Why does a child in auxr-spo(y93 qe )vk)i wagon seem to fall backward when you give the wagon a sharp ux3e)q( -v)ryskoi p9pull forward?

A box rests on the (frif dghxpw7t*5 (ctionless) 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 terms of Newton’s laws, as seen (a) by 7*dgpt5 f whx(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 itxw1tr/5kpjc wd5l0 7l ? Explain.

Only one force acts on an object. Cano pb ; o,leud(lot6eg:x0yo: 2 the object have zero acceleration? Can it have zero velocity? xeo(p, 2oot6yd u; g boll:0e:Explain.

When a golf ball is dropped to the pavement, it 0e9/y kcu/x 1s7q +0i(xj 0hwxqbeeqhbounces back up. (a) Is a force needed to make sh/j0qhbyqwe e/9( xx1e0uic qx70 k+it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, whc bn d+*wj/l,iy does the log move in the opposite direction?* ,wic/+jbd ln

Why might your foot hurt8f.br j 6pt/i3+nnisajdg2 *z if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate qui d 2*twc) s+i2mstciecp fdlcm ,4*1/ackly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum ratetecc*m) ,fpc1+ *sitl22 dmiws/ad c4 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 ceill:gl,ff+9 dg; pif.la ing, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answer, figl.fgad;flp :+l9s.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. v7m0w wc,3j8gy8qnq8c4 qjd j Why then doesn’t the h88q4c wqvjg8w70 ycndj3m ,jqeavier rock fall faster?

Would a spring scale carried to the Moon give accural( qjy4wj vpkb92el tg 3-*:ecte results if the scale had be34kte(wvl-pb9 *ylje jc2q: g en calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictibaarm+2u2tah6 .s8.oito.d oonless table using an attached+ o2a.m2 d.6osorbhi 8tat. ua rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influvajg tuv+6omeu 6k3jxa a yy7 80e,55bence of gravity there is a net force mg exerted on it by the Earth. Yet by Neuao 7xb0vyj55 kuem+ a,6a86tgy3 vjewton’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 1j;o :p9pi; xunn41+ swtiqfn* 0-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the ui1 *qptnxnwns4;+9ijfo; p: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 (Fig. 4–37) pulls wit/ 8x6gak(weyozpp xe pn,6.3difz/s-5v z6xg h equal force on the y/ xgn 3 p65ipze w/ax6.xsvkpz,df8 zgoe(6-other team. What, then, determines which team will win?

A person exerts an upward forcecmz88/ sqjraz9nj s* +4u/iuh of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it z8j i+ hj4*szc/rq98 unmuas /is exerted, and (d) by what object it is exerted.

When you stand still on the ground, hdr+q3rr9)c xy9c pzgcv;z 0p4g8 im:,7 qesqpow large a force does the ground exert on you? Why doesn’t this g+ydpc x4e: ;9z9 3g )scp qvip 0m8,7qqrrzrcforce make you rise up into the air?

Whiplash sometimes results from an automobile accident when thewzf mf/o+0 (vk victim’s car is struck violently fkzf+/m(fov0w rom 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 of a flatbed truck. When the trucesw;re4 9x) lgk accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acce9 ew)e4x rlsg;lerate?

A block is given a push so that it slides up a ramp. After the block. * ,lzb6ko qt1tpdy)tn5d( qt reaches its highest point, it slides back down but the magnitude of its accelera)nqkbt 1t lpz.6do (,*dy5ttq tion is less on the descent than on the ascent. Why?

What would your bathrogkqr7j5 2r dy;om scale read if you weighed yourself on an inclined plane? Assume the mechanism fjr 5d qyk2r;7gunctions properly, even at an angle.

  What force is needed to accelerate a cn*aa8a5h + aikhild on a sled at 1.25m/s$^2$?   

