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Physics: Principles with Applications

Douglas C. Giancoli

Chapter 4

DYNAMICS: NEWTON'S LAWS OF MOTION - all with Video Answers

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Chapter Questions

00:44

Problem 1

(I) What force is needed to accelerate a sled (mass = 55 kg) at 1.4 m/s$^2$ on horizontal frictionless ice?

Chasen Shaw
Chasen Shaw
Numerade Educator
05:29

Problem 2

(I) What is the weight of a 68-kg astronaut ($a$) on Earth, ($b$) on the Moon ($g =1.7 m/s^2$) ($c$) on Mars ($g = 3.7 \,m/s^2$) ($d$) in outer space traveling with constant velocity?

Kathleen Tatem
Kathleen Tatem
Numerade Educator
00:56

Problem 3

I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s$^2$ ?

Donald Albin
Donald Albin
Numerade Educator
01:23

Problem 4

(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
03:02

Problem 5

(II) Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train's mass is $3.6 \times 10^5$ kg how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?

Averell Hause
Averell Hause
Carnegie Mellon University
02:52

Problem 6

(II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?

Lydia Guertin
Lydia Guertin
Numerade Educator
01:31

Problem 7

(II) What average force is required to stop a 950-kg car in 8.0 s if the car is traveling at 95 km/h?

Averell Hause
Averell Hause
Carnegie Mellon University
01:45

Problem 8

(II) Estimate the average force exerted by a shot-putter on a 7.0-kg shot if the shot is moved through a distance of 2.8 m and is released with a speed of 13 m/s.

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
02:20

Problem 9

(II) A 0.140-kg baseball 35.0 m/s traveling strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove?

Averell Hause
Averell Hause
Carnegie Mellon University
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Problem 10

(II) How much tension must a cable withstand if it is used to accelerate a 1200-kg car vertically upward at 0.70 m/s$^2$?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:47

Problem 11

(II) A 20.0-kg box rests on a table. ($a$) What is the weight of the box and the normal force acting on it? ($b$) A 10.0-kg box is placed on top of the 20.0-kg box, as shown in Fig. 4-43. Determine the normal force that the table exerts on the 20.0-kg box and the normal force that the 20.0-kg box exerts on the 10.0-kg box.
(Figure can't copy)Fig. 4-43

Averell Hause
Averell Hause
Carnegie Mellon University
02:09

Problem 12

(II) A 14.0-kg bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant. What is the acceleration of the bucket? Is it up or down?

Vishal Gupta
Vishal Gupta
Numerade Educator
02:50

Problem 13

(II) A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg. How might the thief use this "rope" to escape? Give a quantitative answer.

Averell Hause
Averell Hause
Carnegie Mellon University
04:57

Problem 14

(II) An elevator (mass 4850 kg) is to be designed so that the maximum acceleration is 0.0680$g$. What are the maximum and minimum forces the motor should exert on the supporting cable?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:12

Problem 15

(II) Can cars "stop on a dime"? Calculate the acceleration of a 1400-kg car if it can stop from 35 km/h on a dime (diameter $=$ 1.7 cm). How many $g$'s is this? What is the force felt by the 68-kg occupant of the car?

Donald Albin
Donald Albin
Numerade Educator
02:41

Problem 16

(II) A woman stands on a bathroom scale in a motionless elevator.When the elevator begins to move, the scale briefly reads only 0.75 of her regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
02:18

Problem 17

(II) ($a$) What is the acceleration of two falling sky divers (total mass = 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight? ($b$) After opening the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute? See Fig. 4-44.(Figure can't copy)

Averell Hause
Averell Hause
Carnegie Mellon University
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Problem 18

(II) The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
04:28

Problem 19

(III) A person jumps from the roof of a house 2.8 m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find ($a$) his velocity just before his feet strike the ground, and ($b$) the average force exerted on his torso by his legs during deceleration.

