Fundamentals of Physics

David Halliday, Robert Resnick, Jearl Walker

Chapter 6

Force and Motion-II - all with Video Answers

Educators

Chapter Questions

Problem 1

The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of $0.25$ with the floor. If the train is initially moving at a speed of $48 \mathrm{~km} / \mathrm{h}$, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

Averell Hause

Averell Hause

Carnegie Mellon University

Problem 2

In a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the $3.5 \mathrm{~kg}$ book is pushed from rest through a distance of $0.90 \mathrm{~m}$ by the horizontal $25 \mathrm{~N}$ force from the broom and then has a speed of $1.60 \mathrm{~m} / \mathrm{s}$, what is the coefficient of kinetic friction between the book and floor?

Keshav Singh

Numerade Educator

Problem 3

A bedroom bureau with a mass of $45 \mathrm{~kg}$, including drawers and clothing, rests on the floor. (a) If the coefficient of static friction between the bureau and the floor is $0.45$, what is the magnitude of the minimum horizontal force that a person must apply to start the bureau moving? (b) If the drawers and clothing, with $17 \mathrm{~kg}$ mass, are removed before the bureau is pushed, what is the new minimum magnitude?

Averell Hause

Carnegie Mellon University

Problem 4

A slide-loving pig slides down a certain $35^{\circ}$ slide in twice the time it would take to slide down a frictionless $35^{\circ}$ slide. What is the coefficient of kinetic friction between the pig and the slide?

Supratim Pal

Numerade Educator

Problem 5

ao A $2.5 \mathrm{~kg}$ block is initially at rest on a horizontal surface. A horizontal force $\vec{F}$ of magnitude $6.0 \mathrm{~N}$ and a vertical force $\vec{P}$ are then applied to the block (Fig. $6-17$ ). The coefficients of friction for the block and surface are $\mu_{s}=0.40$ and $\mu_{k}=0.25 .$ Determine the magnitude of the frictional force acting on the block if the magnitude of $\vec{P}$ is (a) $8.0 \mathrm{~N}$,(b) $10 \mathrm{~N}$, and $(\mathrm{c}) 12 \mathrm{~N}$

Keshav Singh

Numerade Educator

Problem 6

A baseball player with mass $m=79 \mathrm{~kg}$, sliding into second base, is retarded by a frictional force of magnitude $470 \mathrm{~N}$. What is the coefficient of kinetic friction $\mu_{k}$ between the player and the ground?

Averell Hause

Carnegie Mellon University

Problem 7

A person pushes horizontally with a force of $220 \mathrm{~N}$ on a $55 \mathrm{~kg}$ crate to move it across a level floor. The coefficient of kinetic friction between the crate and the floor is $0.35 .$ What is the magnitude of (a) the frictional force and (b) the acceleration of the crate?

Averell Hause

Carnegie Mellon University

Problem 8

The mysterious sliding stones. Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if the stones had been migrating (Fig. $6-18$ ). For years curiosity mounted about why the stones moved. One explanation was that strong winds during occasional rainstorms would drag the rough stones

Keshav Singh

Numerade Educator

Problem 9

A $3.5 \mathrm{~kg}$ block is pushed along a horizontal floor by a force $\vec{F}$ of magnitude $15 \mathrm{~N}$ at an angle $\theta=40^{\circ}$ with the horizontal (Fig. 6-19). The coefficient of kinetic friction between the block and the floor is $0.25 .$ Calculate the
magnitudes of (a) the frictional force on the block from the floor and (b) the block's acceleration.

Averell Hause

Carnegie Mellon University

Problem 10

Figure $6-20$ shows an initially stationary block of mass $m$ on a floor. A force of magnitude $0.500 \mathrm{mg}$ is then applied at upward angle $\theta=$ $20^{\circ}$. What is the magnitude of the acceleration of the block across the floor if the friction coefficients are and
(b) $\mu_{s}=0.400$ and $\mu_{k}=0.300 ?$

Keshav Singh

Numerade Educator

Problem 11

$68 \mathrm{~kg}$ crate is dragged across a floor by pulling on a rope attached to the crate and inclined $15^{\circ}$ above the horizontal.
(a) If the coefficient of static friction is $0.50$, what minimum force magnitude is required from the rope to start the crate moving?
(b) If $\mu_{k}=0.35$, what is the magnitude of the initial acceleration of the crate?

Averell Hause

Carnegie Mellon University

Problem 12

In about 1915 , Henry Sincosky of Philadelphia suspended himself from a rafter by gripping the rafter with the thumb of each hand on one side and the fingers on the opposite side (Fig. 6-21). Sincosky's mass was $79 \mathrm{~kg}$. If the coefficient of static friction between hand and rafter was $0.70$, what was the least magnitude of the normal force on the rafter from each thumb or opposite fingers? (After suspending himself, Sincosky chinned himself on the rafter and then moved hand-over-hand along the rafter. If you do not think Sincosky's grip was remarkable, try to repeat his stunt.)

Averell Hause

Carnegie Mellon University

Problem 13

A worker pushes horizontally on a $35 \mathrm{~kg}$ crate with a force of magnitude $110 \mathrm{~N}$. The coefficient of static friction between the crate and the floor is $0.37 .$ (a) What is the value of $f_{s, \max }$ under the circumstances? (b) Does the crate move?
(c) What is the frictional force on the crate from the floor? (d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull that will allow the first worker's $110 \mathrm{~N}$ push to move the crate? (c) If, instead, the second worker pulls horizontally to $\mathrm{F}$ the least pull that will get the crate moving?

Vishal Gupta

Numerade Educator

Problem 14

Figure $6-22$ shows the cross section of a road cut into the side of a mountain. The solid line $A A^{\prime}$ represents a weak bedding plane along which sliding is possible. Block $B$ directly above the highway is separated from uphill rock by a large crack (called a joint), so that only friction between the block and the bedding plane prevents sliding. The mass of the block is $1.8 \times 10^{7} \mathrm{~kg}$, the $d$ plane is $24^{\circ}$, and the coefficient of stat and plane is $0.63 .$ (a) Show that the $b$ these circumstances. (b) Next, water se pands upon freezing, exerting on the $\mathrm{b}$. $A A^{\prime}$. What minimum value of force $\mathrm{m}$ slide down the plane?

Keshav Singh

Numerade Educator

Problem 15

The coefficient of static friction between Teflon and scrambled eggs is about $0.04$. What is the smallest angle from the horizontal that will cause the eggs to slide across the bottom of a Teflon-coated skillet?

