Physics

Robert Resnick, David Halliday, Kenneth S. Krane

Chapter 5

Applications Of Newton'S Laws - all with Video Answers

Educators

Chapter Questions

Problem 1

A charged sphere of mass $2.8 \times 10^{-4} \mathrm{~kg}$ is suspended from a string. An electric force acts horizontally on the sphere so that the string makes an angle of $33^{\circ}$ with the vertical when at rest. Find $(a)$ the magnitude of the electric force and $(b)$ the tension in the string.

Ravindra Yadav

Ravindra Yadav

Numerade Educator

Problem 2

An elevator weighing $6200 \mathrm{lb}$ is pulled upward by a cable with an acceleration of $3.8 \mathrm{ft} / \mathrm{s}^{2}$. (a) What is the tension in the cable? (b) What is the tension when the elevator is accelerating downward at $3.8 \mathrm{ft} / \mathrm{s}^{2}$ but is still moving upward?

Ravindra Yadav

Numerade Educator

Problem 3

A lamp hangs vertically from a cord in a descending elevator. The elevator has a deceleration of $2.4 \mathrm{~m} / \mathrm{s}^{2}$ before coming to a stop. ( $a$ ) If the tension in the cord is $89 \mathrm{~N}$, what is the mass of the lamp? (b) What is the tension in the cord when the elevator ascends with an upward acceleration of $2.4 \mathrm{~m} / \mathrm{s}^{2}$ ?

Ravindra Yadav

Numerade Educator

Problem 4

An elevator and its load have a combined mass of $1600 \mathrm{~kg}$. Find the tension in the supporting cable when the elevator, originally moving downward at $12.0 \mathrm{~m} / \mathrm{s}$, is brought to rest with constant acceleration in a distance of $42.0 \mathrm{~m}$.

Ravindra Yadav

Numerade Educator

Problem 5

A $110-\mathrm{kg}$ man lowers himself to the ground from a height of $12 \mathrm{~m}$ by holding on to a rope passed over a frictionless pulley and attached to a 74 -kg sandbag. ( $a$ ) With what speed does the man hit the ground? (b) Is there anything he could do to reduce the speed with which he hits the ground?

Ravindra Yadav

Numerade Educator

Problem 6

An $11-\mathrm{kg}$ monkey is climbing a massless rope attached to a $15-\mathrm{kg}$ log over a frictionless tree limb.
(a) With what minimum acceleration must the monkey climb up the rope so that it can raise the $15-\mathrm{kg}$ log off the ground? If, after the $\log$ has been raised off the ground, the monkey stops climbing and hangs on to the rope, what will now be $(b)$ the monkey's acceleration and $(c)$ the tension in the rope?

Ravindra Yadav

Numerade Educator

Problem 7

Figure $5-29$ shows a section of an alpine cable-car system. The maximum permitted mass of each car with occupants is $2800 \mathrm{~kg} .$ The cars, riding on a support cable, are pulled by a second cable attached to each pylon. What is the difference in tension between adjacent sections of pull cable if the cars are accelerated up to $35^{\circ}$ incline at $0.81 \mathrm{~m} / \mathrm{s}^{2}$ ?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 8

The man in Fig. 5-30 weighs $180 \mathrm{lb}$; the platform and attached frictionless pulley weigh a total of $43 \mathrm{lb}$. Ignore the weight of the rope. With what force must the man pull up on the rope in order to lift himself and the platform upward at $1.2 \mathrm{ft} / \mathrm{s}^{2} ?$

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 9

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 10

Suppose that only the rear wheels of an automobile can accelerate it, and that half the total weight of the automobile is supported by those wheels. (a) What is the maximum acceleration attainable if the coefficient of static friction between tires and road is $\mu_{\mathrm{s}} ?(b)$ Take $\mu_{\mathrm{s}}=0.56$ and get a numerical value for this acceleration.

Ravindra Yadav

Numerade Educator

Problem 11

What is the greatest acceleration that can be generated by a runner if the coefficient of static friction between shoes and road is $0.95 ?$

Ravindra Yadav

Numerade Educator

Problem 12

A baseball player (Fig. 5-31) with mass $79 \mathrm{~kg}$, sliding into a base, is slowed by a force of friction of $470 \mathrm{~N}$. What is the coefficient of kinetic friction between the player and the ground?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 13

A horizontal bar is used to support a $75-\mathrm{kg}$ object between two walls, as shown in Fig. 5-32. The equal forces $F$ exerted by the bar against the walls can be varied by adjusting the length of the bar. Only friction between the ends of the bar and the walls supports the system. The coefficient of static friction between bar and walls is $0.41$. Find the minimum value of the forces $F$ for the system to remain at rest.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 14

