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Pearson Physics

James S. Walker

Chapter 7

Linear Momentum and Collisions - all with Video Answers

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Chapter Questions

01:12

Problem 1

A Major League pitcher can give a $0.142-\mathrm{kg}$ baseball a speed of $45.1 \mathrm{~m} / \mathrm{s}$. Find the magnitude of the baseball's momentum.

Nishant Kumar
Nishant Kumar
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01:05

Problem 2

The momentum of a $12-\mathrm{kg}$ dog racing to greet its owner has a magnitude of $37 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$. What is the dog's speed?

Nishant Kumar
Nishant Kumar
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02:43

Problem 3

Rank The masses and speeds of four objects are given in the following table. Rank the objects in order of increasing magnitude of their momentum. Indicate
ties where appropriate.
$$
\begin{array}{|l|c|c|c|c|}
\hline & \text { Object A } & \text { Object B } & \text { Object C } & \text { Object D } \\
\hline \text { Mass } & 10 \mathrm{~kg} & 15 \mathrm{~kg} & 5 \mathrm{~kg} & 60 \mathrm{~kg} \\
\hline \text { Speed } & 10 \mathrm{~m} / \mathrm{s} & 4 \mathrm{~m} / \mathrm{s} & 20 \mathrm{~m} / \mathrm{s} & 3 \mathrm{~m} / \mathrm{s} \\
\hline
\end{array}
$$

Nishant Kumar
Nishant Kumar
Numerade Educator
01:32

Problem 4

Should the speed of the goose be increased or decreased to make the total momentum of the three birds add up to zero? Verify your answer by calculating the required speed.

James Kiss
James Kiss
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01:47

Problem 5

A car and a bicycle move toward each other, traveling in opposite directions. Each has a speed of $12.0 \mathrm{~m} / \mathrm{s}$. The mass of the car and its passengers is $1250 \mathrm{~kg}$, and the mass of the bicycle and its rider is
$81.6 \mathrm{~kg}$. What is the total momentum of the system, assuming that the car moves in the positive direction?

Nishant Kumar
Nishant Kumar
Numerade Educator
05:21

Problem 6

A $1200-\mathrm{kg}$ car moves due north with a speed of $15 \mathrm{~m} / \mathrm{s}$. An identical car moves due east with the same speed. What are the direction and the magnitude of the system's total momentum?

Nishant Kumar
Nishant Kumar
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01:47

Problem 7

How does momentum change if the mass of an object is doubled?

Hubert Agamasu
Hubert Agamasu
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01:42

Problem 8

Gexplain How is the direction of momentum related to the direction of velocity?

Nishant Kumar
Nishant Kumar
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01:56

Problem 9

Compare The speed of an object doubles. How does the change in the magnitude of the object's momentum compare to the change in its kinetic energy?

Supratim Pal
Supratim Pal
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02:48

Problem 10

Analyze A system consisting of two particles is known to have zero total momentum. Does it follow that the kinetic energy of the system is zero as well? Explain.

Prabhu Ramji
Prabhu Ramji
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01:42

Problem 11

Calculate What is the momentum of a $0.16-\mathrm{kg}$ apple that moves with a speed of $2.7 \mathrm{~m} / \mathrm{s}$ ?

Hubert Agamasu
Hubert Agamasu
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Problem 12

Calculate A school bus has a mass of $18,200 \mathrm{~kg}$. The bus moves at $12.5 \mathrm{~m} / \mathrm{s}$. How fast must a $0.142-\mathrm{kg}$ baseball move in order to have the same momentum as the bus?

Chasen Shaw
Chasen Shaw
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01:13

Problem 13

Calculate A dog running with a speed of $1.9 \mathrm{~m} / \mathrm{s}$ has a momentum of $17 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$. What is the mass of the dog?

Nishant Kumar
Nishant Kumar
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01:50

Problem 14

Calculate Two carts move directly toward one another on an air track. Cart 1 has a mass of $0.35 \mathrm{~kg}$ and a speed of $1.2 \mathrm{~m} / \mathrm{s}$. Cart 2 has a mass of $0.61 \mathrm{~kg}$ and a speed of $0.85 \mathrm{~m} / \mathrm{s}$. What is the total momentum of the system, assuming that cart 1 moves in the positive direction?

Nishant Kumar
Nishant Kumar
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01:17

Problem 15

You kick a soccer ball, delivering an impulse of $23 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$. If the force you exert on the ball lasts for $0.25 \mathrm{~s}$, what is the magnitude of the force?

Nishant Kumar
Nishant Kumar
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02:40

Problem 16

Triple Choice Apple 1 falls from a tree and drops $2 \mathrm{~m}$ to the ground. Apple 2, which has the same mass as apple 1, falls from the tree and drops $3 \mathrm{~m}$ to the ground. Is the impulse delivered by gravity to apple 1 greater than, less than, or equal to the impulse delivered by gravity to apple 2? Explain.

Supratim Pal
Supratim Pal
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01:40

Problem 17

An impulse of $12.2 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ is delivered to an object whose initial momentum is $4.5 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$. The impulse has the same direction as the initial momentum. What is the object's final momentum?

