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College Physics

Hugh D. Young Philip W. Adams

Chapter 4

Newton's Law of Motion - all with Video Answers

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Chapter Questions

17:49

Problem 1

A warehouse worker pushes a crate along the floor, as shown in Figure 4.36 , by a force of $10 \mathrm{~N}$ that points downward at an angle of $45^{\circ}$ below the horizontal. Find the horizontal and vertical components of the push.

Nicole Steward
Nicole Steward
Numerade Educator
03:01

Problem 2

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is $60.0^{\circ} .$ If $\operatorname{dog} A$ exerts a force of $270 \mathrm{~N}$ and $\operatorname{dog} B$ exerts a force of 300 $\mathrm{N},$ find the magnitude of the resultant force and the angle it makes with $\operatorname{dog} A$ 's rope.

Aaron Shoolroy
Aaron Shoolroy
Numerade Educator
05:08

Problem 3

A man is dragging a trunk up the loading ramp of a mover's truck. (See Figure $4.37 .)$ The ramp has a slope angle of $20.0^{\circ},$ and the man pulls upward with a force $\vec{F}$ of magnitude $375 \mathrm{~N}$ whose direction makes an angle of $30.0^{\circ}$ with the ramp. Find the horizontal and vertical components of the force $\vec{F}$

NJ
Nicholas Johnson
Numerade Educator
02:14

Problem 4

Jaw injury. Due to a jaw injury, a patient must wear a strap (see Figure 4.38 ) that produces a net upward force of $5.00 \mathrm{~N}$ on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
19:59

Problem 5

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in Figure 4.39 .
(a) Find the $x$ and $y$ components of each of the three pulls. (b) Use the components to find the magnitude and direction of the resultant of the three pulls.

Nicole Steward
Nicole Steward
Numerade Educator
01:00

Problem 6

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude $48.0 \mathrm{~N}$ to the box and produces an acceleration of magnitude $3.00 \mathrm{~m} / \mathrm{s}^{2},$ what is the mass of the box?

Farhanul Hasan
Farhanul Hasan
Numerade Educator
01:25

Problem 7

In outer space, a constant force is applied to a $32.5 \mathrm{~kg}$ probe initially at rest. The probe moves a distance of $100 \mathrm{~m}$ in $10 \mathrm{~s}$. (a) What acceleration does this force produce? (b) What is the magnitude of the force?

Supratim Pal
Supratim Pal
Numerade Educator
03:47

Problem 8

A $68.5 \mathrm{~kg}$ skater moving initially at $2.40 \mathrm{~m} / \mathrm{s}$ on rough horizontal ice comes to rest uniformly in $3.52 \mathrm{~s}$ due to friction from the ice. What force does friction exert on the skater?

Kevin Hayakawa
Kevin Hayakawa
University of California - Los Angeles
03:29

Problem 9

Animal dynamics. An adult $68 \mathrm{~kg}$ cheetah can accelerate from rest to $20.1 \mathrm{~m} / \mathrm{s}(45 \mathrm{mph})$ in $2.0 \mathrm{~s} .$ Assuming constant acceleration, (a) find the net external force causing this acceleration. (b) Where does the force come from? That is, what exerts the force on the cheetah?

Nicole Steward
Nicole Steward
Numerade Educator
01:43

Problem 10

A $2 \mathrm{~kg}$ block sits at rest on a frictionless horizontal table. A $10 \mathrm{~N}$ horizontal force is suddenly applied to the block and maintained as the block begins moving. (a) What is the acceleration of the block after the force is applied? (b) What is the speed of the block after it has moved a distance of $0.5 \mathrm{~m} ?$

Supratim Pal
Supratim Pal
Numerade Educator
04:44

Problem 11

A dock worker applies a constant horizontal force of $80.0 \mathrm{~N}$ to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves $11.0 \mathrm{~m}$ in the first $5.00 \mathrm{~s}$. What is the mass of the block of ice?