Averell Hause

Carnegie Mellon University

Problem 16

A loaded penguin sled weighing $80 \mathrm{~N}$ rests on a plane inclined at angle $\theta=20^{\circ}$ to the horizontal (Fig. 6 -23). Between the sled and the plane, the coefficient of static friction is $0.25$, and the coefficient of kinetic friction is $0.15$. (a) What is the least magnitude of the force $\vec{F}$, parallel to the plane, that will prevent the sled from slipping down the mum magnitude $F$ that will start the What value of $F$ is required to move the sled up the plane at constant velocity?

Keshav Singh

Numerade Educator

Problem 17

In Fig. 6-24, a force $\vec{P}$ acts on a block weighing $45 \mathrm{~N}$. The block is initially at rest on a plane inclined at angle $\theta=15^{\circ}$ to the horizontal. The positive direction of the $x$ axis is up the plane. Between block and plane, the coefficient of static friction is $\mu_{s}=0.50$ and the coefficient of kinetic friction is $\mu_{k}=0.34$. In unit-vector notation, what is the frictional force on the block from the plane when $\vec{P}$ is (a) $(-5.0 \mathrm{~N}) \hat{\mathrm{i}},(\mathrm{b})(-8.0 \mathrm{~N}) \hat{\mathrm{i}}$, and $(\mathrm{c})(-15 \mathrm{~N}) \hat{\mathrm{i}} ?$

Keshav Singh

Numerade Educator

Problem 18

You testify as an expert witness in a case involving an accident in which car $A$ slid into the rear of car $B$, which was stopped at a red light along a road headed down a hill (Fig. $6-25$ ). You find that the slope of the hill is $\theta=12.0^{\circ}$, that the cars were separated by distance $d=24.0 \mathrm{~m}$ when the driver of car $A$ put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car $A$ at the onset of braking was $v_{0}=18.0 \mathrm{~m} / \mathrm{s}$. With what speed did car $A$ hit car $B$ if the coefficient of kinetic friction was
(a) $0.60$ (dry road surface) and (b) $0.10$ (road surface covered with wet leaves)?

Keshav Singh

Numerade Educator

Problem 19

$\omega $ A $\mathrm{~N}$ horizontal force $\vec{F}$ pushes a block weighing $5.0 \mathrm{~N}$ against a vertical wall (Fig. $6-26$ ). The coefficient of static friction between the wall and the block is $0.60$, and the coefficient of kinetic friction is $0.40$. Assume that the block is not moving initially. (a) Will the block move tion, what is the force on the block from

Keshav Singh

Numerade Educator

Problem 20

(ao In Fig. 6-27, a box of Cheerios (mass $m_{C}=1.0 \mathrm{~kg}$ ) and a box of Wheaties (mass $m_{W}=3.0$ $\mathrm{kg}$ ) are accelerated across a horizontal surface by a horizontal force $\quad$ Figure 6-27 Problem 20 . $\vec{F}$ applied to the Cheerios box. The magnitude of the frictional force on the Cheerios box is $2.0 \mathrm{~N}$, and the magnitude of the frictional force on the Wheaties box is $4.0 \mathrm{~N}$. If the magnitude of $\vec{F}$ is $12 \mathrm{~N}$, what is the magnitude of the force on the Wheaties box from the Cheerios box?

Keshav Singh

Numerade Educator

Problem 21

An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed $1100 \mathrm{~N}$. The coefficient of static friction between the box and the floor is $0.35$. (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

Averell Hause

Carnegie Mellon University

Problem 22

In Fig. $6-23$, a sled is held on an inclined plane by a cord pulling directly up the plane. The sled is to be on the verge of moving up the plane. In Fig. 628 , the magnitude $F$ required of the cord's force on the sled is
plotted versus a range of values for the coefficient of static friction $\mu_{s}$ between sled and plane:
$F_{1}=2.0 \mathrm{~N}, F_{2}=5.0 \mathrm{~N}$, and $\mu_{2}=$
$0.50 .$ At what angle $\theta$ is the plane inclined? Figure 6-28 Problem 22.

Keshav Singh

Numerade Educator

Problem 23

When the three blocks in Fig. $6-29$ are released from rest, they accelerate with a magnitude of $0.500 \mathrm{~m} / \mathrm{s}^{2}$. Block 1 has mass $M$, block 2 has $2 M$, and block 3 has $2 M$. What is the coefficient of kinetic friction between block 2 and the table?

Averell Hause

Carnegie Mellon University

Problem 24

A $4.10 \mathrm{~kg}$ block is pushed along a floor by a constant applied force that is horizontal and has a magnitude of $40.0 \mathrm{~N} .$ Figure $6-30$ gives the block's speed $v$ versus time $t$ as the block moves along $\operatorname{an} x$ axis on the floor. The scale of the figure's vertical axis is set by $v_{s}=$ $5.0 \mathrm{~m} / \mathrm{s} .$ What is the coefficient of kinetic friction between the block and the floor?

Averell Hause

Carnegie Mellon University

Problem 25

Block $B$ in Fig. $6-31$ weighs $711 \mathrm{~N}$. The coefficient of static friction between block and table is $0.25$; angle $\theta$ is $30^{\circ}$; assume that the cord between $B$ and the knot is horizontal. Find the maximum weight of block $A$ for which the system will be stationary.

Averell Hause

Carnegie Mellon University

Problem 26

ao Figure $6-32$ shows three crates being pushed over a concrete floor by a horizontal force $\vec{F}$ of magnitude $440 \mathrm{~N}$. The masses of the crates are $m_{1}=30.0 \mathrm{~kg}, m_{2}=10.0$
$\mathrm{kg}$, and $m_{3}=20.0 \mathrm{~kg}$. The coefficient of kinetic friction between the floor and each of the crates is $0.700 .$ (a) What is the magnitude $F_{32}$ of the force on crate 3 from crate $2 ?$ (b) If the crates then slide onto a polished floor, where the coefficient of kinetic magnitude $F_{32}$ more than, less than, or coefficient was $0.700 ?$

Keshav Singh

Numerade Educator

Problem 27

ao Body $A$ in Fig. 6 -33 weighs $102 \mathrm{~N}$, and body $B$ weighs $32 \mathrm{~N}$. The coefficients of friction between $A$ and the incline are $\mu_{s}=0.56$ and $\mu_{k}=0.25$. Angle $\theta$ is $40^{\circ}$. Let the positive direction of an $x$ axis be up the incline. In unit-vector notation, what is the acceleration of $A$ if $A$ is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline?

Keshav Singh

Numerade Educator

Problem 28

In Fig. 6-33, two blocks are connected over a pulley. The mass of block $A$ is $10 \mathrm{~kg}$, and the coefficient of kinetic friction between $A$ and the incline is $0.20$. Angle $\theta$ of the incline is $30^{\circ} .$ Block $A$ slides down the incline at constant speed. What is the mass of block $B$ ? Assume the connecting rope has negligible mass. (The pulley's function is only to redirect the rope.)

