Why does a child in a wagon seem to s+.g mx p8;mz+n)wlyz fall backward when you give the wagon a sharp pul8;+lpz m x.gzywm+) snl forward?

A box rests on the (frictionless) bed of a tmr3poljx7 rcx 8(f 9v1ruck. The truck driver starts the truck and accelerates forward. The box immpmo f(cjr97r3vx xl 18ediately 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 (b) by Chris who is riding on the truck

If the acceleration of an oblvtm7s22a4qi ject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accenpe 3 6e5a8kdcleration? Can it have zea c35 pe6de8nkro velocity? Explain.

When a golf ball is dropped to the pavement5:m5)nn bf way, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts ty5bnmn):fa 5w he force?

If you walk along a log floating on a lake, why does the log move in the opvszz42bs/ho-sb4yg gl(o 7-j posite directionbzgvl/4h2gs b o7y-z ( -4joss?

Why might your foot hurt if you kick a heavy dverz p-;qfvd7s.u: + desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicklsck9,so: +t j9 bc5rnny. (a) Wh ,sn +rk9cnb s5:9jtcoat is the origin 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 ceiling; (; ctknrzb zo:oan3j0e) 5zw, 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 dangjb zt 3a zenc0w(z5or)k:n;;o ling thread, where is the thread likely to break: 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 on l q,8rn/,w,wfmw0 zgreat as that on a 1-kg rock. Why then does wrm/ ,z,q0on,n 8wwfln’t the heavier rock fall faster?

Would a spring scale carried to the Moon )nj.u,fwa zh8 give accurate results if the scale had been calibrateh)wzu.j af ,8nd (a) in pounds, or (b) in kilograms?

You pull a box with a constahvb h5n .at:h d-9c-xe5xfw(znt force across 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? Explain-hfdx zex ah-h9n.t 5wbc(v5: .

When an object falls freely e b le56y8fq-tnk;y9lunder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s thirdbqe-e68y kl; lnt9yf5 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 whed:ent:rg352 yt g cl+fn you are on the Moon with tgc e::5t r3 +ntgl2dfyhe force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of xsfnoeu4z i .3to5+, vwar (Fig. 4–37) pulls with equal force on the other team. What, then, dxiotn3.5u+,sz v4o efetermines which team will win?

A person exerts an upwagzm 5av*(wb1grd force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direc5(mgba*zg 1v wtion, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on thvd, 1x*0 mzfz:bc +ptqe ground, how large a force does the ground exert on you? Why doesn’t this+tf1q mvz*b,:z0p cdx force make you rise up into the air?

Whiplash sometimes results from an 9igy7r3c +(q -jsnij qautomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the v7 sjj+i i nr(9-yqqcg3ictim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the q4-tjt nfz-9 r sju/9ctruck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crat-q-jzsttc/fj 4 r99nu e to accelerate?

A block is given a push so that it slif rl /breq3n*o v+i)7odes up a ramp. After the block reaches its highest point, itqo /i)rr*e b 37vfoln+ 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 if you weighed your6:hd-di uw2 -hw 3pw wjhbdn,(self on an inclined plane? Assume t2wwdhw, d jb-6h-(:nhpiu3wdhe mechanism functions properly, even at an angle.

  What force is needed tokla.pejekc5; xg :e3-a -xu 6o accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ritss,v awolv.ac0 71ia4 0ms v7der at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must p /:5il 7no 7v;bxq1k8rnqdfl :az l2fa rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of ajt 2 8y e.4l-nevd)ptd $76-\mathrm{kg}$ 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 stop aq s4-( 4 zerqjk2rctq3n 1100-kg car in 8.0 s if the car is traveling at 95kst(q4ejrr-3c4qq z 2km/h? -  

  What average force is needed to accelerat61ej9 t-ww6rl klun/e7k,p yda5cvy3e a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrknw,e-e t9pad6w y lcj3vr75 u1/kyl6el of a rifle?   