Caleb Huber
Caleb Huber
Numerade Educator
01:19

Problem 12

(a) What is the mass of a book that weighs $3.20 \mathrm{~N}$ in the laboratory? (b) In the same lab, what is the weight of a dog whose mass is $14.0 \mathrm{~kg} ?$

Farhanul Hasan
Farhanul Hasan
Numerade Educator
02:31

Problem 13

Superman throws a $2400 \mathrm{~N}$ boulder at an adversary. What horizontal force must Superman apply to the boulder to give it a horizontal acceleration of $12.0 \mathrm{~m} / \mathrm{s}^{2} ?$

Kevin Hayakawa
Kevin Hayakawa
University of California - Los Angeles
03:40

Problem 14

(a) How many newtons does a 150 lb person weigh? (b) Should a veterinarian be skeptical if someone said that her adult collie weighed $40 \mathrm{~N}$ ? (c) Should a nurse have questioned a medical chart showing that an average-looking patient had a mass of $200 \mathrm{~kg} ?$

Vishal Gupta
Vishal Gupta
Numerade Educator
02:49

Problem 15

(a) An ordinary flea has a mass of $210 \mu$. How many newtons does it weigh? (b) The mass of a typical froghopper is $12.3 \mathrm{mg}$. How many newtons does it weigh? (c) A house cat typically weighs $45 \mathrm{~N}$. How many pounds does it weigh, and what is its mass in kilograms?

Enes Suyabatmaz
Enes Suyabatmaz
Numerade Educator
04:06

Problem 16

Calculate the mass (in SI units) of (a) a 160 lb human being; (b) a 1.9 lb cockatoo. Calculate the weight (in English units) of (c) a $2300 \mathrm{~kg}$ rhinoceros; (d) a $22 \mathrm{~g}$ song sparrow.

Anuraj Sunda
Anuraj Sunda
Numerade Educator
01:59

Problem 17

A standard bathroom scale is placed on an elevator. A $30 \mathrm{~kg}$ boy enters the elevator on the first floor and steps on the scale. What will the scale read (in newtons) when the elevator begins to accelerate upward at $0.5 \mathrm{~m} / \mathrm{s}^{2} ?$

Prashant Bana
Prashant Bana
Numerade Educator
02:10

Problem 18

At the surface of Jupiter's moon Io, the acceleration due to gravity is $1.81 \mathrm{~m} / \mathrm{s}^{2} .$ If a piece of ice weighs $44.0 \mathrm{~N}$ at the surface of the earth, (a) what is its mass on the earth's surface? (b) What are its mass and weight on the surface of Io?

Farhanul Hasan
Farhanul Hasan
Numerade Educator
04:20

Problem 19

A scientific instrument that weighs $85.2 \mathrm{~N}$ on the earth weighs $32.2 \mathrm{~N}$ at the surface of Mercury. (a) What is the acceleration due to gravity on Mercury? (b) What is the instrument's mass on earth and on Mercury?

Caleb Huber
Caleb Huber
Numerade Educator
03:11

Problem 20

Planet X! When venturing forth on Planet X, you throw a $5.24 \mathrm{~kg}$ rock upward at $13.0 \mathrm{~m} / \mathrm{s}$ and find that it returns to the same level 1.51 s later. What does the rock weigh on Planet $X ?$

Farhanul Hasan
Farhanul Hasan
Numerade Educator
03:21

Problem 21

You drag a heavy box along a rough horizontal floor by a horizontal rope. Identify the reaction force to each of the following forces:
(a) the pull of the rope on the box, (b) the friction force on the box,
(c) the normal force on the box, and (d) the weight of the box.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
01:36

Problem 22

A person pushes two boxes with a horizontal force of $100 \mathrm{~N}$. The boxes are on a horizontal frictionless floor as shown in Figure 4.35 . If the mass of box $A$ is $5 \mathrm{~kg}$ and the mass of box $B$ is $2 \mathrm{~kg},$ calculate the magnitude of the action-reaction pair between the two boxes.

