College Physics

Jerry D. Wilson, Anthony J. Buffa, Bo Lou

Chapter 4

Force and Motion - all with Video Answers

Educators

+ 6 more educators

Chapter Questions

Problem 1

(a) If an object is at rest, there must be no forces acting on it. Is this statement correct? Explain. (b) If the net force on an object is zero, can you conclude that the object is at rest? Explain.

Prabhu Ramji

Prabhu Ramji

Numerade Educator

Problem 1

- Which has more inertia, $20 \mathrm{~cm}^{3}$ of water or $10 \mathrm{~cm}^{3}$ of aluminum, and how many times more? (See Table 9.2.)

Narayan Hari

Numerade Educator

Problem 2

When on a jet airliner that is taking off, you feel that you are being "pushed" back into the seat. Use Newton's first law to explain why.

Prabhu Ramji

Numerade Educator

Problem 2

- Two forces act on a $5.0-\mathrm{kg}$ object sitting on a frictionless horizontal surface. One force is $30 \mathrm{~N}$ in the $+x$ -direction, and the other is $35 \mathrm{~N}$ in the $-x$ -direction. What is the acceleration of the object?

Narayan Hari

Numerade Educator

Problem 3

In Exercise 2 , if the 35 -N force acted downward at an angle of $40^{\circ}$ relative to the horizontal, what would be the acceleration in this case?

Narayan Hari

Numerade Educator

Problem 3

An object weighs $300 \mathrm{~N}$ on Earth and $50 \mathrm{~N}$ on the Moon. Does the object also have less inertia on the Moon?

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 4

A net force of 4.0 N gives an object an acceleration of $10 \mathrm{~m} / \mathrm{s}^{2} .$ What is the mass of the object?

Narayan Hari

Numerade Educator

Problem 4

Consider an air-bubble level that is pushed and a force is applied to accelerate it, which way would the bubble move? Which way would the bubble move if the force is then removed and the level slows down, due to friction? (b) Such a level is sometimes used as an "accelerometer" to indicate the direction of the acceleration. Explain the principle involved. [Hint: Think about pushing a pan of water.] sitting on a horizontal surface ( $>$ Fig. 4.27 ). Initially, the air bubble is in the middle of the horizontal glass tube.
(a) If the level is

James Kiss

Numerade Educator

Problem 5

Consider a $2.0-\mathrm{kg}$ ball and a $6.0-\mathrm{kg}$ ball in free fall.
(a) What is the net force acting on each?
(b) What is the acceleration of each?

Melissa Walsh

Numerade Educator

Problem 5

As a follow-up to Conceptual Question $4,$ consider a child holding a helium balloon in a closed car at rest. What would the child observe when the car (a) accelerates from rest and (b) brakes to a stop? (The balloon does not touch the roof of the car.)

James Kiss

Numerade Educator

Problem 6

The following is an old trick ( $\mathbf{r}$ Fig. 4.28 ). If a tablecloth is yanked out very quickly, the dishes on it will barely move. Why?

cm

Charles Magnusen

Numerade Educator

Problem 6

IE oo A hockey puck with a weight of $0.50 \mathrm{lb}$ is sliding freely across a section of very smooth (frictionless) horizontal ice. (a) When it is sliding freely, how does the upward force of the ice on the puck (the normal force) compare with the upward force when the puck is sitting permanently at rest: (1) The upward force is greater when the puck is sliding; (2) the upward force is less when it is sliding; (3) the upward force is the same in both situations? (b) Calculate the upward force on the puck in both situations.

Arun Bana

Numerade Educator

Problem 7

\bullet. A 5.0 -kg block at rest on a frictionless surface is acted on by forces $F_{1}=5.5 \mathrm{~N}$ and $F_{2}=3.5 \mathrm{~N}$ as illustrated in vFig. $4.33 .$ What additional force will keep the block at rest?

Arun Bana

Numerade Educator

Problem 7

Another old one: Referring to
- Fig. 4.29 , (a) how would you pull to get the upper string to break? (b) How would you pull to get the lower string to break?

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 8

IE oo (a) You are told that an object has zero acceleration. Which of the following is true: (1) The object is at rest; (2) the object is moving with constant velocity; (3) either (1) or (2) is possible; or (4) neither 1 nor 2 is possible. (b) Two forces on the object are $F_{1}=3.6 \mathrm{~N}$ at $74^{\circ}$ below the $+x$ -axis and $F_{2}=3.6 \mathrm{~N}$ at $34^{\circ}$ above the $-x$ -axis. Is there a third force on the object? Why or why not? If there is a third force, what is it?

Arun Bana

Numerade Educator

Problem 8

A student weighing $600 \mathrm{~N}$ crouches on a scale and suddenly springs vertically upward. Will the scale read more or less than $600 \mathrm{~N}$ just before the student leaves the scale?

