College Physics

Roger A. Freedman; Todd Ruskell; Philip R. Kesten

Chapter 4

Forces and Motion I: Newton's Laws - all with Video Answers

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Chapter Questions

Problem 1

According to Newton's second law, does the direction of the net force always equal the direction of the acceleration? SSM

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Problem 2

If the sum of the forces acting on an object equals zero, does this imply that the object is at rest?

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Problem 3

What are the basic SI units $(\mathrm{kg}, \mathrm{m}, \mathrm{s})$ for force according to Newton's second law $\sum \mathrm{F} \rightarrow \mathrm{ext}=\mathrm{ma} \rightarrow ? \sum \vec{F}_{\mathrm{ext}}=m \vec{a} ?$

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Problem 4

Explain why the force that a horizontal surface exerts on an object at rest on the surface is called the normal force.

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Problem 5

What is the net force on a bathroom scale when a 75 -kg person stands on it? SSM

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Problem 6

Two forces of $30 \mathrm{~N}$ and $70 \mathrm{~N}$ act on an object. What are the minimum and maximum values for the sum of these two forces?

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Problem 7

You apply a 60-N force to push a box across the floor at constant speed. If you increase the applied force to $80 \mathrm{~N}$, will the box speed up to some new constant speed, or will it continue to speed up until it hits the wall? Assume that the floor is horizontal and the surface is uniform. Explain your answer.

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Problem 8

A definition of the inertia of an object is that it is a measure of the quantity of matter. How does this definition compare with the definition discussed in the chapter?

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Problem 9

Astronomy Why would it be easier to lift a truck on the Moon's surface than it is on Earth? SSM

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Problem 10

When constructing a free-body diagram, why is it a good idea to choose your coordinate system so that the motion of an object is along one of the axes?

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Problem 11

Sports How can a fisherman land a 5-lb fish using fishing line that is rated at $4 \mathrm{lb}$ ?

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Problem 12

List all the forces acting on a bottle of water if it were sitting on your desk.

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Problem 13

Sports A boxer claims that Newton's third law helps him while boxing. He says that during a boxing match the force that his jaw feels is the same as the force that his opponent's fist feels (when the opponent is doing the punching). Therefore, his opponent will feel the same force as he feels and he will be able to fight on without any problems, no matter how many punches he receives or gives. It will always be an "even fight." Discuss any flaws in his reasoning.

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Problem 14

Astronomy We know that the Sun pulls on Earth. Does Earth also pull on the Sun? Why or why not? SSM

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Problem 15

Medical Use Newton's third law to explain the forces involved in walking.

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Problem 16

Biology Use Newton's third law to explain how birds are able to fly forward. SSM

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Problem 17

A certain rope will break under any tension greater than $800 \mathrm{~N}$. How can it be used to lower an object weighing $850 \mathrm{~N}$ over the edge of a cliff
without the rope breaking? SSM

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Problem 18

Tension is a very common force in day-to-day life. Identify five ordinary situations that involve the force of tension.

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Problem 19

A chair is mounted on a scale inside an elevator in the physics building. Describe the variation in the scale reading as the elevator begins to ascend, goes up at constant speed, stops, begins to descend, goes down at a constant speed, and stops again.

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Problem 20

Medical Why does the American Academy of Pediatrics recommend that all infants sit in rear-facing car seats starting with their first ride home from the hospital? Explain your answer.

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Problem 21

Medical Why should the driver and passengers in a car wear seat belts? Explain your answer.

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Problem 22

Medical, Sports Gymnastics routines are done over a padded floor to protect athletes who fall. Why is falling on padding safer than falling on concrete?

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Problem 23

Using physics principles, explain why your hand hurts after punching a solid wall. Assuming your punches are all identical, use physics principles to explain why it hurts less if the wall is padded.

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Problem 24

The net force on a moving object suddenly becomes zero and remains zero. The object will
A. stop abruptly.
B. reduce speed gradually.
C. continue at constant velocity.
D. increase speed gradually.
E. reduce speed abruptly.

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Problem 25

Which has greater monetary value, a newton of gold on Earth or a newton of gold on the Moon?
A. the newton of gold on Earth
B. the newton of gold on the Moon
C. The value is the same, regardless of location.
D. One cannot say without checking the weight on the Moon.
E. the newton of gold on the Moon but only when inside a spaceship

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Problem 26

According to Newton's second law of motion, when a net force acts on an object, the acceleration is
A. zero.
B. inversely proportional to the object's mass.
C. independent of mass.
D. inversely proportional to the net force.
E. directly proportional to the object's mass.

