Why does a child in a wagon seem to fall backward when you give the wagon a ssru.. u-kw0yy r+ x-kfharp pull forwrrxkus. -+yyu . kf0-ward?

A box rests on the (frictionless) bed of a truck. The truck drtu ih.44/fokl;kqk g2zx+ fo8iver 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 terms of Newton’s laws, as seen (a) by Mary standing on tfh4;x og uo28ilqkkf/.k4+tz he ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of - * t/tn i+uaucoh)b7jan object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object chv96q.ecvk *y jziq :z7 ,eq(have zero acceleration? Can it have zero velocity? Eyhec7 cev, iqq6*z .:(zk9jvqxplain.

When a golf ball is dropped to the pavement, it bounces b7rc /h(ate()z 8cr tkpack up. (a) Is a force needed to make7( c)(hp8/ra trczket it bounce back up? (b) If so, what exerts the force?

If you walk along a log 7tfom9tep(iy)5wb kyy9. bgpj .z5r( floating on a lake, why does the log move in the opposite direc7k.9oy5repypjgwt.yb(5i9f )(z tmbtion?

Why might your foot .)wrup mjhv-wbl2(*,1 mv piy ,wwfx7hurt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you md s7:fx+vmntnqfyyus42-5r k l44o8 lust 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 decelerayfn4kq7 : 54+2x8yuls vms 4l-o frdtntion of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling,civ9iu,k)p-c sk :vq :rx-2 /9gth vcf :rcou: 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 tc c:cv r:9)tvkuixu/-,k :ch9qs gop:-vrf i2he 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 as that ond4cx .ib:m6y 8jj fq)m a 1-kg rock. Why then doesn’t the heavier rock my8:.d4x b)jjqf im 6cfall faster?

Would a spring scale carried to the Moon give accurate resultsgi: 5u+m ue)zf yq)erh6 :mih, if the scale had been calibrated (a) in pounds, or q r)fi6m i ,):muy+5zhuhe:eg(b) in kilograms?

You pull a box with a constant force across a fvz(xdz7lw9fq (6n(h uu 76lin6qc5srrictionless table using an attached rope held horizontiqd z9n76u sf6uhz n (5c 67qxlv(rlw(ally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net forcegy)mt )n.q)fbmvt-xqc*sdhw.*z 7. v mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposi-ndgvmyfw hbv qs.*.x m))t.zcq 7*t)te force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force)g8)6c,9a wwyjb 1 zl noj8ddm5 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 t 8ao1)d6c89nyj j5 gdm ,bzwlwhrow a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in 0:n7rt6 5 cz6ylmj iiha tug of war (Fig. 4–37) pulls with er i 5it76j0zylcm: 6hnqual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desqco6v0/rmg.(.w ikt8 b0tld e f*3rbycribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) iyrkbv.wte68f ci.00qom *g( l db3 r/tts direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does thl+va5 dhd g)6ce ground exert on you? Why doesn’)cd+gl56d h vat this force make you rise up into the air?

Whiplash sometimes results idx1m),o8yn k sg zwe+xxhb 9p,td620from an automobile accident when the victim’s car is struck violently from the rear. Explain wh6,d)i1ozpn 82gbm9+hyw xds xk, x 0tey the head of 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 truc(o+sqyk 3 dt3zu v:kw+k accelerates, thvk3u( zdqw:t ++3y skoe crate remains 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. Afte2 qkyaqwa:( a(r the block reaches its highest point, it slides ba(qa aq :k(yw2ack 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 wt:hda-+ lde/ reighed yourself on an inclined plane? Assume the med / a:dhrelt+-chanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled *4t)cen;g x1- g1frjw mcl9d n at 1.25m/s$^2$?   