Narayan Hari

Numerade Educator

Problem 9

An astronaut has a mass of $70 \mathrm{~kg}$ when measured on Earth. What is her weight in deep space, far from any celestial body? What is her mass there?

Linda Winkler

Numerade Educator

Problem 9

IE $\bullet$ A fish weighing $25 \mathrm{lb}$ is caught and hauled onto the boat. (a) Compare the tension in the fishing line when the fish is brought up vertically at a constant speed to the tension when the fish is held vertically at rest for the picture-taking ceremony on the wharf. In which case is the tension largest: (1) When the fish is moving up; (2) when the fish is being held steady; or (3) the tension is the same in both situations? (b) Calculate the tension in the fishing line.

Arun Bana

Numerade Educator

Problem 10

In general, this chapter has considered forces that are applied to objects of constant mass. What would be the situation if mass were added to or lost from a system while a constant force was being applied to the system? Give examples of situations in which this set of events might happen.

Donald Albin

Numerade Educator

Problem 10

. $\bullet$ A 1.5 -kg object moves up the $y$ -axis at a constant speed. When it reaches the origin, the forces $F_{1}=5.0 \mathrm{~N}$ at $37^{\circ}$ above the $+x$ -axis, $F_{2}=2.5 \mathrm{~N}$ in the $+x$ -direction, $F_{3}=3.5 \mathrm{~N}$ at $45^{\circ}$ below the $-x$ -axis, and $F_{4}=1.5 \mathrm{~N}$ in the $-y$ -direction are applied to it. (a) Will the object continue to move along the $y$ -axis? (b) If not, what simultaneously applied force will keep it moving along the $y$ -axis at a constant speed?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 11

The engines of most rockets produce a constant thrust (forward force). However, when a rocket is fired, its acceleration increases with time as the engine continues to operate. Is this situation a violation of Newton's second law? Explain.

Mayukh Banik

Numerade Educator

Problem 11

IE .?? Three horizontal forces (the only horizontal ones) act on a box sitting on a floor. One (call it $F_{1}$ ) acts due east and has a magnitude of $150 \mathrm{lb}$. A second force (call it $F_{2}$ ) has an easterly component of $30.0 \mathrm{lb}$ and a southerly component of $40.0 \mathrm{lb}$. The box remains at rest. (Neglect friction.) (a) Sketch the two known forces on the box. In which quadrant is the unknown third force: (1) the first quadrant; (2) the second quadrant; (3) the third quadrant; or (4) the fourth quadrant? (b) Find the unknown third force in newtons and compare your answer to the sketched estimate.

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 12

A 6.0 -N net force is applied to a 1.5 -kg mass. What is the object's acceleration?

Narayan Hari

Numerade Educator

Problem 12

In football, good wide receivers usually have "soft" hands for catching balls ( $\mathbf{F i g} .4 .30$ ). How would you interpret this description on the basis of Newton's second law?

Manish Kumar

Numerade Educator

Problem 13

A force acts on a $1.5-\mathrm{kg},$ mass, giving it an acceleration of $3.0 \mathrm{~m} / \mathrm{s}^{2} .$ (a) If the same force acts on a 2.5 -kg mass, what acceleration would be produced?
(b) What is the magnitude of the force?

Narayan Hari

Numerade Educator

Problem 14

A loaded Boeing 747 jumbo jet has a mass of $2.0 \times 10^{5} \mathrm{~kg} .$ What net force is required to give the plane an acceleration of $3.5 \mathrm{~m} / \mathrm{s}^{2}$ down the runway for takeoffs?

Narayan Hari

Numerade Educator

Problem 15

IE $\bullet$ A $6.0-\mathrm{kg}$ object is brought to the Moon, where the acceleration due to gravity is only one-sixth of that on the Earth. (a) The mass of the object on the Moon is (1) zero, $(2) 1.0 \mathrm{~kg},(3) 6.0 \mathrm{~kg}$
(4) 36 kg. Why?
(b) What is the weight of the obiect on the Moon?

Arun Bana

Numerade Educator

Problem 16

A gun is fired and a $50-\mathrm{g}$ bullet is accelerated to a muzzle speed of $100 \mathrm{~m} / \mathrm{s}$. If the length of the gun barrel is $0.90 \mathrm{~m}$, what is the magnitude of the accelerating force? (Assume the acceleration to be constant.)

Narayan Hari

Numerade Educator

Problem 17

Fig. 4.34 shows a product label. (a) This label is correct (1) on the Earth; (2) on the Moon, where the acceleration due to gravity is only one-sixth of that on the Earth; (3) in deep space, where there is little gravity; (4) all of the preceding.
(b) What mass of lasagne would a label show for an amount that weighs $2 \mathrm{lb}$ on the Moon?