A fisherman yanks a f gb5 l0s2(auyr01mom2/yuttaish vertically out of the water with an acceleration of 2. a1/ut( 2lmrbyys002tgu oa m55 $\mathrm{~m} / \mathrm{s}^{2}$ 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 quar-ei tu 3nqs4p2c p s5e0ds.k4cter-mile track (402 $\mathrm{~m}$) 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 accelz e;;pcln ztlmp e.y:8 3k9b3beration is 0.0680 g . What are the maximum and minimum forces the ; pl 89pk3z;:lmzycb.eenb3 t motor should exert on the supporting cable? max =    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 ba doxz4zy8fl17throom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the persdy1f oz87zx 4lon’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-;7eb/q8zx9) urxw2unpz zj+hkg elevator has a maximum strength of 21,750 N. What uxx;7bz29r 8q +hn/)uezwpjz maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diver,svmyq . 2c ckv0w;n4fs (mass 132 kg including parachute) when the upward force of air resistance is equalw20 n csvk4f,.m q;cvy 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 3.4 ).oce a*gq djtfet/ /e3ds*ms3t10x ol7uej9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his*/j3j3a tc qso0) .ot gu/eed*elf 4md1x7 tes 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 a0ibh5 a7l(te ;z n)+ lmpw ;wg+mvd7itied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the forceivngmm;)p7;w(ea5 h wil+tb d+ a7z0l that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball puu9 axo g6 19:4matyeplayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body ;cakxx+2glg 9d*4j4 wzis)m.cr; r vi diagram of a baseball (a) at the moment it is hit by the bat,mr*4;;csl r+a.)gx xkv 49zcji 2gwdi and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction.mg)n/2h9 *keatf ,uj8 .7y zaclotu6u A second 650-N force must be exerted in what direction so that the re9afc 7u*nzk ue62)utoha./, yl8mgjt sultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontaw) f0-jueodi(mygs/wb 0 b.m+lly between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is /d) mo. mfwew0 +y0bs -bjui(g 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 mas ke0*6gonh pq,sless cord from another 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 14kzro2v f* f2(w24atro/y5 pkx.0$-\mathrm{kg}$ 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 McMurdo Base, Antarcticc mf.x5j ua*q8a, as shown in Fig. 4-46. The sum of the.ux8m*c5a j fq 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 h+k9 ln :tag(vof the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fgvl9(nt+ kha: irst 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 sedujh v6 ly 8yw7zkg1u+58v5shown in Fig. 4-48.uhyjy8vs+k7v5g ldue51 68z w (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a jpws4:y2zxb6zct o (865$-\mathrm{kg}$ 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 bl.fd,p:l b/w znock (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 horizontal surface are in contact with each :k y2 ns:uddl5i+l gx9other, as shown in i:sk l92dd:y5gl+ u nxFig. 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 in Fig. 4-52 are each initially 1.80 m above the grob5,t 0js6t owmxrg )x;und, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter ob6jrx0w gsbxmtt,5 o);ject 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 "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connectasm8 o(rn 9sm 94z43f8ljyzsqed by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box sz4 l(y9am8f4on 9sj qmz83 rsand the tension at each end of the 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 kinetic friction betw7 *auo qw:rg:been 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 rep/ygh3g5fq3kg e ud, ,quired to start a 5.0$-\mathrm{kg}$ 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. What mid fc +pitgdm244xsl4vo,ls *ko75f 8 xnimum coefficient of static friction must exist betwei8,msc2l5ld k +x7pfo4 4g4*tovsd fx en your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stascx2st) b*7avyf7pmg+z8 p1 y tic friction between the tires and the ground is 0.80?1 tsm 7+byaf7c82s yzvp *gx)p   

  The coefficient of static friction between hard rubber and n2l6 du+zmnne p2/*wenormal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked2pze*m 2+ nw/ udl6nen?   $^{/circ}$

  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 qns oue 7j(v +c2w(+ gyer;7fx-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 o-t gjrs8d8z o6n 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 asphalt surface have a ver+gjbgt 8;2ei3jgm7 g hk+t3e1zo mv.iy high coefficient oo+tz8 ;jtg32g gg evmijmeh+kb1i.73f 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 friction fn3z: i5bdf mp)or 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. 4-3vsxh e290uw) nkq1g.x 2 (Example 4-20) how large a mass would box A have to have to prevent any motion from occegqnk . )x9u10 h2vwsxurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go y:vxd ),j h2 8uy.sxdei*/ipyl8p3 wk, given that the coefficient of kinetic friction is) /dpyu ., 8:*ylkx832ivyj dhwxiep s 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at resev7nq*a*xm4(.jjp y95p/ o) nz: dxs vi +iestt on a horizontal surface (Fig. 4-54). A d9v7v*ex sj:/.+nm ypjis eqon)z *ixat p(45 620$-\mathrm{N}$ 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 crate. The 2 wxxts:kk9usg 9m*ch,1u; h o2ri g)ccoefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid havwu mg ,1is: h2 oxcgck2xs*u9;ht)kr 9ing the crate slide against the cab of the truck?   