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Problem 27

In the absence of a net force, an object can be
A. at rest.
B. in motion with a constant velocity.
C. accelerating.
D. at rest or in motion with a constant velocity.
E. It's not possible to know without more information. SSM

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Problem 28

Medical A car stops suddenly during a head-on collision, causing the driver's brain to slam into the skull. The resulting injury would most likely be to which part of the brain?
A. frontal portion of the brain
B. rear portion of the brain
C. middle portion of the brain
D. left side of the brain
E. right side of the brain

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Problem 29

Medical During the sudden impact of a car accident, a person's neck can experience abnormal forces, resulting in an injury commonly known as whiplash. If a victim's head and neck move in the manner shown in Figure 424 , his car was hit from the
A. front.
B. rear.
C. right side.
D. left side.
E. top during a rollover. SSM

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Problem 30

When a net force acts on an object, the object
A. is at rest.
B. is in motion with a constant velocity.
C. has zero speed.
D. is accelerating.
E. is at rest or in motion with a constant velocity.

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Problem 31

In the absence of a net force, an object cannot be
A. at rest.
B. in motion with a constant velocity.
C. accelerating.
D. moving with an acceleration of zero.
E. experiencing opposite but equal forces.

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Problem 32

How does the magnitude of the normal force exerted by the ramp in Figure 4-25 compare to the weight of the block? The normal force is
A. equal to the weight of the block.
B. greater than the weight of the block.
C. less than the weight of the block.
D. possibly equal to or less than the weight of the block, depending on whether or not the ramp surface is smooth.
E. possibly greater than or equal to the weight of the block, depending on whether or not the ramp surface is smooth.

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Problem 33

While an elevator traveling upward slows down to stop, the normal force on the feet of a passenger is _____ her weight. While an elevator traveling downward slows down to stop, the normal force on the feet of a passenger is _____ his weight.
A. larger than; smaller than
B. larger than; larger than
C. smaller than; smaller than
D. smaller than; larger than
E. equal to; equal to

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Problem 34

Case (a) in Figure 4-26 shows block A accelerated across a frictionless table by a hanging $10-\mathrm{N}$ block $(1.02 \mathrm{~kg})$. In case $(\mathrm{b})$ the same block $\mathrm{A}$ is accelerated by a steady 10-N tension in the string. Treat the masses of the strings, as well as the masses and friction of the pulleys, as negligible. The acceleration of block A in case (b) is
A. greater than its acceleration in case (a).
B. less than its acceleration in case (a).
C. equal to its acceleration in case (a).
D. twice its acceleration in case (a).
E. half its acceleration in case (a).

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Problem 35

Estimate the weight of five common objects using newtons (not pounds or ounces).

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Problem 36

Estimate the normal force acting on an apple that rests on a flat surface. What would this estimate be if the surface were tilted at an incline of $30^{\circ}$ with the horizontal?

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Problem 37

Sports Estimate the average force that a major league baseball pitcher exerts on a baseball when he throws it. SSM

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Problem 38

Estimate the maximum tension in the cable that supports a typical elevator.

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Problem 39

Sports Estimate the average force imparted on a tennis ball as it is fired from a tennis ball machine.

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Problem 40

Sports Estimate the tension in a rope that pulls you on water skis at a constant speed behind a speedboat.

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Problem 41

Estimate the force that is produced with the "jaws of life" (the pneumatic tool used to rip open the jammed doors of a vehicle that is involved in an accident).

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Problem 42

Estimate the force in newtons required to flip on a light switch.

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Problem 43

Estimate the force in newtons associated with snapping your fingers.