Narayan Hari

Numerade Educator

Problem 18

In a college homecoming competition, eighteen students lift a sports car. While holding the car off the ground, each student exerts an upward force of $400 \mathrm{~N}$.
(a) What is the mass of the car in kilograms?
(b) What is its weight in pounds?

Narayan Hari

Numerade Educator

Problem 19

(a) A horizontal force acts on an object on a frictionless horizontal surface. If the force is halved and the mass of the object is doubled, the acceleration will be (1) four times, (2) two times, (3) one-half, (4) one-fourth as great. (b) If the acceleration of the object is $1.0 \mathrm{~m} / \mathrm{s}^{2},$ and the force on it is doubled and its mass is halved, what is the new acceleration?

Arun Bana

Numerade Educator

Problem 20

A force of $50 \mathrm{~N}$ acts on a mass $m_{1}$, giving it an acceleration of $4.0 \mathrm{~m} / \mathrm{s}^{2}$. The same force acts on a mass $m_{2}$ and produces an acceleration of $12 \mathrm{~m} / \mathrm{s}^{2} .$ What acceleration will this force produce if the total system is $m_{1}+m_{2}$ ?

Narayan Hari

Numerade Educator

Problem 21

A student weighing $800 \mathrm{~N}$ crouches on a scale and suddenly springs vertically upward. His roommate notices that the scale reads 900 N momentarily just as he leaves the scale. With what acceleration does he leave the scale?

Narayan Hari

Numerade Educator

Problem 22

The engine of a 1.0 -kg toy plane exerts a 15-N forward force. If the air exerts an 8.0 -N resistive force on the plane, what is the magnitude of the acceleration of the plane?

Narayan Hari

Numerade Educator

Problem 23

When a horizontal force of $300 \mathrm{~N}$ is applied to a 75.0 $\mathrm{kg}$ box, the box slides on a level floor, opposed by a force of kinetic friction of $120 \mathrm{~N}$. What is the magnitude of the acceleration of the box?

Prashant Bana

Numerade Educator

Problem 24

A rocket is far away from all planets and stars, so gravity is not a consideration. It is using its rocket engines to accelerate upward with an acceleration $a=9.80 \mathrm{~m} / \mathrm{s}^{2} .$ On the floor of the main deck is a crate (object with brick pattern) with a mass of $75.0 \mathrm{~kg}$
(a) How many forces are acting on the crate:
(v Fig. 4.35).
(1) zero; (2) one; (3) two; (4) three?
(b) Determine the normal force on the crate and compare it to the normal force the crate would experience if it were at rest on the surface of the Earth.

Narayan Hari

Numerade Educator

Problem 25

An object (mass $10.0 \mathrm{~kg}$ ) slides upward on a slippery vertical wall. A force $F$ of $60 \mathrm{~N}$ acts at an angle of $60^{\circ}$ as shown in r Fig. 4.36 .
(a) Determine the normal force exerted on the object by the wall. (b) Determine the object's acceleration.

Arun Bana

Numerade Educator

Problem 26

In an emergency stop to avoid an accident, a shoulder-strap seatbelt holds a 60 -kg passenger in place. If the car was initially traveling at $90 \mathrm{~km} / \mathrm{h}$ and came to a stop in $5.5 \mathrm{~s}$ along a straight, level road, what was the average force applied to the passenger by the seatbelt?

Narayan Hari

Numerade Educator

Problem 27

A student is assigned the task of measuring the startup acceleration of a large RV (recreational vehicle) using an iron ball suspended from the ceiling by a long string. In accelerating from rest, the ball no longer hangs vertically, but at an angle to the vertical. (a) Is the angle of the ball forward or backward from the vertical? (b) If the string makes an angle of 3.0 degrees from the vertical, what is the initial acceleration of the RV?

Arun Bana

Numerade Educator

Problem 28

A force of $10 \mathrm{~N}$ acts on two blocks on a frictionless surface (vFig. 4.37 ). (a) What is the acceleration of the system? (b) What force does block A exert on block B?
(c) What force does block B exert on block A?

Narayan Hari

Numerade Educator

Problem 29

A 2.0 -kg object has an acceleration of $1.5 \mathrm{~m} / \mathrm{s}^{2}$ at $30^{\circ}$ above the $-x$ -axis. Write the force vector producing this acceleration in component form.

Arun Bana

Numerade Educator

Problem 30

In a pole-sliding game among friends, a $90-\mathrm{kg}$ man makes a total vertical drop of $7.0 \mathrm{~m}$ while gripping the pole which exerts and upward force (call it $F_{\mathrm{p}}$ ) on him. Starting from rest and sliding with a constant acceleration, his slide takes 2.5 s. (a) Draw the man's free body diagram being sure to label all the forces.
(b) What is the magnitude of the upward force exerted on the man by the pole? (c) A friend whose mass is only $75 \mathrm{~kg}$, slides down the same distance, but the pole force is only $80 \%$ of the force on his buddy. How long did the second person's slide take?

