Why does a child in a wagon seem to fall backward when you give the wagon a sh (1ria i6tbgyt73: amwarpi3tw 7:6y tmgb1a(ari pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts x-1rk rlceal 4dqq )n:5ga7u7t;9ryc the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the rc9arq gc4a7q51x)-yk url net: l;d7ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are 7djhii a9+y4rno forces acting on it? Explain.

Only one force acts on an object nqq(axzm85qo1kw 59 g. Can the object have zero acceleration? Can it ha5x1wqo58ma9q(k z gnqve zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is :8sv1 zu qifi,a force needed to make it bounce backuv,:z qi isf81 up? (b) If so, what exerts the force?

If you walk along a log floating pd xsm*sek s+wrl0jr o6663bel-e s58pe 2m(s on a lake, why does the log move in the opposite dirl s-b 62spess(6r*0l+ewe8epds mmo j xk35r6ection?

Why might your foot hurt if you kick 1a3f6qu.wg cq a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicdp::c/xzak)hl9 ez0lkly. (a) What is the orig /hkazd)e:cp 90xl:lzin 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.    m/s$^2$

A stone hangs by a fine thread from the ceiv+ht- mkac ;7pling, 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 danglink-a7;v +hptmc g 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 on a 1-kg rx.okfes acnf*g ;nes,,lt 70;ock. Why then doesn’t the heavier rock fall fasc n 0*s,;e7xfto.nkgel;as f ,ter?

Would a spring scale carried to the Moon give accurate results if the scalx +sverh92 ku+x- rr5fm.6h ake had been calibrated (a) in pounds, or (b) in kilogramrshr k256ek+ f+. vhrxuxm-9as?

You pull a box with a constant force across aspph8ov 77nn8f ;t 6ry frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the hoyvnpn 7 s;p7o8h 8r6tfrizontal (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 ofjm46b*l3 v bc uh,*wrl gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doe4l6lm,bh*v 3crbjuw*sn’t the Earth move?

Compare the effort (or force)ofev.b; i+cp4( p:u ka 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 throc.fpkuev :+o4 (;aib pw 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 (Fig. 4–37) pulls witsl0 uxbo5uj 8b5h 2*8 xtdid4vh equal force on the other t4o8dx b5 2*iuh btusd5j0 xlv8eam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Deou e.1t1e awv+rs*g6 zscribe the “reaction” force (Newton’s thirdsgwvz1 6e1+*ear.uto law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on thc ph-)h3l6way2wb b y8e ground, how large a force does the ground exert on you? Why doesn’t this force makawpb3 c68 y)2yw-hbhle you rise up into the air?

Whiplash sometimes results from an automobile accident when the /dz9se,p fv1wumefrd1(. 0 kgvictim’s car is struck viok e,dg(u rs vw/e9p.1dm0fz1f lently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of3/vu: jha2*bnu (z pms a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, acc /z b3sh:un2*pvja(m uelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches s* +1xfh4 x(kt l6txoeits highest point, it slides back down but the magnitude of its acceleration is less on the descot*ht6x x x4s1e(l kf+ent than on the ascent. Why?

What would your bathroom scale read iyk-is3j 2a0q vf you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an an ai2 v0-3kjsqygle.

