mg metric ton
1000 kg = 10^3
1m^3
1000L
1kg =
1000g
1km
1000m = 10^3
1L
1000mL
1m
100cm = 10^2
In a sample of gas, you pick a particle at random. The mass of the particle is 1.67 × 10-27 kg and you measure its speed to be 1600 m/s. If that particle's kinetic energy is equal to the average kinetic energy of the gas particles, what is the temperature of the sample of gas?
103.3 K https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/kinetic-energy-gases
A delivery truck travels 8 miles in the +x-direction, 5 miles in the +y-direction, and 4 miles again in the +x-direction. What is the magnitude (in miles) of its final displacement from the origin?
13 miles
A small helicopter travels 225 m across a city in a direction 53.1° south of east. What are the components of the helicopter's trip?
135 m east (+x), 180 m south (-y)
1mL
1cm^3
What is Newton's 1st Law of Motion?
1st law: every object continues in a state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces acting upon it.
A non-Carnot heat engine operates between a hot reservoir at 610K and a cold reservoir at 320K. In a cycle, it takes in 6400 J of heat and does 2200 J of work. What is the total change in entropy of the universe over the cycle?
2.6 J/K
An aircraft engine takes in 9 kJ of heat and expels 6.4 kJ of heat each cycle. How much mechanical work does the engine do each cycle?
2.6 kJ
3 moles of an ideal gas fill a cubical box with a side length of 30cm. If the temperature of the gas is 20°C, what is the pressure inside the container?
2.7 × 10^5 Pa https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/ideal-gas-law
The brakes of your car can provide an acceleration of 4.6m/s2. You're speeding at 37.5 m/s and suddenly see a police car, so you slam the brakes. How long will it take for your car to slow down to the speed limit of 25 m/s?
2.7s
If Karen can make 7 cakes in 3 hours, how many cakes can she make in 10 hours?
23.3
You are given a sample of an unknown metal. You weigh the sample and find that its weight is 29.4N. You add 1.25×104 J of heat energy to the sample and find that its temperature increases from 52°C to 70°C. What is the specific heat of this unknown metal?
231.5 J/(kg⋅K) https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/specific-heat
On a very cold day at a temperature of -12°C, a power line made of aluminum between two support towers measures exactly 150.56m. You go out on a hot day and measure the power line to be exactly 150.71m. What is the temperature (in °C) outside? The linear expansion coefficient of aluminum is 2.4×10-5.
29.5 °C https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/zeroth-law-of-thermodynamics
What is Newton's 2nd Law of Motion?
2nd law: when there is a net force acting on an object, the object undergoes an acceleration that is proportional in magnitude and in the same direction of the force. 1. The net force and the acceleration are related as: F=ma 2. If the force F is equal to 0, then also the acceleration a is 0 (the mass is never 0 and it is always constant).
Explain the different processes in the cycle: Point C - D
3) Then again, we put everything in a heat reservoir as we did in point 1, so temperature is constant and now we compress the system a little bit with pressure that is going up, while volume is going down.
How much work is done on a gas that expands from A to B along the path shown in the image?
3.6 × 107 J https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/intro-to-thermal-processes
Calculate the heat required to raise the temperature of 50g of water from 40 degrees C to 55 degrees C.
3140J
PROBLEM: A sled of 20 kg of mass, initially at rest, slides on a plane inclined 30° compared to the ground. Considering that the speed of the sled at the end of the inclined plane is 10 m/s and the coefficient of kinetic friction is 0.1, calculate: a) the work done by the weight force b) the initial height from the horizontal plane c) the work done by the friction force
c) the work done by the friction force = -210J
Given that the specific heat of water is larger than that of steam, which of the following statements does NOT represent a possible physical process? a. It requires more heat to raise the temperature of water by 1°C than it does to raise the temperature of steam by 1°C. b. The specific heat of water is higher because the energy bonds between water molecules are stronger when it is a liquid than when it is a gas. c. During a phase transition from water to steam, if you continue adding heat to the system, some of it will be used to generate the change in the aggregation status of the material and some to increase temperature. d. A change from the liquid to the vapor state of water involves using some energy to change the molecular interactions between water molecules
c. During a phase transition from water to steam, if you continue adding heat to the system, some of it will be used to generate the change in the aggregation status of the material and some to increase temperature.
What is impulse?
change in momentum So the effect of the net torque is creating a variation in the angular momentum of the object (similar to is said about the linear momentum).
Objects in free fall experience ______.
constant vertical acceleration, so we use Kinetics Equations to solve problems.
What is Q in an isovolumetric (aka. isochoric) process?
constant volume (use CV)
In a uniform circular motion the linear velocity is:
constant, but it is greater, the further away you are from the center of the circle (if you were standing on the center, you would be just rotating on yourself, so your velocity would be zero -- the further away youare the larger your velocty -- could see this in a carousel).
At point A, a hiker is 10m east from the origin. After 35s, the hiker arrives at point B 40m at 60° north of east from the origin. Calculate the magnitude and direction of the hiker's displacement.
36m; 73.9° north of east
What is Newton's 3rd Law of Motion?
3rd law: if one object exerts a force F on a second object, then the second object exerts an equal but opposite force -F on the first. For example, in the law of universal gravitation the Earth exerts a force on a generic mass, and the generic mass exerts an equal but opposite force on the Earth.
Explain the different processes in the cycle: Point D - A
4) Finally, we remove again the heat reservoir, we insulate the system and then we have an adiabatic compression, so a real compression without exchange of heat.
You walk to the right at 3m/s for 8s, then turn around and walk backwards at 2m/s for some unknown time. You end up 16m to the right from where you started. How long did you walk backwards?
4.0 s
A refrigerator has a coefficient of performance of 2.4. Each cycle, it takes in 3×10^4 J of heat from the cold reservoir. How much is expelled to the hot reservoir?
4.25×10^4 J
3 moles of an ideal gas are in the left side of an hourglass-shaped container, separated by a thin barrier. The right side is completely empty, but the volume of the left and right sides are equal. The barrier is suddenly removed, and the gas freely expands into the vacuum. What is the change in entropy? sol.
49.9 J/K
Two perpendicular forces act on a box, one pushing to the right and one pushing up. An instrument tells you the magnitude of the total force is 13N. You measure the force pushing to the right is 12N. Calculate the force pushing up.
5 newtons
A car accelerates from 5.0 m/s to 21 m/s at a rate of 3.0 m/s2. How far does it travel while accelerating?
69 m
A boat on a river is traveling from a pier to a point 500 m upstream (against the river's current). The current flows at 4 m/s. If the boat makes the trip in 250 s, what is the speed of the boat relative to the water?