A 53-lb $(=240-\mathrm{N})$ trunk rests on the floor. The coefficient of static friction between the trunk and the floor is $0.41$, while the coefficient of kinetic friction is $0.32 .(a)$ What is the minimum horizontal force with which a person must push on the trunk to start it moving? (b) Once moving, what horizontal force must the person apply to keep the trunk moving with constant velocity? (c) If, instead, the person continued to push with the force used to start the motion, what would be the acceleration of the trunk?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 15

The coefficient of static friction between the tires of a car and a dry road is $0.62$. The mass of the car is $1500 \mathrm{~kg}$. What maximum braking force is obtainable $(a)$ on a level road and $(b)$ on an $8.6^{\circ}$ downgrade?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 16

A house is built on the top of a hill with a $42^{\circ}$ slope. Subsequent slumping of material on the slope surface indicates that the slope gradient should be reduced. If the coefficient of friction of soil on soil is $0.55$, through what additional angle $\phi$ (see Fig. 5-33) should the slope surface be regraded?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 17

A $136-\mathrm{kg}$ crate is at rest on the floor. A worker attempts to push it across the floor by applying a 412-N force horizontally. (a) Take the coefficient of static friction between the crate and floor to be $0.37$ and show that the crate does not move. (b) A second worker helps by pulling up on the crate. What minimum vertical force must this worker apply so that the crate starts to move across the floor? $(c)$ If the second worker applies a horizontal rather than a vertical force, what minimum force, in addition to the original 412-N force, must be exerted to get the crate started?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 18

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 $28.0^{\circ}$, the box starts to slip and slides $2.53 \mathrm{~m}$ down the plank in $3.92 \mathrm{~s}$. Find the coefficients of friction.

Supratim Pal

Numerade Educator

Problem 19

Frictional heat generated by the moving ski is the chief factor promoting sliding in skiing. The ski sticks at the start, but once in motion will melt the snow beneath it. Waxing the ski makes it water repellent and reduces friction with the film of water. A magazine reports that a new type of plastic ski is even more water repellent and that, on a gentle $203-\mathrm{m}$ slope in the Alps, a skier reduced his time from 61 to $42 \mathrm{~s}$ with the new skis. Assuming a $3.0^{\circ}$ slope, compute the coefficient of kinetic friction for each case.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 20

A block slides down an inclined plane of slope angle $\theta$ with constant velocity. It is then projected up the same plane with an initial speed $v_{0} .(a)$ How far up the incline will it move before coming to rest? $(b)$ Will it slide down again?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 21

A piece of ice slides from rest down a rough $33.0^{\circ}$ incline in twice the time it takes to slide down a frictionless $33.0^{\circ}$ incline of the same length. Find the coefficient of kinetic friction between the ice and the rough incline.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 22

In Fig. 5-34, $A$ is a $4.4-\mathrm{kg}$ block and $B$ is a $2.6$ -kg block. The coefficients of static and kinetic friction between $A$ and the table are $0.18$ and 0.15. (a) Determine the minimum mass of the block $C$ that must be placed on $A$ to keep it from sliding. (b) Block $C$ is suddenly lifted off $A$. What is the acceleration of block $A$ ?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 23

A $4.8$ -kg block on a $39^{\circ}$ inclined plane is acted on by a horizontal force of $46 \mathrm{~N}$ (see Fig. $5-35$ ). The coefficient of kinetic friction between block and plane is $0.33 .$ (a) What is the acceleration of the block if it is moving up the plane? $(b)$ With the horizontal force still acting, how far up the plane will the block go if it has an initial upward speed of $4.3 \mathrm{~m} / \mathrm{s}$ ? (c) What happens to the block after it reaches the highest point?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 24

A 12 -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 just start the block moving? ( $b$ ) What is the magnitude of a force acting upward $62^{\circ}$ from the horizontal that will just start the block moving? $(c)$ If the force acts down at $62^{\circ}$ from the horizontal, how large can it be without causing the block to move?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 25

A worker drags a 150 -lb crate across a floor by pulling on a rope inclined $17^{\circ}$ above the horizontal. The coefficient of static friction is $0.52$ and the coefficient of kinetic friction is 0.35. (a) What tension in the rope is required to start the crate moving? (b) What is the initial acceleration of the crate?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 26

A wire will break under tensions exceeding $1.22 \mathrm{kN}$. If the wire, not necessarily horizontal, is used to drag a box across the floor, what is the greatest weight that can be moved if the coefficient of static friction is $0.35 ?$