Nishant Kumar
Nishant Kumar
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02:05

Problem 18

Follow-up Suppose one of the three students in Guided Example $7.6$ stops pushing the car after $6.00 \mathrm{~s}$. In this case the force exerted on the car is $305 \mathrm{~N}$ for the first $6.00 \mathrm{~s}$ and $215 \mathrm{~N}$ for the second $6.00 \mathrm{~s}$.
(a) What is the final momentum of the car?
(b) What is the final speed of the car?

Prabhu Ramji
Prabhu Ramji
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02:45

Problem 19

A baseball player bunts (hits softly) a $0.144-\mathrm{kg}$ baseball thrown at $43.0 \mathrm{~m} / \mathrm{s} .$ If the bat exerts an average force of $6.50 \times 10^{3} \mathrm{~N}$ on the ball for $0.00122 \mathrm{~s}$, what is the final speed of the ball? Assume that the ball is bunted directly back toward the pitcher.

Nishant Kumar
Nishant Kumar
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01:22

Problem 20

When spiking a volleyball, a player changes the velocity of the ball from $4.2 \mathrm{~m} / \mathrm{s}$ to $-24 \mathrm{~m} / \mathrm{s}$ along a certain direction. If the impulse delivered to the ball by the player is $-9.3 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$, what is the mass of the volleyball?

Nick Auwerda
Nick Auwerda
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02:21

Problem 21

As an orange falls vertically downward, its momentum changes by $2.4 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ per second.
(a) What is the weight of the orange?
(b) How much time does it take for the orange's momentum to change by $6.1 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ ?

Nishant Kumar
Nishant Kumar
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01:03

Problem 22

Gr Identify Which (one or more) of the following quantities has the same direction as impulse: momentum, change in momentum, velocity, force, kinetic energy?

Hubert Agamasu
Hubert Agamasu
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01:36

Problem 23

G=xplain Does impulse determine an object's momentum or the change in an object's momentum?

Hubert Agamasu
Hubert Agamasu
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01:42

Problem 24

?nssess Why would a thin steel helmet offer little protection during an accident?

Prabhu Ramji
Prabhu Ramji
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02:59

Problem 25

Rank Impulses are delivered to systems A through D as described below. Rank the systems in order of increasing impulse. Indicate ties where appropriate.

Vishal Gupta
Vishal Gupta
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02:02

Problem 26

Triple Choice An unattended car rolls slowly across an empty parking lot. Consider the following two cases: case 1, the car hits a light pole and comes to rest; case 2 , the car hits a pile of plastic garbage bags and comes to rest.
(a) Is the impulse in case 1 greater than, less than, or equal to the impulse in case 2 ?
(b) Is the average force in case 1 greater than, less than, or equal to the average force in case 2 ?

Prabhu Ramji
Prabhu Ramji
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02:02

Problem 27

Calculate A safety helmet extends the time of impact from $0.005 \mathrm{~s}$ to $0.020 \mathrm{~s}$. By what factor is the average force that causes the impact reduced?

Prabhat Tyagi
Prabhat Tyagi
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01:54

Problem 28

Calculate In a typical golf swing the club is in contact with the ball for about $0.0010 \mathrm{~s}$. If the $45-\mathrm{g}$ ball acquires a speed of $67 \mathrm{~m} / \mathrm{s}$, estimate the magnitude of the force exerted by the club on the ball.

Nishant Kumar
Nishant Kumar
Numerade Educator
01:44

Problem 29

Calculate A $0.50-\mathrm{kg}$ croquet ball is initially at rest on the grass. When the ball is struck with a croquet mallet, the average force exerted on the ball is $230 \mathrm{~N}$. If the ball's speed after being struck is $3.2 \mathrm{~m} / \mathrm{s}$, how long was the mallet in contact with the ball?

Nishant Kumar
Nishant Kumar
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02:04

Problem 30

Calculate the final velocity of each canoe given that the total mass of canoe 1 is $130 \mathrm{~kg}$ and the total mass of canoe 2 is $250 \mathrm{~kg}$. Use your results to determine whether velocity is a conserved quantity.

James Kiss
James Kiss
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01:26

Problem 31

What is the final momentum of each canoe if they are pushed apart with a force of $56 \mathrm{~N}$ for $1.3 \mathrm{~s}$ ?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:53

Problem 32

Two ice skaters stand at rest in the center of an ice rink. When they push off against each other, the $45-\mathrm{kg}$ skater acquires a speed of $0.62 \mathrm{~m} / \mathrm{s}$. If the speed of the other skater is $0.89 \mathrm{~m} / \mathrm{s}$, what is that skater's mass?

Nishant Kumar
Nishant Kumar
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02:14

Problem 33

A 92-kg astronaut holds onto a 1200-kg satellite; both are at rest relative to a nearby space shuttle. The astronaut pushes on the satellite, giving it a speed of $0.14 \mathrm{~m} / \mathrm{s}$ directly away from the shuttle. The astronaut comes into contact with the shuttle $7.5 \mathrm{~s}$ after pushing away from the satellite. What was the initial distance from the shuttle to the astronaut?

Hubert Agamasu
Hubert Agamasu
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01:36

Problem 34

Explain If the total external force acting on a system is zero, what can you say about its total momentum?

Vysakh M
Vysakh M
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02:18

Problem 35

Describe Internal forces can change the momentum of individual objects within a system. How do they affect the total momentum of the system?

Prabhu Ramji
Prabhu Ramji
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Problem 36

Identify Two ice skaters at rest in the center of an ice rink push off each other in opposite directions. Identify the system in which momentum is conserved, and list the internal and external forces acting on the system.