Keshav Singh
Keshav Singh
Numerade Educator
03:13

Problem 20

(I) A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-45). Determine the force that the table exerts on
the box if the weight hanging on the other side of the pulley weighs ($a$) 30.0 N, ($b$) 60.0 N, and ($c$) 90.0 N.
(Fig. 4-45) (Figure can't copy)

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
01:33

Problem 21

(I) Draw the free-body diagram for a basketball player ($a$) just before leaving the ground on a jump,
and ($b$) while in the air. See Fig. 40-46.(Figure can't copy)

Averell Hause
Averell Hause
Carnegie Mellon University
01:09

Problem 22

(I) Sketch the free-body diagram of a baseball ($a$) at the moment it is hit by the bat, and again ($b$) after it has left the bat and is flying toward the outfield. Ignore air resistance.

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
02:30

Problem 23

(II) Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0$^\circ$, as shown in Fig. 4-47. If her mass is 50.0 kg, what is the tension in the rope at this point?
(Figure can't copy)Fig. 4-47

Averell Hause
Averell Hause
Carnegie Mellon University
04:35

Problem 24

(II) A window washer pulls herself upward using the bucket-pulley apparatus shown in Fig. 4-48. ($a$) How hard must she pull downward to raise herself slowly at constant speed? ($b$) If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 72 kg.
(Figure can't copy)Fig. 4-48

Keshav Singh
Keshav Singh
Numerade Educator
05:12

Problem 25

(II) One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord, as shown in Fig. 4-49. ($a$) If the buckets are at rest, what is the tension in each cord? ($b$) If the two buckets are pulled upward with an acceleration of 1.25 m/s$^2$ by the upper cord, calculate the tension in each cord
(Figure can't copy)Fig. 4-49

Averell Hause
Averell Hause
Carnegie Mellon University
04:01

Problem 26

(II) Two snowcats in Antarctica are towing a housing unit north, as shown in Fig. 4-50. The sum of the forces $\vec{F}_A$ and $\vec{F}_B$ exerted on the unit by the horizontal cables is north, parallel to the line L, and $F_A=$ 4500 N Determine $F_B$ and the magnitude of $\vec{F}_A + \vec{F}_B$ .
(Figure can't copy) Fig. 4-50.

Keshav Singh
Keshav Singh
Numerade Educator
01:35

Problem 27

(II) A train locomotive is pulling two cars of the same mass behind it, Fig. 4-51. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car to that between the first car ($F_{T1}$) and the second car ($F_{T2}$) for any nonzero acceleration of the train.
(Figure can't copy) Fig. 4-51

Averell Hause
Averell Hause
Carnegie Mellon University
13:22

Problem 28

(II) The two forces $\vec{F}_1$ and $\vec{F}_2$ shown in Fig. 4-52a and b (looking down) act on an 18.5-kg object on a frictionless tabletop. If $F_1=$ 10.2 N and $F_2=$ 16.0 N, find the net force on the object and its acceleration for (a) and (b).
(Figure can't copy) Fig. 4-52a

Eduard Sanchez
Eduard Sanchez
Numerade Educator
01:31

Problem 29

(II) At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22$^\circ$ angle with respect to the ground. ($a$) What was the horizontal acceleration of the sprinter? ($b$) If the force was exerted for 0.32 s, with what speed did the sprinter leave the starting block?

Averell Hause
Averell Hause
Carnegie Mellon University
04:47

Problem 30

(II) A 27-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire. ($a$) What horizontal force would be necessary to displace its position 0.15 m to one side? ($b$) What will be the tension in the wire?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
02:55

Problem 31

(II) An object is hanging by a string from your rearview mirror. While you are decelerating at a constant rate from 25 m/s to rest in 6.0 s, ($a$) what angle does the string make with the vertical, and ($b$) is it toward the windshield or away from it? [$Hint$: See Example 4-15.]