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 27

Block $B$ in Fig. 5-36 weighs $712 \mathrm{~N}$. The coefficient of static friction between block $B$ and the table is $0.25$. Find the maximum weight of block $A$ for which block $B$ will remain at rest.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 28

Block $m_{1}$ in Fig. 5-37 has a mass of $4.20 \mathrm{~kg}$ and block $m_{2}$ has a mass of $2.30 \mathrm{~kg}$. The coefficient of kinetic friction between $m_{2}$ and the horizontal plane is $0.47$. The inclined plane is frictionless. Find $(a)$ the acceleration of the blocks and $(b)$ the tension in the string.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 29

In Fig. 5-38, object $B$ weighs $94.0 \mathrm{lb}$ and object $A$ weighs $29.0 \mathrm{lb} .$ Between object $B$ and the plane the coefficient of static friction is $0.56$ and the coefficient of kinetic friction is 0.25. (a) Find the acceleration of the system if $B$ is initially at rest. (b) Find the acceleration if $B$ is moving up the plane. ( $c$ ) What is the acceleration if $B$ is moving down the plane? The plane is inclined by $42.0^{\circ}$.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 30

A crate slides down an inclined right-angled trough as in Fig. 5-39. The coefficient of kinetic friction between the crate and the material composing the trough is $\mu_{\mathrm{k}} .$ Find the acceleration of the crate.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 31

A 42 -kg slab rests on a frictionless floor. A $9.7-\mathrm{kg}$ block rests on top of the slab, as in Fig. 5-40. The coefficient of static friction between the block and the slab is $0.53$, while the coefficient of kinetic friction is $0.38$. The $9.7-\mathrm{kg}$ block is acted on by a horizontal force of $110 \mathrm{~N}$. What are the resulting accelerations of $(a)$ the block and $(b)$ the slab?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 32

During an Olympic bobsled run, a European team takes a turn of radius $25 \mathrm{ft}$ at a speed of $60 \mathrm{mi} / \mathrm{h}$. What acceleration do the riders experience $(a)$ in $\mathrm{ft} / \mathrm{s}^{2}$ and $(b)$ in units of $g$ ?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 33

A $2400-\mathrm{lb}(=10.7-\mathrm{kN})$ car traveling at $30 \mathrm{mi} / \mathrm{h}(=13.4 \mathrm{~m} / \mathrm{s})$
attempts to round an unbanked curve with a radius of $200 \mathrm{ft}$ $(=61.0 \mathrm{~m}) .(a)$ What force of friction is required to keep the car on its circular path? ( $b$ ) What minimum coefficient of static friction between the tires and road is required?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 34

A circular curve of highway is designed for traffic moving at $60 \mathrm{~km} / \mathrm{h}(=37 \mathrm{mi} / \mathrm{h}) .(a)$ If the radius of the curve is $150 \mathrm{~m}$
$(=490 \mathrm{ft})$, 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 at this speed?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 35

A conical pendulum is formed by attaching a $53-\mathrm{g}$ pebble to a $1.4$ -m string. The pebble swings around in a circle of radius $25 \mathrm{~cm} .(a)$ What is the speed of the pebble? $(b)$ What is its acceleration? ( $c$ ) What is the tension in the string?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 36

A bicyclist (Fig. 5-41) travels in a circle of radius $25 \mathrm{~m}$ at a constant speed of $8.7 \mathrm{~m} / \mathrm{s}$. The combined mass of the bicycle and rider is $85 \mathrm{~kg}$. Calculate the force - magnitude and angle with the vertical- exerted by the road on the bicycle.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 37

In the Bohr model of the hydrogen atom, the electron revolves in a circular orbit around the nucleus. If the radius is $5.3 \times 10^{-11} \mathrm{~m}$ and the electron makes $6.6 \times 10^{15} \mathrm{rev} / \mathrm{s}$, find
(a) the speed of the electron, $(b)$ the acceleration of the electron, and $(c)$ the force acting on the electron. (This force is the result of the attraction between the positively charged nucleus and the negatively charged electron.)

