Why does a child in a wagon seem to fall backward when you give 5z.z2nj,lm5 r vs n3rlthe wagon a sharp pull forwar5rjmz, .3l lvrs5zn2nd?

A box rests on the (frictionless) bed of qu96mq: 7.u qlr um8drm2hz8g 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 Neh 8u muu gq.69qrqm :8zr7d2lmwton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an o .jtsz;hc g tmy(v.,3ybject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it- o4p up+)ucf:vkmv5c have zero velocity? Explain v5f):o- cu c+upkvmp4.

When a golf ball is dropped to the pave d+p57xxavr5 et il63zment, it bounces back up. (a) Is a force needed to make it bounce back up? (b) Iiz d6e5lax3tv5r+p7x f so, what exerts the force?

If you walk along a log floating on a lake, why does the ltam;nu 7to-l: 1 m2njvog move in the opposite directi7 nojla;t-nvmm u21t:on?

Why might your foot hurt if yoo f*97mg2li) kytq jm7u kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickl64he-opajy 3yl3 2adk y. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experiey6l j43-a kdehpy32aonce) 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 ceiling, and a section of the sp:io, pr2o./iod.ky,mudqk /ame 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 yourqom 2p.: uk iyirdd o,/,./pok answers.

The force of gravity of3hkbl ; wn8-mn a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall faw8n fmhl ;k3b-ster?

Would a spring scale carried to the3bs2co 7zl*ol 7urt8 z Moon give accurate results if the scale had bou t8zzr3ls *l727co been calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table llnc )/77f +r grrx2srusing an attached rope held horizontally. If +/7lfn2) r 7gxlcrrsryou 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 i9;gy xb4cluk-am o( n;nfluence of 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 doesn’t the Eaulocg(km9 ;;-n 4xby arth move?

Compare the effort (or force) needed to lift a 10-kg object when you are /b;mibygue xsv, ,. 6ton the Moon with the force needed to lift m,.vx,/u6t ybeg;sibit on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls1:qd6mnnccu*n(pmt 7 with equal force on the other team. Whq tm(m:dn67cn *pcnu1 at, then, determines which team will win?

A person exerts an upward force of 4e -/sgdg+x(ol xp s .kp.)apn3 z7apd90 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 whatk zo93/nad+s.p7p (p egga p.dxsx)- l object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on ;roo+mcic hyg /* bs2j7 )aht3you? Why doesn’t this force make youg) jbo2soci * r+thy73/amc;h rise up into the air?

Whiplash sometimes results from an automobile accident when the v j+n)df8d*.fgg u5 ji+1s vmlj1so;syictim’s car is struck violently from the rear. Explain why the hy 1 gml nsgu.)jd*jj fofisd;++1sv58 ead 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 ok4bakr(nxv ;-e+v3gtruck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?kgxb n(vke a-34v ;or+

A block is given a puf ;oo mk-+j.cn6yxa1ai +jl -jsh so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascef.-oj+ c;kaj-1 jaonml6 x+i ynt. Why?

What would your bathroom scale read if you weig98hh3 5v ocr ba znzy51ii4-xdhed yourself on an inclined plane? Assume the mechan5hi- ixzy9oa4d5hz 1 bn3cr v8ism functions properly, even at an angle.

  What force is needed to accelerate a chilu1r p+ 2llcg+dd on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and r0c24nah;em kkr; . acwider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension mussuabnv 0lclc lbe*,6x1brr0 6j9;h(vt a rope withstand if 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 of x cn9rlfx +7h;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-k33r ds x0hdqu7b7hz*o *sqvr h9g/ )hyg car in 8.0 s if the car is travelinsd3/yr*qvx7 rhgohd u *7)q9hh z3b s0g at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellerdtut73inqu ejm, )dq .w6 tiagqp8(+*ex7 f+t from rest to 125m/s over a distance tfn 87qtr7pj* mtiw+6 3gqi d.uu( edeq),+xaof 0.800 m along the barrel of a rifle?   

