MCAT Physics & Math
Surface tension
"Skin" on the surface of a liquid - results from cohesion (the attractive force that a molecule of liquid feels toward other molecules of the same liquid)
A low-pressure weather system can decrease the atmospheric pressure from 1 atm to 0.99 atm. By what percent will this decrease the force on a rectangular window from the outside? (Window = 6m by 3m and the glass is 3cm thick) 1% 10% 1/3% 30%
1%
Which of the following processes is LEAST likely to be accompanied by a change in temp? The kinetic energy of a gas is increased thru a chemical reaction Energy is transferred to a solid via electromagnetic waves A boiling liquid is heated on a hot plate A warm gas is mixed with a cold gas
A boiling liquid is heated on a hot plate
Mass (m)
A measure of a body's inertia (the amount of matter in the object) ** Scalar (has magnitude only) - SI unit = kilogram (independent of gravity) F_g = mg - F_g = weight of the object - m = mass - g = acceleration due to gravity (10 m/s^2)
Weight (F_g)
A measure of gravitational force on an object's mass ** Vector (bc it is a force) - SI units = newtons (N) F_g = mg - F_g = weight of the object - m = mass - g = acceleration due to gravity (10 m/s^2)
Work done
A process by which energy is transferred from one system to another - SI unit = joule (J)
Energy
A system's ability to do work (to make something happen)
Friction
A type of force that opposes the movement of objects - ALWAYS opposes an objects motion (causes it to slow or become stationary) Static friction (f_s) = exists b/t a stationary object & the surface upon which it rests Kinetic friction (f_k) = exists b/t a sliding object & the surface over which the object slides
Gravity
An attractive force that is felt by all forms of matter - All objects exert gravitational forces on each other
Order the following units from smallest to largest: centimeter, angstrom, inch, mile, foot
Angstrom, centimeter, inch, foot, mile
Vector addition: component method
Break each vector into perpendicular components - Mostly horizontal & vertical (aka x and y components) ** Given any vector V, we can find the x and y components (X and Y) by drawing a right triangle with V as the hypotenuse (pic) If θ is the angle b/t V and the x-component, then cos θ = X / V and sin θ = Y / V X = V cos θ Y = V sin θ
Open systems
Can exchange both energy and matter with the environment
Closed system
Capable of exchanging energy but not matter w/ their surroundings
Multiplying vectors by scalars
Change in magnitude & its direction will be either parallel or antiparallel to its original direction If vector A is multiplied by the scalar value n, a new vector, B, is created and B = nA - To find magnitude of B multiply the magnitude of A by the absolute value of n - If n is positive then the direction of B points in the same direction of A & if n is negative then B points in the opposite direction of A Ex: A x +3 = B is three times as long as A & points in the same direction
Types of menisci
Concave (a) and convex (b)
Heat transfer (thermodynamics)
Conduction = the direct transfer of energy from molecule to molecule through molecular collisions - Requires direct physical contact Convection = the transfer of heat by the physical motion of a fluid over a material - Liquids & gases ONLY Radiation = the transfer of energy by electromagnetic waves - Works in a vacuum
Conservation of mechanical energy
Conservation of mechanical energy formula: ΔE = ΔU + ΔK = 0 (ΔE, ΔU, ΔK = changes in total mechanical energy, potential energy, and kinetic energy) Conservative forces = path independent & do not dissipate energy (have potential energy) - Ex: gravitational force & electrostatic force When nonconservative forces (friction, air resistance, viscous drag) are present the total mechanical energy is not conserved W_nonconservative = ΔE = ΔU + ΔK
A water tower operator is interested in increasing the pressure of a column of water that is applied to a piston. She hopes that increasing the pressure will increase the force being applied to the piston. The only way to increase the pressure is to alter the speed of the water as it flows through the pipe to the piston. How should the speed of the water be changed to increase the pressure and force? Increase the speed Decrease the speed Release water intermittently against the pipe The speed of water will not change pressure at the piston.