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Problem 44

Medical During an arthroscopic surgery repair of a patient's knee, a portion of healthy tendon is grafted in place of a damaged anterior cruciate ligament (ACL). To test the results the surgeon applies a known force to the ligament and increases it at 1-s intervals for $10 \mathrm{~s}$. Plot the data listed in the table as a function of time in a spreadsheet or on a graphing calculator and extrapolate the best-fit line to estimate the force that would correspond to a time of $15 \mathrm{~s}$.
$$
\begin{array}{cc}
\text { Time (s) } & \text { Force (mN) } \\
\hline 0 & 0 \\
1 & 2.28 \\
2 & 5.73 \\
3 & 11.28 \\
4 & 12.27 \\
5 & 12.54 \\
6 & 12.38 \\
7 & 14.11 \\
8 & 16.79 \\
9 & 21.08 \\
10 & 28.51 \\
\hline
\end{array}
$$

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Problem 45

Use a spreadsheet or graphing calculator to plot the velocity versus height of an express elevator. The elevator starts from rest on the ground floor, has constant acceleration until reaching its maximum speed of $10 \mathrm{~m} / \mathrm{s}$ at the 4 th floor (the distance between each floor is $3.5 \mathrm{~m}$ ), remains at this speed until the 20th floor, and then has constant acceleration until it stops at the 30th floor. Identify the point(s) on the graph when the weight of a rider as measured by a spring scale will reach its maximum value. SSM

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Problem 46

What is the acceleration of a $2.00 \times 103-\mathrm{kg}^{2} .00 \times 10^{3}-\mathrm{kg}$ car if the net force on the car is $4.00 \times 103 \mathrm{~N} ? 4.00 \times 10^{3} \mathrm{~N} ? \underline{\text { Example } 4-1}$

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Problem 47

What net force is needed to accelerate a $2.00 \times 103-\mathrm{kg}^{2.00} \times 10^{3}-\mathrm{kg}$ car at $2.00 \mathrm{~m} / \mathrm{s}^{2} ? \underline{\text { Example } 4-1}$

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Problem 48

Applying a constant net force to an object causes it to accelerate at 10
$\mathrm{m} / \mathrm{s}^{2}$. What will the acceleration of the object be if (a) the force is doubled,
(b) the mass is halved, (c) the force is doubled and the mass is doubled, (d) the force is doubled and the mass is halved, (e) the force is halved, (f) the mass is doubled, (g) the force is halved and the mass is halved, and (h) the force is halved and the mass is doubled? Example $4-1$

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Problem 49

Suppose that the engine of a certain car can result in a maximum force of $15,000 \mathrm{~N}$ being applied to the car from the road. In the absence of any other forces, what is the maximum acceleration this engine can produce in a 1250 -kg car? Example 4-1

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Problem 50

Three rugby players are pulling horizontally on ropes attached to a box, which remains stationary. Player 1 exerts a force $F_{1}$ equal to $1.00 \times 102 \mathrm{~N}$ $1.00 \times 10^{2} \mathrm{~N}$ at an angle $\theta_{1}$ equal to $60.0^{\circ}$ with respect to the $+x$ direction (Figure 4-27). Player 2 exerts a force $F_{2}$ equal to $2.00 \times 102 \mathrm{~N} 2.00 \times 10^{2} \mathrm{~N}$ at an angle $\theta_{2}$ equal to $37.0^{\circ}$ with respect to the $+x$ direction. The view in the figure is from above. Ignore friction and note that gravity can be ignored in this problem. (a) Determine the force $\mathrm{F} 3^{-} \overrightarrow{\boldsymbol{F}_{3}}$ exerted by player 3. State your answer by giving the components of $\mathrm{F} 3^{-} \overrightarrow{\boldsymbol{F}_{3}}$ in the directions perpendicular to and parallel to the positive $x$ direction. (b) Redraw the diagram and add the force $\mathrm{F} 3^{-} \overrightarrow{\boldsymbol{F}_{3}}$ as carefully as you can. (c) Player 3's rope breaks, and player 2 adjusts by pulling with a force of magnitude $\mathrm{F}^{\prime} 2^{\prime}{ }_{2}^{\prime}$ equal to $1.50 \times 102 \mathrm{~N}$ $1.50 \times 10^{2} \mathrm{~N}$ at the same angle as before. In which direction is the acceleration of the box relative to the $+x$ direction shown? (d) In part (c) the magnitude of the acceleration is measured to be $10.0 \mathrm{~m} / \mathrm{s}^{2}$. What is the mass of the box? SSM Example 4-2