Bailey Latka

Numerade Educator

Problem 31

A book is sitting on a horizontal surface. (a) There is (are) (1) one, (2) two, or (3) three force(s) acting on the book.
(b) Identify the reaction force to each force on the book.

Arun Bana

Numerade Educator

Problem 32

In an Olympic figure-skating event, a 65-kg male skater pushes a $45-\mathrm{kg}$ female skater, causing her to accelerate at a rate of $2.0 \mathrm{~m} / \mathrm{s}^{2}$. At what rate will the male skater accelerate? What is the direction of his acceleration?

Narayan Hari

Numerade Educator

Problem 33

A sprinter of mass $65.0 \mathrm{~kg}$ starts his race by pushing horizontally backward on the starting blocks with a force of $200 \mathrm{~N}$. (a) What force causes him to accelerate out of the blocks: (1) his push on the blocks; (2) the downward force of gravity; or (3) the force the blocks exert forward on him? (b) Determine his initial acceleration as he leaves the blocks.

Narayan Hari

Numerade Educator

Problem 34

Jane and John, with masses of $50 \mathrm{~kg}$ and $60 \mathrm{~kg}$, respectively, stand on a frictionless surface $10 \mathrm{~m}$ apart. John pulls on a rope that connects him to Jane, giving Jane an acceleration of $0.92 \mathrm{~m} / \mathrm{s}^{2}$ toward him. (a) What is John's acceleration? (b) If the pulling force is applied constantly, where will Jane and John meet?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 35

During a daring rescue, a helicopter rescue squad initially accelerates a little girl (mass $25.0 \mathrm{~kg}$ ) vertically off the roof of a burning building. They do this by dropping a rope down to her, which she holds on to as they pull her up. Neglect the mass of the rope.
(a) What force causes the girl to accelerate vertically upward: (1) her weight; (2) the pull of the helicopter on the rope; (3) the pull of the girl on the rope; or (4) the pull of the rope on the girl? (b) Determine the pull of the rope (the tension) if she initially accelerates upward at $0.750 \mathrm{~m} / \mathrm{s}^{2}$

Bailey Latka

Numerade Educator

Problem 36

A 75.0 -kg person is standing on a scale in an elevator. What is the reading of the scale in newtons if the elevator is (a) at rest, (b) moving up at a constant velocity of $2.00 \mathrm{~m} / \mathrm{s},$ and $(\mathrm{c})$ accelerating up at $2.00 \mathrm{~m} / \mathrm{s}^{2} ?$

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 37

In Exercise 36 , what if the elevator is accelerating down at $2.00 \mathrm{~m} / \mathrm{s}^{2} ?$

Narayan Hari

Numerade Educator

Problem 38

(a) When an object is on an inclined plane, the normal force exerted by the inclined plane on the object is
(1) less than, (2) equal to, (3) more than the weight of the object. Why? (b) For a $10-\mathrm{kg}$ object on a $30^{\circ}$ inclined plane, what are the object's weight and the normal force exerted on the object by the inclined place?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 39

The weight of a 500 -kg object is 4900 N. (a) When the object is on a moving elevator, its measured weight could be (1) zero, (2) between zero and $4900 \mathrm{~N}$, (3) more than $4900 \mathrm{~N},$ (4) all of the preceding. Why? (b) Describe the motion if the object's measured weight is only $4000 \mathrm{~N}$ in a moving elevator.

Arun Bana

Numerade Educator

Problem 40

A boy pulls a box of mass $30 \mathrm{~kg}$ with a force of $25 \mathrm{~N}$ in the direction shown in $v$ Fig. 4.38 . (a) Ignoring friction, what is the acceleration of the box? (b) What is the normal force exerted on the box by the ground?

Narayan Hari

Numerade Educator

Problem 41

A girl pushes a 25-kg lawn mower as shown in veig. 4.39. If $F=30 \mathrm{~N}$ and $\theta=37^{\circ}$ (a) what is the acceleration of the mower, and (b) what is the normal force exerted on the mower by the lawn? Ignore friction.

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 42

A $3000-\mathrm{kg}$ truck tows a $1500-\mathrm{kg}$ car by a chain. If the net forward force on the truck by the ground is $3200 \mathrm{~N}$, (a) what is the acceleration of the car, and (b) what is the tension in the connecting chain?

Narayan Hari

Numerade Educator

Problem 43

A block of mass $25.0 \mathrm{~kg}$ slides down a frictionless surface inclined at $30^{\circ} .$ To ensure that the block does not accelerate, what is the smallest force that you must exert on it and what is its direction?