6m/s
A gas in a cylinder expands from a volume of 0.10 m3 to 0.320 m3. Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65×105 Pa during the expansion. The total heat added is 1.15×105J. What is the change in internal energy of the gas?
7.87 × 10^4J
A rock is thrown horizontally with a speed of 20 m/s from the edge of a high cliff. It lands 80 m from the cliff's base. How tall is the cliff?
78.4 m
So, temperature is
strictly dependent on velocity. 1. Higher velocity will result in higher kinetic energy, which consequently leads to higher temperature. Vice versa, whenever we heat the gas, we are providing energy to it and to its molecules that will start moving faster. 2. More movement results in an increment of the temperature. On the other side, a lower velocity means lower temperature. Also, lower temperature leads to a decrease of the particle's average movement. 3. Considering ideal conditions, such as a monatomic gas in which all the particles have the same mass (as they belong to the same species), the relation between temperature and kinetic energy is described as follows: Where: -m: mass; -v: velocity; -rms: root mean square (the square root of the mean square, meaning the arithmetic mean of the squares of a set of numbers). - KB: constant of Boltzmann (also useful when talking about entropy). KB constant is fundamental as it constitutes the bridge between the microscopic and the macroscopic worlds. It appears also in other fields, such as biochemistry, chemistry, physiology. When multiplicated by the Avogadro's number, it gives the constant of ideal gases.
4. Uniform Circular Motion With this type of motion, the motion of the point is represented by looking at;
the fraction of the circular path that is travelled during Δt. Instead of looking at the displacement we look at the variation of the angle.
If the particle starts falling, at some point it will reach a condition for which:
the friction force will be equal and opposite to the weight. Weight is always constant, but as the velocity of the falling particle is increasing, the friction will also increase, reaching a point where it will completely balance the weight. When we reach this condition,
The main difference between the law of universal gravitation by Newton and Coulomb's law is that:
the gravitational force expressed by Newton is always attractive, whereas the electromagnetic force described by Coulomb can be either attractive or repulsive (because there are two types of charge: positive and negative).
Ω:
the number of possible microstates corresponding to the macroscopic state of a system.
Conservative forces are...
the ones in which the work done to go from A to B does not depend on the particular path - if we go from a position to another and then we go back to the initial position, the work is zero (it means there is no variation in kinetic energy ∆EK).
We can also consider the angular momentum of a mass (ex: a particle) that is rotating with respect to a particular point O. In this case the moment of inertia is equal to:
the product of the mass by the distance square between the point O and the particle.
What is power?
the rate at which work is done (work over the change in time.
So, we can find temperature as
the square of velocity times mass over three times the Boltzmann's constant. 1. More simply, temperature is determined by the motion of particles, which are free to move, since they are at the gaseous state. 2. For instance, in solids particles are blocked in stricter positions and the only movement allowed is vibration. 3. When the temperature in a solid increases, the vibration motion gets stronger. 4. At a certain point, if the temperature keeps increasing, it will reach a point in which the vibration will be stronger than the interactions between the atoms, starting to break them. 5. That is what happens during phase transitions.
What is the electrical resistance?
the tendency for a material to resist the flow of electrons and to convert electrical energy into other forms of energy. R = p(l/A). What is the name of this law? Ohm's Law.
For monoatomic gases, the translational kinetic energy is...
the total internal energy. This is because its rotational energy can be ignored as its atoms are so small that the moment of inertia is negligible. There are 3 directions it can move in (x, y and z) which contribute 1/2KT each per molecule, therefore the total internal energy for a monatomic gas is 3/2KT. U = 3/2nRT
Work can also be described by:
the variation in kinetic energy of a system (work-energy theorem: W = ∆EK, where EK = ½mv2).
The work done to bring the mass from 0 to a generic point X, can be expressed as:
the variation of kinetic energy (final kinetic energy - initial kinetic energy). The kinetic energy is the energy of the particles. Work means force acting for a given distance and if the work is not zero, it means we are accelerating or changing the velocity of the kinetic energy of the particles.
Only for conservative forces, work from point A to point B can be represented as ______.
the variation of potential energy: WAB=U(A)-U(B) Moreover, WAB = EK(B)-EK(A) = U(A)-U(B) So, WAB=U(B)+EK(B)=U(A)+EK(A)
The Carnot cycle belongs to a class known as:
thermal engines, which can create energy and so work by changing or keeping variables constant, which means this cycle can do this work for a long time, and it can transfer heat or chemical energy in mechanical work.
In thermodynamics, a quasi-static process is a...
thermodynamic process that happens slowly enough for the system to remain in internal physical (but not necessarily chemical) thermodynamic equilibrium. An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process.
Polyatomic gases are the same as diatomic gases except...
they can rotate in the z axes. This means that polyatomic gases can move and rotate in all directions so it has 6 degrees of freedom that contribute 1/2KT each. Therefore U = 6/2nRT (or 3nRT)
Adding vectors graphically:
tip to tail method (connecting the arrows from "tip-to-tail").
Forces acting on a rigid body can generate some ______.
torques inducing rotation in that specific body. -- Therefore, we need to make sure that the net force acting on the body = 0 as well as the sum of all torques.
2 mol of a monoatomic gas follows the cyclic process used in a heat engine. Heat is removed from the gas at constant pressure from A to B, added at constant volume from B to C, then the gas expands isothermally from C to A, doing 2300J of work, and repeats. Calculate a) the heat transfer for each process; b) the total work done by the heat engine. sol.
total work done = area in the loop.
Thermal expansion
with delta we mean final length - initial length, same with delta T. delta A is the increase in surface area, correlated to if there is an increase in temperature. If we consider a metal road the expansion will take place preeminently on the axial direction, so its length will increase by a factor ΔL. This is particularly a kind of notation with which we will become familiar, as we will often speak in terms of variation, defined as the final measure minus the initial one. As shown in the following formula, the variation is proportional to the initial length and to the increment of temperature. α is the coefficient of linear expansion, which depends on the material. Its dimension is the inverse of a Kelvin (or a Celsius) since the two lengths simplify with each other. In the case, for instance, of a disk, the expansion will occur in two dimensions, so there will be an increment in the area. If the object is isotropic (uniform in all the direction), we can assume that the increment of the area will be roughly twice the increment in one direction. Of course, it is not a precise measure, but it is a good approximation. This allows us to use the same coefficient of linear expansion. The same happens when we talk about volume. If we have a block of concrete, it will expand in all three directions and the increment in volume will be roughly three times the increment in one direction. What we have said up to now can be considered true in the case of solids. However, when talking about gases and liquids, it is hard to measure the expansion in one direction, given the fact that they don't have a prescribed shape. In fact, even though they have a fixed mass, they tend to acquire the shape of their container, as they are deformable substances. So, measuring the change of shape in different directions is not possible. What we use is the volume expansion, that considers a different coefficient named β. In this case the measurement is more precise.