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 38

A child places a picnic basket on the outer rim of a merry-goround that has a radius of $4.6 \mathrm{~m}$ and revolves once every $24 \mathrm{~s}$. How large must the coefficient of static friction be for the basket to stay on the merry-go-round?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 39

A disk of mass $m$ on a frictionless table is attached to a hanging cylinder of mass $M$ by a cord through a hole in the table (see Fig. 5-42). Find the speed with which the disk must move in a circle of radius $r$ for the cylinder to stay at rest.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 40

A driver's manual states that a driver traveling at $48 \mathrm{~km} / \mathrm{h}$ and desiring to stop as quickly as possible travels $10 \mathrm{~m}$ before the foot reaches the brake. The car travels an additional $21 \mathrm{~m}$ before coming to rest. (a) What coefficient of friction is assumed in these calculations? (b) What is the minimum radius Ifor turning a corner at $48 \mathrm{~km} / \mathrm{h}$ without skidding?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 41

A banked circular highway curve is designed for traffic moving at $95 \mathrm{~km} / \mathrm{h}$. The radius of the curve is $210 \mathrm{~m}$. Traffic is moving along the highway at $52 \mathrm{~km} / \mathrm{h}$ on a stormy day. ( $a$ ) What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding? $(b)$ With this value of the coefficient of friction, what is the greatest speed at which the curve can be negotiated without sliding?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 42

A 150 -lb student on a steadily rotating Ferris wheel is sitting on a scale that reads $125 \mathrm{lb}$ at the highest point. $(a)$ What is the scale reading at the lowest point? $(b)$ What would be the scale reading at the highest point if the speed of the Ferris wheel were doubled?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 43

A small object is placed $13.0 \mathrm{~cm}$ from the center of a phonograph turntable. It is observed to remain on the table when it rotates at $33 \frac{1}{3}$ rev/min but slides off when it rotates at $45.0$ rev/min. Between what limits must the coefficient of static friction between the object and the surface of the turntable lie?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 44

An airplane is flying in a horizontal circle at a speed of $482 \mathrm{~km} / \mathrm{h}$. The wings of the plane are tilted at $38.2^{\circ}$ to the horizontal; see Fig. 5-43. Find the radius of the circle in which the plane is flying. Assume that the centripetal force is provided entirely by the lift force perpendicular to the wing surface.

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 45

A frigate bird is soaring in a horizontal circular path. Its bank angle is estimated to be $25^{\circ}$ and it takes $13 \mathrm{~s}$ for the bird to complete one circle. ( $a$ ) How fast is the bird flying? ( $b$ ) What is the radius of the circle? (See "The Amateur Scientist" by Jearl Walker, Scientific American, March 1985, p. $122 .$.)

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 46

A model airplane of mass $0.75 \mathrm{~kg}$ is flying at constant speed in a horizontal circle at one end of a 33 -m cord and at a height of $18 \mathrm{~m}$. The other end of the cord is tethered to the ground. The airplane makes $4.4$ rev/min and the lift is perpendicular to the unbanked wings. (a) What is the acceleration of the plane? (b) What is the tension in the cord? ( $c$ ) What is the lift produced by the plane's wings?

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 47

Assume that the standard kilogram would weigh exactly $9.80 \mathrm{~N}$ at sea level on the equator if the Earth did not rotate. Then take into account the fact that the Earth does rotate, so that this object moves in a circle of radius $6370 \mathrm{~km}$ (the Earth's radius) in one day. (a) Determine the centripetal force needed to keep the standard kilogram moving in its circular path. ( $b$ ) Find the force exerted by the standard kilogram on a spring balance from which it is suspended at the equator (its apparent weight).

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 48

The position of a particle of mass $2.17$ kg traveling in a straight line is given by
$$
x=\left(0.179 \mathrm{~m} / \mathrm{s}^{4}\right) t^{4}-\left(2.08 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}+17.1 \mathrm{~m}
$$
Find the $(a)$ velocity, $(b)$ acceleration, and $(c)$ force on the particle at time $t=7.18 \mathrm{~s}$

Ashwin Banarsee

Ashwin Banarsee

Numerade Educator

Problem 49

A particle of mass $m$ is subjected to a net force $\mathbf{F}(t)$ given by $\overrightarrow{\mathbf{F}}(t)=F_{0}(1-t / T) \hat{\mathbf{i}}$; that is, $F(t)$ equals $F_{0}$ at $t=0$ and decreases linearly to zero in time $T .$ The particle passes the ori$\operatorname{gin} x=0$ with velocity $v_{0} \hat{\mathbf{i}}$. Show that at the instant $t=T$ that $F(t)$ vanishes, the speed $v$ and distance $x$ traveled are given by $v(T)=v_{0}+a_{0} T / 2, \quad$ and $x(T)=v_{0} T+a_{0} T^{2} / 3$,
where $a_{0}=F_{0} / m$ is the initial acceleration. Compare these results with Eqs. $2-26$ and $2-28$.

Devi Dutta Biswajeet

Devi Dutta Biswajeet

Numerade Educator