Decrease the speed
The entropy of a system can: Never decrease Decrease when the entropy of the surroundings increases by at least as much Decrease when the system is isolated and the process is irreversible Decrease during an adiabatic reversible process
Decrease when the entropy of the surroundings increases by at least as much
Specific gravity equation
Density of substance / density of water
Gravitational potential energy
Depends on an object's position to some level identified as the datum ("ground" or 0 potential energy position) U = mgh - U = potential energy - m = mass (in kg) - g = acceleration due to gravity - h = height of object above datum
Process functions
Describe path taken to get from one state to another - Ex: work and heat
Which of the following quantities is NOT a vector? Velocity Force Displacement Distance
Distance
Potential energy
Energy that is associated with an object's position in space or other intrinsic qualities of the system
Inclined plane
Example of motion in 2 directions - divide force vectors into components that are parallel & perpendicular to the plane
Translational equilibrium
Exists only when the vector sum of all of the forces acting on an object is zero (first condition of equilibrium) ** When the resultant force on an object = 0 then the object will not accelerate
Conversion equations for measures of temperature
F = 9/5C + 32 K = C + 273
Force (F)
F is vector quantity that is experienced as pushing or pulling on objects - can exist b/t objects that are not touching - SI unit = newton (N) - equivalent for one (kg x m)/(s^2) Ex: gravity
Newton's third law of motion
F_AB = -F_BA Law of action & reaction - for every force exerted by object A on object B, there is an equal but opposite force exerted by object B on object A
Laminar flow
Flows in parallel lines in a smooth progression Rate of laminar flow can be determined by Poiseuille's law: Q = (πr^4ΔP) / (8nL) - Q = flow rate (volume flowin per time) - r = radius of tube - ΔP = pressure gradient - n = fluid viscosity - L = length of pipe
Newton's second law of motion
Fnet = ma - Fnet = net force - m = mass - a = acceleration An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector
Newton's first law of motion
Fnet = ma = 0 - Fnet = net force - m = mass - a = acceleration A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it - Law of inertia
If the newton is the product of kilograms and meters/second^2, what units comprise the pound?
Force is always the product of mass and acceleration, so one pound (lb) is equal to one (slug x ft)/(s^2)
Work: pressure & volume
Gas expansion & compression processes can be represented in graphs (P-V graphs) - shows the pressure-volume curve ** Gas expands = positive work is done by the gas ** Gas is compressed = negative work is done ** If volume is constant & pressure changes then no work is done (isovolumetric / isochoric process)
Which of the following is a conservative force? Air resistance Friction Gravity Convection
Gravity
Closed loop system
Has a nonconstant flow rate (result - Ex: circulatory system
Which of the following is NOT a state function? Internal energy Heat Temperature Entropy
Heat
SI units
Includes the metric system - meters (centimeters), kilograms (grams), seconds
In an adiabatic process, the internal energy of the gas: Increases bc the work done on the gas is negative Increases bc the work done on the gas is positive Decreases bc the work done on the gas is negative Decreases bc the work done on the gas is positive
Increases bc the work done on the gas is positive
Special Types of Thermodynamic Processes
Isothermal = constant temp (no change in internal energy) Adiabatic = no heat exchange Isovolumetric = no change in volume (no work is done)
Centrifugal force is an apparent outward force during circular motion. It has been described as a reaction force according to Newton's third law. Which of the following statements is most likely to be correct regarding centrifugal force? It only exists for uniform circular motion, not nonuniform circular motion It exists only when tension or a normal force provides centripetal acceleration It always acts antiparallel to the centripetal force vector It is a result of repulsive electrostatic interactions
It always acts antiparallel to the centripetal force vector
Molecular / atomic / subatomic units
Length = angstroms (1 Å = 10^-10 m) OR nanometers (1 nm = 10^-9 m) Energy on the atomic scale is expressed in electron-volts (1 eV = 1.6 x 10^-19 J) - Represents the amount of energy gained by an electron accelerating through a potential difference of one volt
Mechanical advantage & efficiency are both ratios. Which of the following is true regarding the quantities used in these ratios? Mechanical advantage compares values of work & efficiency compares values of power Mechanical energy compares values of forces & efficiency compares values of work Mechanical advantage compares values of power & efficiency compares values of energy Mechanical energy compares values of work & efficiency compares values of forces
Mechanical energy compares values of forces & efficiency compares values of work Mechanical advantage = ratio of the output force generated by a particular input force & efficiency = a ratio of the useful work performed on a system compared to the work performed on the system
