Why does a child in a wagon seem to fall backward when you give tb e40fzbz0/td 54 fb9dcf;icd)p8qn0 -jnklwhe wagon a sharp4f cntd8f 0eddq0 -kbfj50l 9w)b/pinb4zz;c pull forward?

A box rests on the (frictiuz/lm 9)5) kgk1 g ys*l3eiewjonless) bed of a truck. The truck driver starts the truck and accelerates forward. The box imm g93j*ekie5w)) ygulsm1kl/ zediately 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 object is zero, arejgo1 -x2d 3j upb7k8vvjgg)v8 no forces acting on it? Explain.

Only one force acts on an object. Can th1u qcv06s8w4 c5as xife object have zero acceleration? Can it have zero v4i uavcqc85fs 1xw0s6elocity? Explain.

When a golf ball is dropped to the pavement, it bounces back uprji.avey68b52 +7pw 3faauci. (a) Is a force neededauwi+ f ic8re5a7y2v p3bj.6a to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log ftwyk k8g/ca)oav9u2j )b33x yloating on a lake, why does the log move in the opposite 9a )kayogkw3c8j/ v y32x)ub tdirection?

Why might your foot hurtm9o,9n6kyvu rel 38t i if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dec hhsflr8aj2.) elerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate .a l)2sjfhrh 8of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ce2nk *q uf,rb4/pj jk212v (nxp p4jlwoiling, 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 break: below the stone or abovp42op 4jfbq*nxp 2wlr, k/(vj 12uknje it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity 6; o*/wl k530)uapf6:fgppelo jcb *qxpvo(ron a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heav fb)op:(6oje ox w/ u5r63pk*fl c;l ppva*gq0ier rock fall faster?

Would a spring scale carried to the Moon give accurate results i)t8w oeoo;z.c,y dkthu ;:pa 4f the scale had been calibrated (a) in p:w t )y, .oakoeohp;4t 8dz;cuounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an att +5t kpmzj1j(g5jrdp i7it59uun0a)a 33 ty rtached 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 t55upj(tn5k)duit zt j7 9am01 g+yi j3arpr3 the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is f38+aej2utu 4die 4 wxa net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. 4e4jdut2e3 a iw+ 8ufxWhy doesn’t the Earth move?

Compare the effort (or force )0n r:*4koaxws es1yv) 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 a 2-kg object horizr*v xnys0 4k:w1as)o eontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug os6fghk+x b; ;gu a xm ;y.vnsm:a*2qi(f war (Fig. 4–37) pulls witvx n;k* bfqmg s.i;gu:s6m( yaa2+;xhh equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to,i edva4:qi :k 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 is exertkivaqi:ed: ,4ed, and (d) by what object it is exerted.

When you stand still sl d.fv 3c+(h x u+qexr7i:juza*g+f6on the ground, how large a force does the ground exert on you? Why doeu37+q+ljrd c* xuiszv(ef+6ax ghf:.sn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile(uk 7qmq7su+ h accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be kq7u mshq(u7+ thrown backward in this situation. Is it really?

A heavy crate rests on to 31lve jtofdx6y/:m4ao /k0 :r xxyb5he bed of a flatbed truck. When the truck accelerates, the crate remains where it is 1v/y5d: 6:mkx3 o 4 ox eabylf/xrtj0oon the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so p *ju3nc) 8lmgn*ip 9r, .isrrthat it slides up a ramp. After the block reaches its highestn n8jgiur9 .,ppc rim*l3sr*) 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 if you weighed yourself on anmbkipy- d ,t0 m mcj1.6b5v0yi inclined plane? Assume the-1mtv0yp ,cidi.ym50b6b kmj mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.2a. b d(cgz5v5d5m/s$^2$?   