  A net force of 265 N acceler1 mi)rwcw a1e+ates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is u2wryw)x6ro o9sed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o;n.ci z2e mvdr5uy z1(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 requirerv 5pfnl.rcwkh 81b,vy,) .i hd to stop an 1100-kg car in 8.0 s if the car is traveling at 95kiwv.r85 yp.vf1,l)knrc b,hhm/h? -  

  What average force is needed to accelerate a 7.00-grrn.)ndft) vj h)dk8:uam pellet from rest to 125m/s over a distance of 0.800 m along the)8r):d)u hn n dftv.kj barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2d r) :jdvhz+5i.5 d jr +i)h:dvz5$\mathrm{~m} / \mathrm{s}^{2}$ 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 cagmt7 4)sw )jksnm2+ qbn cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum accelerat 3ol 2xzx6ez/w4 re2nqion is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting c22z4xzx6 eq r3e/ wnolable? 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 sc d ma*4cszl+/eale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the persoz + elas*4/mdcn’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 21,7tlj7wnc88h j7 50 N. What maximum upwar8n 8w7cl7jthjd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration ody8 548o zqwjb;i m79h ible,of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is eiwimqoy4;,8 b9oh j5eblz 87dqual 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. When he xfvm 1z 2 h0p6x kj7w /,aoao(x1n6x9m1rvfvjstrikes the ground below, he bends his knees so that his jm0 1xo6pv9hnvf f vrk(x jw7/mxa2x1ao1z6,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 thig, xls4r8*cx0gli0h q5),tgvoj5bih u 30qie box runs vertically upward over a pulley and a weight is hung f) l qsi,h,hgj 504ig x3v5g0li ic0torxqb*u8rom the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagramm;9e*mkiix. 1qixte;s 3 a.5yfjvm c9 for a basketball player
(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 baseiufcasl2 b b,9+mc,/mball (a) at the moment it is hit by the bat, a,lcbbmf ,aim c/s92 +und again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forchlh :zu8-4(mq guyvr7e must be exerted in what direction so that the resultant of the two folumv8-h4qyz gu(hr 7:rces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" yipr h t76i*5istrung horizontally between two buildings 10.0 m apart. The sag in the rhtp7yi*5 iir6 ope 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 be29mind.5c2*y pyf38l sxa kis hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0 cppua/kfhqg89yf-3-nzt 6ga zf1 ),n$-\mathrm{kg}$ 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 hon 64gdd fk)k/husing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum gnkf h4d /d)6kof 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 caztn-d:)r evn5 l5cb e;rs of the same mass behind it, Fig. 4-47 . Determine the ratio of the tens5:rntnd e-5 b)elz ;cvion 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-pulnu0v p +ty r :shn;o4;- nwaacimz6r7/4bnau1 ley apparatus shown in Fig. 4-48. (a) How hard au 6:nc 0a1 rbunaysh4+z-n7vit/n;4;omrw p must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a rac5wvddafl+ eq :*;l .on6 )spfge began, 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 fv,j4rc0 p. owp:/hvj c8kh8n$ 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 frice tsx;h +9d+dztionless horizontal surface are in contact with each other, as shown in Fig. 4-51. A force sxz deht+ 9;d+ $\overrightarrow{\mathbf{F}}$ 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 e m+ve+)h8pqc /pqmk5 rieb3 d(ach initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lightvmdpq+5( qkipr 3e/mb8 )+che er 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 frictfkbm lf 02p4+c6o:suj ionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tensio:0bl f42ckjfs m ou6+pn at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friiw + y za08opff96u3pfction 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 required to s4k47nshy. lnihrxx. 5lqowg 5 7ld63vtart 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 acceq;;oq ,gxhuu(xa 3t8 s p0g-xtlerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if su; q0 hx(quxt3tp; x -,og8agyou are not to slide?   

  What is the maximum acceleration a car kx( 8wc0 ev0xap-t xy:can undergo if the coefficient of static friction between the tires and the y x: 0(vx8xct-ea0 kpwground is 0.80?   

