Momentum and Collisions Review

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Part B: Multiple Choice

6. Which of the following objects have momentum? Include all that apply.

a. An electron is orbiting the nucleus of an atom.

b. A UPS truck is stopped in front of the school building.

c. A Yugo (a compact car) is moving with a constant speed.

d. A small flea walking with constant speed across Fido's back.

e. The high school building rests in the middle of town.

 

Answer: A, C, and D

Momentum can be thought of as mass in motion. An object has momentum if it has its mass in motion. It matters not whether the object is of large mass or small mass, moving with constant speed or accelerating; if the object is MOVING, then it has momentum!



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Momentum

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7. A truck driving along a highway road has a large quantity of momentum. If it moves at the same speed but has twice as much mass, its momentum is ________________.

a. zero

b. quadrupled

c. doubled

d. unchanged


Answer: C

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.



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Momentum

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8. TRUE or FALSE:

A ball is dropped from the same height upon various flat surfaces. For the same collision time, impulses are smaller when the most bouncing take place.

a. True

b. False



Answer: B

Since being dropped from the same height, the balls will be moving with the same pre-collision velocity (assuming negligible air resistance). Upon collision with the ground, the velocity will have to be reduced to zero - that is, the ball will cease moving downwards. This decrease in velocity constitutes the first portion of the velocity change. If the ball bounces, then there is an additional velocity change sending the ball back upwards opposite the original direction. Thus, for the same collision time, bouncing involves a greater velocity change, a greater momentum change, and therefore a greater impulse.



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Real-World Applications

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9. Consider a karate expert. During a talent show, she executes a swift blow to a cement block and breaks it with her bare hand. During the collision between her hand and the block, the ___.

  1. time of impact on both the block and the expert's hand is the same
  2. force on both the block and the expert's hand have the same magnitude
  3. impulse on both the block and the expert's hand have the same magnitude
  4. all of the above.
  5. none of the above.

Answer: D

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two colliding objects. The lower mass object always receives the greater velocity change and acceleration.



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Momentum Conservation Principle

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10. It is NOT possible for a rocket to accelerate in outer space because ____. List all that apply.

  1. there is no air in space
  2. there is no friction in space
  3. there is no gravity in outer space
  4. ... nonsense! Rockets do accelerate in outer space.

Answer: D

Rockets accelerate in outer space by means of Newton's third law of motion. It does not matter that there is no air outside of the rocket. Rockets produce their own gas by burning fuels. The combustion of rocket fuels produces gaseous products. The rocket's thrusters push these gases backwards (or rightwards, or leftwards, or ...) and the gases push the rocket forwards (or leftwards, or rightwards, or ...). Thus, rockets indeed can and do accelerate in outer space.



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The Law of Action-Reaction (Revisited)

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11. In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be reduced in size principally because ___.

  1. the resulting impact velocity is lessened
  2. the momentum change is decreased
  3. the time of impact is increased
  4. the time of impact is decreased
  5. none of these

Answer: C

Increasing the time over which the ball's momentum is brought to 0 will decrease the force required to stop it. Suppose a ball is coming at you with 100-units of momentum. An impulse of 100-units would be required to stop the ball. Regardless of how the impulse is accomplished (big F, little t or little F, big t), there must be 100-units of it. Imparting such an impulse over a long time results in a small force.



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Real-World Applications

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12. Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet leaving the muzzle will be the same as the speed of the recoiling gun ____.

  1. because momentum is conserved
  2. because velocity is conserved
  3. because both velocity and momentum are conserved
  4. only if the mass of the bullet equals the mass of the gun
  5. none of these

Answer: D

In any collision or explosion involving two objects, the momentum change for each object is the same. So both the bullet and the gun encounter the same momentum change. The momentum change is simply the mass multiplied by the velocity change. Thus, the velocity change would only be the same if their masses were the same. Otherwise, the smaller-mass object receives a greater velocity change.



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The Law of Action-Reaction (Revisited)

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 13. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater change is momentum?

a. the moth

b. your car

c. both the same


Answer: C

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.



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Momentum Conservation Principle

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 14. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater force?

a. the moth

b. your car

c. both the same


Answer: C

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.



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Momentum Conservation Principle

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15. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater impulse?

a. the moth

b. your car

c. both the same


Answer: C

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.