  A net force of 265 N acceli+pn)xz.afh u*; *m24qfv9vokg: pg yerates 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 a1c cunp)yt/ cjk. ;cg9 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 oro(a;1d a,mjp f 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 an 110*)m 91zu oerdd0-kg car in 8.0 s if the car is tra*r 9 ezd)odum1veling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelubv n 91k7nd4hlet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle? 4dnb unh17v9 k  

A fisherman yanks a fish vertically out of 5 es2qm9 h2ryhthe water with an acceleration of 2.5 eryqhms 2h259$\mathrm{~m} / \mathrm{s}^{2}$ 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 (402p oap o,f76h7x $\mathrm{~m}$) 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 accezl7;qlnik-o)ou5 (oozw/zu -. jjqz5 leration is 0.0680 g . What are the ma zji) 7jou oolq- q/u(n5zzw.zk- 5ol;ximum 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 bi09 h8 aisuc2 ufq;9min a motionless elevator. When the elevator begins to move, tucbi9u 82i ahqs;m9f0he 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-kg elevator has a maximum strength of 21,750 ukj (8gjr8e g47- ikklN. What maximum upward acceleration canu gij8 4r(7g8k ek-jkl it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including q3f; . qgbzhb;parachute) when the upward force of ;.3gf; bqzb qhair resistance 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. vm*2ydfq mxb *; e4ce9When he strikes the ground below, he bends his knees so that his torso 4e v f*cme* 2dq;ybmx9decelerates 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 N6euu deta-p2pus 6 j0: 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. 4-40). Determine the force that the table exerts on the box if uu6a2s0e: - ujdeptp6the 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 playe2ncedmq86. g)w- bjt.tew o)fjm9 pib)+3 fw dr
(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) aq/j8t/u k;afj t the moment it is hit by the bat, and again (b) after it has left the bat and is flying t;kj/a/t 8fuj qoward the outfield.

A 650-N force acts in a northwesterly directglz-xegtj0d)8 :3h jbo) 60ek, jsmnbion. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a ve,6jzsebeg0 ml jk)ojh- bx 0)ng83t:dctor diagram.

  Arlene is to walk acr;ek:*m2n fyk*v yzd2fa + fxq/oss a "high wire" strung horizontally between two buildings 10.0 m2*k dv;*/2nm zkfqe f:xfy+ay apart. The 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 massless cord from nn:t qx/:xtx 6another 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 14.0lcdpon1z hao vsb.11 ex 1b98bio 6/;u$-\mathrm{kg}$ 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 toeoc9g f2b+nd 28i:qyd a new location at McMurdo Base, Antarctica, as shd+29qfb2:eycg8o d in own in Fig. 4-46. The 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- + 2s.orcx ,nrez;xjb547 . Determine the ratio of the tensi, nzej;sr.2xbr x5 +ocon 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 slhu9 grg9 d1j*hown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constdrjl9gh *gu 91ant 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 begawjm7l,kq 3k +cn, 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 block ( yipn0 yq:5fem f,ooyc4663zjmass $ 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 06 -04p ym3ihj 2tnbv-.oml cgkv0*xnv rlu-vhorizontal surface are in contact with each other, as shown in Fig. 4-51. A force ojv-bm.40i3 nrnx p 0h0*v-tluy6v-gc 2v mkl $\overrightarrow{\mathbf{F}}$ 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 1o*ymms 9j9) or.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. Wh*9m9mos r)yoj at 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 doesn't hit the pulley.]   

Suppose two boxes on a fricti;yn-i4czq r)+w7/unz:ppt qoonless 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 th7;wzo /tnrq+pqn 4zui)cy: - pe 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 betwe/+.tajqg af,oee 3wx 0en 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 sc8rvi ah6wu,3d9f -ma 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 minimum :kq5 vgehva2h48d:r tcoeffic:ka: hr t428g vd5hqevient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleratio6sd-cpbg(e9 a 2o*+qweuj - vn1:jwkin a car can undergo if the coefficient of static friction between the tires and the v u-g1k9 ocwapej:dwi(-jnqe2s+b* 6 ground is 0.80?   

  The coefficient of static frifp h:enlq 0p//v8:th yction between hard rubber and normal street pavement:e0qy:phl nvfp8 /t/h is about 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 am/,) :ihdz)uz ygelb :n ddt1,t -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 on a rough 3 ux;3ujnbj+b sigziuc 9f71 890$^{\circ}$ 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 very ysjj g5o 6yvi it21n23-7dh.eba dk7nhigh coefficient of static friv2dy3 7 2-7nh.6gitn bej1 5a djoikysction.

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 kinetrj yzni ;n 83-wrloat3 ;sw/(pic friction 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 t*/bu( j u:hyooo have to prevent any motiooj*/u(o bu :hyn from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across m3fa4hb9 / 2aj ift2s3vodgd; the floor. How far will it go, givsv/ agjfid2am;39f 2 3ob4d then that the coefficient 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 , are in contact and at rest on a hor.+v)io b* jkllizontallb+o).* lkjv i surface (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 crate. The coefficientc* 8.en9gi.gwg(xm qv 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 having the crate slide against the cab of the tr qgi8n vg*w(.ge9m. xcuck?   