  A net force of 265 N aq r6,fy37f-p + )vkvmqwqn:q vccelerates 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 if2pwyapx8: ueylnz ;5 9 it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o1eypj 9xrnqo *6 hf,s7f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the car is tra5-i,mx +z nlqp; med7zveling at 7xenlpz 5;qd -,mz+im 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellp( zg i8q8wn4pet from rest to 125m/s over a distance of 0.800 m algppi8 4 nqz(8wong the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accel5hc,. 2 lmghgvor,aw0eration of 2.h5,crw2,o 0a vlmh .gg5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cark e7i3qe.nbm* (mxpl8 can 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 accele,f1 b8j zpf4v/f/hq xlration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the su,q1fpfljzhv4 b/f/ 8xpporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionle8oqczp dbgd5u +.znk/o:8zm81zq3xv ss elevator. When the elevator begins to move, the sc.zoz5 qumd:q+gzk /x nz8v1db8 pc3o8ale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strn6ax +2 hty(g4vuj6xaength of 21,750 N. What maximum upward acceleration canjgtxa+6xa 2y hv(n4 6u it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two faqh*nt3( 74gvok p7-m* wljnnjlling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of theirh-q77w m4 pv k on(jln*jtg3*n 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 thuzdu 1u/qgv; 7e roof of a house 3.9-m high. When he strikes the ground below, he z 1duguv;7u/qbends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N res3i qus ng+tu5o1a ifp0/gtg5*)lx9 bwts on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the )ua9gi*3txfq s wgu ibl5+tnpo/0 5 1gforce 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 diagrxs :+ph j;;c pjr xz,,ke*u0jfam 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 baseball (a) aq3 4hzhu+k +rwt the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outz uwk+h 43rhq+field.

A 650-N force acts in a northwesterly direc5, xbxtft(k 8d9c /bz j0pmcs1tion. A second 650-N force must be exerted in what direction so that the resultant of the twkx9j,zpf bb/ct8 (tcm1sd 0x5 o forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "highow/6jc yesb7j q5e1 )m wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when sh /ee5m)7j1sjo wcb6qye is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord from hl9 ntksj-;e ez/*;kzanother 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 14qom-j2.+iqfo4m dnj 9.0$-\mathrm{kg}$ 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 hzinlh)0o3,up8w: upo y :/lg unit to a new location at McMurdo Base, Antarctica, ahuo u) zwo30llgh y 8/p:pi:n,s shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of twf+o8)tb 0: fjck.mnehe same mass behind it, Fig. 4-47 . Determine the rat+jfm)wfet0 cbn8:ko .io of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus showjlhjwqq:h, 4 26-g u3:lkoec fn in Fig. 4-48. (a) How o4 u:j: -q, f3 62kgleqhwcjlhhard 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 race beo4 wu xc6,.: kbne.gtm-o(p2w5c skmsgan, 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 bl: / dhxl 8yhaor 3-v6s1u ufmsi+3d/gvock (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 fricte6mh /bfu j58m4mmva;ionless horizontal surface are in contact with each other, as ;ammmvf eju54 8h6b m/shown 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 1.8kyfgz ; smw10p0::hei0 m above the ground, and the masslepi: 0m sy:f kwz;hg10ess 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 its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heag2 *yuigdl .j7vy 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 Fig.idg *jg7 2l.yu 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 kin o gk ua8:*w39(op-:r kpulwswetic friction 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 re qpsk 82cp:8cgw5;cr hquired 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 amyzz-mpg5is a zk+7:se9 +x. s z.p/bbx)a;fg train accelerating at 0.20g. What minimum coefficient of static friction must exist betgm x9bz;.xzg.5 - sk f:iaa s/psz b7em+p)zy+ween your feet and the floor if you are not to slide?   

  What is the maximum accy gw1h,ssvp 0m g.92l /wrpb; t5sie1keleration a car can undergo if the coefficient of static friction between the tires and the gr 1smh;.e29ig k1sg,w p/tlspbyw 05vround is 0.80?   

  The coefficient of static friction q f pqe 81jwkur6ikdj. +oj78/between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum8uk wq/e1.8d+ji jj6opfqrk7 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 kuij bt8 c :4jxiv3,.r -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 roughp 8u 9(me( dil+7 p+u-syhgydj 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 coe iu1t3r5wn7wjfficient of sr1uwt n 3i7w5jtatic 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 friction fo-qn9+ rg6ndjaq2( y eyr a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a masssd.nz) phtvq.7qx3m 2cnq/;wn8 zb8n would box A have to have to prevent any mz 3pq /;s q.nvtmw2n d8xzb)n 7.cnq8hotion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will 3)j*w damyuf f9,( yekit go, given that the coefficien,3(eajdfy uwf)*9k myt of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in conlzdz ju :60t d,6 4ds,uebwrv)tact and at rest on a horizontal surface (Fig. 4-54)0e:6 uu z)l4,dwrt,jsbddvz 6. 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 staefvcgz+u) 4 l we/;1ectic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab +c 4evzf)wc1e; /eugl of the truck?   