Gregory Devenport
Gregory Devenport
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02:05

Problem 37

Assess An object resting on a frictionless surface is struck by a second object.
(a) Is it possible for both objects to be at rest after the collision? Explain.
(b) Is it possible for one of the objects to be at rest after the collision? Explain.

James Kiss
James Kiss
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02:50

Problem 38

Explain If you drop your keys, their momentum increases as they fall. Is the momentum of the keys conserved, or does the momentum of the universe increase as the keys fall? Explain.

James Kiss
James Kiss
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02:28

Problem 39

Calculate Two canoes are touching and at rest on a lake. The occupants push away from each other in opposite directions, giving canoe 1 a speed of $0.58 \mathrm{~m} / \mathrm{s}$ and canoe 2 a speed of $0.42 \mathrm{~m} / \mathrm{s}$. If the mass of canoe 1 is $320 \mathrm{~kg}$, what is the mass of canoe 2 ?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:31

Problem 40

Calculate A 94-kg lumberjack stands on a 1200$\mathrm{kg} \log$ in a pool of water. Initially the lumberjack and the log are at rest. The lumberjack then starts jogging toward shore along the length of the log. If the lumberjack's speed relative to the shore is $2.2 \mathrm{~m} / \mathrm{s}$, what is the log's speed relative to the shore?

James Kiss
James Kiss
Numerade Educator
02:21

Problem 41

Calculate A young hockey player stands at rest on the ice holding a $1.3-\mathrm{kg}$ helmet. The player tosses the helmet directly in front of him with a speed of $6.5 \mathrm{~m} / \mathrm{s}$ and recoils with a speed of $0.25 \mathrm{~m} / \mathrm{s}$. What is the mass of the hockey player?

Nishant Kumar
Nishant Kumar
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02:22

Problem 42

Follow-up If the final speed of the two players is to be zero, should the running back run faster or slower? Explain.

Supratim Pal
Supratim Pal
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Problem 43

Follow-up Check your answer to Problem 42 by calculating the required speed for the running back.

Susan Hallstrom
Susan Hallstrom
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02:30

Problem 44

A $1.35-\mathrm{kg}$ block of wood is at rest on a smooth table. A $0.0105-\mathrm{kg}$ bullet moving horizontally with a speed of $715 \mathrm{~m} / \mathrm{s}$ embeds itself within the block. What is the speed of the bullet-block system after the collision?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:14

Problem 45

A $1200-\mathrm{kg}$ car moving at $2.5 \mathrm{~m} / \mathrm{s}$ is struck directly from behind by a $2600-\mathrm{kg}$ truck moving at $6.2 \mathrm{~m} / \mathrm{s}$. If the vehicles stick together after the collision, what is their speed immediately after colliding? (Assume that external forces may be ignored.)

Nishant Kumar
Nishant Kumar
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01:28

Problem 46

Follow-up Suppose the initial speed of the red car in Guided Example $7.11$ was greater than $16 \mathrm{~m} / \mathrm{s}$. Would the angle in which the vehicles move after the collision be greater than, less than, or equal to 61°? Explain.

James Kiss
James Kiss
Numerade Educator
03:21

Problem 47

Follow-up Suppose the speed and the direction of the vehicles immediately after the collision in Guided Example $7.11$ are known to be $v_{\mathrm{f}}=12.5 \mathrm{~m} / \mathrm{s}$ and $\theta=42^{\circ}$, respectively. Find the initial speed of each vehicle.

James Kiss
James Kiss
Numerade Educator
02:28

Problem 48

An 82-kg football player is running in the positive $y$ direction with a speed of $3.1 \mathrm{~m} / \mathrm{s}$. A $96-\mathrm{kg}$ player from the opposing team is running in the negative $x$ direction with a speed of $2.4 \mathrm{~m} / \mathrm{s}$ when the tackle is made. Assuming that the players remain together, what is their speed immediately after the tackle?

James Kiss
James Kiss
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01:47

Problem 49

Relate When a collision occurs, how are the initial and final momentums of the system related?

James Kiss
James Kiss
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01:18

Problem 50

Describe How is the initial kinetic energy related to the final kinetic energy in an elastic collision?

Nishant Kumar
Nishant Kumar
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01:11

Problem 51

Explain What happens to the kinetic energy that is lost in an inelastic collision?

Vysakh M
Vysakh M
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01:14

Problem 52

Identify What do we call a collision in which the colliding objects stick together?

Nishant Kumar
Nishant Kumar
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Problem 53

What condition is required for momentum to be conserved in a collision?

Gregory Devenport
Gregory Devenport
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01:46

Problem 54

Assess Two cars collide at an intersection. If the cars do not stick together, can you conclude that the collision was elastic? Explain.

James Kiss
James Kiss
Numerade Educator
02:35

Problem 55

Calculate A cart of mass $m=0.12 \mathrm{~kg}$ moves with a speed $v=0.45 \mathrm{~m} / \mathrm{s}$ on a frictionless air track and collides with an identical cart that is stationary. The carts stick together after the collision. What are (a) the initial kinetic energy and (b) the final kinetic energy of the system?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:06

Problem 56

Calculate The collision between a geological hammer and a rock lying loose on the ground can be considered to be approximately elastic. Calculate the final speed of a $0.19-\mathrm{kg}$ rock when it is struck by a $0.55-\mathrm{kg}$ hammer moving with an initial speed of $4.5 \mathrm{~m} / \mathrm{s}$. The rock is initially at rest.