Suzanne W.
Suzanne W.
Numerade Educator
07:23

Problem 32

(II) A pair of fuzzy dice is hanging by a string from your rearview mirror. While you are accelerating from a
stoplight to $28 \mathrm{~m} / \mathrm{s}$ in $6.0 \mathrm{~s},$ what angle $\theta$ does the string make
with the vertical? See Fig. $4-50$.(Figure can't copy)

Eduard Sanchez
Eduard Sanchez
Numerade Educator
04:55

Problem 33

(II) ($a$) If $m_A=$ 13.0 kg and mB= 5.0 kg in Fig. 4-53, determine the acceleration of each block. ($b$) If initially $m_A$ is at rest 1.250 m from the edge of the table, how long does it take to reach the edge of the table if the system is allowed to move freely? (c) If $m_B=$ 1.0 kg, how large must $m_A$ be if the acceleration of the system is to be kept at ${1\over100}g$? (Figure can't copy) Fig. 4-53

Averell Hause
Averell Hause
Carnegie Mellon University
07:37

Problem 34

(III) Three blocks on a frictionless horizontal surface are in contact with each other as shown in Fig. 4-54. A force $\vec{F}$ is applied to block A (mass $m_A$). ($a$) Draw a free-body diagram for each block. Determine ($b$) the acceleration of the system (in terms of $m_A, m_B,$and $m_C$ ), ($c$) the net force on each block, and ($d$) the force of contact that each block exerts on its neighbor. (e) If $m_A=m_B=m_C=$10.0 kg and $F=$96.0 N, give numerical answers to ($b$), ($c$), and ($d$). Explain how your answers make sense intuitively. (Figure can't copy) Fig. 4-54

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
04:51

Problem 35

(III) Suppose the pulley in Fig. 4-55 is suspended by a cord C. Determine the tension in this cord after
the masses are released and before one hits the ground. Ignore the mass of the pulley and cords.
(Figure can't copy)Fig. 4-55

Averell Hause
Averell Hause
Carnegie Mellon University
02:41

Problem 36

(I) If the coefficient of kinetic friction between a 22-kg crate and the floor is 0.30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_k$ is zero?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:23

Problem 37

(I) A force of 35.0 N is required to start a 6.0-kg box moving across a horizontal concrete floor. ($a$) What is the coefficient of static friction between the box and the floor? ($b$) If the 35.0-N force continues, the box accelerates at 0.60 m/s$^2$ What is the coefficient of kinetic friction?

Averell Hause
Averell Hause
Carnegie Mellon University
01:27

Problem 38

(I) Suppose you are standing on a train accelerating at 0.20 $g$. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:03

Problem 39

(II) The coefficient of static friction between hard rubber and normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave a car parked?

Averell Hause
Averell Hause
Carnegie Mellon University
03:54

Problem 40

(II) A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?

Kathleen Tatem
Kathleen Tatem
Numerade Educator
01:41

Problem 41

(II) A 2.0-kg silverware drawer does not slide readily. The owner gradually pulls with more and more force, and when the applied force reaches 9.0 N, the drawer suddenly opens, throwing all the utensils to the floor. What is the coefficient of static friction between the drawer and the cabinet?

Averell Hause
Averell Hause
Carnegie Mellon University
02:36

Problem 42

(II) A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.15 and the push imparts an initial speed of 3.5 m/s?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
04:18

Problem 43

(II) A 1280-kg car pulls a 350-kg trailer. The car exerts a horizontal force of $3.6 \times 10^3$ N against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.

Keshav Singh
Keshav Singh
Numerade Educator
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Problem 44

(II) Police investigators, examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:17

Problem 45

(II) Drag-race tires in contact with an asphalt surface have a very high coefficient of static friction. Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s, starting from rest.

Averell Hause
Averell Hause
Carnegie Mellon University
07:19

Problem 46

(II) For the system of Fig. 4-32 (Example 4-20), how large a mass would box A have to have to prevent any motion from occurring? Assume $\mu _s =$ 0.30.