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Problem 51

Three forces act on a $2.00-\mathrm{kg}$ object at angles $\theta 1=40.0^{\circ}, \theta_{1}=40.0^{\circ}$, $\theta 2=60.0^{\circ}, \theta_{2}=60.0^{\circ}$, and $\theta 3=20.0^{\circ}, \theta_{3}=20.0^{\circ}$, as shown in Figure 4-28. Find
the magnitude of $\mathrm{F} 2 \rightarrow \overrightarrow{\boldsymbol{F}_{2}}$ and $\mathrm{F} 3 \rightarrow \overrightarrow{\boldsymbol{F}_{3}}$ if the magnitude of $F_{1}$ is $1.00 \mathrm{~N}$ and the acceleration of the object is $1.50 \mathrm{~m} / \mathrm{s}^{2}$ toward the $+x$ direction. Example $4-2$

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Problem 52

What is the weight on Earth of a wrestler who has a mass of $120 \mathrm{~kg}$ ? Example 4-3

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Problem 53

A bluefin tuna has a mass of $250 \mathrm{~kg}$. What is its weight? SSM Example $\underline{4-3}$

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Problem 54

Astronomy An astronaut has a mass of $80.0 \mathrm{~kg}$. How much would the astronaut weigh on Mars where surface gravity is $38.0 \%$ of that on Earth? $\underline{\text { Example } 4-3}$

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Problem 55

What is the net force on an apple that weighs $3.5 \mathrm{~N}$ when you hold it at rest in your hand? Example $4-3$

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Problem 56

A $1300-\mathrm{kg}$ car is capable of a maximum acceleration of $5.0 \mathrm{~m} / \mathrm{s}^{2}$. If this car is required to push a stalled car of mass $1700 \mathrm{~kg}$, what is the maximum magnitude of acceleration of the two-car system? Example 4-3

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Problem 57

Draw a free-body diagram for a heavy crate being lowered by a steel cable straight down at a constant speed. Example 4-3

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Problem 58

Draw a free-body diagram for a box being pushed horizontally by a person across a smooth, frictionless floor at a steadily increasing speed. SSM Example 4-3

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Problem 59

Draw a free-body diagram for a bicycle rolling down a hill. Ignore the friction between the bicycle wheels and the hill, but consider any air resistance. Example 4-3

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Problem 60

A tugboat uses its winch to pull up a sinking sailboat with an upward force of $4500 \mathrm{~N}$. The mass of the boat is $200 \mathrm{~kg}$ and the water acts on the sailboat with a drag force of $2000 \mathrm{~N}$. Draw a free-body diagram for the sailboat and describe the motion of the sailboat. Example 4-3

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Problem 61

Box A weighs $80 \mathrm{~N}$ and rests on a table (Figure 4-29). A rope that connects boxes A and B drapes over a pulley so that box B hangs above the table, as shown in the figure. The pulley and rope are massless, and the pulley is frictionless. What force does the table exert on box $\mathrm{A}$ if box $\mathrm{B}$ weighs (a) $35 \mathrm{~N}$, (b) $70 \mathrm{~N},(\mathrm{c}) 90 \mathrm{~N} ? \underline{\text { Example } 4-9}$

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Problem 62

Two forces act on an object of mass $\mathrm{M}=3.00 \mathrm{~kg} M=3.00 \mathrm{~kg}$ as shown in Figure 4-30. Because of these forces, the object experiences an acceleration of $\mathrm{a}=7.00 \mathrm{~m} / \mathrm{s} 2^{a}=7.00 \mathrm{~m} / \mathrm{s}^{2}$ in the $+x$ direction. If $\theta 1=30.0^{\circ}$,
$\theta_{1}=30.0^{\circ}$, (a) calculate the magnitude of $\mathrm{F} 2 \rightarrow \overrightarrow{\boldsymbol{F}_{2}}$ and (b) make a careful drawing to show its direction, given that $\mathrm{F} 1=20.0 \mathrm{~N}^{F_{1}}=20.0 \mathrm{~N} .$ Example 4 $\underline{2}$

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Problem 63

$A 1.00 \times 102-\mathrm{kg} 1.00 \times 10^{2}-\mathrm{kg}$ streetlight is supported equally by two
ropes as shown in Figure 4-31. One rope pulls up and to the right, $40.0^{\circ}$
above the horizontal; the other rope pulls up and to the left, $40.0^{\circ}$ above the horizontal. What is the tension in each rope? SSM Example 4-3

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Problem 64

A $2.00 \times 102-\mathrm{N} 2.00 \times 10^{2}-\mathrm{N}$ sign is supported by two ropes as shown in Figure 4-32. If $\theta \mathrm{L}=45.0^{\circ} \theta_{\mathrm{L}}=45.0^{\circ}$ and $\theta \mathrm{R}=30.0^{\circ}, \theta_{\mathrm{R}}=30.0^{\circ}$, what is the
tension in each rope? Example 4-3