James Kiss
James Kiss
Numerade Educator
07:35

Problem 57

Calculate Suppose the red car in Guided Example $7.11$ has an initial speed of $20.0 \mathrm{~m} / \mathrm{s}$ and the direction in which the wrecked vehicles move after the collision is $40.0^{\circ}$ above the $x$ axis. Find the initial speed of the blue minivan.

Mark J
Mark J
Numerade Educator
02:50

Problem 58

Calculate Brittany stands at rest on a skateboard. The combined mass of Brittany and the skateboard is $61 \mathrm{~kg}$. Dave tosses a 3.7-kg pumpkin to Brittany, and when she catches it, she and the skateboard begin to roll backward with a speed of $0.16 \mathrm{~m} / \mathrm{s}$. What was the speed of the pumpkin?

Nishant Kumar
Nishant Kumar
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02:13

Problem 59

Is it possible for a baseball to have more momentum than a truck? Explain.

Nishant Kumar
Nishant Kumar
Numerade Educator
02:10

Problem 60

A system of particles is known to have zero kinetic energy. What can you say about the momentum of the system?

Nishant Kumar
Nishant Kumar
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Problem 61

A system of particles has a kinetic energy of $10,000 \mathrm{~J}$ but a total momentum of zero. Explain why this is possible.

Gregory Devenport
Gregory Devenport
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02:11

Problem 62

What is the difference between velocity and momentum? How are velocity and momentum similar?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:24

Problem 63

Mass and speed data for four objects are given below. Rank the objects in order of increasing magnitude of momentum. Indicate ties where appropriate.

Vysakh M
Vysakh M
Numerade Educator
02:42

Problem 64

Momentum and speed data for four objects are given below. Rank the objects in order of increasing mass. Indicate ties where appropriate.
$$
\begin{array}{|l|c|c|c|c|}
\hline & \text { A } & \text { B } & \text { C } & \text { D } \\
\hline \text { Momentum (kg } \cdot \mathbf{m} / \mathbf{s}) & 4 & 5 & 1 & 2 \\
\hline \text { Speed }(\mathbf{m} / \mathbf{s}) & 1 & 2 & 4 & 0.5 \\
\hline
\end{array}
$$

Nishant Kumar
Nishant Kumar
Numerade Educator
01:08

Problem 65

A $0.15-\mathrm{kg}$ baseball has a momentum of $0.78 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ just before it lands on the ground. What was the ball's speed just before landing?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:10

Problem 66

A car moving with a speed of $25 \mathrm{~m} / \mathrm{s}$ has a momentum of $32,000 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$. What is the mass of the car?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:03

Problem 67

What is the momentum of a $5.2-\mathrm{kg}$ salmon swimming upstream with a speed of $2.3 \mathrm{~m} / \mathrm{s}$ ?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:51

Problem 68

Soccer player 1 has a mass of $45 \mathrm{~kg}$ and moves to the right with a speed of $1.4 \mathrm{~m} / \mathrm{s}$. Soccer player 2 has a mass of $32 \mathrm{~kg}$ and moves to the left with a speed of $2.1 \mathrm{~m} / \mathrm{s}$. What are the direction and the magnitude of the total momentum of the two players?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:51

Problem 69

Soccer player 1 has a mass of $47 \mathrm{~kg}$ and moves to the right with a speed of $1.1 \mathrm{~m} / \mathrm{s}$. Soccer player 2 has a mass of $38 \mathrm{~kg}$. If the total momentum of the two players is $2.2 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ to the right, what are the speed and the direction of motion of player 2 ?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:33

Problem 70

Two carts move directly toward one another on an air track. Cart 1 has a mass of $0.35 \mathrm{~kg}$ and a speed of $1.2 \mathrm{~m} / \mathrm{s}$. Cart 2 has a mass of $0.61 \mathrm{~kg}$. What speed must cart 2 have if the total momentum of the system is to be zero?

Nishant Kumar
Nishant Kumar
Numerade Educator
05:13

Problem 71

A 280-g ball falls vertically downward, hitting the floor with a speed of $2.5 \mathrm{~m} / \mathrm{s}$ and then rebounding upward with a speed of $2.0 \mathrm{~m} / \mathrm{s}$. (a) What was the ball's momentum just before it hit the floor? (b) What was the ball's momentum just after it rebounded from the floor? (c) What was the ball's change in momentum during its impact with the floor?

Stylianos Gregoriou
Stylianos Gregoriou
Numerade Educator
04:34

Problem 72

A 26-kg dog is running northward at $2.7 \mathrm{~m} / \mathrm{s}$, while a $5.3-\mathrm{kg}$ cat is running eastward at $3.0 \mathrm{~m} / \mathrm{s}$. Find the magnitude and direction of the total momentum for this system.

Prabhat Tyagi
Prabhat Tyagi
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02:03

Problem 73

$$
\text { How does a force differ from an impulse? }
$$

James Kiss
James Kiss
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02:15

Problem 74

Is it possible for a small force to deliver a greater impulse than a large force? If so, explain how.

Vysakh M
Vysakh M
Numerade Educator
01:43

Problem 74

Is it possible for a small force to deliver a greater impulse than a large force? If so, explain how.