What is a lever?
A rigid bar that is free to move around a fixed point
And for a circular motion the angular velocity is equal to:
the tangential velocity divided by R.
In a cyclic process, it is impossible for heat to flow from COLDER to HOTTER temperature without an input of ______.
work; heat ALWAYS flow from hotter to colder, never the other way around.
Find the magnitude and direction of the vector C =2B × A. sol.
|C| = 54; along the +x direction
"G" is a _____. "k" is a ____.
"G" is a tiny number, therefore gravity force is a relatively small force. "k" is a a huge number, therefore electric force is a relatively large force.
Entropy is often called a measure of ______.
"disorder", but a better definition is it's a measure of a system's randomness.
The position-time graph for a moving box is shown. (a) What is the box's average velocity from 0 to 5s? (b) What is the box's average velocity from 0 to 8s? (c) What is the box's velocity in the interval where it's moving fastest? sol.
(a) -1.2 m/s; (b) 0 m/s; (c) -11 m/s
Starting from a pillar, you run a distance 140m east (the + x-direction), then turn around. (a) How far west would you have to walk so that your total distance traveled is 300m? (b)What is the magnitude and direction of your total displacement?
(a) 160 m (b) 20 m, west
A moving box's motion is described by the velocity graph below. The box's initial position is x = 0. (a) How far has the box moved at t = 4? (b) What is the displacement of the box from t=4 to t=10?
(a) 24 m; (b) 0 m
A rock is thrown vertically upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. The rock doesn't hit the building on its way back down and lands in the street below. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street? (+sol part b)
(b) t = 6.49 s
A student throws a set of keys vertically upward to her sorority sister who is in a window 14.00 m above. The second student catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (+sol part b)
(b) vy=2 m/s
Example: Solution
* always have to be in kelvin (K) ** divide the lower temperature by the hotter temperature. Last step = calculate the entropy change for the heat reservoire (not the system, heat is going out = negative = minus) = -QH/TH = -2.18 (would be positive for the opposite).
Thermal expansion
** Don't have to remember these values. The coefficient of linear expansion depends on the material, as shown in the table below: We can see that in linear expansion, metals tend to have higher coefficients than other materials, such as quartz. In volume expansion the coefficients are usually even bigger (order of 10^-3), due to the fact that liquids and gases are flexible materials, so their expansion is greater.
Thermometers and temperature scales: CONVERSIONS --
*** don't learn by heart any constant of specific heat of water, etc. These will be provided in questions. Don't remember how to convert celsius to Fahrenheit. But you should remember how to convert CELSIUS to KELVIN. And do this at the start of a problem.
Heat capacity
***be careful with the signs. Heat is positive, when it is added to the system = temperature will increase (delta T will be positive as well), vice versa. Also depends on the mass of the material. 1. A way to define heat is to measure the temperature variation of an object. So, we give energy to an object, we measure the variation of temperature and we can consequently determine the amount of energy in the form of heat that was given. 2. That is proportional to the properties of the object. For different objects in fact, the same amount of heat will result in different variations of temperature. 3. So, we can introduce a new quantity, heat capacity, defined as the amount of heat given to an object divided by the variation of temperature. 4. So, thanks to this new quantity we can define heat as the product of heat capacity and variation of temperature, as shown in the upper image in yellow.
The internal energy of a system decreases by 500 J, and 230 J of work is done on the system. What is the heat transfer into or out of this system?
- 730 J
Let's give some examples of resolution: -First case: the two objects have the same heat capacity C1=C2
-First case: the two objects have the same heat capacity C1=C2 NB: Even if they have the same heat capacity, they might have different specific heats. Of course, in that case they will also have different masses. (We remind you that C= c m, so the two quantities c and m are inversely proportional).
-Second case: if C2 is ten times C1:
-Second case: if C2 is ten times C1: As the solution highlights, the final temperature will be closer to the initial one of the objects with higher heat capacity. That may become more intuitive if we present a practical example: We consider a large pool and we insert into it a small hot object. The two will reach thermal equilibrium at a temperature much closer to the one of the pool than the one of the small object, since the pool has a much higher heat capacity.
What are the classes of pulleys?
1. Single fixed pulleys 2. Single moveable pulleys
3. Lecture
3. THERMODYNAMIC SYSTEMS AND THE FIRST LAW OF THERMODYNAMICS Learning goals: 1. Understand the definition of isolated, closed, and open thermodynamic systems 2. Recognize the different types of thermodynamic variables and processes 3. Understand the operation of a heat engine 4. Evaluate the thermophysical properties of an ideal gas 5. Recognize and apply the First Law of Thermodynamics 6. Explain the properties of the thermodynamic potential U (internal energy) with respect to the definition of state functions and the case of an ideal gas 7. Recognize the different types of specific heat for an ideal gas with respect to polytropic transformations
A moving hockey puck encounters a patch of rough ice and slides 90cm before coming to a full stop. Assuming a constant deceleration of 8 m/s2, what was the puck's initial speed?
3.79 m/s
4950pm to nm
4.95nm
What is an electric current?
A flow of electric charge (electrons) (around a circuit). +Q move in the direction of the electric field. -Q against it. Charges that move by the actions (forces) in the electric current will accelerate and bump against another particle. Charge will start and stop. Effective friction force (drift velocity). A = the area of the cross-section of the wire I (current) = A * E / p (resistivity = the resistance against the motion of charges in that specific material).
Zeroth Law of Thermodynamics
A law that if two systems are separately found to be in thermal equilibrium with a third system, the first two systems are in thermal equilibrium with each other; that is, all three systems are at the same temperature. Also known as thermodynamic equilibrium. The zeroth law of thermodynamics: If object A is in thermal equilibrium with object B, and object C is also in thermal equilibrium with object B, then objects A and C will be in thermal equilibrium if brought into thermal contact. That is, temperature is the only factor that determines whether two objects in thermal contact are in thermal equilibrium or not.
1. Linear motion with constant velocity
A point is moving in one direction with constant velocity. There is a linear relationship between position and time. The velocity is equal to the average velocity over any time interval (it is constant).
4th process: adiabatic compression
Again, no heat supplied so Q = 0. Temperature increases so internal energy is going to increase so Wd→a is negative as Uc→d = 0 - Wd→a. We find out work the same way as before Wd→a = -3/2nRΔT
Why is a molecule of water polar?
