#6 #12 #18 #28 #34 #36 #38 #42 #48 #586. Can the kinetic energy of an object ever be negative?
No. Kinetic energy is given by one-half times an object's mass times the object's speed squared. Since the mass of an object and the square of a speed can never be less than zero, the kinetic energy can never be negative.
12. Compare the kinetic energies of two identical objects under the following conditions:
a) Object A is traveling in a straight line at the same speed that object B is moving in a circle.
The kinetic energies of the two objects are the same. Note that kinetic energy does not depend upon the direction of the object's velocity.
b) Both objects make one revolution per minute along circular paths. A's circle has only one half the circumference of B's.
The distance that object A travels in a minute is half as far as the distance object B travels in a minute. Thus, object A's speed is half as big as object B's speed. Kinetic energy is one-half times an object's mass times its speed squared. Noting that the masses of our objects are identical, we conclude that the kinetic energy of object A is only one-quarter the size of the object B's kinetic energy.
18. A bowler lifts a bowling ball from the floor and places it on a rack. If you know the weight of the ball, what else must you know in order to calculate the work she does on the ball?
Work is the force in the direction of the motion times the distance. Thus, we must know how high the bowler lifted the ball to determine the work done.
28. Is it possible to change an object's momentum without changing its kinetic energy? What about the reverse situation?
It is possible to change an object's momentum and not alter its kinetic energy. A prime example of this is found in circular motion. In circular motion the object's momentum is constantly changing, but if the object's speed is constant (as it was in our examples in class) its kinetic energy would remain constant.
In contrast, it is not possible to change an object's kinetic energy and leave its momentum unchanged. For an object's kinetic energy to change, its speed must change. Since momentum is dependent upon velocity, the momentum of the object must change if its kinetic energy changes.
34. How is the gravitational potential energy defined?
We write the gravitational potential energy of an object near to the earth's surface as U = mgh. This is the work done by the force of gravity (W=mg) when an object falls through a vertical distance h. An implicit assumption is that the gravitational potential energy of an object on the ground is zero.
36. Does the mechanical energy of a falling ball increase, decrease, or stay the same?
If we ignore air resistance, the mechanical energy of the ball remains the same. The mechanical energy of the ball is the sum of the ball's kinetic energy and its potential energy. As the ball falls, its kinetic energy increases by the amount that its potential energy decreses.
38. Which of the following is conserved as a ball falls freely in a vacuum: the ball's kinetic energy, gravitational potential energy, momentum, or mechanical energy?
Only the ball's mechanical energy is conserved if one leaves the earth out of the "system" to be considered. If the earth is included in the system, then momentum and mechanical energy would be conserved.
42. If we do not ignore air resistance, what happens to the mechanical energy of a falling ball?
Air resistance, like friction, is a not a conservative force. Some of the ball's mechanical energy would be lost due to air resistance. But, if we included the air molecules in our system we would find that this lost mechanical energy was actually transferred to the air molecules as heat and sound.
48. An elephant, an ant, and a professor jump from a lecture table. Assuming no frictional losses, which of the following could be said about their motion just before they hit the floor?
A. They all have the same kinetic energy.
B. They all started with the same gravitational potential energy.
C. They will all experience the same force on stopping.
D. They all have the same speed.
Only D is true. [We are not admitting elephants that tiny or ants that large. :-) ]
58. Which of the following is not a unit of energy: Joule, Newton-meter, kilowatt-hour, or Watt?
All are units of energy except Watt, which is a unit of power.