Work and Energy Review
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Part A: Forced Choice Questions
1. Which of the following statements are true about work? Include all that apply.
 Work is a form of energy.
 A Watt is the standard metric unit of work.
 Units of work would be equivalent to a Newton times a meter.
 A kg•m^{2}/s^{2} would be a unit of work.
 Work is a timebased quantity; it is dependent upon how fast a force displaces an object.
 Superman applies a force on a truck to prevent it from moving down a hill. This is an example of work being done.
 An upward force is applied to a bucket as it is carried 20 m across the yard. This is an example of work being done.
 A force is applied by a chain to a roller coaster car to carry it up the hill of the first drop of the Shockwave ride. This is an example of work being done.
 The force of friction acts upon a softball player as she makes a headfirst dive into third base. This is an example of work being done.
 An eraser is tied to a string; a person holds the string and applies a tension force as the eraser is moved in a circle at constant speed. This is an example of work being done.
 A force acts upon an object to push the object along a surface at constant speed. By itself, this force must NOT be doing any work upon the object.
 A force acts upon an object at a 90degree angle to the direction that it is moving. This force is doing negative work upon the object.
 An individual force does NOT do positive work upon an object if the object is moving at constant speed.
 An object is moving to the right. A force acts leftward upon it. This force is doing negative work.
 A nonconservative force is doing work on an object; it is the only force doing work. Therefore, the object will either gain or lose mechanical energy.
Answer: ACDHIKNO
a. TRUE  Work is a form of energy, and in fact it has units of energy.
b. FALSE  Watt is the standard metric unit of power; Joule is the standard metric unit of energy.
c. TRUE  A N•m is equal to a Joule.
d. TRUE  A kg•m^{2}/s^{2} is a mass unit times a speed squared unit, making it a kinetic energy unit and equivalent to a Joule.
e. FALSE  Work is not dependent on how rapidly the force displaces an object; power is timebased and calculated by force multiplied by speed.
f. FALSE  Since Superman does not cause a displacement, no work is done; he is merely holding the car to prevent its descent down the hill.
g. FALSE  The upward force does not cause the horizontal displacement so this is a NONexample of work.
h. TRUE  There is a component of force in the direction of displacement and so this is an example of work.
i. TRUE  There is a force and a displacement; the force acts in the opposite direction as the displacement and so this force does negative work.
j. FALSE  For uniform circular motion, the force acts perpendicular to the direction of the motion and so the force never does any work upon the object.
k. FALSE  This is clearly work  a force is causing an object to be displaced.
l. FALSE  If a force acts at a 90degree angle to the direction of motion, then the force does not do any work at all. Negative work is done when there is a component of force opposite the direction of motion.
m. FALSE  There are many instances in which an individual force does positive work and yet the object maintains a constant speed. Consider a force applied to lift an object at constant speed. The force does positive work. Consider a car moving at constant speed along a level surface. The force of the road on the tires does positive work while air resistance does and equal amount of negative work.
n. TRUE  A force which acts in a direction opposite the motion of an object will do negative work.
o. TRUE  When nonconservative forces do work upon an object, the object will either gain or lose mechanical energy. Mechanical energy is conserved (neither gained nor lost) only when conservative forces do work upon objects.

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2. Which of the following statements are true about power? Include all that apply.
 Power is a timebased quantity.
 Power refers to how fast work is done upon an object.
 Powerful people or powerful machines are simply people or machines which always do a lot of work.
 A force is exerted on an object to move it at a constant speed. The power delivered by this force is the magnitude of the force multiplied by the speed of the object.
 The standard metric unit of power is the Watt.
 If person A and person B do the same job but person B does it faster, then person A does more work but person B has more power.
 The Newton•meter is a unit of power.
 A 60kg boy runs up a 2.0 meter staircase in 1.5 seconds. His power is approximately 80 Watt.
 A 300Newton force is applied to a skier to drag her up a ski hill at a constant speed of 1.5 m/s. The power delivered by the toe rope is 450 Watts.
Answer: ABDEI
a. TRUE  Power is a rate quantity and thus timebased.
b. TRUE  This is the definition of power.
c. FALSE  This is not always the case. A machine can do a lot of work but if it fails to do it rapidly, then it is not necessarily powerful. In fact two machines can do the same task (and therefore the same work), yet they can have drastically different power ratings.
d. TRUE  An equation for computing work in constant speed situations is P=F•v.
e. TRUE  Watt is the unit of power? Yes!!
f. FALSE  Vice versa. If two people do the same job, then they're doing the same amount of work. The person who does it fastest generates more power.
g. FALSE  A N•m is a Joule and that is a unit of work (not power). Think force (N) times distance (m); that's work (J).
h. FALSE  The work would be (m•g)•d or approximately 1200 J. The power is work divided by time  1200 J/1.5 s = 800 W.
i. TRUE  Since force and speed are given, use Power = F•v. The calculation yields 450 W.

