Why does a child in a wagon seem to fall backward when you give the wagoni3c(zyrbt ur;g u5,2d;z1 edu2x u333hrb sh o a sharp pull forwardu1;3d5icybor33 3uz 2rt u;z2hb,re(u sh d xg?

A box rests on the (frictionless) bed of a truck. Thjju,fndj-c ; 3xp96 qwe truck driver starts the truck and accelerates forward. The b jdwqpx,;c j-3fj 6n9uox 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 is riding on the truck

If the acceleration of an object / h1lm,8:lxl,j0ch oms nvpn.is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can ikiys7 * 1dgo0 wa/2yafh2xu95 x ho3ext have zero velocity? Ex91 dxyf0s5ooe 7hhyx2giw 3/2 kua*axplain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is atvgxo,e, vs)vscvx;f+/x 4 .v force needed to make it bounce back c+xxv )s,4oxvg;. svftv ev /,up? (b) If so, what exerts the force?

If you walk along a log floating a8wu33v wr pt4on a lake, why does the log move in the opposite directionuw8pav3 t w34r?

Why might your foot hurt if you kick 2uhcylf:hby1iw : : ;llfi) jzjuq39:a heavy desk or a wall?

  When you are running and want to stop quickly, you mu7fo x cu-ns uru3o.(:ust decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experie(xr : .uu7-osc3ufonu nce) 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 ceilin ,l 5.rs.w8+lnwcdpt cg, 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 above it? What if the person gives a slow and steady pull? Explai l+.p 5n8c.dctl, srwwn your answers.

The force of gravity on a 2-kg rock is tw.9r)b9zl e gin3yh 9bfice as great as that on a 1-kg rock. Why then doesn’t the heavier rock 9ybr99 zbl n ige.hf3)fall faster?

Would a spring scale carried to the Moon give accurate results if the sazy9pc v (i b+ptb01rjc9-gz, cale had been calibrated (a) in pounds, or 01b-rbajv(9pp,it czcz +y 9g (b) in kilograms?

You pull a box with a constalq3y u *ml;mh,nt force across a frictionless table using an attached rope held horizontally. If you now pull the rope withqlyumm;3 ,h l* 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 thwixxdn0/6u p/cz8 nh 0jzy); he influence of gravity there is a net force mg exerted on it by the Earth. Yet by Nxnh)/z y;ipz/u djwc0 6x0n8hewton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a vxdlocx-ap s6 5i4 y,,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 horizontally with a given speed on the Moon and on Earths6x5yic,v a4pxo,l- d .

According to Newton’s third law, each team in a tug xomiu3f. j6 -3+axtzcof war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will x o-+33xzf jmtu.ic6awin?

A person exerts an upwar.vn gwef fczw)7by9)tr ;s pa(ur;f6(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 is exerted, and (d) by what object itb;g.7f(swe) w 6 fyu;zr r9 n)tcvfpa( is exerted.

When you stand still on the ground, how large a force dfyb l:6 lva3u4oes the ground exert on you? Why doesn’t this force make yolyuaf3: b64lvu rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s v 76r+xi7dnlw-av 8bl car is struck violently from the rear. Explain why the head of vr l+7i 7wvd8-n6xbla the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,)rxw)4 pgpsr dw,cz- rj -:)ad the crate remainsrr)adzp)-w) xpw-c: d srgj,4 where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp.z:-d)jz 3b ftjp-6wqq After the block reaches its highest point,j 6zpfw qt)3q--:zdbj 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 yourselylu00;bnv:iu a zu)ur3g p 0t+f on an inclined plane? ug : )0uplzart; b0un0y +3uviAssume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a ccn7sinon6. 3u hild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.3ia,jrh99rs f60$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to w um c-y .qt01c3;eiltaccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a s,*j5 adkbv+o $76-\mathrm{kg}$ 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 rek6 bwk /zuivk,.-u .kvwr,;5 zi 9kxruquired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? ;ukkriz -6,kw..vzu9w rux /k5,vkb i -  