Prashant Bana
Prashant Bana
Numerade Educator
03:01

Problem 23

The upward normal force exerted by the floor is $620 \mathrm{~N}$ on an elevator passenger who weighs $650 \mathrm{~N}$. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the magnitude and direction of the acceleration?

Aaron Shoolroy
Aaron Shoolroy
Numerade Educator
01:42

Problem 24

A person throws a 2.5 lb stone into the air with an initial upward speed of $15 \mathrm{ft} / \mathrm{s}$. Make a free-body diagram for this stone (a) after it is free of the person's hand and is traveling upward, (b) at its highest point, (c) when it is traveling downward, and (d) while it is being thrown upward but is still in contact with the person's hand.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
01:38

Problem 25

A tennis ball traveling horizontally at $22 \mathrm{~m} / \mathrm{s}$ suddenly hits a vertica brick wall and bounces back with a horizontal velocity of $18 \mathrm{~m} / \mathrm{s}$. Make a free-body diagram of this ball (a) just before it hits the wall, (b) just after it has bounced free of the wall, and (c) while it is in contact with the wall.

Prashant Bana
Prashant Bana
Numerade Educator
09:08

Problem 26

Two crates, $A$ and $B$, sit at rest side by side on a frictionless horizontal surface. The crates have masses $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$. A horizontal force $\vec{F}$ is applied to crate $A,$ and the two crates move off to the right. (a) Draw clearly labeled free-body diagrams for crate $A$ and for crate $B$. Indicate which pairs of forces, if any, are third-law action-reaction pairs. (b) If the magnitude of force $\overrightarrow{\boldsymbol{F}}$ is less than the total weight of the two crates, will it cause the crates to move? Explain.

Caleb Huber
Caleb Huber
Numerade Educator
02:15

Problem 27

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity, and (b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
04:48

Problem 28

A person drags her $65 \mathrm{~N}$ suitcase along the rough horizontal floor by pulling upward at $30^{\circ}$ above the horizontal with a $50 \mathrm{~N}$ force. Make a free-body diagram of this suitcase.

Caleb Huber
Caleb Huber
Numerade Educator
04:58

Problem 29

A factory worker pushes horizontally on a $250 \mathrm{~N}$ crate with a force of $75 \mathrm{~N}$ on a horizontal rough floor. A $135 \mathrm{~N}$ crate rests on top of the one being pushed and moves along with it. Make a free-body diagram of each crate if the friction force exerted by the floor is less than the worker's push.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
03:21

Problem 30

A dock worker pulls two boxes connected by a rope on a horizontal floor, as shown in Figure 4.40 . All the ropes are horizontal, and there is some friction with the floor. Make a free-body diagram of each box.

Caleb Huber
Caleb Huber
Numerade Educator
01:30

Problem 31

A hospital orderly pushes horizontally on two boxes of equipment on a rough horizontal floor, as shown in Figure $4.41 .$ Make a free-body diagram of each box.

Prashant Bana
Prashant Bana
Numerade Educator
03:32

Problem 32

A uniform $25.0 \mathrm{~kg}$ chain $2.00 \mathrm{~m}$ long supports a $50.0 \mathrm{~kg}$ chandelier in a large public building. Find the tension in (a) the bottom link of the chain, (b) the top link of the chain, and (c) the middle link of the chain.

Caleb Huber
Caleb Huber
Numerade Educator
01:21

Problem 33

A $60 \mathrm{~kg}$ circus performer is climbing up a rope (of negligible mass) with an acceleration of $1.2 \mathrm{~m} / \mathrm{s}^{2}$. (a) Draw a free-body diagram for the performer. (b) What is the tension in the rope?

