Why does a child in a wagon seem h9 0taeiehc:4b2 *5f1sfs al uto fall backward when you give the wagon a sharp pu1a i 2ea9csth u4eh:b5 ff0s*lll forward?

A box rests on the (frictionless) bed of a truck. The truck driver s:mi8d/cpit5 xkz27 bjtarts 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 (b) by Chris who is2zip: 7tk 5/ x8imcdbj riding on the truck

If the acceleration of an object is zero, are no forces acting on+hh1sl;a zsky:z 5 42xytl8l x it? Explain.

Only one force acts on an object. Can the object havtp .n i: x5pn32turm:re zero acceleration? Can it have zero ve5utri 3:xnpmpnt2.: r locity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is g6eh65pibh :0x ahfp7a force needed to make it bounce back up? (b) If so, what g56pe h h:0hip6 xbf7aexerts the force?

If you walk along a log float s4d:8m r4k*ef; pstuqing on a lake, why does the log move in the opposite dups8 *4fm 4;sqekt:dr irection?

Why might your foot hurt if you ki8s) ytk o(6wvsck a heavy desk or a wall?

  When you are running and want to stop quicklljis+ 1.56-iw vl /ot 0iphiexy, you must decelerate quickly. (a) What 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 at5/l op ti1h60e +swij l.ixv-i top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sectvz.one3fh09 zd70+ctf n jmj ;ion of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangld03n9z oj tfm0 7h.f+;cvn ejzing 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 1hjtp hp;bh:g4h3 pi:wy+d6da 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fastehgppb4yhd:; j+p6hw 1 3t i:dhr?

Would a spring scale carried to the Moon give hkcmaul* 7hze*2ts c4jk,)dmah;qh k8:, i (raccurate results if the scale had been calibrlh8* jkm qeh d7h4a(zcc:u ,sr2*itam khk,);ated (a) in pounds, or (b) in kilograms?

You pull a box with a constant foed*s n372 qaokw cw.*nrce across a frictionless table using an attache*2.*e3 ow7nnwdck q sad 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.

When an object falls freely under the influence of gravity there is a net forc-dy60/b sas4 jz/dlg be mg exerted on it by the Essdzb db/- j40ga/ 6ylarth. 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 (or7i- r bqz9ch3n:p)vo 2 ty1xah force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw vy9z :-qhabth7 oin2c1r3 x)p 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 war us3eknva agd3-(t v-n; 3k3cw(Fig. 4–37) pulls with equal force on the other team. What, then, de-kvsne33-d; k awvt3(nac3 gutermines which team will win?

A person exerts an upwart7czxbe-8 -ak d 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 direction, (c) on what object it isk-cbe -87 axzt exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large9gwdhld6x-0ce0( 4v)ghd 7uxmov vl4 a force does the ground exert on you? Why doesnvgol h4x-x0d0 hc duvl7ev m96w4 )(dg’t this force make you rise up into the air?

Whiplash sometimes results from an apq ht33k w)lu1utomobile 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 situation. Is it rl1hku3 ) w3pqteally?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerai) w7kphbn*b 1tes, the crate remains where it is on the truck, so it, too, accelerat7hk 1nbb)w p*ies. What force causes the crate to accelerate?

A block is given a push so that x se: h+rz7lw7it slides up a ramp. After the block reaches its highest p+7 h7 :xswrezloint, 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 relzxs ; jo33b/8yqz); lpc6odiad if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even ac;b 3o zjzlo/6pxiy3;sl )d8qt an angle.

  What force is needed to accelerate a child on a sles(i4w 91fnavrd at 1.25m/s$^2$?   

  A net force of 265 N acceler3 u),jsyv lcoeq(bg(1 ates 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 qrj*;29 cfp t+a;s)bbdjnl5wit 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 og272pwx mp u i53k:ludf a $76-\mathrm{kg}$ 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 y2kf1kts52ig sp(9c jan 1100-kg car in 8.0 s if the car is traveling at 95km/h? -(j 5cs912ytkgps2 kf i  

  What average force is needed to accelerate a 7.00-gram pellet8w-jpog e :ut(r6u2 :rervm0zc 6qb t, from rest to 125m/s over a distance of 0.800 m along the barrel e guct2p(z::60q-jmu r brr ,t68o ewvof a rifle?   

