Why does a child in a wagon seem to fall backward when you 1g0qlnizsp j i.luysp. -7l2/give the wagon a sharp pull forl g1u/sj 0n. 2 zlply-ips7q.iward?

A box rests on the (frictionh 2mqu7b ;jg,cless) bed of a truck. The truck driver starts 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 terms2 bcm7h;g,juq 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, are no forces acting on it?(uy mi*,0dd:9 fhxw:an )dj wz Explain.

Only one force acts on an object. Can the object have zero asv6l nd .0a(j a8xani+cceleration? Can it has (.+ lan86va0 jixndave zero velocity? Explain.

When a golf ball is dropped to the pavement, it b()koti 3 7/v6,sk s rsaeco*n- l-cyzwounces back up. (a) Is a force needed to make it bounce w( vkoso*e-tsc/6y-n 3lkaicz ,rs)7 back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move inbahf2/ 0;at 5os 8oss,6kkmzb the opposite directia/ 0s82ooms5bbhk 6z;fa kt,s on?

Why might your foot hurt if you kick a heavy desk or a wajp4sll;m gkfrp98v+t 1)oyo2 ll?

  When you are running and want to stop quickly xx. u,u 5-hvgqm *nk;w65iiwq, 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 at top speed to come to rest uwu .;ixqk,qgh 6xv5*nw -i5m.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a se /p40 hvkgn1xide)ihro *b,(nction of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives0*i n 1bi)d/( voe4hxpgrh,kn 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? Explain your answers.

The force of gravity on a 2-kg rock is twice as great tdj),zd4lsjn/o l uc*/ /,4zdu h n9tnas that on a 1-kg rock. Why thenzd/)l/4 h*ct,j ujlz /odnt4s9nu,n d doesn’t the heavier rock fall faster?

Would a spring scaleds6 l+(0abza g carried to the Moon give accurate results if the scale had been calibrated (a) in pounds,60z+bs ldag(a or (b) in kilograms?

You pull a box with a conh/1x-do9d ots lk 8dud2k oj.1stant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the tablesdk/ 8o.tu1ojl 1x-k9 2dhddo), 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 netk r+yu2i51 xyie h7p rl.9cm9k force mg exerted on it by the Earth. Yet by Nrci2 pmxi yy1.ule+kr5k 99 7hewton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you aref 70jvcani6ga+vsm df21 ;ed3 ;r-ux p on the Moon withfr-s a; ceiv 6 na1duf+d v0;3p2x7gmj 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 Earth.

According to Newton’s third law, each team in a tug of war (Fit(6+syeky. l ag. 4–37) pulls with equal force on the other team. What, then, determintys( lk+. yea6es which team will win?

A person exerts an upward force of 40 N to ht.b(ca4jb/: x m ix)djold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitud xdb)bima t/c(4:j xj.e, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how lpteimc 1pv15-arge a force does the ground exert on you? W mcvi5p1p-t1ehy doesn’t this force make you rise up into the air?

Whiplash sometimes r7esrp ry4vsd*q, q -+-+xyb7dqx 1wueesults from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of thepe+1duse ,7 y -q4q *vx-s7ywrbqr+dx 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 acc3wxidgk4vr e07- 9o-mac ,wnuelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes ta ,9-xc7m ekur 0-vnwow d34ighe crate to accelerate?

A block is given a push so that it slides yl23m sg.r, a n1lhcv-)gd b2bup a ramp. After the block reaches its highest point, it slides baycva 2 ,1llrnhbg.- sgd 3mb)2ck down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read ifvxa30.sil /5 a0oj+mv* kfruca0s w/y you weighed yourself on an inclined plane*/35/vw mvajc yrxu oak0.f0la +ssi0 ? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sledg p;0;tc6ir m ,ptkeu* at 1.25m/s$^2$?   