Ankur S

Numerade Educator

Problem 44

$\bullet$ (a) An Olympic skier coasts down a slope with an angle of inclination of $37^{\circ} .$ Neglecting friction, there is (are)
(1), one, (2) two, (3) three force(s) acting on the skier.
(b) What is the acceleration of the skier?
(c) If the skier has a speed of $5.0 \mathrm{~m} / \mathrm{s}$ at the top of the slope, what is his speed when he reaches the bottom of the 35 -m-long slope?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 45

A car coasts (engine off) up a $30^{\circ}$ grade. If the speed of the car is $25 \mathrm{~m} / \mathrm{s}$ at the bottom of the grade, what is the distance traveled by the car before it comes to rest?

Arun Bana

Numerade Educator

Problem 46

Assuming ideal frictionless conditions for the apparatus shown in $\mathrm{rFig} .4 .40,$ what is the acceleration of the system if (a) $m_{1}=0.25 \mathrm{~kg}, m_{2}=0.50 \mathrm{~kg},$ and $m_{3}=0.25 \mathrm{~kg}$,
and (b) $m_{1}=0.35 \mathrm{~kg}, m_{2}=0.15 \mathrm{~kg},$ and $m_{3}=0.50 \mathrm{~kg} ?$

Aparna Shakti

Numerade Educator

Problem 47

A rope is fixed at both ends on two trees and a bag is hung in the middle of the rope (causing the rope to sag vertically). (a) The tension in the rope depends on (1) only the tree separation, (2) only the sag,
(3) both the tree separation and $\operatorname{sag},(4)$ neither the tree separation nor the sag. $(b)$ If the tree separation is $10 \mathrm{~m},$ the mass of the bag is $5.0 \mathrm{~kg},$ and the sag is $0.20 \mathrm{~m}$, what is the tension in the line?

Arun Bana

Numerade Educator

Problem 48

A 55-kg gymnast hangs vertically from a pair of parallel rings. (a) If the ropes supporting the rings are attached to the ceiling directly above, what is the tension in each rope?
(b) If the ropes are supported so that they make an angle of $45^{\circ}$ with the ceiling, what is the tension in each rope?

Arun Bana

Numerade Educator

Problem 49

A physicist's car has a small lead weight suspended from a string attached to the interior ceiling. Starting from rest, after a fraction of a second the car accelerates at a steady rate for about $10 \mathrm{~s}$. During that time, the string (with the weight on the end of it) makes a backward (opposite the acceleration) angle of $15.0^{\circ}$ from the vertical. Determine the car's (and the weight's) acceleration during the 10 -s interval.

Mehdi Hatefipour

Mehdi Hatefipour

Numerade Educator

Problem 50

A $10-\mathrm{kg}$ mass is suspended as shown in $\mathbf{r}$ Fig. 4.41 What is the tension in the cord between points $\mathrm{A}$ and $\mathrm{B}$ ?

Arun Bana

Numerade Educator

Problem 51

Referring to Fig. 4.41 , what are the tensions in all the cords?

Bailey Latka

Numerade Educator

Problem 52

At the end of most landing runways in airports, an extension of the runway is constructed using a special substance called formcrete. Formcrete can support the weight of cars, but crumbles under the weight of airplanes to slow them down if they run off the end of a runway. If a plane of mass $2.00 \times 10^{5} \mathrm{~kg}$ is to stop from a speed of $25.0 \mathrm{~m} / \mathrm{s}$ on a $100-\mathrm{m}$ -long stretch of formcrete, what is the average force exerted on the plane by the formcrete?

Arun Bana

Numerade Educator

Problem 53

A rifle weighs $50.0 \mathrm{~N}$ and its barrel is $0.750 \mathrm{~m}$ long. It shoots a 25.0-g bullet, which leaves the barrel at a speed (muzzle velocity) of $300 \mathrm{~m} / \mathrm{s}$ after being uniformly accelerated. What is the magnitude of the force exerted on the rifle by the bullet?

Arun Bana

Numerade Educator

Problem 54

A horizontal force of $40 \mathrm{~N}$ acting on a block on a frictionless, level surface produces an acceleration of $2.5 \mathrm{~m} / \mathrm{s}^{2} .$ A second block, with a mass of $4.0 \mathrm{~kg}$, is dropped onto the first. What is the magnitude of the acceleration of the combination of blocks if the same force continues to act? (Assume that the second block does not slide on the first block.)

Narayan Hari

Numerade Educator

Problem 55

The Atwood machine consists of two masses suspended from a fixed pulley, as shown in $v$ Fig. $4.42 .$ It is named after the British scientist George Atwood $(1746-1807),$ who used it to study motion and to measure the value of $g$. If $m_{1}=0.55 \mathrm{~kg}$ and $m_{2}=0.80 \mathrm{~kg}$,
(a) what is the acceleration of the system, and
(b) what is the magnitude of the tension in the string?