  What average force is needed to accelerate a 7.00-gram pellech93b(ma*e9) 5lyq;wjcpm 4-k imk gut from rest to 125m/s over a disg)e*imu9qmw; 4h9by ak lk5(c pm3-jctance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water withtjoy ,1:7kbkn an acceleration of 2.5 , kjbn:koyt17$\mathrm{~m} / \mathrm{s}^{2}$ 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 cover1ts.kxqr;e*d o k cvhg.yv-26 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 maximum acqo ( 7lg3+y)bo/efeqjceleration is 0.0680 g . What ar3q/bol( ge7 fj yq)oe+e the 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)zqym3)6j,vvt k;tujfcnb,y;dd t)50k pt7g a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the t; 7 ;)mv)u,t5tpzk jdf6jdyq )kgn0,tv3 cby acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator hag+lx le eo5ay+hor9(g5lvw8 s4g2 e2e s a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevxhl9v54re+ 2g+2w esyg 5le(aolog 8eator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diversggh3bb k5aw 9dq -o: q 8)nhrp*53enou (mass 132 kg including parachute) when the upward force of air resi3n5 oh*a8b5) kh rpewog u9q nq-b3:gdstance 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-wxiuhl:qd9 7 +m high. When he strikes the ground below,iqux:+l97 d hw he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to wwb*0 jxa(w82xw re9x/z pc)kthe box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hangi x2)8c9b(0w/z rwex wapwjk x*ng 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 plkr huvgkf5h 0;6tsh x 57v1ymti 3e;-gayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the 7s+j2e o0uwpz bat, and again (b) after it has left the bat and is flying toward e+p2 uoj sz07wthe outfield.

A 650-N force acts in a northwesterly directj(*-44 yxb0ptot+sg amo2moeion. 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 vector diagryem+m4t*g4oob0xj( -ts p2 a oam.

  Arlene is to walk across a "high wire" strung horizontally xlmn n)m fq* 3yr-1ta ;zr-78ycqwj u-between two buildings 10.0 m apart. The sag in the rope xlnmcyr m - ;qj*w1yt-)un7-fq8z3rawhen 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 fr4-), u4p3 t d xxfp1vvtj u24qwssfm mgsh:.:fom 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 14.0o tl9a6-o.llo $-\mathrm{kg}$ 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, A7,7 -tixm3qay8hd l::pfff xsntarctica, as shown: l7fd- ,:8xqispmxt 3f afyh7 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. 4-47 . n o: *3.,awb wm3jvvusjg 1f6eyxt,)bDetermim ),t:6 wv3ewbu by3aj x*n,fvojg1 .sne the ratio of the tension 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-pulleyvp ef95g 4 f--ywyxt5z apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hers fgx 5f-e9yt4v p5-zwyelf 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 bej +drncy/rv yy(l 4;eg2:yp 9bgan, 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 (mass yu * 6ixo)p+ds$ 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 aren rn71 ijlu 7-symrb)2 in contact with each other, as jrbly 7im-7 2s1)rn nushown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m aew4rtvil6f21nvt7 / ibove the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter o te627rvn1vf il4wi t/bject 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 connec+l/4qvtj8 sdp xsrmk0r6h *e0 ted by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using theprq sjvt /kmrsed8 +x6 h04*l0 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 between a 35/t+86bbq6 qc 3tor qee$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 6-6q7rzrcdxeci ( 3qb 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 c 3d/kyilaj:g33vi 3sa oefficient of static friction must exist between your feet and the floo 3l 33/vjiky3adsiag:r if you are not to slide?   

  What is the maximum acceleration a car *(k56ip,cvb9 w aseix can undergo if the coefficient of static frii6e,c* i(k as5wp xvb9ction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber anz1.zswyn 2e- rd normal street pavement is about 0.8. On how steep a hill 1ze sryw.-2nz (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 )8 ge8dw p4cvui3/g uh-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 ret df k gz;,8fcpvxz8 cz e7b*e1b24v3xst on 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 v 01l c*7lepqdoery high coefficient of stpl1dq70le c*oatic 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 fr7 q .s4t8semsnnab) (yiction 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 ir/ymq+e2i 8jx-,e;3h op ztna mass would box A have to have to prevent any motion; hxe3in,-j/ 8ipz +y2qe mrot from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides .babg ;iy bhg9/,e (guacross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speedbgh ig.9bb/ae,( g y;u of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact andts dr( -ok 6rp6ob3pd: at rest on a horizontal surface dbs:- opd( o3t6kr pr6(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 ca-ij6o1r y8had89c,r hpkq,j prrying a 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 driver can decelerate and still avoid having the crate slide againstr,j-pp yk18co,q h9iah6rdj 8 the cab of the truck?   

