4A. Translational motion, forces, work, energy, and equilibrium in living systems

*Displacement* How is *displacement* different from *distance*?

*Distance* = scalar quantity = considers the pathway taken *Displacement* = vector quantity = does NOT consider the pathway taken = only considers the *net change* in position from initial to final

*Force* What is the *SI unit* for *Force*?

*Newton* (*N*) = (kg x m)/(s^2)

What are the 2 ways in which *energy can be transferred*?

*Work* and *heat* The transfer of energy by work or heat is the *only way by which anything occurs*

*Pressure, Volume, & Work* 1) What happens to *work* when the *volume stays constant* as pressure changes (delta(V) = 0)? 2) What is an isovolumetric (*isochoric*) process?

1) *No work is done* 2) When volume stays constant as pressure changes

*Conservation of Mechanical Energy* 1) How do you find the *work* done by the *nonconservative forces*? 2) What is this equation actually calculating?

1) *Only* calculates the work done by *nonconservative forces only* 2) The amount of energy "lost" from the system

*Conservation of Mechanical Energy* 1) Are *nonconservative forces* path-dependent or independent? 2) What does this mean in terms of distance traveled and energy?

1) *Path-dependent* 2) The longer the distance traveled, the larger the amount of energy dissipated

*Power* 1) What does *power* refer to? 2) How do you calculate *power*? 3) What is the SI unit for power?

1) *Rate* at which energy is transferred from one system to another 2) P = W/t = (delta(E))/t 3) Watt (W) = J/s

*Conservation of Mechanical Energy* 1) When the *work* done by *nonconservative forces* = 0, or when there are *no* nonconservative forces acting on the system, what happens to the *total mechanical energy*? 2) What is the equation to express *conservation of mechanical energy*?

1) *Stays constant* 2) Delta(E) = Delta(U) + Delta (K) = 0

*Force* *friction* 1) Which coefficient value (static or kinetic) is *always larger*? 2) What does this mean for the relationship between static and kinetic friction?

1) *coefficient of static friction* is *always greater*. 2) Maximum value for static friction will *always be greater* than the constant value for kinetic friction *objects will "stick" until they start moving, and then will slide more easily over one another* *It always requires more force to get an object to start sliding than it takes to eep an object sliding*

*Conservation of Mechanical Energy* 1) In the absence of *nonconservative forces* (like frictional forces), the *sum* of KE and PE will be _______ 2) What are *conservative forces* ? 3) *Conservative forces* have what associated with them?

1) *constant* 2) Those that are *path independent* and do *not dissipate energy* 3) PE

*Potential Energy* 1) When a spring is stretched or compressed from its *equilibrium length*, the spring has what type of *energy*? 2) How do you find *elastic potential energy*? Explain components of the equation. 3) What is the *spring constant (k)*?

1) *elastic potential energy* 2) U = 1/2(kx^2) U = potential energy; k = *spring constant*; x = magnitude of displacement from equilibrium 3) A measure of the stiffness of the spring

*Projectile Motion* 1) Objects in projectile motion on Earth (like baseballs) experience the force and acceleration of gravity in which direction? 2) What does this mean about v(y) and v(x)?

1) *only in the vertical direction* (along the y-axis) 2) v(y) will change at the rate of *g* BUT v(x) will remain *constant*

*Work* 1) What is *work*? 2) Is work a form of energy?

1) *process* by which energy is transferred from one system to another 2) NO! Work is *not* energy, but a measure of *energy transfer*

*Projectile Motion* 1) What distinguishes projectile motion from linear motion? 2) What is the relationship between velocity and acceleration (independent vs dependent)?

1) *projectile motion* = motion that follows a path along *two dimensions* 2) Velocity and accelerations in the *two directions* (usually horizontal and vertical) are *independent* of each other = *analyzed separately*

*Potential Energy* 1) Springs and other elastic systems act to store ______ 2) Every spring has a characteristic length at which it is considered *relaxed*, which is referred to as?