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Momentum Conservation Principle

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16. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which undergoes the greater acceleration?

a. the moth

b. your car

c. both the same


Answer: A

In any collision, there are always four quantities which are the same for both objects involved in the collision. Each object experiences the same force (Newton's third law) for the same amount of time, leading to the same impulse, and subsequently the same momentum change. Only the acceleration and the velocity change can differ for the two objects. The object with the least mass always receives the greatest velocity change and acceleration.



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Momentum Conservation Principle

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17. Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____.

a. 4 N down

b. 5 N down

c. 5 N up

d. 10 N up

e. zero


Answer: E

If an object is at rest, then all the forces acting upon the object must be zero. The net force on any one of the boxes is 0 Newtons. Subsequently, in each case, the support force (which we have called the "normal force throughout this course) acting upwards on any of the boxes must be equal to the force of gravity on that box (i.e., the weight) plus the amount of load exerted from above (which would be equivalent to the weight of the other boxes located above the box). So for box Y, the support force acting upward would be equal to 9 N while the net force is still 0 Newtons. And for box Z, the support force is 19 N, sufficient to balance the 10-N gravitational force plus the 9-N of force resulting from the other two boxes bearing down on it.



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Net Force

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18. In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of _____________. Ignore resistive forces.

a. 0.5 m/s

b. 0.33 m/s

c. 0.67 m/s

d. 1.0 m/s

e. none of these


Answer: A

Use 1 kg as the mass of the carts (or any number you wish) and then set the expression for initial total momentum equal to the expression for the final total momentum:

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

Now solve for v using the proper algebraic steps.

(2 kg•m/s) - (1 kg•m/s) = (2 kg) v

1 kg•m/s = (2 kg)v

(1 kg•m/s) / (2 kg) = v

0.5 m/s = v



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Momentum Conservation Principle || Using the Momentum Equation as a Guide to Thinking

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19. A physics cart rolls along a low-friction track with considerable momentum. If it rolls at the same speed but has twice as much mass, its momentum is ____.

a. zero

b. four times as large

c. twice as large

d. unchanged


Answer: C

The momentum of an object is calculated as the product of mass and velocity. Thus, the momentum is directly proportional to the mass of the object. If the mass of an object is somehow doubled, the momentum is doubled as well.


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Using the Momentum Equation as a Guide to Thinking

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20. The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the rifle's recoil is smaller than the bullet's forward speed 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

 


Answer: C

Please don't answer A (for it will make Newton roll over in his grave and he's getting quite tired of that). Perhaps you've heard that "for every action, there is an equal and opposite ...". Choice B is invalid; speed is not something that becomes concentrated or squeezed into an object. Choice D is invalid; ask anyone who's fired a rifle if the rifle is set into motion by the firing of the bullet. (Of course, since it is set in motion, its momentum is not unchanged.) Because of the large mass of the rifle, the acceleration and the recoil speed of the rifle is small.



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Momentum Conservation Principle || Momentum Conservation in Explosions

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21. Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will reach the ground at the same time but object A will have a greater ___. Choose all that apply.

a. speed

b. acceleration

c. momentum

d. none of the above quantities will be greater


Answer: C

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).



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The Acceleration of Gravity || Momentum

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22. Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than non-padded ones because they ____. List all that apply.

a. increase the impact time

b. decrease an occupant's impulse

c. decrease the impact force

d. none of the above


Answer: AC

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. The passenger still must have his/her mass slowed down from the pre-impact velocity to zero velocity. This means the velocity change is the same whether the collision occurs with a padded dashboard, an air bag or a glass windshield. Since the velocity change is independent of the collision time, the momentum change and the required impulse are also independent of the collision time.



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Real-World Applications

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23. A 4 kg object has a momentum of 12 kg•m/s. The object's speed is ___ m/s.

a. 3

b. 4

c. 12

d. 48

e. none of these.


Answer: A

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



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Momentum

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24. A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___.

a. less than 1 unit

b. 1 unit

c. more than 1 unit

d. not enough information


Answer: B

Before the collision, the total system momentum is 1 unit - all due to the motion of the wad of gum. Since momentum must be conserved, the total momentum of the box and gum after the collision must also be 1 unit.

 


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Momentum Conservation Principle

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25. A relatively large force acting for a relatively long amount of time on a relatively small mass will produce a relatively ______. List all that apply.

a. small velocity change

b. large velocity change

c. small momentum change

d. small acceleration


Answer: B

A large force acting upon 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.