Averell Hause

Carnegie Mellon University

Problem 29

In Fig. 6-34, blocks $A$ and $B$ have weights of $44 \mathrm{~N}$ and 22 $\mathrm{N}$, respectively. (a) Determine the minimum weight of block $\bar{C}$ to keep $A$ from sliding if $\mu_{s}$ between $A$ and the table is $0.20$. (b) Block $C$ suddenly is lifted off $A$. What is the acceleration of block $A$ if $\mu_{k}$ between $A$ and the table is $0.15 ?$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 30

A toy chest and its contents have a combined weight of $180 \mathrm{~N}$. The coefficient of static friction between toy chest and floor is $0.42$. The child in Fig. 6- 35 attempts to move the chest across the floor by pulling on an attached rope. (a) If $\theta$ is $42^{\circ}$, what is the magnitude of the force $\vec{F}$ that the child must exert on the rope to put the chest on the verge of moving? (b) Write an expression for the magnitude $F$ required to put the chest on the verge of moving as a function of the angle $\theta$. Determine (c) the value of $\theta$ for which $F$ is a minimum and (d) that minimum magnitude.

Averell Hause

Carnegie Mellon University

Problem 31

Two blocks, of weights $3.6 \mathrm{~N}$ and $7.2 \mathrm{~N}$, are connected by a massless string and slide down a $30^{\circ}$ inclined plane. The coefficient of kinetic friction between the lighter block and the plane is $0.10$, and the coefficient between the heavier block and the plane is 0.20. Assuming that the lighter block leads, find (a) the magnitude of the acceleration of the blocks and (b) the tension in the taut string.

Averell Hause

Carnegie Mellon University

Problem 32

ao A block is pushed across a floor by a constant force that is applied at downward angle $\theta$ (Fig. 6-19). Figure $6-36$ gives the acceleration magnitude $a$ versus a range of values for the coefficient of kinetic friction $\mu_{k}$ between block and floor: $a_{1}=3.0 \mathrm{~m} / \mathrm{s}^{2}, \mu_{k 2}=$ $0.20$, and $\mu_{k 3}=0.40 .$ What is the value of $\theta$ ?

Keshav Singh

Numerade Educator

Problem 33

A $1000 \mathrm{~kg}$ boat is traveling at $90 \mathrm{~km} / \mathrm{h}$ when its engine is shut off. The magnitude of the frictional force $\vec{f}_{k}$ between boat and water is proportional to the speed $v$ of the boat: $f_{k}=70 v$, where $v$ is in meters per second and $f_{k}$ is in newtons. Find the time required for the boat to slow to $45 \mathrm{~km} / \mathrm{h}$.

Keshav Singh

Numerade Educator

Problem 34

ao In Fig. $6-37$, a slab of mass $m_{1}=40 \mathrm{~kg}$ rests on a frictionless $\mu=0-$ floor, and a block of mass $m_{2}=10$ $\mathrm{kg}$ rests on top of the slab. Between Figure 6
block and slab, the coefficient of static friction is $0.60$, and the coefficient of kineti horizontal force $\vec{F}$ of magnitude $100 \mathrm{~N}$ begins the block, as shown. In unit-vector notation, wh:
accelerations of (a) the block and (b) the slab?

Keshav Singh

Numerade Educator

Problem 35

The two blocks $(m=16$ $\mathrm{kg}$ and $M=88 \mathrm{~kg}$ ) in Fig. $6-38$ are not attached to each other. The coefficient of static friction between the blocks is $\mu_{5}=0.38$, but the surface $\mathrm{Fr}$ beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force $\vec{F}$ required to keep the smaller block from slipping down

Keshav Singh

Numerade Educator

Problem 36

The terminal speed of a sky diver is $160 \mathrm{~km} / \mathrm{h}$ in the spreadeagle position and $310 \mathrm{~km} / \mathrm{h}$ in the nosedive position. Assuming that the diver's drag coefficient $C$ does not change from one position to the other, find the ratio of the effective cross-sectional area $A$ in the slower position to that in the faster position.

Keshav Singh

Numerade Educator

Problem 37

ant Continuation of Problem $8 .$ Now assume that Eq. $6-14$ gives the magnitude of the air drag force on the typical $20 \mathrm{~kg}$ stone, which presents to the wind a vertical cross-sectional area of $0.040 \mathrm{~m}^{2}$ and has a drag coefficient $C$ of $0.80 .$ Take the air density to be $1.21 \mathrm{~kg} / \mathrm{m}^{3}$, and the coefficient of kinetic friction to be $0.80 .$ (a) In kilometers per hour, what wind speed $V$ along the ground is needed to maintain the stone's motion once it has started moving? Because winds along the ground are retarded by the ground, the wind speeds reported for storms are often measured at a height of $10 \mathrm{~m} .$ Assume wind speeds are $2.00$ times those along the ground. (b) For your answer to (a), what wind speed would be reported for the storm? (c) Is that value reasonable for a high-speed wind in a storm? (Story continues with Problem 6.5.)

Keshav Singh

Numerade Educator

Problem 38

Assume Eq. 6-14 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at $1300 \mathrm{~km} / \mathrm{h}$. Assume also that the mass of the seat is equal to the mass of the pilot and that the drag coefficient is that of a sky diver. Making a reasonable guess of the pilot's mass and using the appropriate $v_{t}$ value from Table $6-1$, estimate the magnitudes of
(a) the drag force on the pilot $+$ seat and (b) their horizontal deceleration (in terms of $g$ ), both just after ejection. (The result of
(a) should indicate an engineering requirement: The seat must include a protective barrier to deflect the initial wind blast away from the pilot's head.)

Keshav Singh

Numerade Educator

Problem 39

Calculate the ratio of the drag force on a jet flying at $1000 \mathrm{~km} / \mathrm{h}$ at an altitude of $10 \mathrm{~km}$ to the drag force on a propdriven transport flying at half that speed and altitude. The density

Keshav Singh

Numerade Educator

Problem 40

$ \Rightarrow E$ In downhill speed skiing a skier is retarded by both the air drag force on the body and the kinetic frictional force on the skis. (a) Suppose the slope angle is $\theta=40.0^{\circ}$, the snow is dry snow with a coefficient of kinetic friction $\mu_{k}=0.0400$, the mass of the skier and equipment is $m=85.0 \mathrm{~kg}$, the cross-sectional area of the (tucked) skier is $A=1.30 \mathrm{~m}^{2}$, the drag coefficient is $C=0.150$, and the air density is $1.20 \mathrm{~kg} / \mathrm{m}^{3}$. (a) What is the terminal speed? (b) If a skier can vary $C$ by a slight amount $d C$ by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed?

