# Units 4-5 Review

Momentum and Energy

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15. A person on the edge of a roof throws a ball downward. It strikes the ground with 100 J of kinetic energy. The person throws another identical ball upward with the same initial speed, and this too falls to the ground. Neglecting air resitance, the second ball hits the ground with a kinetic energy of ______________.
 a. 100 J b. 200 J c. less than 100 J d. more than 200 J e. none of these

Quite surprisingly to many, each ball would hit the ground with the same speed. In each case, the PE+KE of the balls immediately after being thrown is the same (they are thrown with the same speed from the same height). Upon hitting the ground, they must also have the same PE+KE. Since the PE is zero (on the ground) for each ball, it stands to reason that their KE is also the same. That's a little physics and a lot of logic - and try not to avoid the logic part by trying to memorize the answer.

Mechanical Energy Conservation (13 seconds)

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16. A 10 N object moves at 1 m/s. Its kinetic energy is approximately ____________.
 a. 0.5 J b. 1 J c. 10 J d. more than 10 J

The KE of any object can be computed if the mass (m) and speed (v) are known. Simply use the equation

KE=0.5*m*v2

In this case, the 10-N object has a mass of 1 kg (use Fgrav = m*g). The speed is 1 m/s. Now plug and chug to yield KE=0.5 J.

Kinetic Energy (4 seconds)

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17. A moving object has __________.
 a. speed b. velocity c. momentum d. energy e. all of these

A moving object has speed and velocity. Since momentum is mass*velocity, a moving object would also has momentum. And since a moving object has kinetic energy (0.5*m*v^2), it would also have energy.

Momentum (7 seconds) | Kinetic Energy (4 seconds)

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18. An object at rest may have __________.
 a. speed b. velocity c. momentum d. energy e. all of these

An object at rest absolutely cannot have speed, velocity or momentum. However, an object at rest could have energy if there is energy stored due to its position; for example, there could be gravitational or elastic potential energy.

Momentum (7 seconds) | Mechanical Energy (15 seconds)

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19. What does an object have when it is moving that it absolutely doesn`t have when at rest?
 a. momentum b. energy c. mass d. inertia e. none of these

When moving, an object has momentum; it definitely would not have this if it were at rest. An object which is moving would have kinetic energy (one of the two forms of mechanical energy); but if at rest, it could still have energy of position (potential energy) even though it would not have energy of motion (kinetic energy). An object has mass and inertia whether it is moving or not.

Inertia (12 seconds) | Momentum (7 seconds) | Mechanical Energy (15 seconds)

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20. If an object has kinetic energy, then it also must have ___________.
 a. impulse b. momentum c. acceleration d. force e. none of these

An object which has kinetic energy has mass and speed (or velocity). For this reason, it would also have momentum.

Momentum (7 seconds) | Kinetic Energy (4 seconds)

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21. If the speed of a moving object doubles, then what else doubles?
 a. momentum b. kinetic energy c. acceleration d. all of the above e. none of these

Momentum is directly proportional to the speed of the object; so if the speed is doubled, the momentum is doubled. However, kinetic energy is directly proportional to the square of the speed; thus, doubling the speed would serve to quadruple the kinetic energy.

Acceleration (12 seconds) | Momentum (7 seconds) | Kinetic Energy (4 seconds)

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22. A feather and a coin are dropped in a vacuum. Each falls with equal __________.
 a. momenta b. kinetic energies c. potential energies d. all of the above e. none of the above

In a vacuum, the feather and the coin will have the same acceleration (10 m/s/s) and the same speed. Yet, momentum, kinetic energy and potential energy are all mass dependent quantities. Thus, owing to their different mass, the momentum, kinetic energy and potential energy of the feather and coin are different.