On an icy day, you worry about parking your cqjl*fw:,mknz epa8d+8lc 39aar in your driveway, which has an inclelzm: n8,al qac3+f9j8d wpk *ine 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 slid wk ,y;fi:ix ssk579d3*yyfrf e 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. 4-4 -bi;5rm1 zgpvbxdrk*raq: 2hvg, o 355 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 spcplx6/4*v 1l urv0ng ieed 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 ry*uv-v :/:y;cjz ewr ca-w4 3z yct6yof 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 ,u nfe bwdgfn a6qj28apv q42/(k2+xoa rough wall by someone pushing on it with a force directed upward at 282f e6qkwx2 8(u aap n2dq+bgj nofv4,/$^{\circ}$ 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 g+i b3td ucv8s:w i8g/yrz-v.become dangerous projectiles as they melt. Consider a chunk of snow at the rid3siwr/cvggd+y:-z8 i 8btv.uge 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 sd9oyh1y 9sww (lep(5wtopping distance for an automobile traveling at speed v is equal w59w(9yde(o1h sywpl 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 foc1y dgr 1el1gy-l 4(bxrward on the dash when the driver decelerates ebg-yd1l41( cxrylg 1 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 speed *t+0(qtzsn h m$ 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 z1e :brjwo* y9 -;ouflbelt 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 thrwzo jl-f*:y9eoub1;e 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 b2 dgwaxr7d m xsol315(etween $m_{1}$ 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) can coast down a 6.0o kj;w 99dhiq7l+w k+s$^{\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 simpliy35osli,vl0 n cf a ,hu2oi:h+fied model of a mammalian heart, at each pulse approximately 20 g o , 53:yluvnih,sao0 filhco+2 f blood 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 the decelerv 6 wbw)py l4y gvp( k2.wn2tja+vch0+ation is no more than w2 6 ( hy +aykwntvpjv0+vpg4bl.)cw230 " 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 earthquake is lr )s.g4gvm(aipt5o) a , and if an object is going to "hold its plt4. v)ga 5poi(m rgsl)ace" on the ground, show that the coefficient 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 scpgclfz ,,pq,wq* -sx:ene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic frictiopqs -,f,xc*p: zgwl ,qn 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; 6+1gvsd(vf(ls. u uhwjfuf,-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the lu u fjw6f.+h,v1(f du s(vs;gbottom 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 from the top of the Leaning Tower s (jbrjfcxt2*r toq-/t1yp38 of Pisa and falls 55 m before reaching the ground with a speed of What was tjqy-*t br83t/jsrf 21(xo t cphe average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s bv 7t+l3xm: r a3gbjik9ut enters a muddy stretch where the effective coeff7ika9v3lxmjgb: t+r3icient 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 redesign of a hilly portion of a city. An i/wb1ndy3*rij x7 ij *smportant consideration is how steep the roads can be so that even low-powered cars can get up the hilsyi/ji nr*731wb *j dxls without 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 zt9pnv.tc 0re6y,e*,9 w aa: g b/9czp- grlzyphysics experiments, 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 sa , 6 bzg,09wgtypn99z:yacer/rzevctp -. *ltring 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 several ramps c m3i3 ;cr0jzbronnecting different parts of th0mbc r3;3 rizje 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 nda,7ixa( v;h is needed to lift the piano (mass M ) using the pulley apparatu,(xi; dhvn7aas 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 acceleratn7irh(h-i /1 ;tua pfsing 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 )67vxn+5a5r/rm) qhoi s qnnofor a child-restraint chair, an engineer considers the following set of conditioo)nvnorni6 qam5) sr/ q5+ 7hxns:
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 mqodqwbfm9bs aug .n;:z19 9*yass 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 Kav zunq-.r6 8t v6j n4jsqvbisgg15/w/ren, use 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'sj-vj z.n5qg/gs4w b6i 1/v v s8nqr6tu 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 is9jy i yx)4um2e 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 is allowed to reach a maximum speed of - fali325m mdbg7+iwp 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 av h;mjc uau un8 oxb+1l6:,q7rre roped together are ascending an ice field inclined at 2 7 v1uuajx;b,6mro8qh u: +cnl1.0$^{\circ}$ 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.