Keshav Singh

Numerade Educator

Problem 41

A cat dozes on a stationary merry-go-round in an amusement park, at a radius of $5.4 \mathrm{~m}$ from the center of the ride. Then the operator turns on the ride and brings it up to its proper turning rate of one complete rotation every $6.0 \mathrm{~s}$. What is the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding (or the cat clinging with its claws)?

William Dunkerton

William Dunkerton

Numerade Educator

Problem 42

Suppose the coefficient of static friction between the road and the tires on a car is $0.60$ and the car has no negative lift. What speed will put the car on the verge of sliding as it rounds a level curve of $30.5 \mathrm{~m}$ radius?

Averell Hause

Carnegie Mellon University

Problem 43

What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is $29 \mathrm{~km} / \mathrm{h}$ and the $\mu_{s}$ between tires and track is $0.32 ?$

Averell Hause

Carnegie Mellon University

Problem 44

During an Olympic bobsled run, the Jamaican team makes a turn of radius $7.6 \mathrm{~m}$ at a speed of $96.6 \mathrm{~km} / \mathrm{h}$. What is their acceleration in terms of $g$ ?

Averell Hause

Carnegie Mellon University

Problem 45

$\underline{\text { S student of weight }} 667 \mathrm{~N}$ rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force $\vec{F}_{N}$ on the student from the seat is $556 \mathrm{~N}$. (a) Does the student feel "light" or "heavy" there? (b) What is the magnitude of $\vec{F}_{N}$ at the lowest point? If the wheel's speed is doubled, what is the magnitude $F_{N}$ at the (c) highest and (d) lowest point?

Averell Hause

Carnegie Mellon University

Problem 46

A police officer in hot pursuit drives her car through a circular turn of radius $300 \mathrm{~m}$ with a constant speed of $80.0 \mathrm{~km} / \mathrm{h}$. Her mass is $55.0 \mathrm{~kg}$. What are (a) the magnitude and (b) the angle (relative to vertical) of the net force of the officer on the car seat? (Hint: Consider both horizontal and vertical forces.)

Averell Hause

Carnegie Mellon University

Problem 47

$.\Rightarrow F$ A circular-motion addict of mass $80 \mathrm{~kg}$ rides a Ferris wheel around in a vertical circle of radius $10 \mathrm{~m}$ at a constant speed of $6.1 \mathrm{~m} / \mathrm{s}$. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point?

Keshav Singh

Numerade Educator

Problem 48

$\infty \Rightarrow \sqrt{\text { A roller-coaster car at an amusement park has a mass }}$ of $1200 \mathrm{~kg}$ when fully loaded with passengers. As the car passes over the top of a circular hill of radius $18 \mathrm{~m}$, assume that its speed is not changing. At the top of the hill, what are the (a) magnitude $F_{N}$ and (b) direction (up or down) of the normal force on the car from the track if the car's speed is $v=11 \mathrm{~m} / \mathrm{s} ?$ What are (c) $F_{N}$ and
(d) the direction if $v=14 \mathrm{~m} / \mathrm{s}$ ?

Keshav Singh

Numerade Educator

Problem 49

ao In Fig. $6-39$, a car is driven at constant speed over a circular hill and then into a circular valley with the same radius. At the top of the hill, the normal force on the driver from the car seat is $0 .$ The driver's mass is $70.0 \mathrm{~kg} .$ What is the magnitude of the normal force on the driver from the seat when the car passes through the bottom of the valley?

Keshav Singh

Numerade Educator

Problem 50

An $85.0 \mathrm{~kg}$ passenger is made to move along a circular path of radius $r=3.50 \mathrm{~m}$ in uniform circular motion. (a) Figure $6-40 a$ is a plot of the required magnitude $F$ of the net centripetal force for a range of possible values of the passenger's speed $v$. What is the plot's slope at $v=8.30 \mathrm{~m} / \mathrm{s} ?$ (b) Figure $6-40 b$ is a plot of $F$ for a range of possible values of $T$, the period of the motion. What is the plot's slope at $T=2.50 \mathrm{~s}$ ?

Keshav Singh

Numerade Educator

Problem 51

An airplane is flying in a horizontal circle at a speed of $480 \mathrm{~km} / \mathrm{h}$ (Fig. 6-41). If its wings are tilted at angle $\theta=40^{\circ}$ to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface.

Averell Hause

Carnegie Mellon University

Problem 52

AE An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weigh $\mathrm{kN}$, and the circle's radius is $10 \mathrm{~m}$. At are the (a) magnitude $F_{B}$ and (b) d the force on the car from the boom if the What are (c) $F_{B}$ and (d) the direction if

Keshav Singh

Numerade Educator

Problem 53

An old streetcar rounds a flat corner of radius $9.1 \mathrm{~m}$, at $16 \mathrm{~km} / \mathrm{h}$. What angle with the vertical will be made by the loosely hanging hand straps?

Averell Hause

Carnegie Mellon University

Problem 54

As In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass $m$ riding around a horizontal circle of radius $r$ at speed $v$. What is the variation $d F$ in the net force magnitude for
(a) a variation $d r$ in the radius with $v$ held constant, (b) a variation

Keshav Singh

Numerade Educator

Problem 55

A bolt is threaded onto one end of a thin horizontal rod, and the rod is then rotated horizontally about its other end. An engineer monitors the motion by flashing a strobe lamp onto the rod and bolt, adjusting the strobe rate until the bolt appears to be in the same eight places during each full rotation of the rod (Fig. $6-42$ ). The strobe rate ond; the bolt has mass $30 \mathrm{~g}$ and is at rac magnitude of the force on the bolt from $\mathrm{t}$

Keshav Singh

Numerade Educator

Problem 56

ao A banked circular highway curve is designed for traffic moving at $60 \mathrm{~km} / \mathrm{h}$. The radius of the curve is $200 \mathrm{~m}$. Traffic is moving along the highway at $40 \mathrm{~km} / \mathrm{h}$ on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

Keshav Singh

Numerade Educator

Problem 57

co A puck of mass $m=1.50 \mathrm{~kg}$ slides in a circle of radius $r=20.0 \mathrm{~cm}$ on a frictionless table while attached to a hanging cylinder of mass $M=2.50 \mathrm{~kg}$ by means of a cord that extends through a hole in the table (Fig. 6-43). What speed keeps the cylinder at rest?