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Problem 65

The distance between two telephone poles is $50.0 \mathrm{~m}$. When a $0.500$ -kg bird lands on the telephone wire midway between the poles, the wire sags $0.15 \mathrm{~m}$. How much tension does the bird produce in the wire? Ignore the weight of the wire. Example 4-3

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Problem 66

A locomotive pulls 10 identical freight cars with an acceleration of $2.0$ $\mathrm{m} / \mathrm{s}^{2}$. How does the force between the third and fourth cars compare to the force between the seventh and eighth cars? Example 4-8

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Problem 67

A locomotive pulls 10 identical freight cars. The force between the locomotive and the first car is $1.00 \times 105 \mathrm{~N}, 1.00 \times 10^{5} \mathrm{~N}$, and the acceleration of the train is $2.00 \mathrm{~m} / \mathrm{s}^{2}$. There is no friction to consider. Find the force between the ninth and tenth cars. SSM Example 4-8

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Problem 68

A $0.0100$ -kg block and a $2.00-\mathrm{kg}$ block are attached to the ends of a rope. A student holds the $2.00$ -kg block and lets the $0.0100-\mathrm{kg}$ block hang below it; then he lets go. What is the tension in the rope while the blocks are falling, before either hits the ground? Air resistance can be neglected. $\underline{\text { Example } 4-8}$

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Problem 69

While parachuting, a $66.0$ -kg person experiences a downward acceleration of $2.50 \mathrm{~m} / \mathrm{s}^{2}$. What is the downward force on the parachute from the person? Example 4-4

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Problem 70

A bicycle and $50.0$ -kg rider accelerate at $1.00 \mathrm{~m} / \mathrm{s}^{2}$ up an incline of $10.0^{\circ}$ above the horizontal. What is the magnitude of the force that the bicycle exerts on the rider? Example 4-6

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Problem 71

A car uniformly accelerates from 0 to $28.0 \mathrm{~m} / \mathrm{s}$. A $60.0$ -kg passenger experiences a horizontal force of $4.00 \times 102 \mathrm{~N} 4.00 \times 10^{2} \mathrm{~N}$. How much time does it take for the car to reach $28.0 \mathrm{~m} / \mathrm{s}$ SSM Example $4-10$
What force does a $65.0$ -kg passenger experience during this acceleration? $\underline{\text { Example } 4-10}$

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Problem 72

A car accelerates from 0 to $1.00 \times 102 \mathrm{~km} / \mathrm{h}^{1.00} \times 10^{2} \mathrm{~km} / \mathrm{h}$ in $4.50 \mathrm{~s}$.
What force does a $65.0$ -kg passenger experience during this acceleration? Example 4-10

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Problem 73

Adam and Ben pull hand over hand on opposite ends of a rope while standing on a frictionless frozen pond. Adam's mass is $75.0 \mathrm{~kg}$, and Ben's mass is $50.0 \mathrm{~kg}$. If Adam's acceleration is $1.00 \mathrm{~m} / \mathrm{s}^{2}$ to the east, what are the magnitude and direction of Ben's acceleration? Example 4-8

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Problem 74

Two blocks of masses $M_{1}$ and $M_{2}$ are connected by a massless string that passes over a massless pulley (Figure 4-33). $M_{2}$, which has a mass of $20.0 \mathrm{~kg}$, rests on a long ramp of angle $\theta=30.0^{\circ} \theta=30.0^{\circ}$. Friction can be ignored in this problem. (a) What is the value of $M_{1}$ for which the two blocks are in equilibrium (no acceleration)? (b) If the actual mass of $M_{1}$ is $5.00 \mathrm{~kg}$ and the system is allowed to move, what is the magnitude of the acceleration of the two blocks? (c) In part (b) does $M_{2}$ move up or down the ramp? (d) In part (b) how far does block $M_{2}$ move in $2.00$ s? Example 4-9

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Problem 75

In Figure 4-34, the block on the left incline is $6.00 \mathrm{~kg}$. If $\theta 1=60.0^{\circ}$ $\theta_{1}=60.0^{\circ}$ and $\theta 2=25.0^{\circ}, \theta_{2}=25.0^{\circ}$, find the mass of the block on the right incline so that the system is in equilibrium (no acceleration). All surfaces are frictionless. SSM Example 4-9