A molecule of water is polar because of the unequal sharing of its electrons in a "bent" structure. A separation of charge is present with negative charge in the middle (red shade), and positive charge at the ends (blue shade).
Pulley systems:
A type of system in which there is a wheel, a rope going around it and as we pull on one side of the rope, the force is transmitted along the rope and is applied in a different direction (upwards in the example). It is a way in which we can change the direction of the force that we apply. This is used in physiatry, in which we use a weight that pushes down to exert a force that pushes up.
What is the mechanical energy conservation theorem?
According to the mechanical energy conservation theorem, ∆EM=∆U+EK=0 and U+EK=constant (for conservative forces only). So the mechanical energy is the sum of potential energy and kinetic energy.
Depending on how many degrees of freedom the atom/molecule has/have the molar heat capacity can be calculated in the following way:
Adiabatic ratio: ratio of the heat capacity at constant pressure to the heat capacity at constant volume. Specific heat at constant pressure, Cp = ((f+2)/2) * R Specific heat at constant volume, Cv = (f/2)R In these formulas f represents the degrees of freedom of the gas. We can calculate the ratio of Cv and Cp which is called adiabatic ratio.
Are V, N, p and T independent to eachother?
All these quantities, V, N, p and T, are not independent from each other, there can be a relation that considers all these variables and this relation, called the equation of state, essentially is the function that takes in account how these variables depend on each other.
What is U (the change in internal energy) of the heat engine vs. refrigerator?
Also, U = 0, because it is just the reverse.
Electric current
Ampere (A)
What is an effective force?
An effective force is defined as the product of a particle's mass and acceleration (F = ma). The system of effective forces acting on a system is equal to the system of external forces acting on that particle.
What is linear momentum?
From 2nd Newton's law (F = ma -> can be written in a slightly different way): Linear momentum: p = mv (linear momentum is a vector defined as the product of a system's mass multiplied by its velocity)
4. Uniform Circular Motion
In a uniform circular motion a point moves with constant speed (or constant v in magnitude) in a circle. The reason for this is that the velocity is tangent to the trajectory with a constant value, but the direction constantly changes.
Which has higher entropy, ice or water?
Because things with higher temperatures have more energy, they have more "randomness"/entropy.
When can we have only radiation?
In a void. The only way to transfer energy in an empty space is through radiation. While, conduction and convection is energy transferred by direct contact (solids) or occurring in liquids & gases. Conduction can not occur when there is an empty space.
2nd process: adiabatic expansion
By definition, work is done but no heat is supplied so Q = 0. This means that Ubc = -Wb → c. As we know from before, the equation for the internal energy of a gas is U = 3/2nRT so Wb → c = 3/2nRΔT. As temperature decreases, internal energy is going to decrease so Work done is positive.
The most famous cycle that produces work is known as:
Carnot cycle.
Types of levers: Class 1 levers
Class 1 levers: The fulcrum is between the resistive force (the one that we're trying to win) and the motor force. The mechanical gain can be greater or smaller than 1, depending on the distances. If bm is larger than br then the gain will be greater than one, if bm is smaller than br, then the gain will be lower than 1. An example of this is a plier. We apply a force (Fm) to generate another one(Fr). The force that we apply on one point is equal to the gain times the other force.
Types of levers: Class 2 levers
Class 2 levers (advantageous levers): The fulcrum is on one extreme, the resistive force in the middle and the motor force on the other extreme. The gain is always larger than 1 as bm is always larger than br. If the distance of where we exert a force with respect to a fulcrum is larger than the distance of the resistive force with respect to the fulcrum means that the force that we have to apply will be lower (because it's the product of the two: the force applied times the distance from the fulcrum). An example of this is the nutcracker. The gain is always larger than 1, so if we apply a force of 1N we could get a resistive force of 5N (example).
Types of levers: Class 3 levers
Class 3 levers: the fulcrum is on one side, the motion force in the center and the resistive force on the other side. br is always larger than bm, by construction the gain is always less than 1. An example of this is tweezers: we have a fulcrum, we apply a force in the middle and it is exerted in the other extreme. The force generated by the object is lower than the one exerted on it. We have a gain lower than 1. It is important for precision (it demagnifies the force than we apply).
Vector F is 65 m long, directed 30.5° below the positive x-axis. (a) Find the x-component, Fx. (b) Find the y-component, Fy.
Fx=56 m, Fy=−33 m
Heat transfer
ENERGY FLOWS FROM WARMER TO COOLER OBJECTS IN THE FORM OF HEAT (Q). T3 will be the intermediate temperature between the two (T1 and T2) = become one. It is typically defined as the flow of energy from an object at a higher temperature to an object at a lower temperature. 1. We consider two objects with two different temperatures, T1>T2, and we place them in contact. Energy flows between them. 2. After some time, the two objects will reach the same temperature T3 which is an intermediate measure between T1 and T2. At this point there will be no more exchange of heat. 3. NB: Only the passage of heat from a warmer to a cooler object is spontaneous: the opposite passage requires an external intervention and the expense of some energy (ex: it is the mechanism used in refrigerators).
Then, we can apply again the conservation of the mechanical energy:
ETOT = kinetic energy + elastic energy =
What is an equilibrium state?
Equilibrium state: A state where there is no change in the variables of the system.
What is the second law of thermodynamics?
Every energy transfer or transformation increases the entropy of the universe (the total entropy of a system + surroundings can never be negative/decrease. If a system is absorbing heat. Then the variation of entropy is always larger than the heat that is exchanged > 0.
Types of thermodynamic variables:
Extensive: proportional to system size V = Volume N = number of particles 1. For example, using a container, if we take one of the variables such as the volume V of the container, we'll see that if we increase the size of the container, also the volume will increase. 2. Another extensive variable is the number of particles N and also in this case if we double the size of a gas system for example, also the number of particles will double. As we have seen, usually we use capital letters to define extensive quantities like volume or number of particles. Intensive: independent of system size p = pressure T = temperature 1. Now let's move on to intensive quantities, which we indicate with small letters, these quantities are independent from the size of the system, for example pressure p or temperature T (which is always written with the capital T because small t can be confused with time).
So, the gravitational force exerted by the Earth on a generic mass m can be written as:
F = mg Practically, g is not always constant: 1. it is slightly greater than 9.8 m/s2 at the poles: the Earth radius at the poles is smaller, therefore g is larger, since r2 is the denominator in the g formula (g=(GME)/R2E) 2. it is slightly smaller than 9.8 m/s2 at the equator: the Earth radius is larger at the equator, therefore g is smaller, since r2 is the denominator *So larger distance means smaller force. **Also the rotation of the Earth decreases g, because it rotates centrifugally.