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3. Consider the following physical situations. For each case, determine the angle between the indicated force (in boldface type) and the displacement ("theta" in the work equation).
a. 0 degrees

b. 180 degrees

c. 90 degrees

d. 30 degrees

e. 60 degrees

 A rightward applied force is used to displace a television set to the right.  Answer: A  0 degrees
 The force of friction acts upon a rightwardmoving car to bring it to a stop.  Answer: B  180 degrees
 A waiter uses an applied force to balance the weight of a tray of plates as he carries the tray across the room.  Answer: C  90 degrees
 The force of air resistance acts upon a verticallyfalling skydiver.  Answer: B  180 degrees
 The force of friction acts upon a baseball player as he slides into third base.  Answer: B  180 degrees
 An applied force is used by a freshman to lift a World Civilization book to the top shelf of his locker.  Answer: A  0 degrees
 A bucket of water is tied to a string and tension supplies the centripetal force to keep it moving in a circle at constant speed.  Answer: C  90 degrees
 An applied force acting at 30degrees to the horizontal is used to displace an object to the right.  Answer: D  30 degrees
 A group of football players use an applied force to push a sled across the grass.  Answer: A  0 degrees
 The tension in the elevator cable causes the elevator to rise at a constant speed.  Answer: A  0 degrees
 In a physics lab, an applied force is exerted parallel to a plane inclined at 30degrees in order to displace a cart up the incline.  Answer: A  0 degrees
 An applied force is exerted upwards and rightwards at an angle of 30degrees to the vertical in order to displace an object to the right.  Answer: E  60 degrees
 A child rests on the seat of a swing which is supported by the tension in its cables; he swings from the highest position to its lowest position.  Answer: C  90 degrees
Answer: See questions above; explanations given below.
a. The forward motion is do to the forward pushing; if the force and motion are in the same direction, then the angle is 0 degrees.
b. Friction opposes motion and as such does negative work; the angle is 180 degrees.
c. The force is vertical and the displacement if horizontal; they make a 90 degree angle.
d. Air resistance opposes motion and as such does negative work; the angle is 180 degrees.
e. Friction opposes motion and as such does negative work; the angle is 180 degrees.
f. The frosh applies an upward force to cause an upward displacement; the angle is 0 degrees.
g. For uniform circular motion, the force is inwards and the displacement at each instant is tangent to the circle; these two vectors make a 90 degree angle.
h. This is a straightforward question; no tricks here.
i. The forward motion is do to the forward pushing; if the force and motion are in the same direction, then the angle is 0 degrees.
j. The cable pulls up on the elevator and the elevator is displaced upward; if the force and motion are in the same direction, then the angle is 0 degrees.
k. The 30degree angle is the incline angle, not necessarily the angle between F and d. The force is parallel to the incline and the cart is displaced along the direction of the incline; so the two vectors are in the same direction and the angle between them is 0 degrees.
l. Compare the wording of this to part h. This one is tricky because the angle between F and d is 60degrees. If you missed it, reread the question, paying careful attention to the "with the vertical" part.
m. As the child swings, she traces out a circular arc and as such the tension (centripetal) is perpendicular to the direction of motion (tangent).

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4. Consider the following physical situations. Identify whether the indicated force (in boldface type) does positive work, negative work or no work.
a. Positive Work

b. Negative Work

c. No Work

Description of Physical Situation

+, , or no Work

a. A cable is attached to a bucket and the force of tension is used to pull the bucket out of a well.

A. Positive Work

b. Rusty Nales uses a hammer to exert an applied force upon a stubborn nail to drive it into the wall.

A. Positive Work

c. Near the end of the Shockwave ride, a braking system exerts an applied force upon the coaster car to bring it to a stop.

B. Negative Work

d. The force of friction acts upon a baseball player as he slides into third base.

B. Negative Work

e. A busy spider hangs motionless from a silk thread, supported by the tension in the thread.

C. No Work

f. In baseball, the catcher exerts an abrupt applied force upon the ball to stop it in the catcher's mitt.

B. Negative Work

g. In a physics lab, an applied force is exerted parallel to a plane inclined at 30degrees in order to displace a cart up the incline.