Attractive forces are between
Molecules with opposite charges - Ex: gravity
Repulsive charges are between
Molecules with the same charge
Which of the following statements is true of movement on a plane with friction? Acceleration is a function of applied force only More force is needed to accelerate a stationary object than an identical moving object The force of friction is independent of the mass of objects
More force is needed to accelerate a stationary object than an identical moving object
Projectile motion
Motion that follows a path along 2 dimensions - The velocities & accelerations in the two directions (usually horizontal & vertical) are independent of each other ** Horizontal velocity is constant
Multiplying vectors
Multiply the magnitudes of the two vectors of interest (force & displacement) and the cosine of the angle b/t the two vectors - Called the dot product (A⋅B) A⋅B = [A] [B] cos θ - [ ] = absolute value ** When generating a third vector, both magnitude & direction needs to be determined - multiply the magnitudes of the 2 vectors of interest and the sine of the angle b/t the two vectors - Cross product (A x B) ** Resultant of cross-product will always be perpendicular to the plane created by the 2 vectors A x B = [A] [B] sin θ
During uniform circular motion, which of the following relationships is necessarily true? No work is done The centripetal force does work The velocity does work Potential energy depends on position of the object around the circle
No work is done
Isolated system
Not capable of exchanging energy or matter w/ their surroundings (total Δ in internal energy is 0) - Universe is considered isolated b/c no surroundings
Vector
Numbers that have magnitude & direction Vector quantities include: displacement, velocity, acceleration, force May be represented by arrows - the direction of the arrow indicates the direction of the vector & the length of the arrow is proportional to the magnitude of the vector quantity (also represented by bold type)
Scalars
Numbers that have magnitude ONLY and no direction Scalar quantities include: distance, speed, energy, pressure, mass Represented by italic type
Rotational equilibrium
Occurs when an object's net torque is zero (second condition of equilibrium) ** Torques that generate clockwise rotation = neg ** Torques that generate counterclockwise rotation = positive
Rotational motion
Occurs when forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point (the fulcrum) - Application of force at some distance from the fulcrum generates torque (t) / the movement of force (generates rotational motion) - Lever arm = the distance b/t the applied force and the fulcrum
Circular motion
Occurs when forces cause an object to move in a circular pathway - Displacement = 0 Uniform circular motion = object is kept in the circular pathway by centripetal force (generates centripetal acceleration)
In experiment A, a student mixes ink with water and notices the two liquids mix evenly. In experiment B, the student mixes oil and water - it separates. The entropy change is: Positive in A and negative in B Positive in A and zero in B Negative in A and positive in B Zero in A and negative in B
Positive in A and zero in B
Pascal's Principle
Pressure applied to a fluid is transmitted throughout the fluid - Fluid is considered incompressible if it is in a closed container
Which of the following choices correctly identifies the following three heat transfer processes? - Heat transferred from the sun to the earth - A metal spoon heating up when placed in hot soup - A rising plume of smoke from a fire Radiation - conduction - convection Conduction - radiation - convection Radiation - convection - conduction Convection - conduction - radiation
Radiation - conduction - convection
Pressure
Ratio of force per unit area - SI unit = pascal (Pa) - Scalar P = F / A - P = pressure - F = magnitude of normal force vector - A = area
Density
Ratio of mass to volume - Scalar - SI units = kg / m^3 OR g / mL OR g / cm^3 p = m / V p = density m = mass V = volume ** Density of water = 1 g / cm^3
A student making a coffee cup calorimeter fails to use a second coffee cup and inadequately seals the lid. What was her initial goal, and what was the result of this mistake? She was trying to create an isolated system but created an open system instead She was trying to create an isolated system but created a closed system instead She was trying to create a closed system but created an open system instead She was trying to create a closed system but created an isolated system instead
She was trying to create an isolated system but created an open system instead
Second law of thermodynamics
States that objects in thermal contact and not thermal equilibrium will exchange heat energy such that the object with a higher temp will give off heat energy to the object with a lower temp until both are the same temp
Archimedes' Principle
States that the buoyant force is equal to the weight of the fluid displaced by an object
First law of thermodynamics