Gravity is _____. The Electric Force can ____.
Gravity is ALWAYS an attractive force. The Electric Force can attract and repel.
What is helmotz free energy?
Helmholtz free energy is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential (the helmotz free energy measures the useful work retrievable from a closed system). It may be described as the following equation: F = U -TS.
What is an impulse?
Impulse: ∆p = F∆t (impulse is a force that acts for a certain time interval and creates a variation in an object's linear momentum = change in momentum) Let's consider an isolated system made of two masses: object A exerts a force on object B, and object B exerts an equal but opposite force on object B, according to 3rd law. ∆(pA+pB)=0 ∆ptot=0 Since the variation in the total linear momentum of the system is 0, we say that the linear momentum conserves itself in the system. The total linear momentum is the sum of all the linear momentum of the particles.
Conditions for equilibrium of a material point?
If we consider just a point with no extension, the condition for equilibrium is just that the net force (which is the vectorial sum of all the forces) must be zero. In that case the force is 0 and the point stays there, so the acceleration is 0. The body will either move with some velocity and continue with this velocity or stay at rest if it was at rest (in any case it will stay in equilibrium). If there are 3 forces acting, this is equivalent to saying that the sum of the components of the 3 axes will be 0. This is the condition that is necessary and sufficient to determine the equilibrium of a material point.
The other mass will induce a counterclockwise rotation, the torque will therefore be positive: t(1) = m(1)∙g∙(l/2) both torques are trying to induce a rotation but as number 2 is stronger, we will have an overall clockwise rotation. The sum of the two torques is not 0 because m2 is larger than m1.
If we sum them, we will get: -m(2)∙g∙(l/2)+m(1)∙g∙(l/2) = g∙(l/2)(m(2)m(1)) < 0 In the second case, if we apply the same reasoning, we will find: - m(2) r(2) ∙ g + m(1) r(1)∙g = g ( - m(2) r(2) + m(1) r(1) ) From the definition of the center of mass, m(2) r(2) = m(1) r(1) so (- m(2) r(2) + m(1) r(1) = 0 and the total torque will be = 0. By definition of center of mass, we are sure that if we hang the object at the center of mass, the sum of all torques will be 0 and there will be no rotation. Gravity is acting on all the masses, but it is concentrated at the center of mass. If we consider gravity, the total torque will be the total mass times the distance from the center of mass: t (tot) = (m(1) + m(2) ) g ∙ r(CM)
Thermal Expansion:
If you increase the temperature of most materials, their size also increases (i.e. they expand). For roughly 1D objects (like a rod), changing temperature (ΔT) also changes the length (ΔL) of the rod.
Units of measurement
In 1960, during the eleventh 'Conférence Générale des Poids et Mesures (CGPM)', the International System of Units (SI) was developed. It now includes two classes of units: the seven base units and the derived units.
How are multiple capacitors connected in parallel? What is its overall capacitance?
In parallel = link both positive sides from terminal A to one terminal (terminal B) that is negative. Share the same terminal on all sides. Capacitance = sum of all capacitance. If we want to increase overall capacitance using 2 capacitance I bought in the store = put capacitance in parallel. Multiple capacitors in parallel higher capacitance than multiple capacitors in series.
How are multiple capacitors connected in series? What is its overall capacitance?
In series = one next to the other one, positive next to negative charge. Electric potential is the same across C1 and C2 = Q (+Q, -Q, +Q, -Q, etc.). Same electric potential. Delta V / Q = 1 / C. 1 / C = the sum of all capacitors (C).
Microscopic description of Entropy: Probability of a possible arrangement.
In terms of probability in thermodynamics -- chamber where we have particles, means that N = 10^23 -- a lot more particles. If there are n number of particles in a chamber connected via a switch to another then there are many possibilities of particle arrangements to be divides amongst the two chambers the following.
When does an increase in entropy not mean a system that is in disorder?
In the case of opal: hydrated amorphous forms of silica. These silica spheres do not interact and settle in regular structures. Regular distribution means that we see these colours. First there is random distribution (disorder), but then there is an increase in entropy once they are equally spaced. Why is there an increase in entropy, because of this order (equal distribution)? If you fill the volume with particles ina regular order, they will be separated (some space between all of them) and they have more space to move (vibrate a little bit). = This is entropically favoured = particles have more freedom. If they are in disorder (irregularly distributed), once we reach a certain distribution, the particles won't be able to move anymore.
This can also be seen by drawing a line with the same direction of the force F, called line of action. With respect to it we can consider the projection of point O to this line, and by drawing the rectangle triangle, we can find the magnitude of the torque with this formula:
In which we consider the magnitude of the force (F), the magnitude of the vector r (distance) and the sine of the angle formed between the vector r and the force, which is equal to the angle shown in the picture. If we call r the distance between O and the line of action, it is equal to r times the sine of ϕ.
What happens to entropy in an irreversible process?
Increases
What forces act on this object?
Indeed, on this mass we have the gravitational force (F = mg) and the reaction of the surface (F = - mg). They are exactly equal and, because they are in opposite directions, they cancel each other out. Even if the mass is not moving, they are acting: if we remove the solid boundary, the mass would just fall.
A fixed mass of an ideal gas undergoes a change in which it is supplied with 3500J of heat. At the same time this gas does 3500J of work on its surroundings. Which type of change does the gas undergo during this time?
Isothermal.
When do you need to consider the Gibbs free energy?
Most processes in chemistry and biology occur at constant temperature and pressure, and so to decide whether they are spontaneous and able to produce non-expansion work we need to consider the Gibbs free energy.
Friction force in liquids and gases: What are solid-gas interfaces?
Motion of a solid object through a gas at high speed We consider a solid object falling in air (in a gas) like for example someone parachuting. In this case there is a drag force that comes from its interaction with the air molecules, which we neglect in experiments most of the times If someone jumps from a plane, he will start falling with a first negligible friction force; at first, we will therefore only have the weight as a force (linear motion with constant acceleration). The velocity at this point increases quite rapidly until it reaches a certain value.
Friction force in liquids and gases: What are solid-liquid interfaces?
Motion of a solid object through a liquid: 1. We consider the motion of a solid object through a liquid; we therefore have an interface between a solid object and a liquid. This can be, for example, a particle that has some weight, (heavier than the liquid) that is falling in the liquid. 2. There is a friction that comes from the interaction between the solid surface and the liquid molecules. 3. There is a weight (Fg), as the particle is falling by the action of gravity, and a friction force (Fd), acting perpendicularly to the motion of these particles. 4. In this case (motion of an object through a liquid) this friction force is proportional to the velocity, so the larger is the velocity at which this object is falling into this liquid, the larger is the drag force.