  A net force of 265 N accelerates a y /zo-.+; tz55pxtj m uffwf1jbike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 960. ce:gjm.s,kob , .pzd$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a 1e y2pxl( (lyej*nji+ $76-\mathrm{kg}$ 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 1100-kg car in 8.00qu1 p wr)q8gx 3tplw9 s if the car is traveling at 95km/h? rpgw8 tx u)1l309qpqw -  

  What average force is needed to accelerate a 7.00-gram pelx 0x(w nuu39krlet from rest to 125m/s over auk3n(r0wx u 9x distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an a)e )vf)lybrquid8k(v;n :6 zxcceleration of 2.5f)i(vkyzl)6qu8bx;: d vr n) e $\mathrm{~m} / \mathrm{s}^{2}$ 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-miless p069d5t5me vk e.vh 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;p br d1hu79e/rufo*m o);zx o be designed so that the maximum acceleration is 0.0680 g . What are the maximum an/f9 )zorbuope;d1uh r7xo*m ; d 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 bathroaar26,sx7aqqto-r hqb m7r84om scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevatohbxsr27taqaq a7mo-6 48r ,rqr, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator r3f8gp lo9w91w58rujpkg 6 k x0hm)jfhas a maximum strength of 21,750 N. What maximum upward acceleration can it give tk horp3pfjgg8 mf9kwrlux89 065 1) wjhe elevator without breaking?    ( two decimal places)

  (a) What is the acceleratilrab(0q 7c ybl7/ hhz31fm)ovpsf15ion of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equalb(a r c7h)ls iqv 0b51y7fpo1l zhf/m3 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 roofhyeje,xn u, y:j6e;. uf iw.q( of a house 3.9-m high. When he strikes the ground below, he bends his knees so that hi.u,n e.y yq:hxfw e(i,uej6;js 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 the box runs vertically uj:xxrrh7,fbf .s d:*k i7y mw1pward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other s7 x:1mdbhy7*wri.frf j ,s :kxide of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball play jy:u7.upmrs8er
(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 th)v x6 llv)kognoqa -93e bat, and again (b) after it has left the bat and 3 k oo-6av)vgql)9xnl is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-b6jm, a1d1 rdjs*sa ;dN force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vd 1sjb6j* ;aads,dr1mector diagram.

  Arlene is to walk across a "high wire" strung horizontally betwdf8z.0 dpd mmb;o+mg4 een two buildings 10.0 m apart. The sag in the rope when she is at the mimp0+ gdd8zmob ;m.d 4fdpoint 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 ujple5 0z8 q**lx. xx1 jzfyy/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.qfrs 2pf5 ofs 71p(f*u0$-\mathrm{kg}$ 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 ms2gxgxlw6 fl94 u;8; -gvyqoto a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The s-l9u sxvylm248 g;;gx6 fwqgoum 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 ixxoun t8r4a, g+fhxz1 (4c1pk s pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomo axu,148z r+kp ghxn(t1cox 4ftive 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 showul eoj.d by9 jfl1,d/hnzsy0v8,k /y2n in Fig. 4-48. (a) How hard must v8 /he0sukjb 1d9,l y2l.jdfyzony,/ she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a ek)jchv+)d (r 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 a zm l:*m27oveow8oz.block (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 contactirtijn.bf, 4lw:58avq2 3b t l with each other, as showrlf2ja3bvnb 4,w8t5:lt q ii. n 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 above the ground, a /(b- 4ghhynrmnd 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 i-h4rmnh(yb/ gts "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy smrq 121irw xm;cqm1*rhsb+ .cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fis;s1h1rqr1 m*b 2m.r+ix qmcw g. 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 fricti9bxs+8brb wpm4ug54nu si5 y5on 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 ijey2p*r1 jf,4gc0ha mqjm- *required 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 minimum co:9g/f4gh g4 ev x.ptmsefficient of static friction must exist between gest/:g xg 44p mvh.f9your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if thpncg nd,n1u6 np)7g) idm4l/6i rscm9gbg-)oe coefficient of static friction between the ticgu irc)9d 6 po)g6g4 d7n- nnb/pig s)1mmln,res and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street panyqy,dn3k*p((j *i w8 .spj uc xlsm;)vement is about 0.8. On how steep a hill (maximum angle) can yoixjsp ls*(nyq, ypk w*mcn.8)(;j3du u 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 w j qr(ox*g-el2 wcy93mzz1/n -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 ro uddcv4 ko)m3,3j/uce ugh 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 a)-bqiz 7yp0 sb7 /bdqxsphalt surface have a very high coefficient of yp d q/0)7zxqb7ib bs-static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of klqu+ -8wp70lexyjntx +*zns +inetic 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 4-2g dwmpg*gz6 930) how large a mass would box A have to have to prevent any motion fr zpggm69wg3 d*om occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, gio9ab,*r m 8/gmuls+caven that the coefficient of kinetic friction is 0.20 8ca/ mu*, or glmsb+9aand the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , arn mx-kxjs z,2+e in contact and at rest on a horizontal surface (Fig. 4-54)m+xzn jx ,2-ks. 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 coefficient of static fricti vbb8 b6g/ 5qlbb/*vhson between the cbv /bv/58 hsql6b *bbgrate 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 truck?   