Keshav Singh

Numerade Educator

Problem 58

$. \Rightarrow \sqrt{\text { Brake or turn? Figure } 6}$ 44 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is $d=107 \mathrm{~m}$, and take the car's mass as $m=1400 \mathrm{~kg}$, its initial speed as $v_{0}=35 \mathrm{~m} / \mathrm{s}$, and the coefficient of static friction as $\mu_{s}=0.50$. Assume that the car's weight is disFigure $6-44$
tributed evenly on the four wheels,

Problem 58 .
even during braking. (a) What magnitude of static friction is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum possible static friction $f_{s, \max } ?(\mathrm{c})$ If the coefficient of kinetic friction between the (sliding) tires and the road is $\mu_{k}=0.40$, at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to keep the car in a circular path of radius $d$ and at the given speed $v_{0}$, so that the car moves in a quarter circle and then parallel to the wall? (e) Is the required force less than $f_{s, \max }$ so that a circular path is possible?

Keshav Singh

Numerade Educator

Problem 59

In Fig. 6-45, a $1.34 \mathrm{~kg}$ ball is connected by means of two massless strings, each of length $L=1.70 \mathrm{~m}$, to a vertical, rotating rod. The strings are tied to the rod with separation $d=1.70 \mathrm{~m}$ and are taut. The tension in the upper string is $35 \mathrm{~N}$. What are the (a) tension in the lower string, (b) magnitude of the net force $\vec{F}_{\text {net }}$ on the ball, and (c) speed of the ball? (d) What is the direction of $\vec{F}_{\text {net }} ?$

Keshav Singh

Numerade Educator

Problem 60

In Fig. $6-46$, a box of ant aunts (total Problem $59 .$ mass $m_{1}=1.65 \mathrm{~kg}$ ) and a box of ant uncles (total mass $m_{2}=3.30 \mathrm{~kg}$ ) slide down an inclined plane while attached by a massless rod parallel to the plane. The angle of incline is $\theta=30.0^{\circ} .$ The coefficient of kinetic friction between the aunt box and the incline is $\mu_{1}=0.226$; that between the uncle box and the incline is $\mu_{2}=0.113 .$ Compute (a) the tension in the rod and (h) the magnitude of the common acceleration of the two boxes. (c) How would the answers to (a) and (b) change if the uncles trailed the aunts?

Keshav Singh

Numerade Educator

Problem 61

A block of mass $m_{t}=4.0 \mathrm{~kg}$ is put on top of a block of mass $m_{b}=5.0 \mathrm{~kg}$. To cause the top block to slip on the bottom one while the bottom one is held fixed, a horizontal force of at least 12 N must be applied to the top block. The assembly of blocks is now placed on a horizontal, frictionless table (Fig. $6-47$ ). Find the magnitudes of (a) the maximum horizontal force $\vec{F}$ that can be applied to the lower block so that the blocks will move together and (b) the resulting acceleration of the blocks.

Averell Hause

Carnegie Mellon University

Problem 62

A $5.00 \mathrm{~kg}$ stone is rubbed across the horizontal ceiling of a cave passageway (Fig. $6-48$ ). If the coefficient of kinetic friction is $0.65$ and the force applied to the stone is angled at $\theta=70.0^{\circ}$, what must the magnitude of the force be for the stone to move at constant velocity?

Averell Hause

Carnegie Mellon University

Problem 63

$ \Rightarrow F$ In Fig. 6-49, a $49 \mathrm{~kg}$ rock climber is climbing a "chimney." The coefficient of static friction between her shoes and the rock is $1.2$; between her back and the rock is $0.80$. She has reduced her push against the rock until her back and her shoes are on the verge of slipping. (a) Draw a free-body diagram of her. (b) What is the magnitude of her push against the rock? (c) What fraction of her weight is supported by the frictional force on her shoes?

Keshav Singh

Numerade Educator

Problem 64

A high-speed railway car goes around a flat, horizontal circle of radius $470 \mathrm{~m}$ at a constant speed. The magnitudes of the horizontal and vertical components of the force of the car on a $51.0 \mathrm{~kg}$ passenger are $210 \mathrm{~N}$ and $500 \mathrm{~N}$, respectively. (a) What is the magnitude of the net force (of all the forces) on the passenger? (b) What is the speed of the car?

Averell Hause

Carnegie Mellon University

Problem 65

$=4=$ Continuation of Problems 8 and 37. Another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped in place in the ice. Then, as air flows across the ice during a wind, the air-drag forces on the ice and stones move them both, with the stones gouging out the trails. The magnitude of the air-drag force on this horizontal "ice sail" is given by $D_{\text {ice }}=4 C_{\text {ice }} \rho A_{\text {ice }} v^{2}$, where $C_{\text {ice }}$ is the drag coefficient $\left(2.0 \times 10^{-3}\right), \rho$ is the air density $\left(1.21 \mathrm{~kg} / \mathrm{m}^{3}\right), A_{\text {ice }}$ is the horizontal area of the ice, and $v$ is the wind speed along the ice.

Assume the following: The ice sheet measures $400 \mathrm{~m}$ by $500 \mathrm{~m}$ by $4.0 \mathrm{~mm}$ and has a coefficient of kinetic friction of $0.10$ with the ground and a density of $917 \mathrm{~kg} / \mathrm{m}^{3} .$ Also assume that 100 stones identical to the one in Problem 8 are trapped in the ice. To maintain the motion of the sheet, what are the required wind speeds (a) near the sheet and (b) at a height of $10 \mathrm{~m} ?$ (c) Are these reasonable values for high-speed winds in a storm?

Paul A.

California State Polytechnic University, Pomona

Problem 66

In Fig. 6-50, block 1 of mass $m_{1}=2.0 \mathrm{~kg}$ and block 2 of mass $m_{2}=3.0 \mathrm{~kg}$ are connected by a string of negligible mass and are initially held in place. Block 2 is on a frictionless surface tilted at $\theta=30^{\circ}$. The coefficient of kinetic friction between block 1 and the horizontal surface is $0.25$. The pulley has negligible mass and friction. Once they are released, the blocks move. What then is the tension in the string?

Averell Hause

Carnegie Mellon University

Problem 67

In Fig. 6-51, a crate slides down an inclined right-angled trough. The coefficient of kinetic friction between the crate and the trough is $\mu_{k} .$ What is the acceleration of the crate in terms of $\mu_{k}, \theta$, and $g$ ?