Internal Energy (U or ΔE(int)) can be changed in 2 ways:
heat and/or work
Heat (Q) always flows from ____ to ____
hot to cold, until they reach equilibrium.
Acceleration is...
how fast your velocity changes.
38.6mm to m
in red is the right answer
We are now finding the torques for the two previous cases:
in this case we assume that the bar has a length l. the mass on the right will induce a clockwise rotation (the torque will be negative),so the torque given by this mass will be: t(2) = - m(2)∙g∙(l/2)
If work is done by the system, its sign is:
NEGATIVE
The SI unit of force is the newton. Express the newton in terms of basic SI dimensions, mass M, length L, and time.
Need to know F = ma a) L M^-1 T^-2 b) L^-1 M^-1 T^2 c) L M T ^-2 (acceleration = m/s^2) d) L M^-1 T^2
Since the mass is accelerated, the velocity _______.
increases and it passes the equilibrium condition and it goes in the opposite way: the mass is then compressing the spring.
What happens to the amount of entropy in a closed system?
Never decreases.
Your friend claims they have a design for a reversible heat engine that can operate between the freezing and boiling temperatures of water that has an efficiency of 30%. Is this possible?
No
If a mass goes to space, will its weight stay the same?
No.
Inclined Plane - Problem: A sled of 20kg of mass, initially at rest, slides on a plane inclined 30 degrees compared to the ground. Considering that the speed of the sled at the end of the inclined plane is 10m/s, calculate (neglecting friction) the initial height from the horizontal plane.
Notice that the motion of the object is forced to be on the plane, it does not follow the direction of g (which is perpendicular), therefore one our calculation we won't use g, but a. We need to decompose W in its two components: W parallel and W perpendicular
When are objects in free fall?
Objects are in free fall if the only force acting on them is gravity (Fg), even if they're moving upwards. eg. the third image has velocity moving it upwards, but that doesn't matter, because when the object falls (after you've thrown it upwards) - the only force acting on it is gravity = free fall.
How do objects in free fall accelerate?
Objects in free fall accelerate down with free fall acceleration (g). §
SI prefixes and scale factors
Order of magnitude.
What is a parallel plate capacitor?
Parallel plate capacitor consists of two conducting plates, each of area A, separated by a gap of thickness d containing a non-conductive medium (dielectric). Conductive: when free charges inside the material are free to move density of charges = sigma = Q (charge) * d (distance between the plates) / A (area) * E (the material of the plates). Capacitance (C) = the relationship between the charge and the electric potential of the object (C / V) = delta V = (total charge <Q> / Capacitance <C>).
When there is a phase transition, entropy
increases, because there is more freedom to the particles as the state changes, the largest increase in entropy is from liquid to gas due to a higher degree of freedom.
Since I ∝ ML^(2) increasing the distance (L) ____ the inertia.
increases; when inertia increases the angular momentum decreases. Hence, the rotation is slower with arms open.
A liquid is characterized by
indefinite shape and fixed volume.
A gas is characterized by
indefinite shape and indefinite volume Break all the bonds between the molecules.
What is Q in an adiabatic process?
Q = 0
Law of Heat Conduction aka. Fourier's Law:
Q = heat/energy = how fast is it to transfer heat through this block (= change in Q over change in time). A: The larger the surface = the larger the area we need to provide the conduction. d: thickness of the block k: thermal conductivity = how fast is the heat transferred. = Substances with high thermal conductivities (k) are good conductors of heat; those with low thermal conductivities are good insulators.
What is a quasistatic process?
Quasistatic process: a process that takes place so slowly that equilibrium can be assumed at all times. No perfect quasistatic processes exist in the real world.
What is the Carnot cycle?
Remember: The Second Law of Thermodynamics says no heat engine can EVER have an efficiency of 100%. The carnot cycle is an ideal "reversible" cycle that has the maximum possible efficiency. An engine is "reversible" if processes happen infinitely slowly and without frictional forces dissipating energy.
Calculate a) the components and b) the absolute angle for the given vector A. sol.
Remember: We always use the reference angle (θx).
3rd process: isothermal compression
Same as isothermal expansion, there is no temperature change during this process so Uc→d = 0 so ΔUc→d = -QL - Wc→d = 0 so Wc→d = -QL (- the heat that is released).
In the conservative forces, the work done doesn't depend on the path, but only on the:
initial and final state. It means that we can define a quantity that is a function of the initial and final state and this is the final potential energy U.
What is the erythrocyte sedimentation rate?
Sedimentation velocity is used in clinical practice; the sedimentation speed of red blood cells (erythrocytes) is a simple hematology test that can give indications of pathological conditions, being a measure of inflammation. It is called ESR (erythrocyte sedimentation rate- in Italian it's used as VES) and it indicates the rate at which red blood cells sediment in period of one hour. To perform this test, non-coagulated blood is placed in an upright tube with a scale (Westergren tube), like the one in the picture. Although we cannot see the motion of the red blood cells, after one hour it is possible to see the meniscus (the level) of red blood cells that have fallen in a certain length. After one hour, it is possible to measure how much the level has fallen, which is equal to the sedimentation velocity. It is possible to use this value by setting an average value for the red blood cells and their radius; this is because red blood cells are discs, so they aren't perfectly spherical.
Kinetic-Molecular Theory =
Set of equations connecting P, V, T with the kinetics (motion) of ideal gas molecules. Aka. Equations connecting P, V, T (macroscoping) to v, K (eg. velocity & temperature = microscopic).
Classes of Pulleys: 1. Single fixed pulleys 2. Single moveable pulleys What are single fixed pulleys?
Single fixed pulleys: in this case the mechanical gain is equal to 1 so the forces applied on both ends are equal.
Friction force in liquids and gases: What are solid-solid interfaces?
So when we have solid-solid interfaces and we have an object that is sliding onto another one, there is a force that is always opposite to the direction of motion, the friction force.
What is static friction?
Static friction. It is the force which acts in the opposite direction when we want to put in motion an object. Ex. we have a big box resting on the force; we want to move it and when we push it, we need to exert some force to start the motion of the box. What is acting against our force? The static friction force, which acts in the opposite direction of our force. If we want to move the box, our force F needs to be higher than the static force FS.
The Carnot cycle can be broken up into 4 different parts;
isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression. Carnot cycle = goes back exactly to the same state. Variation of the internal energy should be equal to 0, because it goes back to the exact same stage.