Momentum (7 seconds) | Kinetic Energy (4 seconds) | Potential Energy (12 seconds)

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23. A popular swinging-balls apparatus consists of an aligned row of identical elastic balls that are suspended by strings so they barely touch each other. When two balls are lifted from one end and released, they strike the row and two balls pop out from the other end. If instead one ball popped out with twice the velocity of the two, this would be violation of conservation of __________.
 a. momentum b. kinetic energy c. both of these d. none of these

Momentum would be conserved in such an instance; yet, kinetic energy would not be conserved in the collision. Consider the balls to have a mass of m (for each ball) and an initial velocity of v. The initial momentum and kinetic energy of the system is given by the following expressions:

 Initial Momentum mv + mv or 2mv Initial Kinetic Energy 0.5*mv2 + 0.5*mv2 or mv2

If one ball (with mass m) popped out with twice the velocity (2v) then the final momentum and kinetic energy would be given by the following expressions:

 Final Momentum m*2v or 2mv (same as initial momentum) Initial Kinetic Energy 0.5*m*(2v)2 = 0.5*m*(4v2) or 2mv2 (this indicates a gain in KE)

Kinetic Energy (4 seconds) | Potential Energy (12 seconds) | Mechanical Energy (15 seconds)

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24. Two identical freight cars roll without friction towards each other on a level track. One rolls at 2 m/s and the other rolls at 1 m/s. After the cars collide, they couple (attach together) and roll together with a speed of _____________.
 a. 0.5 m/s b. 0.33 m/s c. 0.67 m/s d. 1.0 m/s e. none of these

Use m as the mass of the freight cars (or any number you wish) and then set the expression for initial total momentum equal to the expression for the final total momentum:

m*(2) + m*(-1) = m*v + m*v

Now solve for v using the proper algebraic steps.

2m - m = 2mv

m = 2mv

1 = 2v

0.5 m/s = v

(Note that the -1 indicates the second car is traveling in the opposite direction as the first car. Also not that the two cars stick together and so they have the same post-collision velocity.)

Momentum Conservation Principle (16 seconds) | Using the Momentum Equation as a Guide to Thinking (19 seconds)

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25. A freight train rolls along a track with considerable momentum. If it rolls at the same speed but has twice as much mass, its momentum is ____.
 a. zero b. quadrupled c. doubled d. unchanged

Momentum is directly related to the mass of the object. So for the same speed, a doubling of mass leads to a doubling of momentum.

Using the Momentum Equation as a Guide to Thinking (19 seconds)

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26. A rifle recoils from firing a bullet. The speed of the rifle's recoil is small because the ___.
 a. force against the rifle is relatively small. b. speed is mainly concentrated in the bullet. c. rifle has lots of mass. d. momentum of the rifle is unchanged. e. none of these.

Please don't answer A (for it will make Newton roll over in his grave and he's getting pretty tired of that); "for every action, there is an equal ...". Choice B is invalid; speed is not something that becomes concentrated or squeexed into an object. Choice D is invalid; ask anyone who's fired a rifle if the rifle begins to move (of course, since it does, its momentum is not unchanged). Because of the large mass of the rifle, the acceleration is small.

Momentum Conservation Principle (16 seconds) | Momentum Conservation in Explosions (12 seconds)

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27. Two objects, A and B, have the same size and shape, but A is twice as heavy as B. When they are dropped simultaneously from a tower (in the absence of air resistance), they reach the ground at the same time, but A has a higher ___.
 a. speed b. acceleration c. momentum d. all of the above e. none of the above

The two objects free-fall at the same rate of acceleration, thus giving them the same speed when they hit the ground. The heavier object however has more momentum since momentum takes into account both the speed and the mass of the object (p=m*v).

The Acceleration of Gravity (5 seconds) | Momentum (7 seconds)

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28. Padded dashboards in cars are safer in an accident than non-padded ones because they ____.
 a. increase the impact time. b. decrease an occupant's impulse. c. decrease the impact force d. two of the above e. none of the above.

Both A and C are correct. Padded dashboard serve to increase the time over which the momentum of a passenger is reduced to zero. With this increase in time, there is a decrease in force (big T, little f). The impulse acting upon the passenger is not changed since the passenger still must have his/her mass slowed down from the pre-impact velocity to zero velocity.

Real-World Applications (15 seconds)

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