James Kiss
James Kiss
Numerade Educator
00:59

Problem 75

As a school bus approaches a stop sign, the driver applies the brakes and brings the bus to a slow, gradual stop. If the driver had instead stomped on the brakes and brought the bus to a sudden stop, would the magnitude of the impulse be greater than, less than, or equal to the magnitude of the impulse with the gradual stop? Explain.

James Kiss
James Kiss
Numerade Educator
01:49

Problem 76

Automobile air bags, which deploy during a collision, are designed to protect the vehicle's occupants. Using the concept of impulse, explain how air bags protect a car's passengers.

James Kiss
James Kiss
Numerade Educator
02:46

Problem 77

A net force of $200 \mathrm{~N}$ acts on a $100-\mathrm{kg}$ boulder, and a force of the same magnitude acts on a $100-\mathrm{g}$ pebble. (a) Is the change in the boulder's momentum in 1 s greater than, less than, or equal to the change in the pebble's momentum in the same time period? (b) Choose the best explanation from among the following:

A. The larger mass of the boulder gives it the greater change in momentum.

B. The force causes a much greater speed in the $100-\mathrm{g}$ pebble, resulting in a larger change in momentum.
C. Equal force means equal change in momentum for a given time period.

James Kiss
James Kiss
Numerade Educator
02:45

Problem 78

Referring to the boulder and the pebble in Problem 77, (a) is the change in the boulder's speed in $1 \mathrm{~s}$ greater than, less than, or equal to the change in speed of the pebble in the same time period?
(b) Choose the best explanation from among the following:
A. The larger mass of the boulder results in a smaller acceleration.

B. The same force results in the same change in speed for a given time.

C. Once the boulder gets moving, it is harder to stop than the pebble.

Mark J
Mark J
Numerade Educator
02:08

Problem 79

Force and time data for four different impulses are given below. Rank the impulses in order of increasing magnitude. Indicate ties where appropriate.
\begin{tabular}{|l|c|c|c|c|}
\hline & $\mathbf{A}$ & $\mathbf{B}$ & $\mathbf{C}$ & $\mathbf{D}$ \\
\hline Force (N) & $1 \mathrm{~N}$ & $2 \mathrm{~N}$ & $5 \mathrm{~N}$ & $10 \mathrm{~N}$ \\
\hline Time (s) & $1 \mathrm{~s}$ & $0.3 \mathrm{~s}$ & $0.1 \mathrm{~s}$ & $0.07 \mathrm{~s}$ \\
\hline
\end{tabular}

Vysakh M
Vysakh M
Numerade Educator
02:16

Problem 80

A $0.14 \mathrm{~kg}$ baseball is dropped from rest. It has a momentum of $0.78 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ just before it lands on the ground. For what amount of time was the ball in the air?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:08

Problem 81

Find the magnitude of the impulse delivered to a soccer ball when a player kicks it with a force of $1250 \mathrm{~N}$.
Assume that the player's foot is in contact with the ball for $5.95 \times 10^{-3} \mathrm{~s}$.

Nick Auwerda
Nick Auwerda
Numerade Educator
00:51

Problem 82

In a typical golf swing the club is in contact with the ball for about $0.0010 \mathrm{~s}$. If the $45-\mathrm{g}$ ball acquires a speed of $67 \mathrm{~m} / \mathrm{s}$, estimate the magnitude of the force exerted by the club on the ball.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:51

Problem 83

During an intense game of croquet, a $0.52-\mathrm{kg}$ ball at rest on the grass is struck by a mallet with an average force of $190 \mathrm{~N}$. If the mallet is in contact with the ball for $7.2 \times 10^{-3} \mathrm{~s}$, what is the ball's speed just after it is hit?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:00

Problem 84

During a ballistics test a bullet is fired into a thick gel to bring it to a stop. A $5.5-\mathrm{g}$ bullet traveling at $325 \mathrm{~m} / \mathrm{s}$ is brought to a stop in the gel by an average force of $550 \mathrm{~N}$. What amount of time is needed for the bullet to come to rest?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:42

Problem 85

When spiking a volleyball, a player changes the velocity of the ball from $4.2 \mathrm{~m} / \mathrm{s}$ to $-24 \mathrm{~m} / \mathrm{s}$ in a certain direction. If the impulse delivered to the ball by the player is $-9.3 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$, what is the mass of the volleyball?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:31

Problem 86

A $15-\mathrm{g}$ marble is dropped from rest onto the floor $1.4 \mathrm{~m}$ below. (a) If the marble bounces straight upward to a height of $0.64 \mathrm{~m}$, what are the magnitude and the direction of the impulse delivered to the marble by the floor? (b) If the marble bounces to a greater height, is the impulse delivered to it greater than or less than the impulse found in part (a)? Explain.

James Kiss
James Kiss
Numerade Educator
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Problem 87

Which types of forces (internal or external) can change the total momentum of a system?

Gregory Devenport
Gregory Devenport
Numerade Educator
01:42

Problem 88

A system consists of two objects. If the total momentum of the system is conserved, does this mean that the momentum of each object must remain the same? Explain.

James Kiss
James Kiss
Numerade Educator
01:23

Problem 89

Give an example of a situation where momentum is conserved but velocity is not.

James Kiss
James Kiss
Numerade Educator
01:31

Problem 90

Explain how a rocket functions in space even though there is no matter for its exhaust gases to push against.