Eduard Sanchez
Eduard Sanchez
Numerade Educator
03:43

Problem 47

(II) In Fig. 4-56 the coefficient of static friction between mass $m_A$ and the table is 0.40, whereas the coefficient of kinetic friction is 0.20. (a) What minimum value of $m_A$ will keep the system from starting to move? (b) What value(s) of $m_A$ will keep the system moving at constant speed? [Ignore masses of the cord and the (frictionless) pulley.]

Averell Hause
Averell Hause
Carnegie Mellon University
03:05

Problem 48

(II) A small box is held in place against a rough vertical wall by someone pushing on it with a force directed upward at 28$^\circ$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30, respectively. The box slides down unless the applied force has magnitude 23 N. What is the mass of the box?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
08:04

Problem 49

(II) Two crates, of mass 65 kg and 125 kg, are in contact and at rest on a horizontal surface (Fig. 4-57). A 650-N force is exerted on the 65-kg crate. If the coefficient of kinetic friction is 0.18, calculate ($a$) the acceleration of the system, and ($b$) the force that each crate exerts on the other. ($c$) Repeat with the crates reversed.
(Figure can't copy)(Fig. 4-57).

Averell Hause
Averell Hause
Carnegie Mellon University
05:02

Problem 50

(II) A person pushes a 14.0-kg lawn mower at constant speed with a force of $F=$ 88.0 N directed along the handle, which is at an angle of 45.0$^\circ$ to the horizontal (Fig. 4-58). ($a$) Draw the free-body diagram showing all forces acting on the mower. Calculate ($b$) the horizontal friction force on the mower, then ($c$) the normal force exerted vertically upward on the mower by the ground. ($d$) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 m/s in 2.5 seconds, assuming the same friction force? (Figure can't copy) (Fig. 4-58)

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
01:37

Problem 51

(II) A child on a sled reaches the bottom of a hill with a velocity of 10.0 m/s and travels 25.0 m along a horizontal straightaway to a stop. If the child and sled together have a mass of 60.0 kg, what is the average retarding force on the sled on the horizontal straightaway?

Averell Hause
Averell Hause
Carnegie Mellon University
07:21

Problem 52

(II) ($a$) A box sits at rest on a rough 33$^\circ$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box. ($b$) How would the diagram change if the box were sliding down the plane? ($c$) How would it change if the box were sliding up the plane after an initial shove?

Linda Winkler
Linda Winkler
Numerade Educator
07:45

Problem 53

(II) A wet bar of soap slides down a ramp 9.0 m long inclined at 8.0$^\circ$. How long does it take to reach the bottom? Assume $\mu _k=$ 0.060.

Donald Albin
Donald Albin
Numerade Educator
01:58

Problem 54

(II) A skateboarder, with an initial speed of 2.0 m/s rolls virtually friction free down a straight incline of length 18 m in 3.3 s. At what angle $\theta$ is the incline oriented above the horizontal?

Anthony Han
Anthony Han
Numerade Educator
03:32

Problem 55

(II) Uphill escape ramps are sometimes provided to the side of steep downhill highways for trucks with overheated brakes. For a simple 11$^\circ$ upward ramp, what minimum length would be needed for a runaway truck traveling 140 km/h? Note the large size of your calculated length. (If sand is used for the bed of the ramp, its length can be reduced by a factor of about 2.)