On an icy day, you worry about parking your car in your driveway, jfg yxv6 3.ppaww,c8s ks.0z- which has an incline of-.swp zc0 w yk.j6fpvsgx 8,a3 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 a 9mee+j, )qas 81ii lt.ibze5 g28$^{\circ}$ 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 tilt-uz ;aace/ k4yed 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 spel(j g*1v * o8)r:yqwvsbtgs.u ed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 6d/rmavb )yt 1(.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 it wittddrs :gl1+w sk0p 3f *v/yb8ch a force: dt+fgp/ ds*bvcy10rl38k sw 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 roofv,v;z/ rq yxl 5bj*cfqqx galo*/25 2 ny2qdi.s can become dangerous projectiles as they melt. Consi z /iy/d2* ; brcqlqq*v5.x fxjqg 2,yavlon52der a chunk of snow 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 distance foubj7cf fh:sde a15p +y+/q;rwr an automobile traveling at speed v is equal to jbc71/qa dfr5 u;+f+ w:peysh $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 th b8 ;mxpvz7 8fcct2ot5 s3ra:se dash when the driver decelerasa ozp;2c:tb53 8vtm f8x7csrtes 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 mas v89 3s;uv lb4 xnlssr g)v8 yp7n7nw2(4ctnbss 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 wheic* 8;m xh;9zly (rotyre 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 (hiy;xo9ty8zmrl * ;cbox 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 coefficihstaa.lm6q35 1(n lg p(p/ellent 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 tn*ce 2ynoub0e),c k ;fnxmk .+he bicycle) 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 mammalianbb(.yjdae3ne/ f z,ttz7y /7y heart, at each pulse approximately 20 g of blfzdbtj 3a.y(ez//7y t 7b ye,nood 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 chan*6ium :y;zgr0s jt6 sqce of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force ruig066;sy m:sqt *zjon 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 earthquakj8(tx11ggb:ty -kfp d 8m7iive is a , and if an object is going to "hold its place" on the ground, show 8 xy1pijm b g1tfk vt(87:g-idthat 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 anz djjb1bg.* x4:zay 5y accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before c*yajy4d1.b gz 5xzjb: olliding. 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 (ion)+6popt 7k 1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore frpootk i76)pn+ iction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropzvvoxf 6g l;jk5y rs+3:y sy-6ped 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 force of air res-fks:y;jlys6v6z5 xr g +v3oyistance?   

  A cyclist is coastin z6 3fx,q +:sir8bxkzbg at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Wfz,bb :s+6x8z kxi3qr ill the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is wo9h8 d)j ehld.d w8qoj4k5uid 2rking on the redesign 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 par)e8 .5d 4jwduo 9ijlhkd2h8 qdticular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, chb; 422pw bkcdangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airpbwp c2c;2 hbk4ort (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, ther)vuhqor. x6,mx5 j ;sfe are to be several ramps connecting different parts of the ,; q5.r xfu6ohj sx)mvstore.
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 ) usin.vo8 a(. ndid:brqnc ;g the pulley apparatus shown ini(da 8nr ;:nvb.. dcoq

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 n 3g iemgne ,*f.d4ih,3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engine 0 piddojoeyi c7)/*d:er considers the following set of conditionjoi do/7e )ydi0pd:c*s:
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-z((zdwvfpj 0 i659 n 4yqrfc*kcar Italian 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, B lo; w)ihil/of26zua s, n;a7sill and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull zi ua,on2s7/a;iw 6o) h fs;llon him? Which climber is more likely to be hurt?

A fisherman in a boat is using af3vv3in 4r xg eb4hmcj6+:,wg " 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 ak9 0l4fw5jmnpk rp*)o llowed 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 tog87*p- ne/djerxkb as6ether are ascending an ice field inclined at 21. jsb*xn /ed-rkea768p 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.