On an icy day, you worry about parking your car in6dz a5/i)y bw)en)mje your driveway, which has an incline ymw5nidaj)b e)ez 6/) 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 sliu96/ c xpmaht,de 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 planekbb*hqu qu;k9:s4( 7wokis1l 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 speed of 3po)ae19g(w+twc c.a m.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of y8a4+/ tbrptl 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 arj :7t/7iqim *1cj tbcgainst a rough wall by someone pushing on it with a forcqi:jr77 c/*ttmcbji1 e 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 slipperyu b qbx0h/g1x1 roofs can become dangerous projectiles as they melt. Consider a chunk of s0bq1/x gh1ux bnow 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 diljqj4q 5 lb asv;7nfphqx,v0 f.40r2nstance for an automobile traveling at speed v j.2rp0q4qf4sal hf7n 0jqvl,;x5bnvis 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 the dash 7 phk5sm 0wna6when the driver decelerates7 60spnm5kh aw 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 spebuhg q5fu9mw4bq(q;l b7zq4( ed $ 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 w,ys qrsbz.dq,eq; 2(0icuez)here they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The rs0decy2q)qeu(.bz ; z,,sqimost rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic fr 94 ihia1-hm ux7l0kkxiction 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) can coast6 w)uj:tj0)iz k h ofq5,j;bli 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 arrnz i1f9k 08n mammalian heart, at each pulse approximately 20 g of blood is accelerakn91r 0zf rin8ted 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 reasonabl 4orrxgnny054(+mtgp e chance of surviving an automobile crash if the deceleration is no 5rt(n+prg 4ong0 x4y mmore than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an yob09m;,f 7 jw8 h6yr-fm b-58mpiuczdta ex7 object is g7-,m9ry0bwxd 8 bfeuy5 tam7jz6cp m8i o;f-hoing to "hold its place" 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 scene of an accident involving t vw42xv3w cqp qhn/2l-wo cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. 2cnlvqpwv2qh3 /4x- w Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down 54ie x+q 7c.h l-okv2ov pd+iaa 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change +7pkhxoq4ecid+. o 5il2va- vis 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped 0xe.55mf eayot4v0hz*w 5dny from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forcext4w5 m .0zh0ye5e5*yavf nod of air resistance?   

  A cyclist is coasting at a steady speed of ./bm eam(t eoon l7g6)km3(m f12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts )m.agk3ob 7mm /nm e( f6l(teofor 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign8lsd2e u+y3o w of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg 2 yud8+ls we3o, 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 exp cn,1 ia5rev0x(h cj4teriments, dangles her watch from a thin piece of string while the crntcjvhai4ex(15,0 jetliner 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 to be several ramps connecting di:ut. un(tjsawr6e 7 n1fferent parts of the 7a twr1.n(nus: u6etjstore.
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 piaqch srl,o4.7r no (mass M ) using the pulley apparaq4ros.rh,7 c ltus 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 gh vakm s5si6k733-aeg1l cz73.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 engine;j/)cbu fz el b.no:wb52 ab+ser considers the following se.b;:b2fucl)wsn b5e z o+ /bajt of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 6j x.3)hwv bj;q60 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety r(*vppi;qid jtt+id(o i2+ r4n opes 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 their2d+n*i4p p(+qttv;dji io( 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 " 1ihj3a 8xlki dtnb-3y; ad t 2iuq4;(r20-1 $\mathrm{~b}$ 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 buildinc,-c q 1c6 1t 1 bb*:5al)j* ro1ikzhgpqeqizyg is 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 who are roped together are ascending an icewickom6,e+h ; j /6;hqoq0bgl field inclined at l6/h;+ kqh6ob,0 qe o;wijm gc 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.