Why does a child in a wagon seem to fall backward whyxa slkf** --ten you give the wagon a sharp pull forwl tx*ys *akf--ard?

A box rests on the (frictionless) bed of a truck. The truck driv0od8,i r24a rgkfwni6er starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is rid8r fw6go2i 0nk4ir,ading on the truck

If the acceleration of .p)c)x g4ztd wan object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratcgx1iezr2/oaa*n / j3ion? Can it have zg n*zc3a/2a /oe1xjriero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is x0u4ogbc 7 aaa(*xd o. vbjw,1a force needed to mak.xb4g a o7 1wc0o*j vx,aubda(e it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposip: vaq(*fudij /-ux3lte directio*j/uuv: - (3fdaxil qpn?

Why might your foot hurt if you kic4g5d)u+smg.7o nwfnmwbrhy+ x;5ur4k a heavy desk or a wall?

  When you are running and want to stop quickly, you mu6i oa:i7sa x+pv7+qsot 3i1e4xfn bg.st decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your7qxx1 is4b6v if3+n7ig o+ps.a: oate 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 ceiling, and a section of the same t+a(w)7x ) kcht o1 si:b.vmxxchread dangles from the bottom of the stone (Fig. 4–36). If a persatc)mxvxh+ iw:co. ( bkx 17s)on 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 answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg r kp; ,8r *0xsoypt4zhwock. Why then doesn’t th ,*0wh 8prxykpsz 4;ote heavier rock fall faster?

Would a spring scale carried to the Moon give accuratepk:; traji +faqtv;i.7;+ skm results if the scale had been calibrated (a) in poundsi k qstvfpa:j;k 7+; r.;mat+i, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an ate mhrw:i;-4nttached 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) decreeh:mr wi- n;4tase? Explain.

When an object falls freely under the influence of gravit;-cbuc t :eqt1a;hw7gv h( 4vhy there is a net force t-:q 74 hehgc t;(1av;cb huwvmg 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 Earth move?

Compare the effort (or force) needed to lie2nnfz3 7(gch,vim3cs z8 y m ks+60erft a 10-kg object when you are on the Mo 33z(esk8 yhmcgfc0i+2emrvs6,nn z7 on with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls tbo. 06-v ddhoyim 0j2with equal forceioh-t b. 0d0dv26yjom on the other team. What, then, determines which team will win?

A person exerts an upward force of 40c m4tixjhy 019 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 is exerted, and (d) by04ht19 mjxiyc what object it is exerted.

When you stand still on thqbf y;v6b( p*qehwjj e4:m7d5bk*t)ne ground, how large a force does the ground exert on you? Why doesn’t thisbwd bqj 45tn fe ):q;v*6j(mh*bkpe 7y force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’syd*g*72cu k4t 7tyih w car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward igduy7yk7tth*2 w *4ic n this situation. Is it really?

A heavy crate rests on the bed of a flatbed3u (fi,qfirm/ truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. r3imf,u/iqf( What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Afte vsis52qd,dg (r the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the dedgi2(v,d 5ssqscent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pr k9b2dov51 yc26hm;jlhkll8lane? Assume the mechanism functions properly, even at an a2l9yl8rh125cj o6 ; hlkm bvdkngle.

  What force is needed to accelerate a child on a -xdb-q*bhq w 25v(;hdbf+ ip hsled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ride8s1ez. ht1(5en xx zwur 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 acfri)z*:6y5ps z; kxau celerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of av) xhxy4;8l mb9le 6pa $76-\mathrm{kg}$ 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 5di unj3m03cx is trave0m3xduicn 35jling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from 4,:spk9 +smqlq iqsty+k r 2e9rest to 125m/s over a distance of 0.8+l :,9qtkm+ q4k9isp2serq ys00 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of: qhgya5ipu mevyhi483i)(u *7pkmj 5 2.5 *:m h )y45u5pmkiu(qhipya7vgj ei83$\mathrm{~m} / \mathrm{s}^{2}$ 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 coveu;i hgy:jzu6r q8v2 +glsx62m q*y 3zqr 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 de); 0mdh+ krf/cf s ihwq3a.h+nsigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor shou3m;h+f a)/dq 0s.rkhwinc +fhld 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 b5. +plrzsbrh+ athroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s reg+ r hrp5.szlb+ular 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.eger )a*yz 6t of 21,750 N. What maximum upward acceleration can it give the elevator 6 r)t* geezay.without breaking?    ( two decimal places)