A fisherman yanks a fish vepxq3fa *34:sr70 4t rx bupxyp/8jx vnrtically out of the water with an acceleration of 2./ pvxp 8rq3a0tn b3y*p44xjrx :ux7sf5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 canflmgw9i .g;9u cover a quarter-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 max i-sozfrf l )+ hn pquir/1l5zt2,*ps8imum acceleration is 0.0680 g . What are the fl8l)fp5- zin,rpt/+1oz2 ruissqh* maximum and minimum forces the 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 bathroom scale in a motionless elevator. When th);faw*e ra--wx lz bdf6)5gf te elevator begins to move, 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.x a5w-6fe;t rlg*-d))a bzfwf     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum st o. 2ygkqr5-pwjx 19girength of 21,750 N. What maximum upwpiqr5ko9gyg.x 1j-2w ard acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg in. ) h/ e1cix2)ttgmdbncluding parachute) when the upward force of air resistance is equal to oxtbe hnm)t/cdg2)i .1ne-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 wdjc9(,uvm x8 6g nk6pof a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates overk 6wx mc (dv9gn,86pju 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 q objsrq2 .o53N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. b3o2s.oj 5qrq 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playerv,k niam)6i5 u
(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 basebal ;dyo1 vqhdyd;o)o; (pxno7k+l (a) at the moment it is hit by the bat, and a o k+oxd o7o1ydpqh; dv(;;ny)gain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A ser7gty o0b1;7zu +sh wzcond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your ah07gzt o 7 bw;r+y1uzsnswer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between twoorexw3u+. matfecl 2 7(4ml2 a buildings 10.0 m apart. Thw 3af4(.7c2exl t+ueamolm2r e sag in the rope 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 masslesez zl(dl ,.i4os 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 14.0ftzoz.p6:8oktl +pf r6df)fc:k ed og3 -9w9s$-\mathrm{kg}$ 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 9awp) n9k9gb70az zkg to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. a0zw zagg99k )9nbp 7kThe sum of 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, Fig. 4-4ms+ijrsq 0 yjrt2 p:q3ra 88+f7 . Determine the ratio of the tensi r+832:qiajpytqj80rsf+s mr on in the coupling 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 sh7 ojhkwb 0sy1( ws-yn;own in Fig. 4-48. (a) How hard must she pull downward to raise bjw w 71-hyoksny;s(0 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,.f,edd .b5g9p,p6ahgq 6t kug 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 blocsepta7 f ,.14elz,jjck (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 wk+ j)jpyr6qg+.h9 cm hith each other, as shown in Fig. 4-51. A force9hy )qj+ ckpj+hm.6 gr $\overrightarrow{\mathbf{F}}$ 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 initgvxku3 ,q g.vysh+35pially 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 "launch" speed. Assume it does3xug sv,.v 3+yg5khqpn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of lfe6o0 (mzqr* mp2yppr,+pn *kfl*5imass 1.0 kg 5f m2l*p,qlp*+oer f6pnz pr * miky0(. Calculate the acceleration of each box and 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 kin3ws29wj z-stb+t.as0xb g p9/hglj xz/b t/ y7etic 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 requij/g1 hj 1,y/9ji.fynj p-w onnred 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 mingy7yoo:jx2 ,abmliqt,b4. j*imum coefficient of static frictaigx4lo :,jq2t bm,yb.yo7 *jion 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 coefficxg20-pcnutj 6,ctq )h ient of static friction between the tires 0tqtx)h2 ,p6 cjcu- ngand the ground is 0.80?   