The phase of a material = sate of matter (eg. ice = solid; water = liquid; steam = gas) usually depends on temperature. Remember: When a material absorbs or loses heat, it changes ______.
Temperature OR Phase, but not BOTH.
What is angular momentum?
The 2nd Newton's Law states that F = ma where a = v/; we have expressed this force as the variation in linear momentum. We can say the same for rotational motion. This quantity is called angular momentum.
Why is the carnot cycle important?
The Carnot cycle is also important because it is the simplest case of a thermal engine and it's also the engine that has the highest efficiency.
What is the Coulomb (C)?
The Coulomb (C) is the standard (SI) unit of electric charge in the International System of Units (SI). This is the unit charge of an electron (with negative sign). A proton has the same charge (but positive). A neutron has zero charge.
What is Coulomb's Law?
like charges repel, unlike charges attract The magnitude of the force of attraction or repulsion between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Resistors in parallel have a
lower resistance than resistors in series.
The Gravitational Force is based on _____. While Coulomb's Law is based on ____.
The Gravitational Force is based on MASS. While Coulomb's Law is based on CHARGE.
The work done to go from A to B is defined as the variation of potential energy from A to B. For conservative forces, it is always true that the sum of the potential energy and the kinetic energy, known as: ________.
mechanical energy EM, is constant (this is true if there are only conservative forces)
Length
meter (m)
The work done from A to B and back to A is ______.
not equal to zero as in the conservative forces, but is different from zero. That's why the friction force is dissipative. 1. The same process even if we consider a long path rather than a short one: the longer is the path, the longer and higher would be the work done by the friction force. 2. Because it is a dissipative force, some kinetic energy is dissipated (typically it is dissipated as heat).
A quasistatic process is
not necessarily reversible, but almost always.
The position of an object vibrating on a moving spring is represented by the diagram below. Which of the following options is true of the velocity and acceleration at Point P? sol.
The velocity is negative and the acceleration is positive.
What is the ideal gas law equation?
p*V = n*Na*Kb*T = n*R*T Kb is the Boltzmann constant, and the product of the Avogadro's number Na and Boltzmann constant Kb define what is known as ideal gas constant R.
The gravitational force field g of the Earth is represented by...
parallel vectors that point vertically (and perpendicularly) towards the surface of the Earth, which is imagined as a flat horizontal surface.
Gravitational force is a conservative force and so we can define a ______.
potential energy. 1. We consider a skier who is at a certain height with respect to the horizontal plane. By the action of gravity, the man falls. 2. The height is called Z. The starting point is A and the final point is B. 3. The gravitational force acts with a vertical direction.
If a body has a temperature of 0 Kelvin, this means that:
The body has 0 kinetic energy.
The work divided by the time interval defines what is known as:
power.
The total number of microstates Ω is
proportional to Volume to the power of n, which is number of particles. This is in the initial state.
Formula for the internal energy of an ideal gas:
The formula v=... defines the behaviour of particles inside a gas. As the temperature increases, the molecules have more energy, therefore move faster (-> the collision frequency increases as well). Not only do particles collide more often but also they collide harder. Putting together different formulas we obtain the formula of the internal energy: U = (3/2)*n*R*T
Now, if we are in a liquid medium and the sphere is falling, we'll see that the force will be different and, more importantly, we'll have a friction force (drag force) that is _____.
proportional to the velocity at which this particle is falling.
Thermometers and temperature scales
The pressure in a gas is proportional to its temperature. The proportionality constant is different for different gases, but they all reach zero pressure at the same temperature, which we call absolute zero (AT ZERO KELVIN = we have 0 kinetic energy). In this graph we see 3 different types of gasses, if we increase the temperature, the gases will increase their kinetic energy and in turn increase the pressure of the gas. It is shown that considering three different gases, by measuring the pressure at different temperatures, it is possible to detect a linear relationship between pressure and temperature in a gas. Of course, with different slopes, but they all align as long as they are ideal gases, a concept that we will clarify during the course. In all of them pressure is proportional to the temperature. Even with different slopes, they will all intersect in the same point, which corresponds to pressure = 0. They reach a pressure of 0 at a temperature of -273.15 Celsius, that is for that defined as the absolute zero. In result, Kelvin has only positive values, from zero to infinity. All of the lines intersect, where the pressure of the gas = 0.
In the end, the conditions of equilibrium define 3 relationships:
The sum of all forces acting in the horizontal direction is zero, the sum of all forces acting in the vertical direction is zero, and the sum of all momentum, so the sum of all the torques defined by the forces, which are perpendicular to the plane of the body (z direction), must be zero.
What is the weight?
The weight is the force that acts on a generic mass by the action of the gravitational field created by the Earth. W (weigth) = F = mg Weight differs from mass: the mass is the quantity of a material expressed in kg, and it is constant; weight is expressed in Newtons (N) and it changes if we change g.
What is work?
The work (W) done by a force (F) is defined as the scalar product (product of 2 vectors = scalar) of the force F, the displacement s of the system (due to the action of F), and the cosine of the angle between vector F and vector s: W = F s cos(a)
What is the work done by the gravitational force to bring the skier from A to B?
The work done is force x displacement, which acts in the same vertical direction. The force is mass x acceleration (in this case the acceleration is g), while the displacement is Z.
There could be other types of processes, such as the isobaric process, in which the pressure is constant and it can be represented in:
There could be other types of processes, such as the isobaric process, in which the pressure is constant and it can be represented in a graph P over V like in the image above, in this case we change volume but pressure remains constant. Then we also have the isovolumetric process, in which pressure changes but volume is constant.
What is a thermodynamic process?
Thermodynamic process: A change in the state of the system from one equilibrium state to another 1. When we have a system that is defined by some variables, the system starts from an equilibrium state, so it means that all the variables that we measured (volume, pressure...) are constant and they're not changing with time. 2. Starting from an equilibrium state, if we act in some ways on the system, there will be a change in the state of the system, so the variables will change, and this is called the thermodynamic process.
Work can also be written as the difference between 2 potential energies:
UB (final potential energy) - UA (initial potential energy). W = mass * g (gravitational acceleration) * z (height) = UB - UA = U(z) 1. By definition, the potential energy in B (ground level - h=0) is zero. The ground level is where the gravitational force cannot change anything, where the skier cannot fall below. 2. The potential energy in A can now be calculated as the product mgz. 3. In other words, the gravitational potential energy can be expressed as the product between mass, acceleration and height. It increases while we increase the position of the object from the horizontal plane. If we move parallel to the horizontal plane, the potential energy doesn't change. It changes only when we move in an opposite direction with respect to gravity, we move against the gravitational field.