On an icy day, you worry about par 23uc:xyav,vsj zt 7t(king your car in your driveway, which has an incline of sy(t2t7: jvuvz ax3c, 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 s3s apwv,fo5 /w1m,pnyg.s j0u. pnh y7lide 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 lies on a plane tilty( 5lpmkg(l 6led 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 speed of 3.0 3d8tqe4c a jzg q0.bff/ v//mt3lt4tn$\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a s)n,mryx- o8 s unu8(ihsnf5p2 peed 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 againvexo jr3nf,.) st a rough wall by someone pushing on it with a force directed upward nj.3,or)f vxe 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 he;cy reemq l /)v4*7mcan become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roovhe ;y4)m7e/c mr*lq ef 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 automobile tr kvk2c5x-4atqe,12t pzj.iut aveling at speed c1uj t. ie2,pztq5 2xak4kt- v v 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 tnl9ed: ) orr2wm*x ra(es20d ,pvkd-phe dash when the driver deceleratesx, 0*pkeewd vdo 2)r29n-rslr :md(ap 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 initia( o*jwr 1h34t xv,d9gbnb5lbpl speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they (hiox)j mva71 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 the coefficient of static friction between a box and the belt is 0.60, what is the minimum transiji1(o7)hx avmt 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 80:vy-tl ou pfy,xg,yof kinetic friction 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) cjfw 7f,pvvr0l ;f py+1qh7(us an 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,f/jc (t) tugejo:.ifb.3d0bi at each pulse approximately 20 g of blood is accelerated from fb0otjib.ge j3fc )u t :i.d(/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 reaso1hwxldcms;+15 z//l 3jml35(l k m*ftsp czhvnable chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force o x;zvs3fclcm3 + hlph5t(1mw1kzjd5/mls* /ln 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 , and if ana,p.e 6(rv dbe object is going to "hold its place" on the ground, show that the coefe pbev r.(,d6aficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two cars, *whpq)12 nr:4vibrj smeasure 72-m-long skid marks of one of the cars, which4r* ip:j v h2nw1rqbs) 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 vqhct9zics,,w- t 9/ ndown a 1-in-4 hill (1-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 bottom after traveling 55 m? (a) Ignorcqit9, wvsc-h n,/t9 ze friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaningr)3vy/c cwldcr h7- 4)z/ m odccf4fv; Tower of Pisa and falls 55 m before reaching the gro -h4y;)7f3c/d) ccd c crflzv ovm4w/rund with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but ew7iw;s4 f8 yibh-hz, anters a muddy stretch where the effective,8iww4ihahfy s-;7 zb 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 red +eum*v3gpor) esign of a hilly portion of a city. An important consideration is how s)pm3o+uv* gerteep 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 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 experiments, dan atf1o-3u bqy1gles her watch from a thin piece of string while the b ouaq-fy3t11jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are toj4d /k;0gfhs*j,d zj: s.,oxwm6 wjni be several ramps connecting different parts ofwj:im 6o4js; 0wk n,,z* /.dgxdsj jhf the 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 g65r:.xuwb-nu4 bhq s lift the piano (mass M ) using the pulley apparatus shown iuxn6.wq h- b:5us b4rgn

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 ) buv8 dbvu72fx1muk *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 chair, an engineer conshop 3sh*f3as(z v+ ckgcc81+7v /oohoiders the following set of conditionoh(szh v 13oavps /c g7k+h*oo8cc+ 3fs:
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 (660,0en1fmpovv*b0e ;g:h q 9ns8(z00 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropi sc,agvy dqt c-(;;.aes of similar length. Karen's rope is more elastic, called a dynamic rope- dgs;cy;t.qca,(vi a 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 likely to be hurt?

A fisherman in a boat is using a,i obb6wapqn 9hs9ho3(yzx*1 " 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 al; +ukxoxnmch. . qstu,c22lx4lowed 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 who are roped together are ascending an ud/nap:1r6zfb vjx,3o79c ksice field inclined at 21.s 6jru:n/xk 7pc,vabo 3zd1f90$^{\circ}$ 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.