A. Positive Work

h. A pendulum bob swings from its highest position to its lowest position under the influence of the force of gravity.

A. Positive Work

Answer: See table above; explanations provided below.
a. The force is upwards and the displacement is upwards. When the force and the displacement act in the same direction, positive work is done.
b. The force is horizontal and the displacement is horizontal. When the force and the displacement act in the same direction, positive work is done. (It is true that the wall is doing negative work upon the nail but this statement is about the hammer's force on the nail.)
c. The force is backwards and the displacement is forwards. When the force and the displacement act in the opposite direction, negative work is done.
d. The force is backwards and the displacement is forwards. When the force and the displacement act in the opposite direction, negative work is done.
e. If the force does not cause the object to be displaced (the object hangs motionless), then no work is done.
f. The force is backwards and the displacement is forwards. When the force and the displacement act in the opposite direction, negative work is done.
g. The force is upwards and parallel to the incline and the displacement is in the same direction parallel to the incline. When the force and the displacement act in the same direction, positive work is done.
h. As the bob swings downwards from its highest position, the motion is downwards (and rightwards); the force is also downwards and as such there is a component of force in the direction of motion. When the force and the displacement act in the same direction, positive work is done. (Note that if the bob was swinging upwards from its lowest position to its highest position, then gravity would be doing negative work.)

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5. Which of the following statements are true about conservative and nonconservative forces? Include all that apply.
 A force is regarded as a conservative force if it does work but does not remove mechanical energy from a system of objects.
 A force is regarded as a nonconservative force if it does not add mechanical energy to a system of objects.
 The force of gravity and elastic (spring) force are both examples of a conservative forces.
 Applied forces, air resistance, friction forces, and tension are common examples of nonconservative forces.
 Physicists envy biologists' ability to instill order on the world of animal species through their taxonomic system. So physicists have made a habit of identifying forces as conservative and nonconservative forces in order to instill order on the world of forces.
 If a nonconservative force acts upon an object, then the object will either gain or lose mechanical energy.
 If the only forces which do work upon an object are conservative forces, then the object will conserve its mechanical energy.
 If the sum of an object's KE and PE is remaining constant, then nonconservative forces are NOT doing work.
 If work is NOT done on an object by a nonconservative force, then the object will experience a transformation of energy from kinetic to potential energy (or vice versa).
 An object starts from an elevated position with 50 J of potential energy and begins its fall towards the ground. If nonconservative forces can be assumed to NOT do work, then at some point during the fall the object will have 20 J of potential energy and 30 J of kinetic energy.
Answer: A(sort of) CDGH I(sort of) J
a. TRUE (sort of)  If a force does work, yet does not remove mechanical energy from an object, then it is definitely a conservative force. The sort of indicates that a force is also considered a conservative force if it does work and does not add mechanical energy to an object.
b. FALSE  If a force does not add mechanical energy to a system of objects, then it is likely a conservative force (provided it doesn't remove mechanical energy either). Nonconservative forces are those which either add or remove energy from a system of objects.
c. TRUE  You must know this!
d. TRUE  These are all nonconservative forces. You can add normal force to the list as well.
e. FALSE  Whether there is envy in a physicist's heart is not for us to tell; the evil found within one's heart is often vast and mysterious ... . We can however definitively say that a physicist classifies forces in order to analyze physical situations in accord with the classification. If only conservativeclassified forces do work, then KE_{i} + PE_{i} = KE_{f} + PE_{f}. On the other hand if one or more nonconservativeclassified forces are doing work, then KE_{i} + PE_{i} + W_{nc} = KE_{f} + PE_{f}.
f. FALSE  Not only must the force act upon the object, it must also be doing work upon the object. As you sit in your chair, there is a nonconservative force (normal force) acting upon your body. But since it does not do work (it's being assumed that you are not sitting in one of those fancy lounge chairs that has more controls than a TV set), your mechanical energy is not changing.
g. TRUE  This is a big principle. You must know this one!
h. TRUE  Non conservative forces would alter the total mechanical energy; that is, the PE + KE would not be a constant value.
i. TRUE (sort of)  This statement is true (sort of); when only conservative forces are doing work, an object has its kinetic energy transformed into potential energy (or vice versa) without the total amount of the two being altered. It would however be possible that work is not done by a nonconservative force and there be no transformation of energy at all; i.e., the object remains at rest. A conservative force must be doing work in order for there to be a transformation of energy.
j. TRUE  One would notice that the PE would begin to drop from 50 J to 0 J and that the KE would increase from 0 J to 50 J. And of course there would be a point at which the PE/KE would be distributed with 20 J to PE and 30 J to KE.