Averell Hause
Averell Hause
Carnegie Mellon University
02:49

Problem 56

(II) A 25.0-kg box is released on a 27$^\circ$ incline and accelerates down the incline at 0.30 m/s$^2$. Find the friction force impeding its motion. What is the coefficient of kinetic friction?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:59

Problem 57

(II) The block shown in Fig. 4-59 has mass $m=$ 7.0 kg and lies on a fixed smooth frictionless plane tilted at an angle $\theta = 22.0^\circ$to the horizontal. ($a$) Determine the acceleration of the block as it slides down the plane. ($b$) If the block starts from rest 12.0 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline? (Figure can't copy) Fig. 4-59

Guilherme Barros
Guilherme Barros
Numerade Educator
04:24

Problem 58

(II) A block is given an initial speed of 4.5 m/s up the 22.0$^\circ$ plane shown in Fig. 4-59. ($a$) How far up the plane will it go? ($b$) How much time elapses before it returns to its starting point? Ignore friction. (Figure can't copy) Fig. 4-59

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
04:03

Problem 59

(II) The crate shown in Fig. 4-60 lies on a plane tilted at an angle $\theta = 25.0 ^\circ$ to the horizontal, with $\mu _k =$ 0.19. ($a$) Determine the acceleration of the crate as it slides down the plane. ($b$) If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate's speed when it reaches the bottom of the incline? (Figure can't copy) Fig. 4-60

Averell Hause
Averell Hause
Carnegie Mellon University
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Problem 60

(II) A crate is given an initial speed of 3.0 m/s up the 25.0$^\circ$ plane shown in Fig. 4-60. ($a$) How far up the plane will it go? ($b$) How much time elapses before it returns to its starting point? Assume $\mu_k =$ 0.12. (Figure can't copy) Fig. 4-60

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
04:14

Problem 61

(II) A car can decelerate at $-$3.80 m/s$^2$ without skidding when coming to rest on a level road. What would its deceleration be if the road is inclined at 9.3$^\circ$ and the car moves uphill? Assume the same static friction coefficient.

Averell Hause
Averell Hause
Carnegie Mellon University
02:04

Problem 62

(II) A skier moves down a 12$^\circ$ slope at constant speed.What can you say about the coefficient of friction, $\mu_k$? Assume the speed is low enough that air resistance can be ignored.

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:57

Problem 63

(II) The coefficient of kinetic friction for a 22-kg bobsled on a track is 0.10. What force is required to push it down along a 6.0$^\circ$ incline and achieve a speed of 60 km/h at the end of 75 m?

Averell Hause
Averell Hause
Carnegie Mellon University
03:37

Problem 64

(II) On an icy day, you worry about parking your car in your driveway, which has an incline of 12$^\circ$. Your neighbor's driveway has an incline of 9.0$^\circ$, and the driveway across the street is at 6.0$^\circ$. The coefficient of static friction between tire rubber and ice is 0.15. Which driveway(s) will be safe to park in?

Anthony Han
Anthony Han
Numerade Educator
08:07

Problem 65

(III) Two masses $m_A=$2.0 kg and $m_B=$5.0 kg are on inclines and are connected together by a string as shown in Fig. 4-61. The coefficient of kinetic friction between each mass and its incline is $\mu _k=$ 0.30. If $m_A$ moves up, and $m_B$ moves down, determine their acceleration. [Ignore masses of the (frictionless) pulley and the cord.] (Figure can't copy)Fig. 4-61

Averell Hause
Averell Hause
Carnegie Mellon University
13:41

Problem 66

(III) A child slides down a slide with a 34$^\circ$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

Kathleen Tatem
Kathleen Tatem
Numerade Educator
05:43

Problem 67

(III) (a) Suppose the coefficient of kinetic friction between $m_A$ and the plane in Fig. 4-62 is $\mu_k =$ 0.15, and that $m_A = m_B=$ 2.7 kg. As $m_B$ moves down, determine the magnitude of the acceleration of mA and mB, given $\theta =$ 34$^\circ$. (b) What smallest value of $\mu_k$ will keep the system from accelerating? [Ignore masses of the (frictionless) pulley and the cord.] (Figure can't copy) Fig. 4-62

Keshav Singh
Keshav Singh
Numerade Educator
04:01

Problem 68

A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 27 m/s. What was the average force of air resistance?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:52