1) *store energy* 2) *in equilibrium*

*Newton's Laws* What is *Newton's First Law*?

1) 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* Fnet = mass(acceleration)=0

*Mechanical Advantage* 1) What is *mechanical advantage*? 2) What is a *simple machine*? How does it relate to *mechanical advantage*? 3) What are the 3 most frequently tested *simple machines* for the MCAT?

1) A measure of the *increase in force* accomplished by *using a tool* 2) For any given quantity of work, any device that allows for work to be accomplished through a *smaller applied force* = said to *provide mechanical advantage* 3) Inclined plane, lever, and pulley (but can also include wedge, wheel and axle, and screw)

*Energy* 1) what is *energy*? 2) Do different forms of energy have the capacity to perform different actions? Give example

1) A system's ability to do work -- to make something happen 2) Yes! Ex: mechanical energy can cause objects to move or accelerate. Nuclear binding energy can be released during fission reactions to run power plants.

*Force* 1) What is *friction*? 2) Does *friction force* speed up or slow down an object?

1) A type of force that *opposes* the movement of objects 2) ALWAYS *opposes* an object's motion = cause it to *slow down* or *become stationary*

*Vector Subtraction* How do you subtract vectors? What are the 2 methods?

1) Adding a vector with equal magnitude (but *opposite direction*) to the first vector. *A-B = A+(-B)* - Simply flipping the direction of the vector being subtracted and then following the same rules as adding tip-to-tail 2) Component method -- x-component of resultant vector = difference of x-components of the vectors being subtracted. (same for y-component of resultant)

*Force* 1) What is *gravity*? 2) How do you find the magnitude of the *gravitational force* between two objects? Explain the components of the equation. 3) If r is halved, what happens to Fg?

1) An attractive *force* that is felt by ALL forms of matter 2) G = universal gravitational constant (6.67x10^-11 Nm^2/kg^2) m1 & m2 = masses of the 2 objects r = distance between their centers of mass 3) Fg quadruple (Fg is inversely related to the square of the distance)

*Displacement* 1) What is *displacement* (x or d)? 2) Is *displacement* a vector or scalar quantity? 3) The *displacement* vector connects (in a straight line) what?

1) An object in motion may experience a change in its position in space (which is known as *displacement*) 2) *Vector* = has magnitude and direction 3) Connects the object's *initial* position and its *final* position

*Newton's Laws* 1) What is *Newton's 2nd Law*? 2) How do you find Fnet? 3) Do the Fnet and acceleration vectors always face in the same direction?

1) An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector 2) Image 3) YES!

*Potential Energy* 1) What does *gravitational PE* depend on? 2) How is *gravitational potential energy calculated*? Explain components of the equation.

1) An object's position with respect to some level identified as the "ground" 2) U = mgh U = PE; m = mass in kg; g = acceleration due to gravity; h = height of the object above the "ground"

*Vector Addition* 1) Besides *tip-to-tail addition*, what is another way to find the *resultant* of several vectors? 2) In most cases, what are these components?

1) Breaking each vector into perpendicular *components* 2) in most cases, these components are x- and y-components OR parallel and perpendicular to some other surface

*Inclined Planes* 1) When working with inclined planes, it's often best to do what? 2) Most of the time, what do you have to do with *gravity*? 3) Draw the components (types of forces) on an object on an inclined plane

1) Divide force vectors into components that are parallel and perpendicular to the plane 2) *split* gravity into *components*

*Vector Addition* 1) Given any vector *V*, how can you find the x- and y-components (*X and Y*)? 2) If theta is the angle between *V* and the x-component, then how do you find *X* (x-component)? 3) If theta is the angle between *V* and the x-component, then how do you find *Y* (y-component)?

1) Draw a right triangle with *V* as the hypotenuse 2) X = Vcos(theta) 3) Y = Vsin(theta)

*Potential Energy* 1) What is *potential energy*? 2) PE is often said to have the *potential* to do what?