Averell Hause

Carnegie Mellon University

Problem 68

Engineering a highway curve. If a car goes through a curve too fast, the car tends to slide out of the curve. For a banked curve with friction, a frictional force acts on a fast car to oppose the tendency to slide out of the curve; the force is directed down the bank (in the direction water would drain). Consider a circular curve of radius $R=200 \mathrm{~m}$ and bank angle $\theta$, where the coefficient of static friction between tires and pavement is $\mu_{s} .$ A car (without negative lift) is driven around the curve as shown in Fig. 6-11. (a) Find an expression for the car speed $v_{\max }$ that puts the car on the verge of sliding out. (b) On the same graph, plot $v_{\max }$ versus angle $\theta$ for the range $0^{\circ}$ to $50^{\circ}$, first for $\mu_{s}=0.60$ (dry pavement) and then for $\mu_{s}=0.050$ (wet or icy pavement). In kilometers per hour, evaluate $v_{\max }$ for a bank angle of $\theta=10^{\circ}$ and for (c) $\mu_{s}=0.60$ and (d) $\mu_{s}=$ $0.050 .$ (Now you can see why accidents occur in highway curves when icy conditions are not obvious to drivers, who tend to drive at normal speeds.)

Averell Hause

Carnegie Mellon University

Problem 69

A student, crazed by final exams, uses a force $\vec{P}$ of magnitude $80 \mathrm{~N}$ and angle $\theta=70^{\circ}$ to push a $5.0 \mathrm{~kg}$ block across the ceiling of his room (Fig. $6-52$ ). If the coefficient of kinetic friction between the block and the ceiling is $0.40$, what is the magnitude of the block's acceleration?

Averell Hause

Carnegie Mellon University

Problem 70

Figure $6-53$ shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of $0.040 \mathrm{~kg}$, the string has length $L=0.90 \mathrm{~m}$ and negligible mass, and the bob follows a circular path of circumference $0.94 \mathrm{~m}$. What are (a) the tension in the string and (b) the period of the motion?

Averell Hause

Carnegie Mellon University

Problem 71

An $8.00 \mathrm{~kg}$ block of steel is at rest on a horizontal table. The coefficient of static friction between
the block and the table is $0.450 .$ A force is to be applied to the block.

Keshav Singh

Numerade Educator

Problem 72

A box of canned goods slides down a ramp from street level into the basement of a grocery store with acceleration $0.75 \mathrm{~m} / \mathrm{s}^{2}$ directed down the ramp. The ramp makes an angle of $40^{\circ}$ with the horizontal. What is the coefficient of kinetic friction between the box and the ramp?

Averell Hause

Carnegie Mellon University

Problem 73

In Fig. 6-54, the coefficient of kinetic friction between the block and inclined plane is $0.20$, and angle $\theta$ is $60^{\circ} .$ What are the (a) magnitude $a$ and
(b) direction (up or down the plane) of the block's acceleration if the block is sliding down the plane? What are (c) $a$ and (d) the direction if the block is sent sliding up the plane?

Averell Hause

Carnegie Mellon University

Problem 74

A $110 \mathrm{~g}$ hockey puck sent sliding over ice is stopped in $15 \mathrm{~m}$ by the frictional force on it from the ice. (a) If its initial speed is $6.0 \mathrm{~m} / \mathrm{s}$, what is the magnitude of the frictional force? (b) What is the coefficient of friction between the puck and the ice?

Averell Hause

Carnegie Mellon University

Problem 75

A locomotive accelerates a 25 -car train along a level track. Every car has a mass of $5.0 \times 10^{4} \mathrm{~kg}$ and is subject to a frictional force $f=250 v$, where the speed $v$ is in meters per second and the force $f$ is in newtons. At the instant when the speed of the train is $30 \mathrm{~km} / \mathrm{h}$, the magnitude of its acceleration is $0.20 \mathrm{~m} / \mathrm{s}^{2}$. (a) What is the tension in the coupling between the first car and the locomotive? (b) If this tension is equal to the maximum force the locomotive can exert on the train, what is the steepest grade up which the locomotive can pull the train at $30 \mathrm{~km} / \mathrm{h}$ ?

Averell Hause

Carnegie Mellon University

Problem 76

A house is built on the top of a hill with a nearby slope at angle $\theta=45^{\circ}$ (Fig. 6-55). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the coefficient of static friction between two such layers is $0.5$, what is the least angle $\phi$ through which the present slope should be reduced to prevent slippage?

Averell Hause

Carnegie Mellon University

Problem 77

What is the terminal speed of a $6.00 \mathrm{~kg}$ spherical ball that has a radius of $3.00 \mathrm{~cm}$ and a drag coefficient of $1.60 ?$ The density of the air through which the ball falls is $1.20 \mathrm{~kg} / \mathrm{m}^{3}$.

Averell Hause

Carnegie Mellon University

Problem 78

A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches $30^{\circ}$, the box starts to slip, and it then slides $2.5 \mathrm{~m}$ down the plank in $4.0 \mathrm{~s}$ at constant acceleration. What are (a) the coefficient of static friction and (b) the coefficient of kinetic friction between the box and the plank?

Averell Hause

Carnegie Mellon University

Problem 79

Block $A$ in Fig. 6-56 has mass $m_{A}=4.0 \mathrm{~kg}$, and block $B$ has mass $m_{B}=2.0 \mathrm{~kg}$. The coefficient of kinetic friction between block $B$ and the horizontal plane is $\mu_{k}=0.50$. The inclined plane is frictionless and at angle $\theta=30^{\circ} .$ The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks.

Keshav Singh

Numerade Educator

Problem 80

Calculate the magnitude of the drag force on a missile $53 \mathrm{~cm}$ in diameter cruising at $250 \mathrm{~m} / \mathrm{s}$ at low altitude, where the density of air is $1.2 \mathrm{~kg} / \mathrm{m}^{3}$. Assume $C=0.75$.

Averell Hause

Carnegie Mellon University

Problem 81

A bicyclist travels in a circle of radius $25.0 \mathrm{~m}$ at a constant speed of $9.00 \mathrm{~m} / \mathrm{s}$. The bicycle-rider mass is $85.0 \mathrm{~kg} .$ Calculate the magnitudes of (a) the force of friction on the bicycle from the road and (b) the net force on the bicycle from the road.

Averell Hause

Carnegie Mellon University

Problem 82

In Fig. $6-57$, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius $R=250 \mathrm{~m}$. What is Figure 6-57 Problem 82. the greatest speed at which he can drive without the car leaving the road at the top of the hill?

Keshav Singh

Numerade Educator

Problem 83

You must push a crate across a floor to a docking bay. The crate weighs $165 \mathrm{~N}$. The coefficient of static friction between crate and floor is $0.510$, and the coefficient of kinetic friction is $0.32$. Your force on the crate is directed horizontally. (a) What magnitude of your push puts the crate on the verge of sliding? (b) With what magnitude must you then push to keep the crate moving at a constant velocity? (c) If, instead, you then push with the same magnitude as the answer to (a), what is the magnitude of the crate's acceleration?