  The coefficient of static fv 5e yw2qb;ww8riction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle)y w8e v5wq2wb; 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 vl (am7;t+hze -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 roud5 47 uzfn-krd+t;.n)t7odff5reqjigh 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 very high coefficiens*huch2u1 g m,ud e)2et of stcuu * s,1dh2em h2)gueatic 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 frict e/wvhm;+ lcr,ep y-:ae9xi 8cion 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 4-2rx- ,4) bcj gvvpkk*p(0) how large a mass would box A have to g v)kb4xcppj(k- , v*rhave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Hr xynxs8m2 mq+yt1s+ ny* 8/ibow far will it go, given that the coefficient of kinetic friction sxrm 2y*88 yqtibmnn/x ys +1+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 anni (. y,f/ pi(rdphp31z ( lp1g9nzknkd at rest on a horizontal surface (Fig. 4-54). A (r13l, pd.py(npi z(f/kg k1z9nhn i p620$-\mathrm{N}$ 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 carr(0rfus9my o/7 oi;j cu3dp5ttying 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 (03o ;jsup t 9/yurito75dfmcwhich the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry afd 2-)g yb7c oxom30hkbout parking your car in your driveway, which has an incline of 12gy)ox2h dko-0m fc3 b7$^{\circ}$ . 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 slix(*)yoc9 r/8k /wx2e g ijpfqfde 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 re dbtqd4s*8vq5.jb4tilted 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 32ga bdtt8*3lxcai;f ( .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 g( u 4oqlvi;dd+o( /9 yki ,+qklslfy:top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rn:qz.9*.mdxm9yq8y f k c9l bfough wall by someone pushing on it with a force directed upward8*9.xy qyf lfm. q:cdkmzb9n9 at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiledjy8y -a5 1oi9,yolums as they melt. Consider a chunk of snow at the ridge of a roof with a pit ua59yjyly i8mo,do- 1ch 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 stoppingc)3ycbdja,;-aam 7mlu i*1vr distance for an automobile traveling at speed v is equal to ad rabjm)v *l-;7yi3cuc1am, $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 870,mv w..f:bb7y fi aubhbe wslides forward on the dash when the driver decelerates fyw7fhe : .b,biba7v0 8 mf.uwbrom 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 i8r 3h)sslegc: s given an initial 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 bel*.h q(n)sp4n jkbusnk+7r-mrt 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 the coefficient of static friction between a box and the belt is 0.sqhb-n7r+mkp u .kns)nr* j(460, 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 coefficiez 20 w3,r lc(sjs,ftwcnt of 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 bicyclp* z3yum a 34pqgemf00e) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at armms bf7g u+ )gx4:lq63qfl 1each pulse approximately 20 g of bloour ):s3l6m1qfambx4f7gq l +gd 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 4k*2)vwe6loop9 cid2;yxj zichance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a 70o4pzde w )92 v c*;2jkyoli6ix$-\mathrm{kg}$ 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 acceleraticxx)m la(ics*a : .i v/2/pxkv4b v*mqon produced by an earthquake is a , and if an object is going to "hold its plasc4l avim)k*i(x/m/2 q*x xv :. pcbvace" 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 ;nrv8 t 1iz+/8dzofpx 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 friction between rubber and the pavement is about 0.80. Estimate the initial speed oztfz;+xr8/v in o8pd1f that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means r2,9heywl :9 ymi6yguthat for each 4 m traveled along the road, mhuir y 2glw69ey,9:ythe elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pis;v28b .* cx*tnp ecespa and falls 55 m before reaching the ground with a speed of What ct**;v2spne bcep8x .was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters ::8mnx n :qumx)g*lavrkhm0/a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to peda g0mul:nv:qr *m 8:hk mx)xna/l 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.fwih/7p 73ocbm4s9y m An important consideration is how steep the roads can be so that even low-powered cars ic9 4mb /77pswfymo h3can 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 experimentszz8 r7xl8up5i , dangles her watch from a thin piece of string while the jetliner she is in tail5rz87zu x p8kes 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 q ) 3y5eycngg j9zr1w3ramps connecting differentg eycw13gzn9qj)r53 y parts of 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 lift the piano (mass M ) using ,-atc r5c i9z5f gej,lthe pulley apparatus shown in f eraccg,jtl ,5z -5i9

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 atvck).pj1rm l b-y(g5x 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 fygl-e0qbk g;jj4llpa6+(b x m: g-vf*or a child-restraint chair, an engineer considers the following set of condi-:+agg 4xejl qk0jl6;-pb flb(m*y vgtions:
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 k qu gz4ao6x8,ydl.tww x 67m7Italian train has a mass 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 Karen, use safety ropes of similar lx.: 3j7wbqyl b6b d0ztu(c: rbrv,)nz ength. 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. (Expre3,d6j: .qb ybb7n czw: ( vxlzbu)rrt0ss 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 boatx/w, 7fecxj0bt6ypx* jd7 frf8; aog qo8,b0 n is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed265 de5pcouf b;z9p lv 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 ascend b z2i,bjb89deing an ice field inclined at 21.zbib ej 2d8,b90$^{\circ}$ 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.