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Problem 76

A reckless coyote engineer straps on a pair of ice skates and attaches a rocket capable of producing $5.0 \times 103 \mathrm{~N} 5.0 \times 10^{3} \mathrm{~N}$ of thrust to his back. Together, the coyote and the rocket have a mass of $120 \mathrm{~kg}$. If the coyote starts at rest on level, frictionless ice and bends over such that the rocket thrust is directed parallel to the ice, what is his final speed if the rocket burns for $5.0$ s? Example 4-5

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Problem 77

You stand at the base of a $4.00$ -m long frictionless ramp that is inclined at an angle of $9.00^{\circ}$. You want to slide a $2.00$ -kg object up the ramp so that it stops just as it reaches the top. What initial velocity must you give the object? Example 4-5

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Problem 78

You and a friend are ice skating. Standing in the middle of the rink, you give your $85-\mathrm{kg}$ friend a push with a force of $3.0 \times 102 \mathrm{~N} 3.0 \times 10^{2} \mathrm{~N}$. Assuming that the ice surface is frictionless, what magnitude of acceleration does your friend experience? Example 4-5

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Problem 79

A skier starts at rest atop a ski slope that has a slope of exactly $40.0^{\circ}$. Her total mass is $72.0 \mathrm{~kg}$. Approximating the slope to be frictionless and assuming that the skier skis straight down the slope, what will her speed be after $25.0 \mathrm{~s}$ ? $\underline{\text { Example } 4-5}$.

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Problem 80

A 5.0-kg block slides in a straight line. The velocity of the block as a function of time is displayed in the $v_{x}-\operatorname{tg}$ gaph in Figure 4-35. Calculate the net force on the block for the time intervals $t=0$ to $1 \mathrm{~s}, 1$ to $3 \mathrm{~s}, 3$ to $5 \mathrm{~s}, 5$ to $6 \mathrm{~s}$, and 6 to $7 \mathrm{~s}$.

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Problem 81

In an Atwood's machine, box A of unknown mass is attached to box B that has a mass of $2.00$ kg (Figure 4-36). The two boxes are attached by a massless rope that hangs over a massless, frictionless pulley. When in motion, it is found that box B moves upward with an acceleration of $3.00$
$\mathrm{m} / \mathrm{s}^{2}$. (a) What is the tension in the rope?
(b) What is the mass of box A? Example 4-9

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Problem 82

Medical, Astronomy A spaceship takes off vertically from rest with an acceleration of $29.0 \mathrm{~m} / \mathrm{s}^{2}$. What force is exerted on a $75.0$ -kg astronaut during takeoff? Express your answer in newtons and also as a multiple of the astronaut's weight on Earth. Example 4-1

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Problem 83

A girl of mass $50.0 \mathrm{~kg}$ is standing on a weight scale in an elevator that is initially at rest. As the elevator begins to move, the scale displays a value of $350 \mathrm{~N}$. (a) What is the magnitude of the acceleration that the girl experiences? (b) Is the elevator moving up or down? Example 4-7

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Problem 84

A child on a sled starts from rest at the top of a $20.0^{\circ}$ slope. Assuming that there are no forces resisting the sled's motion, how long will the child take to reach the bottom of the slope, $210 \mathrm{~m}$ from the top? Example $4-10$

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Problem 85

A car is proceeding at a speed of $14.0 \mathrm{~m} / \mathrm{s}$ when it collides with a stationary car in front. During the collision, the first car moves a distance of $0.300 \mathrm{~m}$ as it comes to a stop. The driver is wearing her seat belt, so she remains in her seat during the collision. If the driver's mass is $52.0 \mathrm{~kg}$, how much force does the belt exert on her during the collision? Neglect any friction between the driver and the seat. Example $4-10$

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Problem 86

Your friend's car runs out of fuel, and you volunteer to push it to the nearest gas station. You carefully drive your car so that the bumpers of the two cars are in contact and then slowly accelerate to a speed of $2.00 \mathrm{~m} / \mathrm{s}$ over the course of $1.00 \mathrm{~min}$. If the mass of your friend's car is $1200 \mathrm{~kg}$, what is the contact force between the two bumpers? Example 4-10