Bailey Latka

Numerade Educator

Problem 56

An Atwood machine (see Fig. 4.42 ) has suspended masses of $0.25 \mathrm{~kg}$ and $0.20 \mathrm{~kg} .$ Under ideal conditions, what will be the acceleration of the smaller mass?

Arun Bana

Numerade Educator

Problem 57

One mass, $m_{1}=0.215 \mathrm{~kg},$ of an ideal Atwood machine (see Fig. 4.42) rests on the floor $1.10 \mathrm{~m}$ below the other mass, $m_{2}=0.255 \mathrm{~kg},$ (a) If the masses are released from rest, how long does it take $m_{2}$ to reach the floor? (b) How high will mass $m_{1}$ ascend from the floor? (Hint: When $m_{2}$ hits the floor, $m_{1}$ continues to move upward.)

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 58

IE . co Two blocks are connected by a light string and accelerated upward by a pulling force $F$. The mass of the upper block is $50.0 \mathrm{~kg}$ and that of the lower block is $100 \mathrm{~kg}$. The upward acceleration of the system as a whole is $1.50 \mathrm{~m} / \mathrm{s}^{2} .$ Neglect the mass of the string.
(a) Draw the free-body diagram of each block. Use the diagrams to determine which of the following is true for the magnitude of the string tension $T$ compared to other forces: $(1) T>w_{2}$ and $T<F ;(2) T>w_{2}$ and $T>F ;$ (3) $T<w_{2}$ and $T<F ;$ or $(4) T=w_{2}$ and $T<F ?$
(b) Apply Newton's laws to find the required pull, $F$.
(c) Find the tension in the string, $T$.

Steven Brown

Numerade Educator

Problem 59

Two blocks on a level, frictionless table are in contact. The mass of the left block is $5.00 \mathrm{~kg}$ and the mass of the right block is $10.0 \mathrm{~kg}$, and they accelerate to the left at $1.50 \mathrm{~m} / \mathrm{s}^{2}$. A person on the left exerts a force $\left(F_{1}\right)$ of $75.0 \mathrm{~N}$ to the right. Another person exerts an unknown force $\left(F_{2}\right)$ to the left. (a) Determine the force $F_{2}$.
(b) Calculate the force of contact $N$ between the two blocks (that is, the normal force at their vertical touching surfaces).

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 60

In the frictionless apparatus shown in $\mathbf{r}$ Fig. 4.43 , $m_{1}=2.0 \mathrm{~kg} .$ What is $m_{2}$ if both masses are at rest? How about if both masses are moving at constant velocity?

Narayan Hari

Numerade Educator

Problem 61

In the ideal setup shown in Fig. $4.43, m_{1}=3.0 \mathrm{~kg}$ and $m_{2}=2.5 \mathrm{~kg} .$ (a) What is the acceleration of the masses? (b) What is the tension in the string?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 62

A 20-kg box sits on a rough horizontal surface. When a horizontal force of $120 \mathrm{~N}$ is applied, the object accelerates at $1.0 \mathrm{~m} / \mathrm{s}^{2} .$ (a) If the applied force is doubled, the acceleration will (1) increase, but less than double; (2) also double;
(3) increase, but more than double. Why? (b) Calculate the acceleration to prove your answer to part (a).

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 63

The coefficients of static and kinetic friction between a $50.0-\mathrm{kg}$ box and a horizontal surface are 0.500 and 0.400 respectively. (a) What is the acceleration of the object if a 250-N horizontal force is applied to the box?
(b) What is the acceleration if the applied force is $235 \mathrm{~N}$ ?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 64

In moving a 35.0 -kg desk from one side of a classroom to the other, a professor finds that a horizontal force of $275 \mathrm{~N}$ is necessary to set the desk in motion, and a force of $195 \mathrm{~N}$ is necessary to keep it in motion at a constant speed. What are the coefficients of (a) static and
(b) kinetic friction between the desk and the floor?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 65

A 40 -kg crate is at rest on a level surface. If the coefficient of static friction between the crate and the surface is 0.69 , what horizontal force is required to get the crate moving?

Narayan Hari

Numerade Educator

Problem 66

A packing crate is placed on a $20^{\circ}$ inclined plane. If the coefficient of static friction between the crate and the plane is $0.65,$ will the crate slide down the plane if released from rest? Justify your answer.

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 67

A 1500 -kg automobile travels at $90 \mathrm{~km} / \mathrm{h}$ along a straight concrete highway. Faced with an emergency situation, the driver jams on the brakes, and the car skids to a stop. What is the car's stopping distance for
(a) dry pavement and (b) wet pavement?