1) Energy that is associated with a given object's *position* in space or other intrinsic qualities of a system 2) *potential to do work*

*Force* *friction* 1) What is *kinetic friction* (fk)? 2) What is the equation that describes the magnitude of static friction?

1) Exists between a *sliding* object and the surface over which the object slides

*Force* *friction* 1) Where does *static friction* (fs) exist? 2) What is the equation that describes the magnitude of static friction? Explain the components

1) Exists between a *stationary* object and the surface upon which it rests 2) u(s) = coefficient of static friction (unitless quantity that is dependent on the 2 materials in contact) N = magnitude of the normal force

*Pressure, Volume, & Work* For a gas system contained in a cylinder with a movable *piston*, we can analyze the relationship between pressure, volume, and work. 1) When gas *expands*, what happens to the *volume*? 2) When gas *compresses*, what happens to the *volume*? 3) When is *work* being done in a system like this? (How does pressure, volume, and work relate?)

1) Gas expands = pushes against piston = exerts force that causes piston to move up = *volume of system increases* 2) Gas compressed = piston pushes down on gas = exerts force that *decreases the volume* of the system 3) *Work* is being done when the *volume* of the system *changes* due to an *applied pressure*

*Conservation of Mechanical Energy* 1) What are the 2 most commonly encountered *conservative forces*? 2) When can *elastic forces* be approximated to be conservative?

1) Gravitational and Electrostatic 2) When frictional forces are *ignored*

*Conservation of Mechanical Energy* How do you find out if a force is *conservative*?

1) If the *change in energy* around any *round-trip path is zero* 2) If the *change in energy* is *equal* despite taking any path between 2 points

*Work-Energy Theorem* 1) How is the *work-energy theorem* useful? 2) What is the *work-energy theorem* equation? How do you find the *net work done by forces acting on an object*?

1) It provides a *direct* relationship between the work done by all the forces acting on an object and the *change in KE* of that object 2) Image

*Total Mechanical Energy* 1) If *frictional forces* are present, what will happen to some of the *mechanical energy*? 2) Is this a violation of the *first law of thermodynamics*?

1) It will be transformed into thermal energy and will be *"lost"*. 2) NO! a full accounting of all forms of energy (KE, PE, thermal, sound, light, etc.) will reveal NO net gain or loss of total energy. Just a transformation of some energy from one form to another.

*Kinetic Energy* 1) What is the relationship between KE and *speed*? 2) Is KE related to *velocity*? 3) Does an object have the same KE regardless of the direction of its velocity vector? 4) Do only objects falling down have KE?

1) KE is a function of the *square of the speed* = If speed doubles, the KE will quadruple (assuming mass is constant) 2) NO! *speed* NOT velocity 3) YES! 4) NO! Objects that move in other ways (like fluid flowing or objects that slide down inclined planes) have KE

*Mass and Weight* 1) What is *mass*? Scalar or vector? 2) What is the SI unit for mass? 3) What is *weight*? Scalar or vector? 4) What is the Si unit for weight?

1) Mass (m) = *scalar* = measure of body's *inertia* (the amount of matter in the object) 2) mass = kilogram (kg) (independent of gravity) 3) Weight (Fg) = *vector* = measure of gravitational foce (usually Earth's) on an object's mass 4) weight = newtons (N)

*Potential Energy* Does the "ground" always have to be the actual ground? What is "ground" referring to?

1) No. "Ground" is the *zero potential energy position* that is usually chosen for convenience

*Work* 1) Only forces (or components of forces) _________ or __________ will do *work* (transfer energy) 2) What is the SI unit for work?

1) Parallel or antiparallel to the *displacement vector* 2) Joule (J) BUT work is NOT a form of energy. It's the process by which a quantity of energy is moved from one system to another

*Pressure, Volume, & Work* 1) What is a *isobaric* process? 2) How is *work* calculated in an *isobaric* process?