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Numerade Educator

Problem 87

A $30.0$ -kg golden retriever stands on a scale in an elevator. Calculate the reading on the scale when the elevator (a) accelerates at $3.50 \mathrm{~m} / \mathrm{s}^{2}$ downward, (b) when the elevator cruises down at a steady speed, and (c) when the elevator accelerates at $4.00 \mathrm{~m} / \mathrm{s}^{2}$ upward. SSM Example 4-7

Prabhu Ramji

Numerade Educator

Problem 88

A person weighs 588 N. If she stands on a scale while riding on the Inclinator (the lift at the Luxor Hotel in Las Vegas), what will be the reading on the scale? Assume the Inclinator moves at a constant acceleration of $1.25$ $\mathrm{m} / \mathrm{s}^{2}$, in a direction $39.0^{\circ}$ above the horizontal, and that the rider stands vertically in the elevator car. Example 4-7

Prabhu Ramji

Numerade Educator

Problem 89

A rider in an elevator weighs $700 \mathrm{~N}$. If this person stands on a scale in an elevator, describe the variation in the scale readings as the elevator initially starts from rest, accelerates upward at $3.00 \mathrm{~m} / \mathrm{s}^{2}$, cruises upward at $4.00 \mathrm{~m} / \mathrm{s}$, slows to a stop at $2.00 \mathrm{~m} / \mathrm{s}^{2}$, then free-falls all the way to the bottom of the elevator shaft before striking springs that bring the car to a safe stop. $\underline{\text { Example } 4-7}$

Prabhu Ramji

Numerade Educator

Problem 90

A fuzzy die that has a weight of $1.80 \mathrm{~N}$ hangs from the ceiling of a car by a massless string. The car travels with a forward acceleration of $2.70 \mathrm{~m} / \mathrm{s}^{2}$ on a horizontal road. The string makes an angle $\theta$ with respect to the vertical, shown in Figure 4-37. What is the angle $\theta$ ? Example 4-4

Prabhu Ramji

Numerade Educator

Problem 91

ABiology On average, froghopper insects have a mass of $12.3 \mathrm{mg}$ and jump to a height of $428 \mathrm{~mm}$. The takeoff velocity is achieved as the little critter flexes its legs over a distance of approximately $2.00 \mathrm{~mm}$. Assume a vertical jump with constant acceleration. (a) How long does the jump last (the jump itself, not the time in the air), and what is the froghopper's acceleration during that time? (b) Make a free-body diagram of the froghopper during its leap (but before it leaves the ground). (c) What force did the ground exert on the froghopper during the jump? Express your answer in millinewtons and as a multiple of the insect's weight. SSM Example 4-10

Linda Winkler

Numerade Educator

Problem 92

Medical A car traveling at $28.0 \mathrm{~m} / \mathrm{s}$ hits a bridge abutment. A passenger in the car, who has a mass of $45.0 \mathrm{~kg}$, moves forward a distance of $55.0 \mathrm{~cm}$ while being brought to rest by an inflated air bag. Assuming that the force that stops the passenger is constant, what is the magnitude of this force? Example 4-10

Prabhu Ramji

Numerade Educator

Problem 93

Two mountain climbers are working their way up a glacier when one falls into a crevasse (Figure 4-38). The icy slope, which makes an angle of $\theta=45.0^{\circ} \theta=45.0^{\circ}$ with the horizontal, can be considered frictionless. Sue's weight is pulling Paul up the $45.0^{\circ}$ slope. If Sue's mass is $66.0 \mathrm{~kg}$ and she falls $2.00 \mathrm{~m}$ in $10.0 \mathrm{~s}$ starting from rest, calculate (a) the tension in the rope joining them and (b) Paul's mass. SSM Example 4-9

Prabhu Ramji

Numerade Educator

Problem 94

Medical During a front-end car collision, the acceleration limit for the chest is $60 \mathrm{~g}$. If a car was initially traveling at $48.0 \mathrm{~km} / \mathrm{h}$, (a) how much time does it take for the car to come to rest, assuming a constant acceleration equal to the threshold acceleration for damage to the chest? (b) Draw a free-body diagram of a person during the crash. (c) What force in newtons does the air bag exert on the chest of a $72.0$ -kg person? The trunk of the body comprises about $43.0 \%$ of body weight. (d) Why doesn't this force injure the person? Example 4-10