Nishant Kumar
Nishant Kumar
Numerade Educator
06:10

Problem 34

A $275 \mathrm{~N}$ bucket is lifted with an acceleration of $2.50 \mathrm{~m} / \mathrm{s}^{2}$ by a $125 \mathrm{~N}$ uniform vertical chain. Start each of the following parts with a free-body diagram. Find the tension in (a) the top link of the chain, (b) the bottom link of the chain, and (c) the middle link of the chain.

Caleb Huber
Caleb Huber
Numerade Educator
01:19

Problem 35

Human biomechanics. World-class sprinters can spring out of the starting blocks with an acceleration that is essentially horizontal and of magnitude $15 \mathrm{~m} / \mathrm{s}^{2}$. (a) How much horizontal force must a 55-kg sprinter exert on the starting blocks during a start to produce this acceleration? (b) What exerts the force that propels the sprinter, the blocks or the sprinter himself?

Farhanul Hasan
Farhanul Hasan
Numerade Educator
03:02

Problem 36

A chair of mass $12.0 \mathrm{~kg}$ is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force $F=40.0 \mathrm{~N}$ that is directed at an angle of $37.0^{\circ}$ below the horizontal, and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts
on the chair.

Aaron Shoolroy
Aaron Shoolroy
Numerade Educator
02:25

Problem 37

Human biomechanics. The fastest pitched baseball was measured at $46 \mathrm{~m} / \mathrm{s}$. Typically, a baseball has a mass of $145 \mathrm{~g}$. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of $1.0 \mathrm{~m},$ (a) what force did he produce on the ball during this record-setting pitch? (b) Make free-body diagrams of the ball during the pitch and just after it has left the pitcher's hand.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
04:41

Problem 38

You walk into an elevator, step onto a scale, and push the "down" button to go directly from the tenth floor to the first floor. You also recall that your weight is $625 \mathrm{~N}$. Start each of the following parts with a free-body diagram. (a) If the elevator has an initial acceleration of magnitude $2.50 \mathrm{~m} / \mathrm{s}^{2},$ what does the scale read? (b) What does the scale read after the elevator reaches it final speed as it heads to the bottom floor?

Andres Mejia
Andres Mejia
Numerade Educator
02:41

Problem 39

A woman is standing in an elevator holding her $2.5 \mathrm{~kg}$ briefcase by its handles. Draw a free-body diagram for the briefcase if the elevator is accelerating downward at $1.50 \mathrm{~m} / \mathrm{s}^{2},$ and calculate the downward pull of the briefcase on the woman's arm while the elevator is accelerating.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
03:31

Problem 40

An advertisement claims that a particular automobile can "stop on a dime." What net force would actually be necessary to stop an $850 \mathrm{~kg}$ automobile traveling initially at $45.0 \mathrm{~km} / \mathrm{h}$ in a distance equal to the diameter of a dime, which is $1.8 \mathrm{~cm} ?$

Alex Garger
Alex Garger
Numerade Educator
06:38

Problem 41

A rifle shoots a $4.20 \mathrm{~g}$ bullet out of its barrel. The bullet has a muzzle velocity of $965 \mathrm{~m} / \mathrm{s}$ just as it leaves the barrel. Assuming a constant horizontal acceleration over a distance of $45.0 \mathrm{~cm}$ starting from rest, with no friction between the bullet and the barrel, (a) what force does the rifle exert on the bullet while it is in the barrel? (b) Draw a free-body diagram of the bullet (i) while it is in the barrel and (ii) just after it has left the barrel. (c) How many $g$ 's of acceleration does the rifle give this bullet? (d) For how long a time is the bullet in the barrel?

Alex Garger
Alex Garger
Numerade Educator
04:06

Problem 42

A parachutist relies on air resistance (mainly on her parachute) to decrease her downward velocity. She and her parachute have a mass of $55.0 \mathrm{~kg},$ and at a particular moment air resistance exerts a total upward force of $620 \mathrm{~N}$ on her and her parachute. (a) What is the weight of the parachutist? (b) Draw a free-body diagram for the parachutist (see Section 4.6). Use that diagram to calculate the net force on the parachutist. Is the net force upward or downward? (c) What is the acceleration (magnitude and direction) of the parachutist?