1) Process when *pressure remains constant* as volume changes 2) Work = P(delta(V))

*Mechanical Advantage* 1) How do you calculate *mechanical advantage*? 2) What is the SI unit for mechanical advantage?

1) Ratio of magnitudes of the force exerted on an object by a simple machine (Fout) to the force actually applied on the simple machine (Fin) MA = (Fout)/(Fin) 2) NO units = dimensionless because it's a ratio

*Vector Addition* To find the resultant (*R*) using the *components method*, what steps do you follow?

1) Resolve the vectors to be added into their x- and y-components 2) Add the x-components to get the x-component of the resultant (*Rx*). Add the y-components to get the x-component of the resultant (*Ry*). 3) Find the magnitude of the resultant using the Pythagorean theorem.

*Velocity* 1) What is speed (v)? 2) Will average speed always be equal to the magnitude of the average velocity? Why or why not? 3) Average speed accounts for what?

1) Speed (v) = rate of actual distance traveled in a given unit of time 2) NO! Because, *average velocity* = ratio of the *displacement vector* over the change in time (*vector*) and *average speed* (*scalar*) is the ratio of the *total distance* traveled over the change in time 3) *actual* distance traveled (whereas average *velocity* does NOT)

*Vector Right-Hand Rule* For resultant *C* where *C = AxB*, what are the steps for finding the direction of *C*?

1) Start by pointing your thumb in the direction of vector *A* 2) Extend your fingers in the direction of vector *B*. You may need to rotate your wrist to get the correct configuration of thumb and fingers. 3) Your palm establishes the plane between the 2 vectors. The direction of your palm points is the direction of the resultant *C*.

*Mechanical Advantage* 1) What is the *cost* (what has to change) of reducing the force needed to accomplish a given amount of work (mechanical advantage)? 2) Why does the actual distance traveled from the initial to final position not matter (assuming all forces are conservative)?

1) The *distance* through which the *smaller force* must be applied in order to do the work must be *increased* 2) Because displacement is *pathway independent* = so, applying a lesser force over a greater distance to achieve the same change in position (displacement) accomplishes the same amount of work

*Total Mechanical Energy* 1) What is *total mechanical energy*? 2) How do you find *total mechanical energy*?

1) The *sum* of an object's *potential and kinetic energies* 2) E = U + K

*Velocity* 1) The *instantaneous speed* of an object will always be equal to what? 2) What is *instantaneous velocity* a measure of?

1) The magnitude of the object's *instantaneous velocity* 2) The *average velocity* as the change in time approaches *zero*

*Force* *friction* 1) What are *contact points*? 2) If the normal force (N) increases, what happens to the *total area of contact*? 3) As the *total area of contact* increases, what happens to the *frictional forces*?

1) The places where friction occurs between 2 rough surfaces *sliding* past each together. 2) Also increases 3) Also increases (it's this increase in total area of contact that governs the degree of friction, more than the surface's roughness)

1) What is an object's *center of mass*? 2) The center of mass of a *uniform object* is where?

1) The single point at which one can conceptualize gravity acting on an object 2) At the geometric center of the object

*Vector Addition* 1) What is a *resultant* of vectors? 2) When adding vectors, always add _______

1) The sum or difference of two or more vectors 2) *always add tip-to-tail*

*Total Mechanical Energy* 1) The *first law of thermodynamics* accounts fro the *conservation of mechanical energy.* What does this mean? 2) Does this mean that total mechanical energy will remain *constant*?

1) This law posits that energy is *never created nor destroyed* -- it is merely *transferred* from one form to another 2) NO!

*Circular Motion* 1) The object moving in the circular path has a tendency (inertia) to do what? 2) Why does this NOT happen? What force? Points in what direction?

1) To break out of its circular pathway and move in a linear direction along the tangent 2) It's kept from doing so by a *centripetal force* that always points *radially inward*

Define: 1) Vector 2) What are some common vector quantities? 3) Scalar 4) What are some common scalar quantities?