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Momentum and Impulse Connection || Real-World Applications

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26. Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and momentum. Force and time is related to momentum change in the same manner as force and displacement pertains to ___________.

a. impulse

b. work

c. energy change

d. velocity

e. none of these.


Answer: C

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 displacement gives work which will cause (and be equal to) an energy change. Take the time to reread those two sentences because it relates two big concepts.



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Momentum and Impulse Connection || Analysis of Situations Involving External Forces

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27. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. This impulse causes the momentum change of the ball to be ____ kg•m/s.

a. -2.5

b. -10

c. -18

d. -45

e. none of these


Answer: C

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).

There is a second means of determining the momentum change of an object (though it does not need to be used in this problem). 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.



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Momentum and Impulse Connection

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28. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse experienced by the ball is ____ N•s.

a. -2.5

b. -10

c. -18

d. -45

e. none of these


Answer: C

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 #27). Thus, the impulse is -18 N•s.



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Momentum and Impulse Connection

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29. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse is encountered by the ball for a time of ____ seconds.

a. 1.8

b. 2.5

c. 3.6

d. 10

e. none of these


Answer: C

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)

t = 3.6 s



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Momentum and Impulse Connection

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30. 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


Answer: B

The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged 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.



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Momentum and Impulse Connection || Real-World Applications

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31. 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


Answer: B

The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged 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.



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Momentum and Impulse Connection || Real-World Applications

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32. 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 (1/2)M in a time of (1/2)t is ____.

a. 2F

b. 4F

c. (1/2)*F

d. (1/4)*F

e. none of these


Answer: E

The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged 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, halving the mass (from M to 1/2-M) will half 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 the same size as 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.



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Momentum and Impulse Connection || Real-World Applications

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33. 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 (1/2)M in a time of 4t is ____.

a. 2F

b. 8F

c. (1/2)*F

d. (1/8)*F

e. none of these


Answer: D

The impulse-momentum change theorem states that F*t = m*(Delta vel.). This equation can be rearranged 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, halving the mass (from M to 1/2-M) will halve the force and quadrupling the time (from t to 4t) will quarter the force. The combined effect of these two changes will make the new force eight times smaller (i.e., one-eighth the size) 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.



Useful Web Links
Momentum and Impulse Connection || Real-World Applications

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34. A 0.5-kg ball moving at 5 m/s strikes a wall and rebounds in the opposite direction with a speed of 2 m/s. If the impulse occurs for a time duration of 0.01 s, then the average force (magnitude only) acting upon the ball is ____ Newtons.

a. 0.14

b. 150

c. 350

d. 500

e. none of these


Answer: C

This is a relatively simple plug-and-chug into the equation

F*t = m*(Delta vel.)

with m=0.5 kg, t=0.01 s and Delta vel.=-7 m/s. (The change in velocity is -7 m/s since the ball must first slow down from 5 m/s to 0 m/s and then be thrown back in the opposite direction at 2 m/s.) Using these numbers and solving for force yields -350 N. The magnitude of the force is 350 N and the "-" sign indicates the direction of the force.



Useful Web Links
Momentum and Impulse Connection

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35. If mass and collision time are equal, then impulses are greater on objects which rebound (or bounce).

a. TRUE

b. FALSE


Answer: A

The impulse is equal to the momentum change. And when there is a rebound, the momentum change is larger since there is a larger velocity change. For instance, a ball thrown at a wall at 5 m/s may rebound at -3 m/s yielding a velocity change of -8 m/s. An egg thrown at the same wall at the same speed of 5 m/s hits and stops, thus yielding a velocity change of -5 m/s. More velocity change means more momentum change and thus more impulse.



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Effect of Rebounding

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36. Consider the head-on collision between a lady bug and the windshield of a high speed bus. Which of the following statements are true? List all that apply.

  1. The magnitude of the force encountered by the bug is greater than that of the bus.
  2. The magnitude of the impulse encountered by the bug is greater than that of the bus.
  3. The magnitude of the momentum change encountered by the bug is greater than that of the bus.
  4. The magnitude of the velocity change encountered by the bug is greater than that of the bus.
  5. The magnitude of the acceleration encountered by the bug is greater than that of the bus.

Answer: D and E

In any collision between two objects, the force, impulse, and momentum change are the same for each object. (This makes statements A, B, and C false.) However, the smaller mass object encounters a greater acceleration and velocity change. (This makes statements D and E true).



Useful Web Links
The Law of Action-Reaction (Revisited)

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