Problem 69

A crane's trolley at point P in Fig. 4-63 moves for a few seconds to the right with constant acceleration, and the 870-kg load hangs on a light cable at a 5.0$^\circ$ angle to the vertical as shown. What is the acceleration of the trolley and load?
(Figure can't copy)Fig. 4-63

Averell Hause
Averell Hause
Carnegie Mellon University
06:51

Problem 70

A 75.0-kg person stands on a scale in an elevator. What does the scale read (in N and in kg) when ($a$) the elevator is at rest, ($b$) the elevator is climbing at a constant speed of 3.0 m/s, ($c$) the elevator is descending at 3.0 m/s, ($d$) the elevator is accelerating upward at 3.0 m/s$^2$, ($e$) the elevator is accelerating downward at 3.0 m/s$^2$?

Jose Carlos
Jose Carlos
Numerade Educator
02:29

Problem 71

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to 21 m/s (75 km/h) in 12.5 s. Using these data, calculate the maximum steepness of a hill.

Averell Hause
Averell Hause
Carnegie Mellon University
11:50

Problem 72

If a bicyclist of mass 65 kg (including the bicycle) can coast down a 6.5$^\circ$ hill at a steady speed of 6.0 km/h because of air resistance, how much force must be applied to climb the hill at the same speed (and the same air resistance)?

Kathleen Tatem
Kathleen Tatem
Numerade Educator
02:34

Problem 73

Francesca dangles her watch from a thin piece of string while the jetliner she is in accelerates for takeoff, which takes about 16 s. Estimate the takeoff speed of the aircraft if the string makes an angle of 25$^\circ$ with respect to the vertical, Fig. 4-64. (Figure can't copy)

Averell Hause
Averell Hause
Carnegie Mellon University
09:44

Problem 74

Bob traverses a chasm by stringing a rope between a tree on one side of the chasm and a tree on the opposite side, 25 m away, Fig. 4-65. Assume the rope can provide a tension force of up to 29 kN before breaking, and use a "safety factor" of 10 (that is, the rope should only be required to undergo a tension force of 2.9 kN). (a) If Bob's mass is 72.0 kg, determine the distance $x$ that the rope must sag at a point halfway across if it is to be within its recommended safety range. ($b$) If the rope sags by only one fourth the distance found in ($a$), determine the tension force in the rope. Will the rope break? (Figure can't copy)Fig. 4-65

Kathleen Tatem
Kathleen Tatem
Numerade Educator
05:04

Problem 75

Piles of snow on slippery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a slope of 34$^\circ$. ($a$) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down? ($b$) As the snow begins to melt, the coefficient of static friction decreases and the snow finally slips. Assuming that the distance from the chunk to the edge of the roof is 4.0 m and the coefficient of kinetic friction is 0.10, calculate the speed of the snow chunk when it slides off the roof. ($c$) If the roof edge is 10.0 m above ground, estimate the speed of the snow when it hits the ground.

Averell Hause
Averell Hause
Carnegie Mellon University
04:51

Problem 76

($a$) What minimum force $F$ is needed to lift the piano (mass $M$) using the pulley apparatus shown in Fig. 4-66? ($b$) Determine the tension in each section of rope: $F_{T1}, F_{T2}, F_{T3}$ and $F_{T4}$. Assume pulleys are massless and frictionless, and that ropes are massless. (Figure can't copy)Fig. 4-66

Surendra Kumar
Surendra Kumar
Numerade Educator
01:57

Problem 77

In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps and it is desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force required is no more than 18 N. Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full 25-kg cart?