Averell Hause

Carnegie Mellon University

Problem 84

In Fig. $6-58$, force $F$ is applied to a crate of mass $m$ on a floor where the coefficient of static friction between crate and floor is $\mu_{s}$. Angle $\theta$ is initially $0^{\circ}$ but is gradu- $\quad$ Figure 6-58 Problem 84 . ally increased so that the force vector rotates clockwise in the figure. During the rotation, the magnitude $F$ of the force is continuously adjusted so that the crate is always on the verge of sliding. For $\mu_{s}=0.70$, (a) plot the ratio $F / m g$ versus $\theta$ and (b) determine the angle $\theta_{\text {inf }}$ at which the ratio approaches an infinite value. (c) Does lubricating the floor increase or decrease $\theta_{\text {inf }}$, or is the value unchanged? (d) What is $\theta_{\text {inf }}$ for $\mu_{s}=0.60 ?$

Paul A.

California State Polytechnic University, Pomona

Problem 85

In the early afternoon, a car is parked on a street that runs down a steep hill, at an angle of $35.0^{\circ}$ relative to the horizontal. Just then the coefficient of static friction between the tires and the street surface is $0.725 .$ Later, after nightfall, a sleet storm hits the area, and the coefficient decreases due to both the ice and a chemi-

Keshav Singh

Numerade Educator

Problem 86

$ \Rightarrow \sqrt{2}$ A sling-thrower puts a stone $(0.250 \mathrm{~kg})$ in the sling's pouch $(0.010 \mathrm{~kg})$ and then begins to make the stone and pouch move in a vertical circle of radius $0.650 \mathrm{~m}$. The cord between the pouch and the person's hand has negligible mass and will break when the tension in the cord is $33.0 \mathrm{~N}$ or more. Suppose the slingthrower could gradually increase the speed of the stone. (a) Will the breaking occur at the lowest point of the circle or at the highest point? (b) At what speed of the stone will that breaking occur?

Keshav Singh

Numerade Educator

Problem 87

ssM A car weighing $10.7 \mathrm{kN}$ and traveling at $13.4 \mathrm{~m} / \mathrm{s}$ without negative lift attempts to round an unbanked curve with a radius of $61.0 \mathrm{~m}$. (a) What magnitude of the frictional force on the tires is required to keep the car on its circular path? (b) If the coefficient of static friction between the tires and the road is $0.350$, is the attempt at taking the curve successful?

Keshav Singh

Numerade Educator

Problem 88

In Fig. $6-59$, block 1 of mass $m_{1}=2.0 \mathrm{~kg}$ and block 2 of mass $m_{2}=1.0 \mathrm{~kg}$ are connected by a string of negligible mass. Block 2 is pushed by force $\vec{F}$ of magnitude 20 $\mathrm{N}$ and angle $\theta=35^{\circ} .$ The coefficient of kinetic friction between each block $0.20 .$ What is the tension in the string?

Keshav Singh

Numerade Educator

Problem 89

ssm A filing cabinet weighing $556 \mathrm{~N}$ rests on the floor. The coefficient of static friction between it and the floor is $0.68$, and the coefficient of kinetic friction is $0.56 .$ In four different attempts to move it, it is pushed with horizontal forces of magnitudes (a) $222 \mathrm{~N}$,
(b) $334 \mathrm{~N}$, (c) $445 \mathrm{~N}$, and
(d) $556 \mathrm{~N}$. For each attempt, calculate the magnitude of the frictional force on it from the floor. (The cabinet is initially at rest.) (e) In which of the attempts does the cabinet move?

Keshav Singh

Numerade Educator

Problem 90

In Fig. 6-60, a block weighing $22 \mathrm{~N}$ is held at rest against a vertical wall by a horizontal force $\vec{F}$ of magnitude $60 \mathrm{~N}$. The coefficient of static friction between the wall and the block is $0.55$, and the coefficient of kinetic friction between them is $0.38$. In six experiments, a second force $\vec{P}$ is applied to the block and directed parallel to the wall with these magnitudes and directions: (a) $34 \mathrm{~N}$, up, (b) $12 \mathrm{~N}$, up, (c) $48 \mathrm{~N}$, up, (d) $62 \mathrm{~N}$, up, $(\mathrm{e}) 10 \mathrm{~N}$, down, and $\quad$ Figure $6-60$
(f) $18 \mathrm{~N}$, down. In each experiment, what is the Problem 90 . magnitude of the frictional force on the block? In which does the block move (g) up the wall and (h) down the wall?
(i) In which is the frictional force directed down the wall?

Tanner Manwaring

Tanner Manwaring

Numerade Educator

Problem 91

A block slides with constant velocity down an inclined plane that has slope angle $\theta$. The block is then projected up the same plane with an initial speed $v_{0}$. (a) How far up the plane will it move before coming to rest? (b) After the block comes to rest, will it slide down the plane again? Give an argument to back your answer.

Averell Hause

Carnegie Mellon University

Problem 92

A circular curve of highway is designed for traffic moving at $60 \mathrm{~km} / \mathrm{h}$. Assume the traffic consists of cars without negative lift.
(a) If the radius of the curve is $150 \mathrm{~m}$, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at $60 \mathrm{~km} / \mathrm{h} ?$

Averell Hause

Carnegie Mellon University

Problem 93

A $1.5 \mathrm{~kg}$ box is initially at rest on a horizontal surface when at $t=0$ a horizontal force $\vec{F}=(1.8 t) \hat{\mathrm{i}} \mathrm{N}$ (with $t$ in seconds) is applied to the box. The acceleration of the box as a function of time $t$ is given by $\vec{a}=0$ for $0 \leq t \leq 2.8 \mathrm{~s}$ and $\vec{a}=(1.2 t-2.4) \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}^{2}$ for $t>$
$2.8 \mathrm{~s}$. (a) What is the coefficient of static friction between the box and the surface? (b) What is the coefficient of kinetic friction between the box and the surface?

Averell Hause

Carnegie Mellon University

Problem 94

A child weighing $140 \mathrm{~N}$ sits at rest at the top of a playground slide that makes an angle of $25^{\circ}$ with the horizontal. The child keeps from sliding by holding onto the sides of the slide. After letting go of the sides, the child has a constant acceleration of $0.86 \mathrm{~m} / \mathrm{s}^{2}$ (down the slide, of course). (a) What is the coefficient of kinetic friction between the child and the slide? (b) What maximum and minimum values for the coefficient of static friction between the child and the slide are consistent with the information given here?