James Kiss
James Kiss
Numerade Educator
01:51

Problem 91

An astronaut carrying a large wrench is tethered to a space shuttle by a wire. Explain how the astronaut can use the wrench to return to the space shuttle after the tether wire breaks.

James Kiss
James Kiss
Numerade Educator
01:40

Problem 92

At the instant a bullet is fired from a gun, the bullet and the gun have equal and opposite momentums. Which object, the bullet or the gun, has the greater kinetic energy? Use your answer to explain why the recoil of the gun is not harmful but the speeding bullet is dangerous.

James Kiss
James Kiss
Numerade Educator
01:54

Problem 93

Two ice skaters stand at rest in the center of an ice rink. When they push off against one another, the $45-\mathrm{kg}$ skater acquires a speed of $0.62 \mathrm{~m} / \mathrm{s}$. If the speed of the other skater is $0.89 \mathrm{~m} / \mathrm{s}$, what is that skater's mass?

Nick Auwerda
Nick Auwerda
Numerade Educator
02:14

Problem 94

Two rollerbladers face each other and stand at rest on a flat parking lot. Tracey has a mass of $32 \mathrm{~kg}$, and Jonas has a mass of $45 \mathrm{~kg}$. When they push off against one another, Jonas acquires a speed of $0.55 \mathrm{~m} / \mathrm{s}$. What is Tracey's speed?

Nishant Kumar
Nishant Kumar
Numerade Educator
04:51

Problem 95

A 63-kg canoeist stands in the middle of her 32-kg canoe. Initially, both the canoeist and the canoe are at rest, and the canoe is pointing directly toward the shore. (a) If the canoeist begins to walk toward one end of the canoe with a speed of $0.95 \mathrm{~m} / \mathrm{s}$ relative to the shore, what is the speed of the canoe relative to the shore? (b) If the mass of the canoe were increased, would the speed found in part (a) be greater than, less than, or the same as before? Explain. (c) Calculate the speed in part (a) for a 39-kg canoe.

Mark J
Mark J
Numerade Educator
01:13

Problem 96

A 92-kg astronaut and a 1200-kg satellite are at rest relative to a space station. The astronaut pushes on the satellite, giving it a speed of $0.14 \mathrm{~m} / \mathrm{s}$ directly away from the station. Seven and a half seconds later the astronaut comes into contact with the station. What was the initial distance from the station to the astronaut?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
05:57

Problem 97

An 85-kg lumberjack stands at one end of a $380-\mathrm{kg}$ floating log, as shown in Figure $7.16$. Both the log and the lumberjack are at rest initially. (a) The lumberjack then trots toward the shore with a speed of $2.7 \mathrm{~m} / \mathrm{s}$ relative to the shore. What is the speed of the log relative to the shore? Ignore friction between the log and the water. (b) If the mass of the log were greater, would its speed relative to the shore be greater than, less than, or the same as the speed found in part (a)? Explain. (c) Check your answer to part (b) by calculating the speed relative to the shore for a $450-\mathrm{kg}$ log.

Mark J
Mark J
Numerade Educator
01:35

Problem 98

What distinguishes a completely inelastic collision from other inelastic collisions?

James Kiss
James Kiss
Numerade Educator
01:42

Problem 99

Momentum is conserved during the collision of two billiard balls. Is the momentum of each ball conserved during the collision? Explain.

James Kiss
James Kiss
Numerade Educator
01:03

Problem 100

What two physical quantities are conserved in an elastic collision?

Vysakh M
Vysakh M
Numerade Educator
00:51

Problem 101

What physical quantity is not conserved in an inelastic collision?

Vysakh M
Vysakh M
Numerade Educator
02:16

Problem 102

In a two-dimensional elastic collision momentum must be conserved in both the $x$ and the $y$ directions. What about the kinetic energy? Must it be conserved in both directions too? Explain.

James Kiss
James Kiss
Numerade Educator
01:01

Problem 103

Can two objects on a horizontal frictionless surface have a collision in which all the initial kinetic energy of the system is lost? Explain why not if your answer is no, and give a specific example if your answer is yes.

James Kiss
James Kiss
Numerade Educator
02:16

Problem 104

A $0.10-\mathrm{kg}$ cart moves with a speed of $0.66 \mathrm{~m} / \mathrm{s}$ on a frictionless air track and collides with a stationary cart whose mass is $0.20 \mathrm{~kg}$. If the two carts stick together after the collision, what is the final kinetic energy of the system?

Nishant Kumar
Nishant Kumar
Numerade Educator
03:31

Problem 105

A $25,000-\mathrm{kg}$ train car moving at $2.50 \mathrm{~m} / \mathrm{s}$ collides with and connects to a train car of equal mass moving in the same direction at $1.00 \mathrm{~m} / \mathrm{s}$. (a) What is the speed of the connected cars? (b) How much does the kinetic energy of the system decrease during the collision?

James Kiss
James Kiss
Numerade Educator
09:23

Problem 106

A 732-kg car stopped at an intersection is rear-ended by a $1720-\mathrm{kg}$ truck moving with a speed of $15.5 \mathrm{~m} / \mathrm{s}$. If the car was in neutral and its brakes were off, so the collision is approximately elastic, find the final speed of both vehicles after the collision.