  (a) What is the acceleration of two ft2-mt14.ecms md+x oyalling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of theirsy.mt2md cm+1-xt o4e 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 rt0*ugao 25vax; / wkwa house 3.9-m high. When he strikes the ground below, he bends his knee/a*w;xovr0g2 wtk ua5s 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 rests on a table. A rope tied to the box runs vesyr(j-3j4dcu .r,u tyrtically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the(j3ur,s uc .d4 ryy-tj 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 n+8lg nq 3dud:qk wx6 +idh3-mplayer
(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) atb7 yt rgq6lvhbxvd0*yyq; u4 )*j;:vx the moment it is hit by the bat, and again (b) after it hhul 7**qqy jxvv;d:gxrty );by 604v bas left the bat and is flying toward the outfield.

A 650-N force acts in a northwer6x7vwmbm ee176mg)w sterly direction. A second 650-N force must be exerted in what direction so that the resultan vb71 r wg66)wmmeexm7t of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally bt: csnx rn0lj) e5m.2: u7mkzuetween two buildings 7t c mm:x)unun 0 5szeljr.:2k10.0 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a md ;m8nc.1 ;cyq/ wjzy( diuaj;assless 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.ug9 tf99h cgz*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 un9y(r; i w7tghyit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum t7iy 9;g y(rwhof 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 o*um e0-9brffcf the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couplin 0ubc-9refm *fg 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 he+ /i 2c3m:kviaat2ubbrself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constan:aui2m i2b3bkt+/vac t 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 begac*2tu2n o :gafjz;2p rcn4+nan, 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 blocko.4 n;k,vfcza (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact wie1ti4 ag3do, 5we rpl:th each other, as shown in Fig. 4-51. A forctd :3we5oilg 1r4pa,e e $\overrightarrow{\mathbf{F}}$ 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 grounaf3s/1cru3t nkc7b5 ubts. ;oep/x,o d, 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? [Hintfer1 /k 5ssuo;/cb7.n3p u x3,tco abt: 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 azx.b ftmkfrxzw jz-+/ :)8+n (*bgtvgre connected by a heavy 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. 4-53. Assumek8zz. )*gn +/jxxt-(vfbfrw z+ :gmb t $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 friction between ajj-/ei wi n:,h6(y naeyqaw740wc:hw 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 isejii-s s-pft:ec:mb q2/kga2 x3- d/m required to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing onomt4,o/s k.0ke6gluc a train accelerating at 0.20g. What minimum coefficient of static friction must exist between yourl, /.6 4 cokesgmk0tou feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffo :9.gl d-dxv78dl+dd8c-jytkurx 9hicient of static friction between thedkdtv x8-hj:-x87 u9y9 gd+dldcl o.r tires and the ground is 0.80?   

  The coefficient of static frial 2 tdkf 0f-lxp8i(5fction between hard rubber and normal street pavement is about 0.8. Ol-5daitp82l0 fk( xffn 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 deceleratebsjzii;m7 h4b) wx+z6 at -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 wf2p27k +ystm+f97kn7xf5 n juolv z5a rough 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 cu l1 ;o2jk7gm8npvg+5so* 4pig0 d uvzoefficient of4*zgivjg 2up+g d0nul 7k1s8moo5pv; static friction.

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

  The coefficient of kinetic friction for08 t;locbw (ao 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 ajbusm.qw c):qe jp,ywib6+ .; mass would box A have to have to prevent any motion frwy,m)j.ecj 6pqbqb.+ ;:sui wom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. 3 j1, ,q.d*-cb geigl*qk*mb;vrzrun How far will it go, given that the coefficient of kinetic friction is 0.2l qgd,rigm*cb** -n3 er,;j 1qzkb .uv0 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 at rest on a hort6mq dtl rg(nkbn hv3x,6m- 94izontal surface (Fig. 4-56t m q 3 vg4-l6nrt,mhnbd9x(k4). 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 crg -) y3sdst)inate. The coefficient of static 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 agai )g)-sd 3tyisnnst the cab of the truck?   