  What force is needed to accelerate a *gjam bw759a8zq jzo 4 4sl0yichild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridedfj5c-w53wl)k 5 lsadr 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 +.fvx7b0;dkgfiz jid0 rr8h (accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of aj6y e,o q3dkv2 $76-\mathrm{kg}$ 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-kgk8s +tz2hu(bqg jcw 95 car in 8.0 s if the car is traveling at 95km/h? q5k8b t hwc9z2s+u(gj -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125m/ :s0:hb/qhc 1 lfgwd9ys9c10sfy :lhdhwb /:qg over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of th- roy3zb// terl(,ep5euw8w ae water with an acceleration of 2./ /,-8 (3r5wrpeblywetauez o5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 hj a+ u9*,j7 ewkney3sa 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 tfl31eh; k0ga u94c alko be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the mc1kaeuhgl9fk;0 4a3 lotor 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 ihj c/ 6(sr0g. 32kg q:7(osu ogm ho(xfzlhsg)n 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 elevator, and find the direction of acceleratio/3sh7s2ok( fg: 6lg0h(roc)qozxm hug(gj.sn.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum streng 29bkg32ue chzth of 21,750 N. What maximum upward acceleratio3 ebc2kg u92zhn can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of t9jh eam8(m(x zki:0qywo falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth (0k: 9emz(hyaij8m xq 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 houwx 1z.xt.7 g -k8yolvbse 3.9-m high. When he strikes the ground below, 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 y7vx xtwb1 k .go8l-.z
(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 6p - gbbfvhh2/upward over a pulley and a weigbh6/bp vgh f-2ht 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 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 player 09gnslw gvm o 9*n 480myivtthd q6;,n
(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 bcexmd *.ro9:t 7u1trn y the bat, and again (b) after it has left the bat and is flying toward the outfid motcu .*r917etn:r xeld.

A 650-N force acts in a northwesterly direction. A / 5g0rntizy(k+f;jp :bl fj 9asecond 650-N force must be exejnkz / f +;y0p fab5tir:ljg(9rted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strut041sx dg8f4uj.ipdj,vw p b:ng horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 1j1pg0t.s wx bvfd, ui44:dj8p0.0$^{\circ}$ 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 is7jk ogtbi).plify1-2 g0v1 rg 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 14.0iyp; fkd34 cs*$-\mathrm{kg}$ 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 locatiogb 1 vxdqbrqe0 +f(9 fpdd7p.v53d;iun at McMurdo Base, Antarctica, as shown in Fig b(p5gqruvf 09;3bi1.vexdd dp+f7d q. 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 tgm9y 9 *.epmtewo cars of the same mass behind it, Fig. 4-47 . Detere9t9p. *megmymine 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 ym3fhjrl,x lawc;:uq /mr ovyr+705. upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must j7 cwfq,r5u ly+:v;m. /0rxroahl ym3 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 racgb -jqrz t0m16e 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 (mas- h/wnx l6su:os $ 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 friv g2/vqe ,d,v6icznf;ctionless horizontal surface are in contact with each other, as shown in Fig. 4-51. A force / vcdv6,ifegvz;n,q 2$\overrightarrow{\mathbf{F}}$ 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,ynd/w fl /wi3, 1ofvp-52 are each 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 acceleio,3fyl/,pf/ nww v d1ration 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 arep;l7s drp-1e- o5zvtv connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of ea el1;z 7vvotd-r-p 5spch box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic e mp li9e,xb;3pw01ew-f9mssfriction 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 startq8a5b+0k ijn77mg/ lo vunz;w 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 mc d4hd hw34-y3n,)lm5aqsi i finimum coefficient of static friction m3yshc,5qd h) w-da434mfniliust exist between your feet and the floor if you are not to slide?   

  What is the maximum acceug)m pb:co(y46yb,uwf u x p( 6z,b;ccleration a car can undergo if the coefficient of static friction betwouy)6czu,gwb m(x ,;(cbu :pb 6 c4ypfeen the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber ;fro9-w4/kuck edb s)and normal street pavement is9; deckor4swkf )ub-/ about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at tw6(o(bz gp,l -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 3045dst (ck(nkxchxm 0 :$^{\circ}$ 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 a+/ptkg+ / qolyt8jphor6 kb58t 7ius;n asphalt surface have a very high coefficient of static t; lqkihypu+78bg58t+pj/oo 6r sk/tfriction.