Nick Auwerda
Nick Auwerda
Numerade Educator
10:13

Problem 107

A 92-kg rugby player running at $7.5 \mathrm{~m} / \mathrm{s}$ collides in midair with a $112-\mathrm{kg}$ player moving in the opposite direction. After the collision each player has zero velocity. (a) Diagram the situation before and after the collision, identifying masses and speeds. (b) What is the initial momentum of the $92-\mathrm{kg}$ player? (c) What is the change in momentum of the $92-\mathrm{kg}$ player due to the collision? (d) How is the change in momentum of the $92-\mathrm{kg}$ player related to the change in momentum of the 112-kg player? (e) What was the initial speed of the $112-\mathrm{kg}$ player before the collision?

Mark J
Mark J
Numerade Educator
03:22

Problem 108

Two $72.0-\mathrm{kg}$ hockey players skating at $5.45 \mathrm{~m} / \mathrm{s}$ collide and stick together. If the angle between their initial directions was $90^{\circ}$, what is their speed after the collision?

Nishant Kumar
Nishant Kumar
Numerade Educator
01:19

Problem 109

Two curling stones collide on an ice rink. Stone 1 has a mass of $21 \mathrm{~kg}$ and an initial velocity of $1.7 \mathrm{~m} / \mathrm{s}$ to the north. Stone 2 has a mass of $16 \mathrm{~kg}$, and was at rest initially. The stones collide dead center. (a) What was the final velocity of stone 2 ? (b) What was the final velocity of stone 1 ?

James Kiss
James Kiss
Numerade Educator
03:23

Problem 110

Two curling stones collide on an ice rink. Stone 1 has a mass of $16 \mathrm{~kg}$ and an initial velocity of $1.5 \mathrm{~m} / \mathrm{s}$ to the north. Stone 2 was at rest initially. The stones collide dead center, giving stone 2 a final velocity of $0.69 \mathrm{~m} / \mathrm{s}$ to the north. (a) What was the mass of stone 2? (b) What was the final velocity of stone 1 ?

Prabhakar Kumar
Prabhakar Kumar
Numerade Educator
03:40

Problem 111

A bullet with a mass of $4.0 \mathrm{~g}$ and a speed of $650 \mathrm{~m} / \mathrm{s}$ is fired at a block of wood with a mass of $0.095 \mathrm{~kg}$. The block rests on a frictionless surface,
and it is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is $23 \mathrm{~m} / \mathrm{s}$. (a) What is the speed of the bullet when it exits the block? (b) Is the final kinetic energy of this system greater than, less than, or equal to the initial kinetic energy? Explain. (c) Verify your answer to part (b) by calculating the initial and final kinetic energies of the system.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:55

Problem 112

A $0.430-\mathrm{kg}$ block is attached to a horizontal spring that is at its equilibrium length and has a spring constant of $20.0 \mathrm{~N} / \mathrm{m}$. The block rests on a frictionless surface. A $0.0500-\mathrm{kg}$ wad of putty is thrown horizontally at the block with a speed of $2.30 \mathrm{~m} / \mathrm{s}$. The putty sticks to the block. How far does the putty-block system compress the spring?

James Kiss
James Kiss
Numerade Educator
12:48

Problem 113

A velocity amplifier The three air-track carts shown in Figure $7.17$ have masses, from left to right, of $4 m, 2 m$, and $m$, respectively. The most massive cart has an initial speed of $v$; the other two carts are at rest initially. All three carts are equipped with spring bumpers that give elastic collisions. (a) Find the final speed of each cart. Notice that the smallest cart has a final speed greater than $v$. We refer to this effect as an amplification of the initial velocity. (b) Verify that the final kinetic energy of the system is equal to the initial kinetic energy. Assume that the air track is long enough to accommodate all collisions. (An example of velocity amplification is shown in Figure 7.18. Notice that the speed of the lightweight green ball is increased by its collision with the heavier orange ball, which sends it much higher than the original drop height.)

Mark J
Mark J
Numerade Educator
00:25

Problem 114

Object A has a mass $m$, object B has a mass $2 m$, and object $C$ has a mass $m / 2$. Rank these objects in order of increasing kinetic energy, given that they all have the same momentum. Indicate ties where appropriate.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:27

Problem 115

Object A has a mass $m$, object B has a mass $4 m$, and object $C$ has a mass $m / 4$. Rank these objects in order of increasing momentum, given that they all have the same kinetic energy. Indicate ties where appropriate.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:46

Problem 116

A block of wood is struck by a bullet. (a) Is the block more likely to be knocked over if the bullet is metal and embeds itself in the wood or if the bullet is rubber and bounces off the wood? (b) Choose the best explanation from among the following:

A. The change in momentum when a bullet rebounds is twice as much as when it is brought to rest.
B. The metal bullet does more damage to the block.
C. Since the rubber bullet bounces off, it has little effect on the block.

James Kiss
James Kiss
Numerade Educator
01:28

Problem 117

Small navigational rockets are used to change the speed and direction of the space probe Voyager II. If a rocket exerts a force of $25 \mathrm{~N}$, how long must the rocket fire to change the speed of the $722-\mathrm{kg}$ probe by $1.0 \mathrm{~m} / \mathrm{s}$ ?