A fisherman yanks a f3mwfgjt(, +s gng,1bhish vertically out of the water with an acceleration of 2.+h,mgtnj13swf gg(, b5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cr5 vw-m 7oqha4an 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 maximu9+xs0+egbz 0 d88zczrzpzg5 d m acceleration is 0.0680 g . What are the maximum and minimum forces the motor zc +p59sz b0dx 0 dg+gezzrz88should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a movjp owqeu-ym ,k 01dh,c vp1/u 3,ve-otionless elevator. When the elevator begins to move, the scale - q, ,0kyv 1oepuw3 dmvvo cphu1j-,e/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 strength of 21,750 N. Wha3f iur2qy6hu0vo/5zh3 o:drwda*p,s 3bau) at maximum upward acceleration can it give the elevator witrr u/3 oh2uab vpqds:iz3 wyo3*h6aua,df)05 hout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inrz5up4 ca02ycuc-p 7u0p)p cxcluding parachute) when the upward force of air resistance is e4 ucc -ru2z0ppxy0apuc5)p7 c qual 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 hous :+p vp+dzxa2ge 3.9-m high. When he strikes the ground below, he bends his knees so that :p+g+vz2 pdxahis 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 tip. h f):a o4p ukxis3.ltcza;2ed to the box runs vertically upward over a pulley and a weight is hfix;ku.2opza .asc l34 pht):ung 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 for5 w7th57 mv( b7 hfv:n)mbxrbi 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) at the moment it ii :*v.x n7vl 1zue5f1awb-t-5ykj txjs hit by the bat, and again (b) after it has left the bat and is flya* vkxje vj nx5l7wzy.bt tu1:5i-- f1ing toward the outfield.

A 650-N force acts in a nok-xe h*3:h u6jrc7(t)fpb sffrthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of3(utcphhf j k e*-6f:rsbf 7x) the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wisnkt 928c9a fxp95dfsre" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the 8 ac9nstpf s5d2x9k 9fmidpoint 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 another car.dny19,n fik :mj g52t2l z 3ls:s7iv4dyu 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 1c. z:mj4*s-d/mazjw d4.0$-\mathrm{kg}$ 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 uni tf 7vocfmz tu;+s2+bhe(f0;pt to a new location at McMurdo Base, Antarctica, as shown in ;fvtuepzfh ;ct7sf2b0(o+ m+ 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:af nt;3 mi2t wn2m8cr pulling two cars of the same mass behind it, Fig. 4-47 . Determine the rat2wt8f3ta 2m;cni n:rmio 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) cru(cdz3x(u k(a(my bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant cc ru(am duz)3y(x (k(speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a ,efq(m wj4pq1 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 x3lm;xal5.lk block (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizonta mwx1sz0 ls8:vl surface are in contact with each other, as shown in Fig. 4-51. A force 0ss1lxzwv8m :$\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the ground,:6hes k;zxnix jxe)5 ) v+m7xee;safe37gre, 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 lighter mass and then its velocity at the moment the heavier one hits the g xxe vs:)ees3rxez7;5f7 ex)enk+ijg, h6 m;around. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tah hjk)- iry2 glz* s50n.fxap/ble are connected by a heavy cord of mass 1.0 kg . C sf /rp nzxkhgh-layj25.)0i*alculate the acceleration of each 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 ofc.*ugtoak)9l- c ph;o kinetic 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 required to star 7nvxamwu6ak29w5tr1 z9)+lgqgu z,gt a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimum ckb:1 avd0.i wnoefficient of static friction must exist between you:a nv.d0w1bi kr feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo v(ir1m9k jbj+ if the coefficient of static friction between the tires and t(+j b mvri91jkhe ground is 0.80?   