States that the change in total internal energy of a system = amount of energy transferred in the form of heat to the system minus the amount of energy transferred from the system in the form of work Change in internal energy = ΔU = Q - W - ΔU = change in internal energy - Q = energy transferred into the system as heat - W = work done by the system
Substances A and B have the same freezing and boiling points. If solid samples of both substances are heated in the exact same way, substance A boils before substance B. Which of the following would NOT explain this phenomenon? Substance B has a higher specific heat Substance B has a higher heat of vaporization Substance B has a higher heat of fusion Substance B has a higher internal energy
Substance B has a higher internal energy
Vector subtraction
Subtracting one vector from another can be accomplished by adding a vector with equal magnitude (but opposite direction) to the first vector A - B = A + (-B) (-B = a vector with the same magnitude as B but points in the opposite direction)
Specific heat (c)
The amount of energy required to raise one gram of a substance by one degree C or one unit K q = mcΔT - m = mass - c = specific heat of a substance - ΔT = change in temp (C or K) Ex: specific heat of water = 1 cal / g⋅K
Adhesion
The attractive force between two particles of different substances
Displacement
The change in position of an object (x or d) ** Vector quantity (has magnitude & direction) Distance (d) = considers the pathway taken & is a scalar quantity
A hydraulic lever is used to lift a heavy hospital bed, requiring an amount of work (W). When the same bed if lifted with a patient in it, the work is doubled. How can the cross-sectional area of the platform that the bed is lifted on be changed so that the pressure on the hydraulic lever remains constant? The cross-sectional area must be doubled The cross-sectional area must be halved The cross-sectional area must be divided by 4 The cross-sectional area must remain constant
The cross-sectional area must be doubled
The speed of blood in the aorta is much higher than the speed of blood through a capillary bed. How can this fact be explained using the continuity equation, assuming that we are interested in average flow and that there is no net fluid loss? The aorta is located higher than the capillary bed The pressure in the aorta is the same as the pressure in the capillary bed The cross-sectional area of all the capillaries added together is much greater than the cross-sectional area of the aorta The cross-sectional area of a capillary is much smaller than the cross-sectional area of the aorta
The cross-sectional area of all the capillaries added together is much greater than the cross-sectional area of the aorta
Kinetic energy
The energy of motion - SI unit = joule (J) K = 1/2 mv^2 - K = kinetic energy - m = mass (in kg) - v = speed (in m/s^2)
Third Law of Thermodynamics
The entropy of a perfectly organized crystal at absolute zero is zero
Thermal expansion
The expansion of matter when it is heated ** The amount of length change is proportional to the original length of the solid and the increase in temperature ΔL = αLΔT - ΔL = change in length - α = the coefficient of linear expansion - ΔT = change in temp ** Coefficient of linear expansion = a constant that characterizes how a specific material's length changes as the temp changes (units = K^-1) Volumetric thermal expansion (applicable to liquids & solids) ΔV = βVΔT - ΔV = change in volume - β = coefficient of volumetric expansion (= 3x the coefficient of linear expansion for same material) - V = original volume - ΔT = change in temp
A parachutist jumps from a plane. Beginning at the point when she reaches terminal velocity (constant velocity during freefall) which of the following is / are true? The jumper is in translational equilibrium The jumper is not being acted on by any forces There is an equal amount of work being done by gravity and air resistance
The jumper is in translational equilibrium AND There is an equal amount of work being done by gravity and air resistance
If the gravitational potential energy of an object has doubled in the absence of nonconservative forces, which of the following must be true? Assume the total mechanical energy of the object is constant The object has been lifted to twice its initial height The kinetic energy of the object has been halved The kinetic energy has decreased by the same quantity as the potential energy increased The mass of the object has doubled
The kinetic energy has decreased by the same quantity as the potential energy increased
Linear motion
The object's velocity and acceleration are along the line of motion, so the pathway of the moving object continues along a straight line ** Air resistance opposes the motion of an object - its value increases as the speed of the object increases ** An object in free fall will experience a growing drag force as the magnitude of the velocity increases - drag force will eventually be equal in magnitude to the weight of the object & will fall with constant (terminal velocity)
A massless spring initially compressed by a displacement of 2cm is now compressed by 4cm. How has the potential energy of this system changed? The potential energy has not changed The potential energy has doubled The potential energy has increased by 2 joules The potential energy has quadrupled