The total electric potential energy stored in a capacitor is:
Uc = (1/2) * Q * delta V = (1/2) * C * delta V^2 𝑄 is the charge stored in the capacitor, Δ𝑉 is the voltage across the capacitor, and 𝐶 is the capacitance. Another way to express this is C = Q / delta V. Q = C * delta V. Eg. C = 1 millifarad * 1 Volt = charge = Q = 1 milliq. What is the job of the capacitor? = to store energy = if we charge the capacitors we can use them as battery = to do work. The total amount of electric potential energy that can be stored in a capacitor is Uc. = The larger the capacitance = the larger the total electric potential energy you can store. V = Uel / q Uel = V * q = electrical energy * charge.
How are multiple resistors connected in series? What is its overall resistance?
Va - Vb is different across resistors, but current (I1 vs. I2) will be the same.
How are multiple resistors connected in parallel? What is its overall resistance?
Va - Vb is the same across both resistors, but current (I1 vs. I2) will be different.
Vector Composition vs. Vector Decomposition
Vector Composition: find the hypotenuse. Vector Decomposition: find the legs.
Differently from mass, the electric charge is ___.
quantized, i.e., any process occurring with a transfer of charge occurs only in multiples of an elementary charge (e).
If vector F and vector s have opposite directions, then...
W = -Fs. The work done by friction is always negative.
What does this graph show us? What is the the function of W?
W = radiated power P. SI unit of this radiated powe P = W.
Levers and pulley systems
We consider objects that are anchored(fixed) in one point, called the fulcrum. The object is fixed in its position but it can still rotate. The condition for the equilibrium is now that the sum of all the torques generated by all the forces applied on this object must be equal to 0. It is a necessary and sufficient condition for equilibrium because the object is fixed to the fulcrum (so is in translational equilibrium). If we consider a bar with a force acting on it(red sketch), the condition of the net force equal to 0 is respected, as there are two equal and opposite forces: the one exerted on the bar(F) and the reaction force(R) given by the fixed point. So in order for a leaver to be in equilibrium the sum of the torques must be 0.
Biomechanics: Achille's Tendon This is another simple example where we can find out the amount of force exerted by the Achilles' tendon in the moment of walking:
We know the following information: 1. FP : Reaction of the soil on the sole of the foot caused by the weight of the body. 2. F0 : Strength exerted by the bones of the leg (tibia and fibula) on the heel. 3. FT : Force applied by the Achilles tendon on the calcaneus. We don't know any of these forces, but here too the conditions of equilibrium are applied and the final force is found.
How would you calculate the electric potential energy (J)?
What is the gravitational potential energy? Gravitational potential energy (U) U = mgh. Electric potential energy (U) = E*q*y Electric potential energy / charge = electric potential -- V = U / q -- unit = J / C = V (volts). Volts = difference of electric potential between two plates.
Temperature: 'macroscopic view' - thermal equilibrium
When 2 objects have the same temperature, they are in thermal equilibrium, , a condition in which there is no more net exchange of energy (in the form of heat). The two objects in contact will reach the same temperature. It is very important, as it allows us to measure the temperature of our body. A thermometer measures it OWN temperature.
second law of thermodynamics: Irreversible Process
When a process is spontaneous = irreversible. Where heat goes from hot to cold. Heat flows spontaneously from a body at high temperature to a body at low temperature (Clausius).
Why did we neglect friction when solving the sleigh problem?
When we have solved the problem with the sleigh, we intentionally neglected the normal force because we have just considered the parallel component of the weight. In fact, it is the only force which makes the sleigh move on the plane. However, if we want to have the precise condition of equilibrium of the forces acting on the sleigh, we have also to consider the normal force because the weight is acting both on the direction parallel and perpendicular to the plane. The perpendicular component of weight is completely balanced by the normal force N (in fact, the sleigh cannot go through the horizontal plane). This is important when talking about friction because the larger is the weight (and, as a consequence, the normal force), the stronger is the interaction between the two boundaries (object and plane). If we have a small normal force, we have a small contact area. Friction always acts in the opposite direction of the motion of the object and it is proportional to the normal force.
Volume Thermal Expansion:
When you increase the temperature of a 3D object (eg. a sphere or a cube their volume also increases
What is the value of work when we go from the starting point A to point B and then back to point A?
Work is 0 when we go from the starting point A to point B and then back to point A: this is why work is a conservative force. The variation of kinetic energy is equal to 0 too. Instead, with regard to dissipative forces, work is different from 0 when we go from A to B and back to A. The variation of kinetic energy is different from 0 too (we lose some kinetic energy).
What type of force is work?
Work is a conservative force: the work done by the force F does not depend on the choice of the path.
If a mass goes to space, will it stay the same?
Yes.
2. Linear motion with constant acceleration This is a useful formula for free fall motion, which is ...
a common type of linear motion with constant acceleration (neglects friction), where (see image). Another example could be an object that is sliding down a plane under the action of gravity. In this case acceleration is not gravitational acceleration, but the projection of gravity along the plane → a= gᐧ sinθ. We won't go deeper in the topic because we'll learn it later.
What is an electric circuit?
a complete, unbroken path through which electric charges can flow. Simplest case: connect a battery (that creates a voltage difference = delta V) to a resistor. eg. 10 V / 10 R = 1 Ampere
A solid is characterized by
a definite (fixed) volume and a fixed shape.
Complete this table: Solution
change in entropy = (delta S) heat transfer = (delta Q) temperature = (T).
What is enthalpy?
the heat content of a system (H). The energy released as heat by a system which can easily expand or contract when a process occurs and is distinct from the total energy released in the same process is exactly equal to the change in enthalpy of the system.
Displacement is the movement of an object in a specific direction, but we need to follow the position of an object through space by what we call its:
trajectory; position of the object at s(t1) can be identified for example by a vector, etc. The position is a vector that moves with time = function of time. Changes over time. In general, if we call 𝒔 the part of trajectory that a body follows in a time 𝑡, we can fully describe the motion by the time-law of motion: 𝒔 = 𝒔(𝑡) → 𝑥 = 𝑥 (𝑡) ; 𝑦 = 𝑦 (𝑡) ; 𝑧 = 𝑧 (𝑡). Observing the motion of a particle from 3 perspectives (x,y,z).
Dimensional analysis is important
when trying to figure out if the dimensions (units) of a solution are correct.
What is the formula for multiple / systems of objects' entropy changes?
ΔS(tot) is always increasing.
The angle that the point has travelled would be:
Δθ for a given time Δt; we call this angular velocity (variation of angle in a circular motion), that is constant and expressed as units of angle (radians) over seconds or simply 1/s:
