Units 4 Review

Momentum

 Units 4 Review - Answers: [ #14 | #15 | #16 | #17 | #18 | #19 | #20 | #21 | #22 | #23 | #24 | #25 | #26 ]

14. 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)

15. 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)

16. 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)

17. 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)

18. A 4 kg ball has a momentum of 12 kg*m/s. The ball's speed is ___ m/s.
 a. 3 b. 4 c. 12 d. 48 e. none of these.

This is a relatively simple plug-and-chug into the equation p=m*v with m=4 kg and p=12 kg*m/s.

Momentum (7 seconds)

19. A piece of putty moving with 1 unit of momentum strikes and sticks to a heavy bowling ball that is initially at rest. After the putty sticks to the ball, both are set in motion with a combined momentum that is ___.
 a. less than 1 unit b. more than 1 unit c. 1 unit d. not enough information

Since momentum must be conserved, the total momentum of the ball and putty must be 1 unit. (Before the collision, the total system momentum is also 1 unit - all due to the motion of the putty.)

Momentum Conservation Principle (16 seconds)

20. A large force acting for a long amount of time on a small mass will produce a ______.
 a. small velocity change b. large velocity change c. small momentum change d. small acceleration e. two of the above

A large force on a small mass will result in a large acceleration (a=F/m) and subsequently a large velocity change (Delta v = a*t). This rules out choices A and D. A large force and for a long time will result in a large impulse and therefore a large momentum change. This rules out choice C.

Momentum and Impulse Connection (14 seconds) | Real-World Applications (15 seconds)

21. Force and time pertains to momentum change in the same manner as force and distance pertains to ___________.
 a. impulse b. work c. energy change d. velocity e. none of these.

A force multiplied by a time gives an impulse which will cause (and be equal to) a momentum change. In the same manner, a force multiplied by a distance gives work which will cause (and be equal to) an energy change. Re-read those two sentences because it relates two big concepts.

Momentum and Impulse Connection (14 seconds) | Analysis of Situations Involving External Forces (21 seconds)

22. A 5-N force is applied to a 3-kg object to change its velocity from +9 m/s to +3 m/s. The momentum change of the object is:
 a. -2.5 kg*m/s b. -10 kg*m/s c. -18 kg*m/s d. -45 kg*m/s e. none of these

Don't make this harder than it is; the momentum change of an object can be found if the mass and the velocity change are known. In this equation, m=3 kg and the velocity change is -6 m/s. When finding the velocity change, always subtract the initial velocity from the final velocity (vf - vi). The momentum change can also be found if the force and the time are known. Multiplying force*time yields the impulse and the impulse equals the momentum change.

Momentum and Impulse Connection (14 seconds)

23. A 5-N force is applied to a 3-kg object to change its velocity from +9 m/s to +3 m/s. The impulse experienced by the object is:
 a. -2.5 N*s b. -10 N*s c. -18 N*s d. -45 N*s e. none of these

Impulse is defined as a force acting upon and object for a given amount of time. Impulse can be computed by multiplying force*time. But in this problem, the time is not known. Never fear - the impulse equals the momentum change. The momentum change in this problem is -18 kg*m/s (see question #22). Thus, the impulse is -18 N*s.

Momentum and Impulse Connection (14 seconds)

24. A 5-N force is applied to a 3-kg object to change its velocity from +9 m/s to +3 m/s. The impulse acts for a time period of
 a. 1.8 s b. 2.5 s c. 3.6 s d. 10 s e. none of these

Use the impulse momentum change theorem with F=5 N, m=3 kg and Delta v=-6 m/s. Solving for time involves the following steps.

t = m*(delta v)/F = (3 kg)*(-6 m/s)/(5 N) = 3.6 s

Momentum and Impulse Connection (14 seconds)

25. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of 2M in a time of (1/2)t is
 a. 2F b. 4F c. (1/2)*F d. (1/4)*F e. none of these

The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be re-arranged to locate the F by itself on one side of the equation; rearranging yields

F = m*(Delta vel.)/t

The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, doubling the mass (from M to 2M) will double the force and halving the time (from t to 1/2-t) will double the force. The combined effect of these two changes will make the new force four times bigger than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

Momentum and Impulse Connection (14 seconds) | Real-World Applications (15 seconds)

26. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the same velocity change of v, the force experienced by a mass of 2M in a time of (1/4)t is
 a. 2F b. 8F c. (1/2)*F d. (1/8)*F e. none of these

The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be re-arranged to locate the F by itself on one side of the equation; rearranging yields

F = m*(Delta vel.)/t

The equation shows that force is directly related to the mass, directly related to the change in velocity, and inversely related to the time. So any change in mass will result in the same change in force; and any change in time will result in the inverse effect upon the force. In this case, doubling the mass (from M to 2M) will double the force and quartering the time (from t to 1/4-t) will quadruple the force. The combined effect of these two changes will make the new force eight times bigger than the old force. This is a case of where equations can be a guide to thinking about how a change in one variable (or two variables) impacts other dependent variables.

Momentum and Impulse Connection (14 seconds) | Real-World Applications (15 seconds)