Caleb Huber
Caleb Huber
Numerade Educator
07:19

Problem 43

As shown in Figure $4.42,$ force vector $\vec{F}_{1}$ always points in the $+x$ direction, but $\vec{F}_{2}$ makes an angle $\theta$ with the $+x$ axis. A physics student is given the task of graphically determining the $x$ and $y$ components of the sum of these vectors, $\vec{F}=\vec{F}_{1}+\vec{F}_{2},$ for several different values of $\theta .$ The magnitudes of $\vec{F}_{1}$ and $\vec{F}_{2}$ remain unchanged; only the angle $\theta$ is varied. The table shows the student's results:
$$
\begin{array}{lcc}
\hline \theta & F_{x}(\mathbf{N}) & F_{y}(\mathbf{N}) \\
\hline 20^{\circ} & 11.4 & 3.1 \\
35^{\circ} & 10.4 & 5.2 \\
60^{\circ} & 7.5 & 7.8 \\
75^{\circ} & 5.3 & 8.7 \\
\hline
\end{array}
$$
(a) Write an expression for $F_{x}$ in terms of $\theta, F_{1},$ and $F_{2} .$ (b) Make a linearized graph of the $x$ component data with the $F_{x}$ values on the $y$ axis and the appropriate trig function of $\theta$ on the $x$ axis. (c) Draw a best-fit line through your plotted points and use this line to determine the magnitudes $F_{1}$ and $F_{2}$. (d) Repeat this process for the $F_{y}$ data and compare your result with what you obtained in part (c).

Morgan Cheatham
Morgan Cheatham
Numerade Educator
06:35

Problem 44

A spacecraft descends vertically near the surface of Planet X. An upward thrust of $25.0 \mathrm{kN}$ from its engines slows it down at a rate of $1.20 \mathrm{~m} / \mathrm{s}^{2},$ but it speeds up at a rate of $0.80 \mathrm{~m} / \mathrm{s}^{2}$ with an upward thrust of $10.0 \mathrm{kN}$. (a) In each case, what is the direction of the acceleration of the spacecraft? (b) Draw a free-body diagram for the spacecraft. In each case, speeding up or slowing down, what is the direction of the net force on the spacecraft? (c) Apply Newton's second law to each case, slowing down or speeding up, and use this to find the spacecraft's weight near the surface of Planet X.

Vipender Yadav
Vipender Yadav
Numerade Educator
03:34

Problem 45

A standing vertical jump. NFL player Gerald Sensabaugh recorded a 46 inch standing vertical jump at the 2005 NFL Combine, at that time the highest for any NFL player in the history of the Combine. Sensabaugh weighed about $200 \mathrm{lb}$ when he set the record. (a) What was his speed as he left the floor? (b) If the jump motion took $0.300 \mathrm{~s}$, what were the magnitude and direction of his acceleration (assuming it to be constant) while he was pushing against the floor? (c) Draw a free-body diagram of Sensabaugh during the jump. (d) Use Newton's laws and the results of part (b) to calculate the normal force on his feet as he jumped.

Supratim Pal
Supratim Pal
Numerade Educator
02:58

Problem 46

You leave the doctor's office after your annual checkup and recall that you weighed $683 \mathrm{~N}$ in her office. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevator's acceleration if the scale reads (a) $725 \mathrm{~N},$ (b) $595 \mathrm{~N}$.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
03:37

Problem 47

Human biomechanics. The fastest served tennis ball, served by Samuel Groth in $2012,$ was measured at $73 \mathrm{~m} / \mathrm{s}$. The mass of a tennis ball is $57 \mathrm{~g}$, and the ball is typically in contact with the tennis racquet for $30.0 \mathrm{~ms}$, with the ball starting from rest. Assuming constant acceleration, (a) what force did Groth's tennis racquet exert on the tennis ball if he hit it essentially horizontally? (b) Make a free-body diagram of the tennis ball during the serve and one just after it has moved free of the racquet.