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6. Which of the following statements are true about kinetic energy? Include all that apply.
 Kinetic energy is the form of mechanical energy which depends upon the position of an object.
 If an object is at rest, then it does not have any kinetic energy.
 If an object is on the ground, then it does not have any kinetic energy.
 The kinetic energy of an object is dependent upon the weight and the speed of an object.
 Faster moving objects always have a greater kinetic energy.
 More massive objects always have a greater kinetic energy.
 Kinetic energy is a scalar quantity.
 An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy would be 80 J.
 An object has a kinetic energy of 40 J. If its speed were twice as much, then its kinetic energy would be 80 J.
 Object A has a mass of 1 kg and a speed of 2 m/s. Object B has a mass of 2 kg and a speed of 1 m/s. Objects A and B have the same kinetic energy.
 An object can never have a negative kinetic energy.
 A falling object always gains kinetic energy as it falls.
 A 1kg object is accelerated from rest to a speed of 2.0 m/s. This object gains 4.0 Joules of kinetic energy.
 If work is done on an object by a nonconservative force, then the object will either gain or lose kinetic energy.
Answer: BGHK
a. FALSE  Kinetic energy depends upon the speed of the object; potential energy depends upon the position of the object.
b. TRUE  Kinetic energy depends upon speed. If there is no speed (the object is at rest), then there is no kinetic energy.
c. FALSE  If an object is on the ground, then it does not have potential energy (relative to the ground).
d. FALSE (sort of)  Kinetic energy depends upon mass and speed. Two objects of the same mass could have different weights if in a different gravitational field; so it is not appropriate to say that kinetic energy depends upon weight.
e. FALSE  Faster moving objects would have more kinetic energy than other objects of the same mass. However, another object could have less speed and make up for this lack of speed in terms of a greater mass.
f. FALSE  More massive objects would have more kinetic energy than other objects with the same speed. However, another object could have less mass and make up for this lack of mass in terms of a greater speed.
g. TRUE  Kinetic energy does not have a direction associated with it; it is a scalar quantity.
h. TRUE  Kinetic energy is directly related to the mass of an object.
i. FALSE  Kinetic energy is directly related to the square of the speed of an object. So a doubling of the speed would result in a quadrupling of the kinetic energy  the new KE would be 160 J.
j. FALSE  When it comes to kinetic energy, speed is doubly important (recall v^{2}). So in this case, object A would have more kinetic energy. Doing the calculation yields 2 J for object A and 1 J for object B.
k. TRUE  Kinetic energy is determined by the equation 0.5•m•v^{2}. the quantity m is always positive. And even if v is negative, v^{2} will always be positive. Therefore, kinetic energy can never be a negative value.
l. FALSE  If an object is falling at a constant velocity (i.e., the air resistance force equals the downward force of gravity), then there is not an increase in kinetic energy. It is true however that freefalling objects always increase their kinetic energy as they fall.
m. FALSE  The kinetic energy increases from 0 J to 2 J (0.5•1•2^{2}); that's an increase by 2 J.
n. FALSE  Such an object will definitely gain or lose mechanical energy but not necessarily kinetic energy.

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7. Which of the following statements are true about potential energy? Include all that apply.
 Moving objects cannot have potential energy.
 Potential energy is the energy stored in an object due to its position.
 Both gravitational and elastic potential energy are dependent upon the mass of an object.
 The gravitational potential energy of an object is dependent upon the mass of the object.
 If the mass of an elevated object is doubled, then its gravitational potential energy will be doubled as well.
 Gravitational potential energy is lost as objects freefall to the ground.
 The higher that an object is, the more potential energy which it will have.
 The unit of measurement for potential energy is the Joule.
 A 1kg mass at a height of 1 meter has a potential energy of 1 Joule.
 A 1kg object falls from a height of 10 m to a height of 6 m. The final potential energy of the object is approximately 40 J.
 If work is done on an object by a nonconservative force, then the object will either gain or lose potential energy.
Answer: BDEFGH
a. FALSE  Potential energy has nothing to do with speed; an object could be moving at an elevated position. It is this elevation above zero level which gives an object potential energy.
b. TRUE  This is the definition of potential energy.
c. FALSE  Gravitational potential energy is dependent upon the mass of the object (PE_{grav} = m•g•h) but elastic potential energy is dependent upon the spring constant and the compression or stretch length of the spring (PE_{elastic} = 0.5•k•x^{2}).
d. TRUE  The equation states that PE_{grav} = m•g•h; PE is dependent upon mass.
e. TRUE  The equation states that PE_{grav} = m•g•h; if the h is doubled, then the PE will be doubled as well.
f. TRUE  As objects freefall, the height (h) decreases; subsequently, the PE decreases.
g. TRUE  The equation states that PE_{grav} = m•g•h; PE is directly related to height.
h. TRUE  The Joule (abbrev. J) is the standard metric unit of energy  all forms of energy.
i. FALSE  The final potential energy is calculated as PE = m•g•h = (1 kg)•(~10 m/s/s)•(1 m) = ~10 J.
j. FALSE  The final potential energy is calculated as PE = m•g•h = (1 kg)•(~10 m/s/s)•(6 m) = ~60 J; the loss in potential energy during this 4m fall is 40 J.
k. FALSE  The object will either gain or lose mechanical energy, but not necessarily potential energy.

