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•m²/s² 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 time-based 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 NON-example 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 90-degree 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 non-conservative 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.

Answer: ABDEI

a. TRUE - Power is a rate quantity and thus time-based.

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.

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 30-degree 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 60-degrees. 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).

a. Positive Work

b. Negative Work

c. No 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.)

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). Non-conservative 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 non-conservative 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 conservative-classified forces do work, then KE_i + PE_i = KE_f + PE_f. On the other hand if one or more non-conservative-classified 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 non-conservative 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 non-conservative 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.

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 v²). 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•v². the quantity m is always positive. And even if v is negative, v² 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 free-falling objects always increase their kinetic energy as they fall.

m. FALSE - The kinetic energy increases from 0 J to 2 J (0.5•1•2²); that's an increase by 2 J.

n. FALSE - Such an object will definitely gain or lose mechanical energy but not necessarily kinetic 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•x²).

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 free-fall, 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 4-m fall is -40 J.

k. FALSE - The object will either gain or lose mechanical energy, but not necessarily potential energy.

Answer: AEFGH

a. TRUE - This is the definition of mechanical energy.

b. FALSE - Heat or thermal energy is a non-mechanical 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 non-conservative forces do not do work upon the object.

d. FALSE- If a non-conservative 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 non-conservative force) does a little work and so one might notice a very slight change in mechanical energy.

f. TRUE - Friction is a non-conservative 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 non-conservative force doing work.

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.

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/s²)•(2.0 m) = ~100 J

Object B: PE = (10.0 kg)•(~10 m/s²)•(3.00 m) = ~300 J

Object C: PE = (1.0 kg)•(~10 m/s²)•(5.0 m) = ~50 J

Object D: PE = (5.0 kg)•(~10 m/s²)•(4.0 m) = ~200 J

The order is evident once the calculations are performed.