  The coefficient of static friction between hx1r /:wv 3gxnoard rubber and normal street pavemen:xnwg3/x r1ovt is 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 6 hgoq3u11ibw-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 rs z(kamm yx v*3(j.1lrough 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 asp:vgsaow+ 7jk9 e5ch x.halt surface have a very high coefficient of stati +5 gs.ajw7cxvoek:h9 c 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 friqes(i -z2br +2u ekych(2:bo fction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A haw q 0;7hn rr.:vz4g wwm(,tqozve to have to prevent any mo,40:tw rzzo (; wnh qq7g.mvwrtion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so thhh;7is3 q5 btt 4dm-mhat it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts a h4-7 ;t3qh5 mdhsmtbin initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact )i/1ejiu z( yxlk.kyeq;x6 u :and at rest on a horizontal surface (Fig. 4-546:zuexk)u/ jiq.yexi;y1 ( k l). 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 coefficiz324:ady o- 6z tfzafkent of static friction between the crate and the bed of the truck-a f2z4 otd6:zy fak3z 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 lseliviju.u(7u zvgz d51:87 in your driveway, which has an incline ofu d5i8z.(:julivszue 17l 7gv 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 wgu2 jhu27f.jf ith 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 til.yv-/w+y vc wlted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 0r-g spbmv0 k6ydb4x- $\mathrm{~m} / \mathrm{s}$ 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 kr k61 z0lx4uog1zfiw7u.-2 sw b/ck gthe 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 bjk) u o6pb1zzs-q;9,,dx hxwz y someone pushing on it with a qp1 ),b9xujw- zz,d ;xozs6 khforce 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 slippq r:x4slqq504bfx2 xwu l*o*jfzqn;4ery roofs can become dangerous projectiles as they melt. Consider a chunk of s045x *brj qn42qfxfqxu ;l 4zwlsq*:o now 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 for an automobile traveling a /3rc tu4bb0dht speed v isu/4bd3btch0r equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash mcntyux3b5 08h4k cxz5 wio8 ,when the driver decelerates 0 kb,icwtnyo43 hc858xm5ux zfrom 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initialxoj09ove7pil7 r:x qtq:s+5l 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 whx:.pm4rb1fe rvnk7cl3u 8s f,ere 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.r7 cfm4 un:,fs pv1blr8 3xek for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinet,c v+wexpz8l;ic 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 w6x71x e goe7 o vzgz7d0uyqa)8:o.robicycle) 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 each pulse apwl8fiw cd1h0* tmv3e8proximately 20 g of blood is accelerated fwm81wh08 *die c3 tlvfrom 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 survivin8 oa9*pu l ukn1t l8lyu/rbr;1g an automobile crash if the deceleration is no more than 30 " g 's." Calcul a/lo lyrrul8 8*npt9ubuk1;1ate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration pr+w5qq6vf q nx6oduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show t6w+ 6nqv 5qqxfhat 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 ofsn*ju+.j1 mb3 )a g)yfewbpb+ an accident 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 kineti megfj+y)+.b p1asn3bb u)wj *c 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 downx17v.n;ml23 o i aa5m:pr yfau a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom 7. flp52v r;an ymaiuma:o 3x1after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppnvi 15hxv+1 xoed 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 5o 1x x+hv1vinresistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wheroa vtdui; 35xfnj lf;/ (s)(hie the effective coefficient ola(idv/s( ht)u f oix j5n;f;3f friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hill(vpigo,b(vr 5ovc v ).y portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get uo,vpgvob(c) r 5.viv(p the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thiw(m4-sqwkg +dn piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25(m +wsq4d gw-k$^{\circ}$ 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 conit* pj2e):r+9wzkc evnecting different parts of the st:)2j zrte9w ke+cv* piore.
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 pia5dmt2a, exdq85m -s wm4ldz 6)b wbv,h sf+5ilno (mass M ) using the pul-d,sm6l5 dqm2z5m)wb v, w4i5h8sf+xb datle ley apparatus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is acceleratingn7f *tyco,,ls at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer comn68 ixwa5olb ql-)7i nsiders the following setix6-l5qonaim w b7)8l of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass ofjh+(i4q7fuk z 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, Bw: (bfczgt 4j66d awp2ill 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 6(ga 2 4zctwbf:6wp djlarge a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " /g 5wuz bdeq*z:v.jc5; rvyq0 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 ma(bj8*vabp ;usj ;8xoxximum 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 aredb4x soj-6j7t q cvrmu,z,;q2 roped together are ascending an ice field inclined at 2r 647d;jb,vz jt, qxosc2u-mq1.0$^{\circ}$ 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.