Bailey Latka

Numerade Educator

Problem 68

A hockey player hits a puck with his stick, giving the puck an initial speed of $5.0 \mathrm{~m} / \mathrm{s}$. If the puck slows uniformly and comes to rest in a distance of $20 \mathrm{~m}$, what is the coefficient of kinetic friction between the ice and the puck?

Arun Bana

Numerade Educator

Problem 69

A crate sits on a flat-bed truck that is traveling with a speed of $50 \mathrm{~km} / \mathrm{h}$ on a straight, level road. If the coefficient of static friction between the crate and the truck bed is 0.30 , in how short a distance can the truck stop with a constant acceleration without the crate sliding?

Arun Bana

Numerade Educator

Problem 70

A block is projected with a speed of $2.5 \mathrm{~m} / \mathrm{s}$ on a horizontal surface. If the block comes to rest in $1.5 \mathrm{~m},$ what is the coefficient of kinetic friction between the block and the surface?

Arun Bana

Numerade Educator

Problem 71

A block is projected with a speed of $3.0 \mathrm{~m} / \mathrm{s}$ on a horizontal surface. If the coefficient of kinetic friction between the block and the surface is 0.60 , how far does the block slide before coming to rest?

Arun Bana

Numerade Educator

Problem 72

A person has a choice while trying to push a crate across a horizontal pad of concrete: push it at a downward angle of $30^{\circ},$ or pull it at an upward angle of $30^{\circ} .$
(a) Which choice is most likely to require less force on the part of the person: (1) pushing at a downward angle;
(2) pulling at the same angle, but upward; or (3) pushing or pulling shouldn't matter? (b) If the crate has a mass of $50.0 \mathrm{~kg}$ and the coefficient of kinetic friction between it and the concrete is $0.750,$ calculate the required force to move it across the concrete at a steady speed for both situations.

Steven Brown

Numerade Educator

Problem 73

Suppose the slope conditions for the skier shown in vFig. 4.44 are such that the skier travels at a constant velocity. From the photo, could you find the coefficient of kinetic friction between the snowy surface and the skis? If so, describe how this would be done.

Arun Bana

Numerade Educator

Problem 74

A 5.0 -kg wooden block is placed on an adjustable wooden inclined plane. (a) What is the angle of incline above which the block will start to slide down the plane?
(b) At what angle of incline will the block then slide down the plane at a constant speed?

Bailey Latka

Numerade Educator

Problem 75

A block that has a mass of $2.0 \mathrm{~kg}$ and is $10 \mathrm{~cm}$ wide on each side just begins to slide down an inclined plane with a $30^{\circ}$ angle of incline ( $\mathbf{r}$ Fig. 4.45 ). Another block of the same height and same material has base dimensions of $20 \mathrm{~cm} \times 10 \mathrm{~cm}$ and thus a mass of $4.0 \mathrm{~kg} .$ (a) At what critical angle will the more massive block start to slide down the plane? Why? (b) Estimate the coefficient of static friction between the block and the plane.

Steven Brown

Numerade Educator

Problem 76

In the apparatus shown in vFig. $4.46, m_{1}=10 \mathrm{~kg}$ and the coefficients of static and kinetic friction between $m_{1}$ and the table are 0.60 and 0.40 , respectively.
(a) What mass of $m_{2}$ will just barely set the system in motion?
(b) After the system begins to move, what is the acceleration?

Bailey Latka

Numerade Educator

Problem 77

In loading a fish delivery truck, a person pushes a block of ice up a $20^{\circ}$ incline at constant speed. The push is $150 \mathrm{~N}$ in magnitude and parallel to the incline. The block has a mass of $35.0 \mathrm{~kg}$. (a) Is the incline frictionless?
(b) If not, what is the force of kinetic friction on the block of ice?

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 78

An object (mass $3.0 \mathrm{~kg}$ ) slides upward on a vertical wall at constant velocity when a force $F$ of $60 \mathrm{~N}$ acts on it at an angle of $60^{\circ}$ to the horizontal.
(a) Draw the freebody diagram of the object.
(b) Using Newton's laws find the normal force on the object. (c) Determine the force of kinetic friction on the object.

Christopher Dzorkpata

Christopher Dzorkpata

Numerade Educator

Problem 79

In the apparatus shown in Fig. $4.43, m_{1}=2.0 \mathrm{~kg}$ and the coefficients of static and kinetic friction between $m_{1}$ and the inclined plane are 0.30 and 0.20 , respectively.
(a) What is $m_{2}$ if both masses are at rest? (b) What is $m_{2}$ if both masses are moving at constant velocity?