Linda Winkler

Numerade Educator

Problem 95

A window washer sits in a bosun's chair that dangles from a massless rope that runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is $95.0 \mathrm{~kg}$. With how much force must he pull downward to raise himself (a) at constant speed and (b) with an upward acceleration $1.50 $\mathrm{m} / \mathrm{s}^{2} ?$

Prabhu Ramji

Numerade Educator

Problem 96

A $2.00 \times 102-\mathrm{kg}^{2} .00 \times 10^{2}-\mathrm{kg}$ block is hoisted by pulleys that are massless and frictionless, as shown in Figure 4-39. If a force of $1.50 \times 103 \mathrm{~N}$ $1.50 \times 10^{3} \mathrm{~N}$ is applied to the massless rope, what is the acceleration of the suspended mass? Example 4-9

Prabhu Ramji

Numerade Educator

Problem 97

Two blocks connected by a light string are being pulled across a frictionless horizontal tabletop by a hanging 10.0-N weight (block C) (Figure 4-40). Block A has a mass of $2.00 \mathrm{~kg}$. The mass of block $\mathrm{B}$ is only $1.00 \mathrm{~kg}$. The strings remain taut at all times. Assuming the pulley is massless and frictionless, what are the values of the tensions $T_{1}$ and $T_{2}$ ? SSM Example 4-8

Prabhu Ramji

Numerade Educator

Problem 98

Three boxes are lined up so that they are touching each other on a nearly frictionless plane, as shown in Figure 4-41. Box A has a mass of $20.0$ $\mathrm{kg}$, box $\mathrm{B}$ has a mass of $30.0 \mathrm{~kg}$, and box $\mathrm{C}$ has a mass of $50.0 \mathrm{~kg}$. If an external force $(F)$ pushes on box A toward the right, and the force that box $B$ exerts on box $\mathrm{C}$ is $2.00 \times 102 \mathrm{~N}, 2.00 \times 10^{2} \mathrm{~N}$, what is the acceleration of the boxes and the magnitude of the external force $F$ ? Ignore friction. Example 4 8

Prabhu Ramji

Numerade Educator

Problem 99

A $2.00-\mathrm{kg}$ object $A$ is connected with a massless string across a massless, frictionless pulley to a $3.00-\mathrm{kg}$ object $B$ (Figure 4-42). The smaller object rests on a nearly frictionless plane, which is tilted at an angle of $\theta=40.0^{\circ} \theta=40.0^{\circ}$ as shown. What are the acceleration of the system and the tension in the string? Example $4-9$

Prabhu Ramji

Numerade Educator

Problem 100

A $1.00$ -kg object $A$ is connected with a string to a $2.00$ -kg object $B$, which is connected with a second string over a massless, frictionless pulley to a $4.00-\mathrm{kg}$ object $C$ (Figure 4-43). Calculate the acceleration of the system and the tension in both strings. The strings have negligible mass and do not stretch, and the level tabletop is frictionless. Example 4-8

Prabhu Ramji

Numerade Educator

Problem 101

A $1.00$ -kg object $A$ is connected with a string to a $2.00-\mathrm{kg}$ object $B$, which is connected with a second string over a massless, frictionless pulley to a $4.00$ -kg object $C$ (Figure 4-44). The first two objects are placed onto a frictionless inclined plane that makes an angle $\theta=30.0^{\circ} \theta=30.0^{\circ}$ as shown. Calculate the acceleration of the masses and the tensions in both strings. Example 4-8

Prabhu Ramji

Numerade Educator

Problem 102

Sports An athlete drops from rest from a platform $10.0 \mathrm{~m}$ above the surface of a 5.00-m-deep pool. Assuming that the athlete enters the water vertically and moves through the water with constant acceleration, what is the minimum average force the water must exert on a $62.0$ -kg diver to prevent her from hitting the bottom of the pool? Express your answer in newtons and also as a multiple of the diver's weight. Air resistance during the athlete's dive can be ignored in this problem. Example 4-10

Supratim Pal

Numerade Educator

Problem 103

A person pulls three crates over a smooth horizontal floor as shown in Figure 4-45. The crates are connected to each other by identical horizontal strings $\mathrm{A}$ and $\mathrm{B}$, each of which can support a maximum tension of $45.0 \mathrm{~N}$ before breaking. (a) What is the largest pulling force that can be exerted without breaking either of the strings? (b) What are the tensions in A and B just before one of the strings breaks? Example 4-8

Linda Winkler

Numerade Educator