  The coefficient of static friction babmxzt yu3h+ wy3m:29sq7*nl etween hard rubber and normal street pavement is :9sy2q ywtn 7+baz*33h ummxlabout 0.8. On how steep a hill (maximum angle) 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 -4.8-s 6 bkgk;n0ii0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 on a ro++6);xh giqq e- -afz8bli twcugh 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 surfewc0m* toh +zs7bv7 *dace have a very high coefficient of stat7o0ztw ce*s +7*mbdvhic 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 fricti(;5mojw bbwo0on 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 a mass would box A have w8ah+)je9.ftsdu e2m2 j p8ip0)pz pu to have to prevent any motion from occurring? Ass) )9wjtu8ez ep+ ph 82s0pa.upmi2jdf ume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wi r h+ntqw hp;v2z5b;7vll it go, given that the coefrwztn+hbh vq ; pv;572ficient of kinetic friction is 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 ,7n-fdq0t47 0x- qxnwk kgm )qs are in contact and at rest on a horizontal surface (F 7 sqkxdq4xq) -t070f- kmgwnnig. 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 u:xv o/qy0 hw v:ecvax(+x+ ,ba heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the dr,be0x vvxcv wx: /(qo +h+a:yuiver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in yom0 -j5*dkwmhjur driveway, which has an incj0 d*khj5m- wmline 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 a 28tu.:s 7k8s7mj lpkag0 $^{\circ}$ 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 lies on a plane tilted at av wf4wj);uc/z n 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 inite)qqp yok:i,b ck.f sil;d5o6zy .fw+bi65g9ial 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 reachws bwt+n4 n3co8k 3h/yes 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 place against a rough wall by someon lqp2i-kyl w; * u1lqnr.3-sdde pushing on it with aiqp-3lydn s21 q-ldkl;.*u rw force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become ddydz o.en0w*7angerous projectiles as they melt. Consid ez.7w nyo0dd*er a chunk of snow at the ridge of a roof 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 stopping distance for an ask+ ;a-bqri t8utomobile traveling at speed v sk+ria8 tb-q; is equal 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 forward on th:vnjg +n m3.7xk8k zwq8y7anje dash when the driver decel:jk7wjn.y8 aq n+v7n 3mx g8zkerates 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 spe n1*f,mnomzdh- +v* imy5 09ebt9q bxeed $ 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 are filled to the pa m*qfx4,gg:3g0azehb cking 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 the coefficient of static friction between a box an3*xa0q:gfzhgg4, b e md 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 fr pxyh x49jaejy9w+8v: iction 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 bicycle) c. c srm:-i dap 1aeu:0x5j)ycvan 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 apprss1x3c t*7i9 xlvs:,3k gxusboximately 20 g of blood is accelerated from 0.25 s xsc*g s7stbk31:u 9,x3xlvi$\mathrm{~m} / \mathrm{s}$ 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 autkyw r0; kc 0h0dx)q5hfomobile crash if the deceleration is no more than 30 " g 's." Calculate thq5;f)x0k khc0 rw0ydh e 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 earthquake is a , and43p5dy5fopn + 5s)xmsm jnnt* if an object is going to "hold its place" on the ground, show that the coeffic4st*3 5x5pn+mdny smjo ) n5pfient 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 scenek.i g;-drpevv2nyn2q,( s4nf of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before collidinf4iqr -,pvg knne22v(.;dys ng. 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 eachmrx,e) h6nmv o )dv0 u2;wx,us 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 mn ;)dxm,0vm2 exuv6) suhrow,? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of nirh),3q1 c +y9fy5oi wmmt5fthe Leaning Tower of Pisa and falls 55 m before ii,3t hyfmr5f5y1q)w +no9 cm reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enter7 1s 0av-vi c8i buano0yf:)uys a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from theun0 1ybfa:uv8 -)0ysvcai7 oi 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 ; kd; 80vin ke9;6pgm d/frng4dee9goportion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from renrf 0pgend ;6igg/kmo8 vd9k;4ee;9dst 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 experiments, dangles her watch dncl5 ;2ke h:gvtw/f8 from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She none ;:wd/2klvg 8 5htcftices 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, t7 ysz)m ql)bwqthuj1;/c4 9 kzhere are to be several ramps connecting different parts of th1 qu) j qs9lym;c)tb z7kzh4w/e 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 is needed to lift the piano (mass M ) e90 9z7+r2 b rqvdeqymusing the pulley apparatusv b2m0edqy9 7r9r+qez 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 pcqa3km ph +rcby*20wphb..4 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-rlteh1xr9i q05. f8i6ixrlv5dohu -x,estraint chair, an engineer considers the following set of con5,dh h1x -lfltixi5iouqr6 ex0r 9v8. ditions:
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 tons (660,0 wkmzl +l0p*cr82rj1m00 $\mathrm{~kg}$) . 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 g):( dnu+chaa safety 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 then 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 a )n:hc+d(auglikely to be hurt?

A fisherman in a boatn wu3g9 hii4lg j:( 3uw1uv6le is using 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 iss f wh5jbard/-xe* p4bu ep,0: allowed to reach a maximum 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 za (7q;q9do tnwho are roped together are ascending an ice field inclined aoq n9q( a7d;tzt 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.