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 friction fo+o+g c4 lfrhu6c1o+w ur 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 (Exam:;-gl ekk2j wth2w, mzple 4-20) how large a mass would box A have to 2:m 2g ekw;jwt hlzk,-have to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so th7z0)i8dveogsm.z9gjm - c lg6 at it slides across the floor. How far will it go, given that the coefficient of kinetic lmd)6g.s0v7- ggejozz8 m i9cfriction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and h. lo-rm. cgdix irs1)3ox g y d.q6+ba*62yogat rest on a horizontal surface (Fig. 4-54.a6yomic ghi)y+qd*ob .or xg -d s1x .3g62lr). 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 frictq(pp77 l:vidkion between the crv qk:7 p(il7pdate 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 in your driveway, whict w8w39o- bmckh has an inc3b t98mow-ckw line of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with 8avr 0ajr1q/j7 mm9fga 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 ong)8jgz u:vcso3sk(, j a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of xdlrb3: m(f o1 mvz;p*l0 .kpo 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches o/nyq:x7v j3m)ycl 8i a8,cao the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on ite.yz(7s4 or wz with a forc7yzw .o(z4 erse directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectib.ac*bh pg9*agtq++ekuv/ bvr,vyp ks.f:3 4les as they melt. Consider a chunk of snow at the ridge o ++.9pe.tbkyrag*q va :cpv*bhs /v gf3u4,kbf 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 stn7 cik91 r3d6 upq3ejsopping distance for an automobile traveling at speed p91c763er3qjui ksdn 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 formq n/9pk;);pm ll /cpbward on the dash when the driver demqc; mln/ p lkp/b)p9;celerates 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 uwn8qv9s1e1uv .sm ka8to y/p q6f. m is 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 belt from wherb3fn uf/i8v y .h2,bhge 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 thifv2y ,u3gn8. fh bbh/e 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 kine49uqnt6; ssp-i 8ok adtic 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 bicyz lat)a ;l-4fbt++h*whoa nq1cle) 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 simplifiedn:pu dq ij0) hru7 y7*edl1fq. model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from ejf7.il yun 1h*p:70dudr q)q 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crass y 7t(b+-reuih if the deceleration is no more than 30 " g 's." Calculate the forcestr(b 7y+ue-i 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 produce-qji /ce5c 5aa8-aecgd by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction witijeaa-cqg5/ac e 8c- 5h 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 ofk ) gresk1cdvobxji9 3*5 (-wo an accident involving two cars, measure 72-m-long skid marks of one ofbo-w5kk(s i1 9ecx g3d jrv*o) 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 of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4u(+ usd 3f 1:sh2 1mzehx8uxeh means that for each 4 m traveled along the road, the elevation chae(h1eu8 2 z3+mhu:fx dsx1sh unge 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 droppe s )sr)4cwm qakg5 rr*xy9bg:.d from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was therg* c4rwr)q)95mk sa.g bx: sy average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mud.8rsa( c0lzrylq bjd3nv sa x9as./**dy 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 for 11 m? If so, what will be the speed upon emes8nj rl qz bsac(.axda*. 9 yl*rv/s03rging?   

  A city planner is working on the redesign of a hillyjsq 6*0t h9phn 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 , can accelerate on a level road from rest to n6*q 9thsh0 jp 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, danglsrfb m o(02v zc av(c46w5z redh r*zrt:n)-k8es her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that v6c m84e0* r(hor2bzwcv5)s:z r-ztaf( n rkdthe 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 diffe+pf+, hqh1dy n ap9:3 hothzj5rent parts of the storf 1+h+yz,h5at h :p hjp3noqd9e.
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 pi)ujcxm r/:t*(alup1z ano (mass M ) using the pulley apparatus sho(zrp)1m xt/ calu*j:uwn 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 3 +y x38plf:ytt.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 copc6fzu5c s5ymxeh8h m;..t6unsiders the following set of pxhhf5 6y5m6euu.c 8.ztms;cconditions:
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 masgy4br 0tsdsm2 nusyh2zn m1) 78w+ji 2s 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,.sycgp5w: a, t9np/ 2durjt4u use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) uw, :ugncts .9pp 245ar /ytdj(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 boatuss3*ubcf 1 puah ( 1jl:+d*te 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 allowed to reach a maximum speed 8k ynr xe1ws.x.;:cc7ki2b gm+-x dz sof 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 b:t yh u( 3lv,-4lwznqare roped together are ascending an ice field inclined at vl:q z,(3w 4unb h-ylt 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.