Averell Hause

Carnegie Mellon University

Problem 95

In Fig. 6-61 a fastidious worker pushes directly along the handle of a mop with a force $\vec{F}$. The handle is at an angle $\theta$ with the vertical, and $\mu_{s}$ and $\mu_{k}$ are the coefficients of static and kinetic friction between
the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass $m$ is in its head. (a) If the mop head Figure 6-61 Problem 95 . moves along the floor with a constant velocity, then what is $F ?$ (b) Show that if $\theta$ is less than a certain value $\theta_{0}$, then $\vec{F}$ (still directed along the handle) is unable to move the mop head. Find $\theta_{0}$.

Keshav Singh

Numerade Educator

Problem 96

A child places a picnic basket on the outer rim of a merrygo-round that has a radius of $4.6 \mathrm{~m}$ and revolves once every $30 \mathrm{~s}$.
(a) What is the speed of a point on that rim? (b) What is the lowest value of the coefficient of static friction between basket and merry-go-round that allows the basket to stay on the ride?

Keshav Singh

Numerade Educator

Problem 97

A warehouse worker exerts a constant horizontal force of magnitude $85 \mathrm{~N}$ on a $40 \mathrm{~kg}$ box that is initially at rest on the horizontal floor of the warehouse. When the box has moved a distance of $1.4 \mathrm{~m}$, its speed is $1.0 \mathrm{~m} / \mathrm{s}$. What is the coefficient of kinetic friction between the box and the floor?

Averell Hause

Carnegie Mellon University

Problem 98

In Fig. 6-62, a $5.0 \mathrm{~kg}$ block is sent sliding up a plane inclined at $\theta=37^{\circ}$ while a horizontal force $\vec{F}$ of magnitude $50 \mathrm{~N}$ acts on it. The coefficient of kinetic friction between block and plane is $0.30 .$ What are the (a) magnitude and (b) direction (up or down the plane) of the block's acceleration? The block's initial speed is $4.0$ $\mathrm{m} / \mathrm{s}$. (c) How far up the plane does the block go? (d) When it reaches its highest point, does it remain at rest or slide back down the plane?

Averell Hause

Carnegie Mellon University

Problem 99

An $11 \mathrm{~kg}$ block of steel is at rest on a horizontal table. The coefficient of static friction between block and table is $0.52 .$ (a) What is the magnitude of the horizontal force that will put the block on the verge of moving? (b) What is the magnitude of a force acting upward $60^{\circ}$ from the horizontal that will put the block on the verge of moving? (c) If the force acts downward at $60^{\circ}$ from the horizontal, how large can its magnitude be without causing the block to move?

Averell Hause

Carnegie Mellon University

Problem 100

A ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of kinetic friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting layer of water. A magazine reports that a new type of plastic ski is especially water repellent and that, on a gentle $200 \mathrm{~m}$ slope in the Alps, a skier reduced his top-to-bottom time from $61 \mathrm{~s}$ with standard skis to $42 \mathrm{~s}$ with the new skis. Determine the magnitude of his average acceleration with (a) the standard skis and (b) the new skis. Assuming a $3.0^{\circ}$ slope, compute the coefficient of kinetic friction for (c) the standard skis and (d) the new skis.

Keshav Singh

Numerade Educator

Problem 101

A ski that is placed on snow will stick to the snow. However, when the ski is moved along the snow, the rubbing warms and partially melts the snow, reducing the coefficient of kinetic friction and promoting sliding. Waxing the ski makes it water repellent and reduces friction with the resulting layer of water. A magazine reports that a new type of plastic ski is especially water repellent and that, on a gentle $200 \mathrm{~m}$ slope in the Alps, a skier reduced his top-to-bottom time from $61 \mathrm{~s}$ with standard skis to $42 \mathrm{~s}$ with the new skis. Determine the magnitude of his average acceleration with (a) the standard skis and (b) the new skis. Assuming a $3.0^{\circ}$ slope, compute the coefficient of kinetic friction for (c) the standard skis and (d) the new skis.

Keshav Singh

Numerade Educator

Problem 102

A $100 \mathrm{~N}$ force, directed at an angle $\theta$ above a horizontal floor, is applied to a $25.0 \mathrm{~kg}$ chair sitting on the floor. If $\theta=0^{\circ}$, what are (a) the horizontal component $F_{h}$ of the applied force and
(b) the magnitude $F_{N}$ of the normal force of the floor on the chair? If $\theta=30.0^{\circ}$, what are (c) $F_{h}$ and $($ d $) F_{N}$ ? If $\theta=60.0^{\circ}$, what are (e) $F_{h}$ and (f) $F_{N}$ ? Now assume that the coefficient of static friction between chair and floor is $0.420$. Does the chair slide or remain at rest if $\theta$ is $(\mathrm{g}) 0^{\circ},(\mathrm{h}) 30.0^{\circ}$, and (i) $60.0^{\circ} ?$

Averell Hause

Carnegie Mellon University

Problem 103

A certain string can withstand a maximum tension of $40 \mathrm{~N}$ without breaking. A child ties a $0.37 \mathrm{~kg}$ stone to one end and, holding the other end, whirls the stone in a vertical circle of radius $0.91$ $\mathrm{m}$, slowly increasing the speed until the string breaks. (a) Where is the stone on its path when the string breaks? (b) What is the speed of the stone as the string breaks?

Averell Hause

Carnegie Mellon University

Problem 104

$ \Rightarrow F$ A four-person bobsled (total mass $=630 \mathrm{~kg}$ ) comes down a straightaway at the start of a bobsled run.The straightaway is $80.0 \mathrm{~m}$ long and is inclined at a constant angle of $10.2^{\circ}$ with the horizontal. Assume that the combined effects of friction and air drag produce on the bobsled a constant force of $62.0 \mathrm{~N}$ that acts parallel to the incline and up the incline. Answer the following questions to three significant digits. (a) If the speed of the bobsled at the start of the run is $6.20 \mathrm{~m} / \mathrm{s}$, how long does the bobsled take to come down the straightaway? (b) Suppose the crew is able to reduce the effects of friction and air drag to $42.0 \mathrm{~N}$. For the same initial velocity, how long does the bobsled now take to come down the straightaway?

Keshav Singh

Numerade Educator

Problem 105

As a $40 \mathrm{~N}$ block slides down a plane that is inclined at $25^{\circ}$ to the horizontal, its acceleration is $0.80 \mathrm{~m} / \mathrm{s}^{2}$, directed up the plane. What is the coefficient of kinetic friction between the block and the plane?

Averell Hause

Carnegie Mellon University