Alex Garger
Alex Garger
Numerade Educator
04:09

Problem 48

Extraterrestrial physics. You have landed on an unknown planet, Newtonia, and want to know what objects will weigh there. You find that when a certain tool is pushed on a frictionless horizontal surface by a $12.0 \mathrm{~N}$ force, it moves $16.0 \mathrm{~m}$ in the first $2.00 \mathrm{~s}$, starting from rest. You next observe that if you release this tool from rest at $10.0 \mathrm{~m}$ above the ground, it takes 2.58 s to reach the ground. What does the tool weigh on Newtonia, and what would it weigh on Earth?

Farhanul Hasan
Farhanul Hasan
Numerade Educator
08:01

Problem 49

Jumping to the ground. $\mathrm{A} 75.0 \mathrm{~kg}$ man steps off a platform $3.10 \mathrm{~m}$ above the ground. He keeps his legs straight as he falls, but at the moment his feet touch the ground his knees begin to bend, and, treated as a particle, he moves an additional $0.60 \mathrm{~m}$ before coming to rest. (a) What is his speed at the instant his feet touch the ground?
(b) Treating him as a particle, what are the magnitude and direction of his acceleration as he slows down if the acceleration is constant?
(c) Draw a free-body diagram of this man as he is slowing down.
(d) Use Newton's laws and the results of part (b) to calculate the force the ground exerts on him while he is slowing down. Express this force in newtons and also as a multiple of the man's weight.
(e) What are the magnitude and direction of the reaction force to the force you found in part (c)?

Farhanul Hasan
Farhanul Hasan
Numerade Educator
03:16

Problem 50

Forces on a dancer's body. Dancers experience large forces associated with the jumps they make. For example, when a dancer lands after a vertical jump, the force exerted on the head by the neck must exceed the head's weight by enough to cause the head to slow down and come to rest. The head is about $9.4 \%$ of a typical person's mass. Video analysis of a $65 \mathrm{~kg}$ dancer landing after a vertical jump shows that her head slows down from $4.0 \mathrm{~m} / \mathrm{s}$ to rest in a time of $0.20 \mathrm{~s}$
What is the magnitude of the average force that her neck exerts on her head during the landing?
A. $0 \mathrm{~N}$
B. $60 \mathrm{~N}$
C. $120 \mathrm{~N}$
D. $180 \mathrm{~N}$

Alex Garger
Alex Garger
Numerade Educator
00:35

Problem 51

Compared with the force her neck exerts on her head during the landing, the force her head exerts on her neck is
A. the same.
B. greater.
C. smaller.
D. greater during the first half of the landing and smaller during the second half of the landing.

Kevin Hayakawa
Kevin Hayakawa
University of California - Los Angeles
01:07

Problem 52

While the dancer is in the air and holding a fixed pose, what is the magnitude of the force her neck exerts on her head?
A. $0 \mathrm{~N}$
B. $60 \mathrm{~N}$
C. $120 \mathrm{~N}$
D. $180 \mathrm{~N}$

Kevin Hayakawa
Kevin Hayakawa
University of California - Los Angeles
01:36

Problem 53

The forces on a dancer can be measured directly when a dancer performs a jump on a force plate that measures the force between her feet and the ground. Figure 4.43 is a graph of force versus time throughout a vertical jump performed on a force plate. What is happening at $0.4 \mathrm{~s} ?$ The dancer is
A. bending her legs so that her body is accelerating downward.
B. pushing her body up with her legs and is almost ready to leave the ground.
C. in the air and at the top of her jump.
D. landing and her feet have just touched the ground.

Kevin Hayakawa
Kevin Hayakawa
University of California - Los Angeles