Averell Hause
Averell Hause
Carnegie Mellon University
06:04

Problem 78

A jet aircraft is accelerating at 3.8 m/s$^2$ as it climbs at an angle of 18$^\circ$ above the horizontal (Fig. 4-67). What is the total force that the cockpit seat exerts on the 75-kg pilot? (Figure can't copy)(Fig. 4-67)

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
04:37

Problem 79

A 7180-kg helicopter accelerates upward at 0.80 m/s$^2$ while lifting a 1080-kg frame at a construction site, Fig. 4-68. ($a$)What is the lift force exerted by the air on the helicopter rotors? ($b$) What is the tension in the cable (ignore its mass) which connects the frame to the helicopter? ($c$) What force does the cable exert on the helicopter? (Figure can't copy) Fig. 4-68

Averell Hause
Averell Hause
Carnegie Mellon University
02:42

Problem 80

An elevator in a tall building is allowed to reach a maximum speed of 3.5 m/s going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1450 kg including occupants?

Nishant Kumar
Nishant Kumar
Numerade Educator
03:42

Problem 81

A fisherman in a boat is using a "10-lb test" fishing line. This means that the line can exert a force of 45 N without breaking (1 lb $=$ 4.45N) ($a$) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? ($b$) If he accelerates the fish upward at 2.0 m/s$^2$ what maximum weight fish can he land? ($c$) Is it possible to land a 15-lb trout on 10-lb test line? Why or why not?

Averell Hause
Averell Hause
Carnegie Mellon University
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Problem 82

A "doomsday" asteroid with a mass of $1.0 \times 10^{10}$ kg is hurtling through space. Unless the asteroid's speed is changed by about 0.20 m/s, it will collide with Earth and cause tremendous damage. Researchers suggest that a small "space tug" sent to the asteroid's surface could exert a gentle constant force of 2.5 N. For how long must this force act?

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
03:41

Problem 83

Three mountain climbers who are roped together in a line are ascending an icefield inclined at 31.0$^\circ$ to the horizontal (Fig. 4-69). The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg, calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers. (Fig. 4-69)(Figure can't copy)

Averell Hause
Averell Hause
Carnegie Mellon University
06:32

Problem 84

As shown in Fig. 4-70, five balls (masses 2.00, 2.05, 2.10, 2.15, 2.20 kg) hang from a crossbar. Each mass is supported by "5-lb test" fishing line which will break when its tension force exceeds 22.2 N ($=$ 5.00 lb).When this device is placed in an elevator, which accelerates upward, only the lines attached to the 2.05 and 2.00 kg masses do not break.Within what range is the elevator's acceleration? (Figure can't copy)Fig. 4-70

Eduard Sanchez
Eduard Sanchez
Numerade Educator
06:09

Problem 85

Two rock climbers, Jim and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a $dynamic$ $rope$ by climbers. Jim has a $static$ $rope$, not recommended for safety purposes in pro climbing. ($a$) Karen (Fig. 4-71) falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m. Estimate how large a force (assume constant) she will feel from the rope. (Express the result in multiples of her weight.) ($b$) In a similar fall, Jim's rope stretches by only 30 cm. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?(Fig. 4-71)(Figure can't copy)

Averell Hause
Averell Hause
Carnegie Mellon University
06:28

Problem 86

A coffee cup on the horizontal dashboard of a car slides forward when the driver decelerates from 45 km/h to rest in 3.5 s or less, but not if she decelerates in a longer time. What is the coefficient of static friction between the cup and the dash? Assume the road and the dashboard are level (horizontal).

Kathleen Tatem
Kathleen Tatem
Numerade Educator
03:57

Problem 87

A roller coaster reaches the top of the steepest hill with a speed of 6.0 km/h It then descends the hill, which is at an average angle of 45$^\circ$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_k=$ 0.12.

Averell Hause
Averell Hause
Carnegie Mellon University
06:57

Problem 88

A motorcyclist is coasting with the engine off at a steady speed of 20.0 m/s but enters a sandy stretch where the coefficient of kinetic friction is 0.70.Will the cyclist emerge from the sandy stretch without having to start the engine if the sand lasts for 15 m? If so, what will be the speed upon emerging?