Aparna Shakti

Numerade Educator

Problem 80

For the apparatus shown in Fig. 4.40 , what is the minimum value of the coefficient of static friction between the block $\left(m_{3}\right)$ and the table that would keep the system at rest if $m_{1}=0.25 \mathrm{~kg}, m_{2}=0.50 \mathrm{~kg},$ and $m_{3}=0.75 \mathrm{~kg} ?$

Linda Winkler

Numerade Educator

Problem 81

If the coefficient of kinetic friction between the block and the table in Fig. 4.40 is 0.560 , and $m_{1}=0.150 \mathrm{~kg}$ and $m_{2}=0.250 \mathrm{~kg},$ (a) what should $m_{3}$ be if the system is to move with a constant speed? (b) If $m_{3}=0.100 \mathrm{~kg}$, what is the magnitude of the acceleration of the system?

Linda Winkler

Numerade Educator

Problem 82

One block (A, mass $2.00 \mathrm{~kg}$ ) rests atop another (B, mass $5.00 \mathrm{~kg}$ ) on a horizontal surface. The surface is a powered walkway accelerating to the right at $2.50 \mathrm{~m} / \mathrm{s}^{2}$. $\mathrm{B}$ does not slip on the walkway surface, nor does A slip on B's top surface.
(a) Sketch the free-body diagram of each block. Use these to determine the force responsible for A's acceleration. Is it (1) the pull of the walkway, (2) the normal force on A by the top surface of $B$, (3) the force of static friction on the bottom surface of $\mathrm{B}$, or (4) the force of static friction acting on A due to the top surface of B? (b) Determine the forces of static friction on each block.

Linda Winkler

Numerade Educator

Problem 83

Two blocks (A and B) remain stuck together as they are pulled to the right by a force $F=200 \mathrm{~N}$ ( $\mathbf{r}$ Fig. 4.47 ). $\mathrm{B}$ is on a rough horizontal tabletop (coefficient of kinetic friction of 0.800 ). (a) What is the acceleration of the system?
(b) What is the force of friction between the two objects?

Linda Winkler

Numerade Educator

Problem 84

To haul a boat out of the water for the winter, a worker at the storage facility uses a wide strap with cables operating at the same angle (measured from the horizontal) on either side of the boat (vFig. 4.48 ). (a) As the boat comes up vertically and $\theta$ decreases, the tension in the cables (1) increases, (2) decreases, (3) stays the same. (b) Determine the tension in each cable if the boat has a mass of $500 \mathrm{~kg}$ and the angle of each cable is $45^{\circ}$

Linda Winkler

Numerade Educator

Problem 85

You are in charge of an accident reconstruction case for the local police department. In order to determine car speeds, skid mark lengths are measured. To determine the coefficient of kinetic friction, you get into an identical car, and at a speed of $65.2 \mathrm{mi} / \mathrm{h}$, you lock its brakes and skid $51.5 \mathrm{~m}$ to rest. (a) Determine the car's deceleration.
(b) What is the coefficient of kinetic friction between the tires and road surface? (c) The car in the accident actually skidded $57.3 \mathrm{~m}$. What was its initial speed?

Linda Winkler

Numerade Educator

Problem 86

Compare two different situations in which a ball and hard surface exert forces on one another. First, a putty ball is placed gently on the floor and left at rest. Then it is dropped from a height of $2.00 \mathrm{~m}$ and comes to rest without a bounce, leaving a $1.15-\mathrm{cm}$ -deep dent in the putty. (a) In which case does the ball exert more force on the floor? In which case is it most likely to dent the floor? Explain. (b) Calculate the force exerted by the ball on the floor (in terms of its weight $w$ ) in the first case. (c) Determine the average acceleration of the ball and the average force exerted by the ball on the floor (in terms of the ball's weight $w$ ) in the second case.

Linda Winkler

Numerade Educator

Problem 87

A hockey puck impacts a goalie's plastic mask horizontally at $122 \mathrm{mi} / \mathrm{h}$ and rebounds horizontally off the mask at $47 \mathrm{mi} / \mathrm{h}$. If the puck has a mass of $170 \mathrm{~g}$ and it is in contact with the mask for $25 \mathrm{~ms},$ (a) what is the average force (including direction) that the puck exerts on the mask? (b) Assuming that this average force accelerates the goalie (neglect friction with the ice), with what speed will the goalie move, assuming she was at rest initially and has a total mass of $85 \mathrm{~kg}$ ?

Linda Winkler

Numerade Educator

Problem 88

A $2.50-\mathrm{kg}$ block is placed on a rough surface inclined at $30^{\circ} .$ The block is propelled and launched at a speed of $1.60 \mathrm{~m} / \mathrm{s}$ down the incline and comes to rest after sliding $1.10 \mathrm{~m} .$ (a) Draw the free-body diagram of the block while it is sliding. Also indicate your coordinate system axes. (b) Starting with Newton's second law applied along both axes of your coordinate system, use your free-body diagram to generate two equations. (c) Solve these equations for the coefficient of kinetic friction between the block and the incline surface. [Hint: You will need to first determine the block's acceleration.]

Linda Winkler

Numerade Educator