On an icy day, you worry aboutcda 7th)70 hdf parking your car in your driveway, which has an inclin7 0d)fhat7 dche 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 a 2ix .fz:ot t55( by2ydk8$^{\circ}$ 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 pl 1yd/d;k4xuxru3 t6 4otm le b0qh(x3wane 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 g z5,gfj)1qm:8i *q1a 8 h akhdkgz.ry3.0 $\mathrm{~m} / \mathrm{s}$ 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 steepe7tk0 wc;6f ku+-rd)ne9tcoqp st 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 i +9bu4sz)du zt3tmmf /t with a force dis3 zu+mfbm9tz ut)4d/rected 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 projectiles as0xe rsw)9rp 8q they melt. Consider a chunk 8p 0xsr9wq)erof 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 distast.ywx+/w w)k nce for an automobile traveling at speed v is equaxk)wsw/.y+ t wl 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 carw e5+svx/u*:m6sud hl slides forward on the dash when the driver decelerates fre:*wsd5/ usl6hum x+ vom 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 initialf u4shg/ulx54em du5 1 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 where they are filled to the pkli4p ag xc5lgc7*gs80pi1g : acking 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 decele l5s0gk8 4ig*7lxcgpi1ga:p crates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction + gq *)h61j(g+ ril,u9umcbx /p2yevjj.nw chbetween $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast do:n+7 m sb,igf1i. cdpdy 6b*t1aru:mhwn 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, pm*+medf(a- (g , duuix//zee at each pulse approximately 20 g of blooud/ped-i+m ,ez*/g(a m ex f(ud 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 chance of surviving an automobile b-.c)56gbm2evd c jq vcrash if the deceleraqem 6. -c)j vbvdc5bg2tion is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if h0zkxt nx75 2xan object is going to "hold its place" on thn2xt z0h 5kxx7e ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scejtxw )) gnzt)ni.kps*, 9-n dune of 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 kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a levu insptjz,-n) ktd)xg w9). *nel road.   

  A car starts rolling down a 1-in-7 /v )m3)zenuk2 h cfyv*wr1+u/bf hgb4 hill (1-in-4 means that for each 4 m traveled along the road, the elevh1bbmwk f +)r2*/)gfv/u cy3 hvu7zenation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top2g9qvnwudjee*a-1 t5 of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Whaqje u5 tg19-2avdw*en t was the average force of air resistance?   

  A cyclist is coasting at :b,lw 4 b5tpqaa steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cycb:4wa5,l bp qtlist 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 hilly portion of a city. An d zamu h4+mucrdi )+vt 04,hr9important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowmc4vamu ,ih+rztd9 hdr0 u4) +ing 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 experimkx34j/wv1 f fyents, dangles her watch from a thin piece of string jf4yx1w/v 3 kfwhile the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps connecting diffk;( wa; x-tb q9c,ih)-jedl mterent parts of the store. x -bme waj,h-d9;t(lckitq) ;
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 c8hfs+tr0y o*y+svr*;ydi1l the piano (mass M ) using the pulleif* 0stlsc v81+yyor*+drh;yy 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 accelerating at 3jm3a el cx+*d+.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 d;3q vurk j 9js.k gzjpsmsq 4c7n:(05considers the following set of conditio(4k0sc3:ks9s nq jzjvp ;5mrgu7q jd .ns:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of p8bwax;0 jxdj4-0yyuc) x :ku :)jlru660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes oat dd0/n lqf6*+xy84g ydss o/vc/4xof similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety pur 4n ly4ogqa8ftxds c06vyo/ +s/dx*d /poses 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 on him? Which climber is more likely to be hurt?

A fisherman in a boat is us0nwag8 a)c3x.p 8/w7mmc m xx3h0pgvding 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 srlm,1 zpwxsjxi ,1 f45)f/dxspeed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are aja7+3 hbht :cqv+/q twscending an ice field inclined at 21tqq w7hthjb+:/va c+3 .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.