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8. Which of the following statements are true about mechanical energy? Include all that apply.
 The total amount of mechanical energy of an object is the sum of its potential energy and the kinetic energy.
 Heat is a form of mechanical energy.
 The mechanical energy of an object is always conserved.
 When nonconservative forces do work, energy is transformed from kinetic to potential (or vice versa), but the total mechanical energy is conserved.
 A bowling ball is mounted from a ceiling by way of a strong cable. It is drawn back and released, allowed to swing as a pendulum. As it swings from its highest position to its lowest position, the total mechanical energy is mostly conserved.
 When a friction force does work on an object , the total mechanical energy of that object is changed.
 The total mechanical energy of an object remains constant if the only forces doing work on the object are conservative forces.
 If an object gains mechanical energy, then one can be certain that a nonconservative force is doing work.
Answer: AEFGH
a. TRUE  This is the definition of mechanical energy.
b. FALSE  Heat or thermal energy is a nonmechanical form of energy. Potential and kinetic energy are the only forms of mechanical energy.
c. FALSE  The mechanical energy of an object is only conserved if nonconservative forces do not do work upon the object.
d. FALSE If a nonconservative force does work upon an object, then the total mechanical energy of that object is changed. Energy will not be conserved.
e. TRUE  Tension does not do work upon the object and so the total mechanical energy is conserved. The presence of air resistance (a nonconservative force) does a little work and so one might notice a very slight change in mechanical energy.
f. TRUE  Friction is a nonconservative force and thus alters the total mechanical energy of an object.
g. TRUE  This is the conservation of energy principle and one that you need to firmly understand.
h. TRUE  If there is any change in the total mechanical energy of an object (whether a gain or a loss), then you know for certain that there is a nonconservative force doing work.

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9. Rank these four objects in increasing order of kinetic energy, beginning with the smallest.
Object A

Object B

Object C

Object D

m = 5.0 kg
v = 4.0 m/s
h = 2.0 m

m = 10.0 kg
v = 2.0 m/s
h = 3.00 m

m = 1.0 kg
v = 5.0 m/s
h = 5.0 m

m = 5.0 kg
v = 2.0 m/s
h = 4.0 m

Answer: D < C < B < A
This is probably best done by performing a calculation of KE and comparing the results:
Object A: KE = 0.5•(5.0 kg)•(4.0 m/s)^{2} = 40. J
Object B: KE = 0.5•(10.0 kg)•(2.0 m/s)^{2} = 20. J
Object C: KE = 0.5•(1.0 kg)•(5.0 m/s)^{2} = ~13 J (12.5 J)
Object D: KE = 0.5•(5.0 kg)•(2.0 m/s)^{2} = 10. J
The order is evident once the calculations are performed.

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10. Rank these four objects in increasing order of potential energy, beginning with the smallest.
Object A

Object B

Object C

Object D

m = 5.0 kg
v = 4.0 m/s
h = 2.0 m

m = 10.0 kg
v = 2.0 m/s
h = 3.00 m

m = 1.0 kg
v = 5.0 m/s
h = 5.0 m

m = 5.0 kg
v = 2.0 m/s
h = 4.0 m

Answer: C < A < D < B
This is probably best done by performing a calculation of PE and comparing the results. Using the approximation that g = ~10 m/s/s gives much quicker results.
Object A: PE = (5.0 kg)•(~10 m/s^{2})•(2.0 m) = ~100 J
Object B: PE = (10.0 kg)•(~10 m/s^{2})•(3.00 m) = ~300 J
Object C: PE = (1.0 kg)•(~10 m/s^{2})•(5.0 m) = ~50 J
Object D: PE = (5.0 kg)•(~10 m/s^{2})•(4.0 m) = ~200 J
The order is evident once the calculations are performed.

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