The potential energy has quadrupled Elastic potential energy = U = 1/2 kx^2 2^2 = 4
Heat (thermodynamics)
The process by which a quantity of energy is transferred between two objects as a result of a difference in temp - SI unit = joule (J) 1 Cal = 10^3 cal = 4184 J = 3.97 BTU
Which of the following data sets is sufficient to determine the linear speed through an area of rigid pipe? The cross-sectional area in another segment of pipe and the cross sectional area in the region of interest They Reynolds number, viscosity of the fluid, density, and diameter of the pipe The radius of the pipe, pressure gradient, viscosity, and the length of the pipe The absolute pressure & density
The radius of the pipe, pressure gradient, viscosity, and the length of the pipe
Work: power
The rate at which energy is transferred from one system to another - SI unit = watt (W)
Speed (v)
The rate of actual distance traveled in a given unit of time
Acceleration (a)
The rate of change of velocity that an object experiences as a result of some applied force - Vector - SI units = m/s^2 Average acceleration (a) = Δv / Δt - Δv = change in velocity - Δt = change in time Pic = instantaneous acceleration formula
Mechanical advantage
The ratio of magnitudes of the force exerted on an object by a simple machine (Fout) to the force applied on the simple machine (Fin) Mechanical advantage = F_out / F_in Ex: pulley (the 2 ropes each carry 1/2 of load)
Bernoulli's equation is the reason for the upward force that permits airplane flight. Which statement best summarizes the equation's relationship to flight? The speed of airflow is equal on the top and bottom of a wing, resulting in non-turbulent flight The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight The speed of the airflow on the flat bottom of the wing is greater than over the curved top of the wing, resulting in more pressure below the wing and the production of a net upward force on the wing, resulting in flight The weight of the wing is directly proportional to the weight of the air it displaces
The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight
Base units vs. derived units
The standard units around which the system itself is designed VS. Created by associating base units with each other
Electrostatics
The study of stationary charges and the forces that are created by and act upon those charges
Total mechanical energy
The sum of an object's potential and kinetic energies E = U + K - E = total mechanical energy - U = potential energy - K = kinetic energy
Vector addition: tip-to-tail method
The sum or difference of two or more vectors is called the resultant of the vectors Tip-to-tail method: place tail of B at the tip of A without changing the length or direction of either arrow - Arrow lengths must be proportional to the magnitude of the vectors
Absolute (hydrostatic) pressure
The total pressure that is exerted on an object that is submerged in a fluid P = Po + pgz - P = absolute pressure - Po = incident / ambient pressure - p = density of the fluid - g = acceleration due to gravity - z = depth of the object
Which of the following best characterizes the work-energy theorem? The work done by any force is proportional only to the magnitude of that force The total work done on any object is equal to the change in kinetic energy for that object The work done on an object by any force is proportional to the change in kinetic energy for that object The work done by an applied force on an object is equal to the change in kinetic energy of that object
The total work done on any object is equal to the change in kinetic energy for that object
Work-energy theorem
The work done on an object equals the change in kinetic energy of the object - Can be applied to changes in other forms of energy
State functions
Thermodynamic properties that are a function of only the current equilibrium state of a system - Independent of the path taken to get to a particular equilibrium state - Ex: internal energy, pressure, density, temp., volume, entropy, gibbs free energy
Velocity
Vector - it's magnitude is measured as the rate of change of displacement in a given unit of time - SI unit = m/s Instantaneous velocity = measure of the average velocity as the change in time (Δt) approaches zero ** Instantaneous speed always = magnitude of instantaneous velocity
Work: force & displacement equation
W = F⋅d = Fd cos θ - W = work - F = magnitude of the applied force - d = magnitude of the displacement thru which the force is applied - θ = the angle b/t the applied force vector & the displacement vector
Elastic potential energy
When a spring is stretched or compressed from its equilibrium length, it has elastic potential energy U = 1/2 kx^2 - U = potential energy - k = spring constant (measure of spring stiffness) - x = magnitude of displacement from equilibrium
Zeroth Law of Thermodynamics
When one object is in thermal equilibrium with another object, and the second object is in thermal equilibrium with a third object, then the first and third object are also in thermal equilibrium
Phase change equation
q = mL q = amount of heat gained or lost m = mass L = heat of transformation (latent heat)
Change in entropy equation
ΔS = Qrev / T ΔS = change in entropy Qrev = heat gained or lost in a reversible process T = temp in K
