Why does a child in a wagon seem to fall backward whew fflga/tlv8:au n,4; n you give the wagon a sharp pull4fv/,w8gt aau:l n;lf forward?

A box rests on the (frictionless) bed of a truck. The truck driver startsdrni-lo:t (c3b6fm 5q q2k, ujkdeja) ch(;9s the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (bdd kqb)o (ki; 2qel,um tjs:9ccrn-j (fh653a) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on kjq)o(c v-v t2ty.mk, it? Explain.

Only one force acts on an object. Can thk;pas7 /dgmo4e /,axbsg )5tpe object have zero acceleration? Can it hav5x,74sopgaka )bmd s; /epgt/e zero velocity? Explain.

When a golf ball is dropped to the pavement, it 6 yofhznop4)n)x0;j mb ;z:lr bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, yx n6;zjr;mn)zo:l o phfb)04 what exerts the force?

If you walk along a log floating on a lake, why d9gdrh/8)nzc; jilnf ;g3; bkvoes the log move in the opposite direction?b ;3d8;ngrcfnk)ivj/l9h zg ;

Why might your foot hurt if you /6ifv) u iohuwxx *l,1kick a heavy desk or a wall?

  When you are runningk8i *n1wlqk ck ja:jz; ;wij5e -eu(t9 and want to stop quickly, you must decelerate quickly. (a) What is the ow jkeqkkc-l8nwtz1i(u*5i9; aj :;jerigin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ki++czrngtq3 6 r.ui(ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to r.6 kqg i+zu+i3 nc(rtbreak: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as thneo+1zxg2qss/ r+ o7nat on a 1-kg rock. Why then doesn’t /n1g7 os+e+z2 sonrqx the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the s l :yk/gsq+y/ncale had been calibrated (a) in pounds, or (b) /gnyy :s +/klqin kilograms?

You pull a box with a constant force acrj s;df(0yegm8 oss a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Ex0jg8es;dm y( fplain.

When an object falls freely under tw(ow:q- q6s xcp -1x9tie8fylhe influence of gravity there is a net force mgq-tsxw x:fc iq-16(w8 y9 elpo exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are ovm:ow, h)e 0trn the Moon with the force needed to lift it on Earth. Compare the force needed :t,o)rhme0 wvto throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’o+ 7zsdh*di i8owg4,fs third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win8dgii*+ow7f dzs o4,h?

A person exerts an upward force of 40 N to hold a bag of groceries. Defx/; *zhou5kdw 1+zg0dt6s px scribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (5ux*w f6g/t khz0;1 z oxsdp+dd) by what object it is exerted.

When you stand still on the ground, how large a force does the9 ;2eio3nlv3hzin/d5:z xoyf0u wx1x ground exert on you? Why doesn’t this force make you rise 5o1h/xi33n y:xn udxle90;2fi o zvz wup into the air?

Whiplash sometimes resul vawpk2:jd+m:t5g v ;dt 1v;c7yhnnq9 ts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situatio:d 1qtv5 cv;ynpaj+dh9 nv2kwt:g;m7n. Is it really?

A heavy crate rests on the bed of a flatbed trucc q.jntv 8hxieh12 1du0 *dm0tk. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accexm t*jt nde1 qh.h u0c120id8vlerate?

A block is given a push so that it sl :,lfp qe7fq a-;cn+jhides up a ramp. After the block reaches its highe;f,+qe hq7pc- jfn: alst point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read a)m6z,8qfsqjd6xj r5if you weighed yourself on an inclined plane? Assume the mechan ,z)6aqq6jxdrs8j fm5ism functions properly, even at an angle.

  What force is needed to accelerate a child onvez c 8yo8cwjaqd7d, a.qj i,0 zl2g53 a sled at 1.25m/s$^2$?   

  A net force of 265 N accelera rd6m:k3yl xbiou4*rl: cb ry1j 006dwtes a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used l8e1aa7 nm73qe c *boqw+xpo3to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a cs 3-,tc:8qnuq2dz ls$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to sto e*3(vkqm 9 xakvnc2l5p an 1100-kg car in 8.0 s if the car is traveling at 95 a vkec3vkmxln 9(q*25km/h? -  

  What average force is needed to accelerate a 7.00-gr9rm h8 7pkvimg: 6zuv wmp*+h8am pellet from rest to 125m/s o8v m:u87hhr*impkpz6 m9w+ gv ver a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water w984.r*ofj g pkjl0tj yith an acceleration of 2.tlkj9.8y0 4 *jfp grjo5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ 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? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (4v,(9 a;ltbiz) hox7 jins/ f3ig bb7q/02 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ 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?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratt51e-addcfy8/ r .kuwxqgw efx.7 1c7ion is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max faw71 cxe.8krcu/ wg.1ydfet-dx7q5=    min =   

A 75$-\mathrm{kg}$ 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.