James Kiss
James Kiss
Numerade Educator
01:45

Problem 118

A car moving with an initial speed $v$ collides with a stationary car that is one-half as massive. After the collision the first car moves in the same direction as before with a speed $v / 3$. (a) Find the final speed of the second car. (b) Is this collision elastic or inelastic?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:12

Problem 119

An apple that weighs $2.7 \mathrm{~N}$ falls vertically downward from rest for $1.4 \mathrm{~s}$. (a) What is the change in the apple's momentum per second? (b) What is the total change in its momentum during the $1.4$-s fall?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:31

Problem 120

A young hockey player stands at rest on the ice holding a $1.3-\mathrm{kg}$ helmet. The player tosses the helmet with a speed of $6.5 \mathrm{~m} / \mathrm{s}$ in a direction $11^{\circ}$ above the horizontal, and then recoils with a speed of $0.25 \mathrm{~m} / \mathrm{s}$. Find the mass of the hockey player.

Nick Auwerda
Nick Auwerda
Numerade Educator
02:21

Problem 121

A friend climbs an apple tree and drops a $0.22-\mathrm{kg}$ apple from rest to you, standing $3.5 \mathrm{~m}$ below. When you catch the apple, you bring it to rest in $0.28 \mathrm{~s}$. (a) What was the speed of the apple just before you caught it? (b) What average force did you exert on the apple to bring it to rest? (Hint: Be sure to include both the weight of the apple and the force needed to bring it to rest.)

James Kiss
James Kiss
Numerade Educator
01:37

Problem 122

The Force of a Storm During a severe storm in Palm Beach, Florida, on January 2, 1999, $79 \mathrm{~cm}$ (31 in) of rain fell in a period of 9 hours. Assuming that the raindrops hit the ground with a speed of $10 \mathrm{~m} / \mathrm{s}$, estimate the average upward force exerted by 1 square meter of ground to stop the falling raindrops during the storm. (One cubic meter of water has a mass of $1000 \mathrm{~kg}$.)

James Kiss
James Kiss
Numerade Educator
02:12

Problem 123

At a busy intersection a $1540-\mathrm{kg}$ car traveling west with a speed of $12 \mathrm{~m} / \mathrm{s}$ collides head-on with a minivan traveling east with a speed of $9.4 \mathrm{~m} / \mathrm{s}$. The cars stick together and move with an initial velocity of $1.5 \mathrm{~m} / \mathrm{s}$ to the east after the collision. What is the mass of the minivan?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
03:38

Problem 124

A 1.7-kg block of wood rests on a rough surface. A $0.011-\mathrm{kg}$ bullet strikes the block with a speed of $670 \mathrm{~m} / \mathrm{s}$ and embeds itself. The bullet-block system slides forward $2.4 \mathrm{~m}$ before coming to rest. What is the coefficient of kinetic friction between the block and the surface?

James Kiss
James Kiss
Numerade Educator
03:02

Problem 125

A 1.35-kg block of wood sits at the edge of a table, $0.782 \mathrm{~m}$ above the floor. A $0.0105-\mathrm{kg}$ bullet moving horizontally with a speed of $715 \mathrm{~m} / \mathrm{s}$ embeds itself within the block. What horizontal distance does the block cover before hitting the ground?

Nick Auwerda
Nick Auwerda
Numerade Educator
04:07

Problem 126

The three air-track carts shown in Figure $7.19$ have masses, from left to right, of $m, 2 m$, and $4 m$, respectively. Initially, the cart on the right is at rest, whereas the other two carts are moving to the right with a speed $v$. All three carts are equipped with putty bumpers that make them have completely inelastic collisions. (a) Find the final speed of the carts. (b) Calculate the ratio of the final kinetic energy of the system to the initial kinetic energy.

Vishal Gupta
Vishal Gupta
Numerade Educator
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Problem 127

Write a paragraph describing in detail the forces involved when two objects collide. Choose a specific collision to write about, such as a tennis ball being hit with a tennis racket. Be sure to discuss action and reaction forces, time of contact, and impulse.

James Kiss
James Kiss
Numerade Educator
02:08

Problem 128

Collisions conserve momentum, but not velocity. What is the difference between momentum and velocity? To illustrate your answer, give an example of objects that have the same momentum but different velocities. Similarly, give an example of objects that have different momentums but the same velocity.

James Kiss
James Kiss
Numerade Educator
00:51

Problem 129

From the perspective of an observer on the planet, what is the spacecraft's speed of approach?
A. $v_{\mathrm{i}}+u$
C. $u-v_{\mathrm{i}}$
B. $v_{\mathrm{i}}-u$
D. $v_{\mathrm{f}}-u$

James Kiss
James Kiss
Numerade Educator
01:05

Problem 130

From the perspective of an observer on the planet, what is the spacecraft's speed of departure?
A. $v_{\mathrm{f}}+u$
C. $u-v_{\mathrm{f}}$
B. $v_{\mathrm{f}}-u$
D. $v_{\mathrm{i}}-u$

James Kiss
James Kiss
Numerade Educator
00:53

Problem 131

Set the speed of departure from Problem 130 equal to the speed of approach from Problem 129. Solving this relation for the final speed, $v_{\mathrm{f}}$, yields
A. $v_{\mathrm{f}}=v_{\mathrm{i}}+u$
C. $v_{\mathrm{f}}=v_{\mathrm{i}}+2 u$
B. $v_{\mathrm{f}}=v_{\mathrm{i}}-u$
D. $v_{\mathrm{f}}=v_{\mathrm{i}}-2 u$

James Kiss
James Kiss
Numerade Educator