1) Vector = numbers that have *magnitude* and *direction* 2) Vector quantities = displacement, velocity, acceleration, and force 3) Scalar = number that only has *magnitude* 4) Scalar quantities = distance, speed, energy, pressure, and mass

*Equilibrium* 1) When does *translational motion* occur? 2) When does *translational equilibrium* exist? 3) What is the *first condition of equilibrium*?

1) When forces cause an object to *move without any rotation* 2) *only* when the vector sum of all the forces acting on an object is *zero* 3) Statement #2 = if there is *no acceleration*, then there is *no net force* on the object

*Circular Motion* 1) When does *circular motion* occur? 2) Upon completion of *one cycle*, what is the *displacement* of the object?

1) When forces cause an object to move in a circular pathway 2) *Zero*

*Work* 1) Energy is *transferred* through the process of *work* when what happens? 2) What is the equation for *work*? Explain the components.

1) When something exerts *forces* on or against something else 2) W = F(d) = F(d)cos(theta) W = work F = *magnitude* of the applied force d = *magnitude* of the displacement through which the force is applied theta = angle between the applied force vector and the displacement vector

*Equilibrium* 1) When does an object experience *zero acceleration*? (2 situations) 2) An object experiencing *translational equilibrium* will have what velocity?

1) When the resultant force upon an object is *zero* = when object is *stationary* OR when object is moving with a *constant nonzero velocity* 2) *constant velocity* = constant speed (can be zero or nonzero) AND constant direction

*Equilibrium* 1) When does *rotational equilibrium* exist? 2) What is the *second condition of equilibrium*?

1) When the vector sum of all the torques acting on an object is zero. All positive torques exactly cancel out all of the negative torques. 2) Statement #1

*Pressure, Volume, & Work* 1) When is work said to be *positive*? 2) When is work said to be *negative*?

1) When work is done *by the system* (gas expands) 2) When work is done *on the system* (gas compresses)

*Circular Motion* 1) What is *uniform circular motion*? 2) In *uniform circular motion*, what is the direction of the *instantaneous velocity vector*?

1) Where the speed of the object is *constant* 2) *always tangent* to the circular path

*Circular Motion* 1) In uniform circular motion, the tangential force is always what? 2) As a force, the *centripetal force* generates what?

1) ZERO, because there is *no change* in the speed of the object 2) *centripetal acceleration*

*Acceleration* 1) What is *acceleration (a)*? Scalar or vector? 2) SI units? 3) How do you find *average acceleration*?

1) a = *vector* = rate of change of velocity that an object experiences as a result of some applied force 2) m/s^2 3) a = (change in velocity)/(change in time)

*Force* 1) Every change in velocity is motivated by what? 2) What is a *force* (*F*)? Scalar or vector? 3) Can force exist between objects that aren't even touching? What are some examples?

1) a push or pull -- a *force* 2) *vector* that is experienced as pushing or pulling on objects 3) YES! Gravity or electrostatic forces between point charges

*Mechanical Advantage* Why do sloping *inclines* (like hillsides and ramps) make it easier to lift objects?

1) because they distribute the required work over a *larger distance* = *decreasing the required force*

*Vector Right-Hand Rule* 1) What do you use the *right-hand rule* for?

1) determine the *direction* of a resultant vector (by multiplication)

*Conservation of Mechanical Energy* 1) What happens to *total mechanical energy* when *nonconservative forces* are present? 2) What are some common types of *nonconservative forces*?

1) it is NOT conserved 2) Friction, air resistance, viscous drag (resistance force created by fluid viscosity)

*Equilibrium* 1) Torques that generate *clockwise rotation* are considered +/-? 2) Torques that generate *counterclockwise rotation* are considered +/-?

1) negative 2) positive

*Equilibrium* 1) How do you find *torque*? What does *torque* depend on? 2) When is *torque* the greatest? 3) What is the torque when the force is applied *parallel* to the lever arm?