  A person stands on a 5d m2qu b/v-i/ gecz:gbathroom scale in a motionless elevator. When the elevator begins to move-g/ 2vzqei:d/mbc5 gu, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg6u/dg:fzewcjh gg* o(r 9,ur2 elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it giveg9,ugw2 cz6rhdfjreg:/u* o ( the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 h ; *uzf5nfnkzk )rq)/o9b2, taeglw7kg including parachute) when the upward force of air rektfu a /2ln ,h5 brg )f9q;zw)e7nk*ozsistance is equal to one-fourth of their weight?   
(b) After popping open 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. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ) +ymz ra+cvpff60ac: ground below, he bends his knees so :vcm+ f6aar+z0 y) pfcthat 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.   

  A box weighing 77.0 N rests on a table. A rope tied ;u)luyyhap8+to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pul 8uaup) ;yyhl+ley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a bas2pbgm s( hd-gxq 0pac 8+;hrf;i8sh-tketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit)zp zg8dnm s0) by the bat, and agaz)s8nzg md 0p)in (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A s3.5tr58zr t+utwhzb vecond 650-N force must be exerted in what direction so that the resultant of the tw5zz w 3ttutb .rvr5+h8o forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally bejm 0 ) ey yqzwj o3g.(u7tlz,zcj/*py4tween two buildings 10.0 m apart. The sag in the rj q/g3jyj4m(uy ,cyoz0p7)*.ztz w leope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord from anothe ls+p(*gh(sqhxas;2jr 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0 spuvv42(o xsy04blc/ $-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(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 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdou*ai1)ysfe6y x*mo ,h Base, Antarctica, as shown in Fig. 4-46. The sum ofa) yu*o*h1 yefs6 xi,m the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, igm-2xhcr 37p3 nt;;e yf zi*xFig. 4-47 . Determine the ratio of the tension in the coreptf7 -mi2 i3* yx3;gh ;znxcupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus shown ), lyaxcsg4y,iff,bg6sb 6 y3in Fig. 4-48. (a) How hard must she pull downwa4,lggayss,b, by3)cx6fiy f 6rd 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 65 kg .   

  At the instant a racewyw3ntg e5+.l began, a 65$-\mathrm{kg}$ 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?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a blyfve9/v7b h h)evyv3zhks*9 7 9 /vynf:tcn u/ock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horiz l 1x,0m0lzfneontal surface are in contact with each other, 0nm1lz f0le,x as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown nhtes fpk2- ;*in Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launcht k*-nh sp2e;f" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictio5 4 qpwwqa5:0lrk3f 5cvj ste7r7kfs8nless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of th:k50s7 e 5vft45fj7wqplk 8qrscwr3a e cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kine530wjzk5po2kcl poxv 7w8- sltic friction between a 35$-\mathrm{kg}$ 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 $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a .lg 2aryben 3t79ju (0 q68rrnfifzk05.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. j4/8 1 g/l7 z/ cwgkkygdr)hcoWhat minimum coefficieyk rg/zlc/ 7d c)okwh4/ jg8g1nt of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient o y0mij 7pxic02/jdtv15k; l kh)wdo8uf static fricivp k8ho5ki)/ ym0 wd1 uj;0 ldx72tcjtion between the tires and the ground is 0.80?   

  The coefficient of static friction betweeg h/:d.hd .x(uczm qw3n hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum qx.wc:3z udm/.h(gdhangle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at xa: + tkrzx6l- -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest onl,wi2gvoe8a ),mu ,4lz,satn( 1dv- 0lraxmj a rough 30$^{\circ}$ 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?

  Drag-race tires in contact with an asphav b cpber5m8g :1vat:9lt surface have a very high coefficient of :evrm vb98tcpg:5ab1 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.   

  The coefficient of kinetic froc9ynwcz+njz 0j2ngq:5(9 bsiction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a2f9p e7,2j d ekdt1tuf mass would box A have to have to prevent any motion from occurring? Ass tk, d2ft1jeu7de2p9fume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go,+f qkxm2h7,)onu(oyzni p 97 mu5aa wuj*(ln/ given that the coefficient of kinetic frilw9i /uapn(*oz j7m(n+ o5ukmy 2,x h f)aqnu7ction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 1101cceu:0 .sbly hc d(5jj2 f8ff kg , are in contact and at rest on a horizontal surfa(sd u f821cl.:yfjce bj hf50cce (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate3han,c p, hjug xj-eh5.fl(0ln ;zwq 2. The coefficient of static friction between the crate and the bhng 3lq (e hj,fxjanp-c,0h 25uzw.l;ed 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?   