On an icy day, you worry about parking younl r40sn w:i:bmg3z zu4 xa4:m2v1gpur car in your driveway, which has an incline of mug:2wl 4g:4 z vz4nr:pbx0manis 1u312$^{\circ}$ . 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 37ek- ki/tkz k lz(wkgcun07/slide with 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. 4-55 lie3yh v ..bz0x2i+ ahfxqs 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 initialqz9y; sj1*x qbc3 swf, speed 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 reachertzmqb 1*9e1)q*wa3t g qh zx9s the top of the 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 plw,wlo1,: wzhh56 /mo ng fhn:uace against a rough wall by someone pushing on it with a for w5 ,nlf onz6m:,wuhg:whh o/1ce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slipperc l1 3jia runo/-*m+rqy roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a n/or+ui*ac qrl- 13mjroof with 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 u9 .jlqqinq5 ;dj07lq stopping distance for an automobile traveling at speed v is equal lq0jq 7ql5 ndi;.qj9u to $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 pn/l,f*2fzb)j0rhyjs tf 3 0g forward on the dash when the driver deceleratesgj0hpl 0f, fn /tfy 2)r3bzs*j 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 is given an initial sp ja9y581ux iia) vvny)eed $ 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 xpc4 137uot7 jglvu fm 1zp m+fj*;da*belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish 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 7cogl* 3m jp ; 1mdp7fztua4j+v1xf*u 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 friction between hr+ph ,s52f mk$m_{1}$ 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 kg3h+ sum -rkcsv2(t*qs (including the bicycle) 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 mo0yul7 j4/6qf 4 shvhv+q zfex,del of a mammalian heart, at each pulse approximately 20 g of blevfv h4ulhs,xz +76/0 qyqjf4 ood is accelerated from 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 reasonable chance of surviving an automobile crash if kzsb7:- gzv b)the deceleration is no more than 30 " g 's." Calculate the force on a 7:z bgv-zbsk ) 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 accel/0czk4a ujok4 eration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at le0cuz /o4 kjka4ast $\mu_{\mathrm{s}}=a / g$ . (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,+ 1al ybh6vh)c bieyc.j2 ig0. examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the care.).y1 2hv lbb gccii0a+yjh6s, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m 6-/bh/l 6evssocqmg *traveled along the road, the elevation changeh6ob*cs/ -/ lvqsme6 g is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped s m/w2 r(pnb;u h+8vhcfrom the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Wham+vhch 8b(wsr; /n 2upt was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 1/q s jdymy1:5 l+hg1)wgnx-(awd f*o 3zk 7jdy2m/s but enters a muddy stretch where ty y1(d fnjhm gdw*k13) zd7gqay-xolj s:+ /5whe effective coefficient of friction is 0.60. Will the cyclist 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 redqjda +o-hfqsy+;y,c4 esign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills withqq; yc 4 ,jfd+y+hs-aoout slowing down. A particular small car, with a mass of 1100 kg , can 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 experimen8:nx 3nz0d.h +5ymhxy0nmc e:-sndsdts, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle shx m cn0m85 nx0e dy3n:nsdh.:d-yz+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 supermiqb5**31puwt rai (udarket, there are to be several ramps connecting different parts of the sp *53(1q wdatu biur*itore.
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 is neededi8b mi1zw 06tt to lift the piano (mass M ) using the pulley at16 z ti0m8iwbpparatus 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 accelerating at ;)h0)ogzsym v5dtct* 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-restraint chrm-,cf m7h- kmair, an engineer considers the following set of condit ,7rm -mmckf-hions:
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 Italian train has a mass of 660 metric tonstj tgwu-v6,4 r)3b) 3o pffljpg:m0ugca0cf9 (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 six ;5a ue/w 82em)htu jzs/u+oafety ropes 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 tta)xm/ s/w oh e;u+u5uz8 ei2jhen the rope stops her over a distance 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 using a " 10- edjo;2fhm j(f9n fq.b;y ) wgmnvn62)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 maximum9zphq,r7eef * 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 ryzshvcz+hr;;r niii ; /, k1m(oped together are ascending an ice field inclined cri;(ksi;z v/,m z+;iy rnh1h 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.