1) r = length of the lever arm F = magnitude of the force theta = angle between the lever arm and force vectors 2) When sin(90) = 1 = when the force is applied 90 degrees (perpendicular) to the lever arm 3) Zero = no torque (sin(0) = 0)

*Kinetic Energy* 1) What is *kinetic energy*? 2) How is *kinetic energy calculated*? 3) What is the SI unit for all forms of energy (including kinetic energy)?

1) the energy of *motion* 2) KE = 1/2(mv^2) 3) Joules (J) = (kg x m^2)/s^2

*Linear Motion* 1) Explain what's happening to an object's velocity and acceleration during *linear motion* 2) Do *falling objects* exhibit linear motion? What about their acceleration?

1) the object's velocity and acceleration are *along the line of motion* = so pathway of the moving object continues along a straight line 2) YES! Linear motion with *constant acceleration*

*Linear Motion* Equations for free-falling objects in one-dimensional motion (Kinematic equations): 1) Velocity (given time) 2) Displacement (can be either x or y) 3) Velocity (given displacement) 4) Displacement (without acceleration)

1) v = v0 + at (v0=initial velocity) 2) x = (v0)(t) + (1/2)(at^2) 3) v^2 = v0^2 + 2ax 4) x = avg(v) x t

*Velocity* 1) How is the *magnitude* of velocity calculated? 2) What is the *SI unit* for *velocity*? 3) The direction of the velocity vector is the same as what?

1) velocity = rate of change of displacement in a given unit of time 2) meters per second (m/s) 3) Same as the displacement vector

*Equilibrium* 1) When does *rotational motion* occur? 2) Application of force at some distance from the *fulcrum* will generate what? 3) What is actually generating the rotational motion?

1) when forces are applied against an object in such a way to cause the object to *rotate around a fixed pivot point* (known as the *fulcrum*) 2) *Torque* = movement of force 3) the torque (not just the application of the force itself)

*Pressure, Volume, & Work* How can the work done on or by the system undergoing a thermodynamic process be determined using *Pressure-Volume Graph*?

By finding the area enclosed by the corresponding pressure-volume curve

*Circular Motion* What is the equation that describes *circular motion*? Both *centripetal force* and *centripetal acceleration*

Fc = magnitude of centripetal force m = mass v = speedr = radius of the circular path

*Mass and Weight* How do you find *weight*? Explain the components

Fg = mg Fg = weight of the object m = object's mass g = acceleration due to gravity (10 m/s^2)

*Force* *friction* Why does the fk equation have an equal sign but the fs equation doesn't? What 2 factors don't matter for *kinetic friction*?

Kinetic friction (fk) will have a constant value for any given combination of coefficient of kinetic friction and normal force. *Kinetic friction = does NOT matter how much surface area is in contact or even the velocity of the sliding object*

*Force* *friction* What are the 2 types of *friction*?

Static and kinetic friction

*Newton's Laws* 1) What is *Newton's 3rd Law*?

To every action, there is always an opposed but equal 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

*Total Mechanical Energy* How is it possible that energy can never be created or destroyed (*first law of thermodynamics*) but total mechanical energy isn't always constant?

Total mechanical energy equation only accounts for PE and KE. It does *NOT* account for other forms of energy, such as thermal energy that is transferred as a result of friction (heat).

*Mechanical Advantage* How do you find the *efficiency* of simple machines?

Wout = product of load and load distance (load = the weight of object being lifted/moved) Win = product of effort and effort distance (effort = force actually applied to object)

*Inclined Planes* 1) How do you find the component of gravity *parallel* to the plane (oriented down the plane)? 2) How do you find the component of gravity *perpendicular* to the plane (oriented into the plane)?

m = mass g = acceleration due to gravity theta = angle of the incline

*Force* *friction* What is the *normal force (N)*?

the component of the force between the 2 objects in contact that is *perpendicular* to the plane of contact between the object and the surface upon which it rests