On an icy day, you worry about parking yourt::bmc(im4agn5 h1 dl car in your driveway, which has an img(:cth bd:1 4ima 5lnncline 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?

  A child slides down a slide with 88.rxua1 dtfoj*a ;qw a 28$^{\circ}$ 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.   

  The carton shown in Fig. 4-5)r :zfl0:kau( iq.m yt5 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speej 57dzldzc2fdb9 e1pmpg ;-e8el(1pz,7 st qfd of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of theun19hoz.a) -rt6yt jt steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{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 $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place agai,bebf h9 rn-e o-a7h:dp-8zll nst a rough wall by someone pushing on it with a force directed uph fl89n--,ezhbp-l d o 7b:raeward 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 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they me9wjkk mf0( p1jlt. Consider a chunk of snow at the ridge of a roof with09w 1 (kmpjfkj a pitch of $ 30^{\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 eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at sqz:q jyg7 tj+8v(pl3jpeed v is equal tql 78q( gyp+ 3jzvj:jto $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forwardkdw;o4m8u:(6l z1e rdsap) ku on the dash when the driver decelerates(6sp)ku:d 1kad 8u4e ;owzlmr from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m p 6uy ,z1(znvwzt+v 2fz2bz 4w is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 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 friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they ar6h -maf(kmn-a k4i2yee filled to the packing station 11.0 m away. The belt is initially stationary and must finish2n-imm(ehk46 fykaa - with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic :o uhs; r9a1op;cnm :efriction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bk.+r)( fii egs, te0xjq)wtn1icycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxima4zccj b(4f; n.rqvvb g5) bphl.t7 dq8tely 20 g of blood is accelerated f5nqrl8jch.fqv z) bt4bv(;g.c b 7pd 4rom 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonawh;pgnft7kwp7 lyf 941: ,np oble chance of surviving an automobile crash if the deceleration is noyw: nk7w4hnf 7ftg lppp1;9,o more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an erh : 6q/lta;:gmu,:r h8ikq:(jzuf qzarthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficlrmk8 :ug:,qqf iq z6hr aj(tu:z;h :/ient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~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.   

  Police investigators, examining the scene of an accident inv+u*:y i t*tuovolving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before col * ouu:i+*vttyliding. 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.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m trav cas;* 0f ry6q7vjfi21sfaor, eled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveli s*cv qjfryo0if7r a;f,s2a16ng 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppds5 tq nvmt/a0qb;/b4ed from the top of the Leaning Tower of Pisa and falls 55 m before reaching the /a bv/05qb4nt;sqtdm ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady0 elxqz6z(nwx(23h f 8e38c gepl4v cb speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cy230n(p clfc eqex8vb4g wz hl6z(e3x 8clist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a cit( o4y+q rjmqzt8e2bv8 y. 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 1100 kg , bv mt q (8o2qeryzj+48can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experimez/ b:7 djc6ltonts, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Ai7blz6/:dtjo crport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . 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.   

  In the design of a supermarket, there are to be sei39(m0 arogb)hr qi e,v/r sy2veral ramps connecting different parts of t rvmqe) 3bsyg 2rarh0i,/(o9 ihe store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F 9:i1jap5hcdm+ h5jid is needed to lift the piano (mass M ) using the pulley apparatu+j5d 5phhci1 aj9m :dis shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accele2c r)6 itc+mibrating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-r54lt 6 maa8(oxav v ijq5th3d.estraint chair, an engineer considers the following set ot3a58 t(i6 4qv5x aldaohmv.j f conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(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) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car t/a9 fh qw9m7)3wryxy Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ 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 $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety /eeo.h+ ugdw7ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distandweg ho./7e +uce of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is n5;+p n0zops9kj:a vlusing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (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 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a 8 xnk:) +ijtvq-xp 8 k*fq,jydmaximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ 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 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

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

  Three mountain climbers who are roped together are ascending an ice sec- h d6/:h 4aq6n8av,ltrxb field inclins:tqe4db8 6l/ xara6h- ,cvnhed at 21.0$^{\circ}$ to the horizontal. 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.