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
03:16

Problem 89

The 70.0-kg climber in Fig. 4-72 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his
back and the wall, are 0.80 and 0.60, respectively. What is the minimum normal force he must
exert? Assume the walls are vertical and that the static friction forces are both at their maximum. Ignore his grip on the rope.(Figure can't copy)Fig. 4-72

Vishal Gupta
Vishal Gupta
Numerade Educator
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Problem 90

A 28.0-kg block is connected to an empty 2.00-kg bucket by a cord running over a frictionless pulley (Fig. 4-73). The coefficient of static friction between the table and the block is 0.45 and the coefficient of kinetic friction between the table and the block is 0.32. Sand is gradually added to the bucket until the system just begins to move. ($a$) Calculate the mass of sand added to the bucket. ($b$) Calculate the acceleration of the system. Ignore mass of cord.(Fig. 4-73)(Figure can't copy)

Darshan Maheshwari
Darshan Maheshwari
Numerade Educator
06:35

Problem 91

A 72-kg water skier is being accelerated by a ski boat on a flat ("glassy") lake. The coefficient of kinetic friction between the skier's skis and the water surface is $\mu_k=$ 0.25 (Fig. 4-74). ($a$) What is the skier's acceleration if the rope pulling the skier behind the boat applies a horizontal tension force of magnitude $F_T=$ 240 N to the skier ($\theta=0^\circ$)? ($b$) What is the skier's horizontal acceleration if the rope pulling the skier exerts a force of $F_T=$ 240 N on the skier at an upward angle $\theta= 12^\circ$?($c$) Explain why the skier's acceleration in part ($b$) is greater than that in part ($a$).(Figure can't copy)(Fig. 4-74)

Averell Hause
Averell Hause
Carnegie Mellon University
18:46

Problem 92

A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28$^\circ$ incline (Fig. 4-75). After sliding down the 110-m-long incline (on which the coefficient of kinetic friction is $\mu_k=$ 0.18 ), the snowboarder has attained a velocity $v$. The snowboarder then slides along a flat surface (on which $\mu_k=$ 0.15 ) and comes to rest after a distance $x$. Use Newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface. Then use these accelerations to determine $x$.(Fig. 4-75)(Figure can't copy)

Kathleen Tatem
Kathleen Tatem
Numerade Educator
01:39

Problem 93

($a$) If the horizontal acceleration produced briefly by an earthquake is a, and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_s= a/g$. ($b$) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 m/s$^2$ in the San Francisco Bay Area. Would a chair have started to slide on a floor with coefficient of static friction 0.25?

Averell Hause
Averell Hause
Carnegie Mellon University
19:28

Problem 94

Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle to the horizontal, Fig. 4-76 (block $B$ is above block $A$). The masses of the blocks are $m_A$ and $m_B$ and the coefficients of friction are $\mu_A$ and $\mu_B$. If $m_A=m_B=$ 5.0 kg and $\mu_A=$ 0.20 and $\mu_B=$ 0.30, determine (a) the acceleration of the blocks and (b) the tension in the cord, for an angle $\theta =$ 32$^\circ$.(Figure can't copy) Fig. 4-76

Kathleen Tatem
Kathleen Tatem
Numerade Educator
04:16

Problem 95

A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the sloping road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? ($a$) Ignore friction. ($b$) Assume an effective coefficient of friction equal to 0.10.

Averell Hause
Averell Hause
Carnegie Mellon University
02:16

Problem 96

A 65-kg ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_k=$ 0.10, how fast was she moving at the start of her coast?

Anthony Han
Anthony Han
Numerade Educator
01:49

Problem 97

An 18-kg child is riding in a child-restraint chair, securely fastened to the seat of a car (Fig. 4-77). Assume the car has speed 45 km/h when it hits a tree and is brought to rest in 0.20 s. Assuming constant deceleration during the collision, estimate the net horizontal force $F$ that the straps of the restraint chair exert on the child to hold her in the chair. (Fig. 4-77)(Figure can't copy)

Averell Hause
Averell Hause
Carnegie Mellon University