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1. Which of the following statements are true about work? Include all that apply.
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. TRUE  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. 

Definition and Mathematics of Work 
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2. Which of the following statements are true about power? Include all that apply.
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. 

Power 
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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).





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). 

Definition and Mathematics of Work 
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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 

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

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

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. 

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

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

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

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. 

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

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.) 

Definition and Mathematics of Work 
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5. Which of the following statements are true about conservative and nonconservative forces? Include all that apply.
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. 

Internal (i.e., Conservative) vs. External (i.e., Nonconservative) Forces 
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6. Which of the following statements are true about kinetic energy? Include all that apply.
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 object's 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. 

Kinetic Energy 
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7. Which of the following statements are true about potential energy? Include all that apply.
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. 

Potential Energy 
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8. Which of the following statements are true about mechanical energy? Include all that apply.
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. 

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




v = 4.0 m//s h = 2.0 m 
v = 2.0 m//s h = 3.00 m 
v = 5.0 m/s h = 5.0 m 
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 The order is evident once the calculations are performed. 

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




v = 4.0 m//s h = 2.0 m 
v = 2.0 m//s h = 3.00 m 
v = 5.0 m/s h = 5.0 m 
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 The order is evident once the calculations are performed. 

Potential Energy 
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