Why does a child in a wagon seem zm 70ap pr3fu0to fall backward when you give the wagon a sharp pull forwauf0r0 7pmpza3 rd?

A box rests on the (frictionless) bed of a truck. The truck driv72rctaw e94ca 44bua u*e zhlc.g,.lker starts the truck and accelerates forward. The box immediately star.elebg tl 2.ha u,*r44974kacuc wzcats 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 riding on the truck

If the acceleration of an object is zero, juivo2vh*w;. are no forces acting on it? Explain.

Only one force acts on an object. Can the object ha)* ays+caudpwe1 g4 1eve zero acceleration? Can it have zero velocity? Explain.e4c+g11ad s )wu*paye

When a golf ball is dropped to the pavement,(sd,6uim8zz s lvqyjx2 (6o w6 it bounces back up. (a) Is a force needed to make it bounce back up? (b) If s2wmv i6z zl8d(6, uy6q(ojsxs o, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppogth1r-atb p +.sittat rg hb1p.-+e direction?

Why might your foot hurt if you kick a heb ;)n x) /p-vfyp,;dj edl3qkbavy desk or a wall?

  When you are running and want to stop qt v mg2x9,vw 1x:tncr f*ity-wg- l3p9uickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come w1t 9v-i3wmtgynf-*v,:px x9 t l2gcrto rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, 5pfhz-4gdy p2 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 p2 45 -hzpfygdthe 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 twkfl26:v,(w ltwe t9gbice as great as that on a 1-kg rock. Why then doesn’t the heavier rock 6twvwg, 2efb(l 9:kl tfall faster?

Would a spring scale carysq,c7m1t )4gs-cs amried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) i4, ta m-y gs17)cmscsqn kilograms?

You pull a box with a constant force across a frictionless table w03tu f8 ero6vrucs95 using an attached rope held horizontally. If you now pull the ropuu cost3 8 56er9wfv0re 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 freeaood1b ;sdl;k qp(:rdj hr;7b 6bi y--ly under the influence 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 dr6 rpksodhbb1yajd;-q ob (i;:-l;7the Earth move?

Compare the effort (or force) needed to lift a 10-kg15;k- 4+zumaz.jnly c0lw4tzqzf 2ehv8g* t t object when you are on the Moon with the force needed to lift it on Earth. Compare the faz2j*zz5 + uqvh 0kt.4;fngctyw el -l t8z41morce 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 t: y3rb, j)zl c6qj3joohs (er8*2mxw7dy3neiug of war (Fig. 4–37) pulls with equal force on the other team. What, then, deterxqsn6r iyye zmow( l3 jc:e783j3hdjb)r 2o*,mines which team will win?

A person exerts an upward force of 40 +yn203js wpqxg;pf b. 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+y p2q0;fb jgsw3n.p x (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on ys1qv* ch ;r8ugz5 oo6q 5b2lxmou? Why doesn’t this force make you rise up into the a 86bcrh5g;ms zu q xloqo*15v2ir?

Whiplash sometimes results from an automobileal)ahk vj c r/:k-4 ,g/nylf-g accident when the victim’s car is struck violently from the rear. Explain why the head of the ,hn)v4a-jl:agg fl rkyk-c//victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the d-d.l6pwzld :,q y7 giej- 4glbed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force 6pi e4 zd7 ,wyqgj- l:g-ldl.dcauses the crate to accelerate?

A block is given a push so that it so a5; z tnt90t,5wa.o) yszefyi)xid ;lides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleratioo)t) 5x59 it tszid; , a;.wn0oyayfezn is less on the descent than on the ascent. Why?

What would your bathr1;l.fuj5 eh :rtccui0oom scale read if you weighed yourself on an inclined plane? Assume :0cf.h;tuu1r ecj5l ithe mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled 5fplls9f/l. tlk/k 6v at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.vmcxyrs3ns96,xlm 57v/;kn 6jw1 ua p30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if im6; bolri/rn* 8e:i sst 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 a r1/m8/3 xrz+) 1s8 co ml-gdprrs icov$76-\mathrm{kg}$ 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 tra.8 3kipt6q yfmo/wlo: vei3/w.f tyo 6q o8pmlk:ling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125m/n.;wh c+ pvqd9 xm:6otduz5.us over a distan.6pomh zu+d;ct:u q.9wx5dvnce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically o6+1qdpjs i +feut of the water with an acceleration of 2.6jpf+1+ieqs d 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 coss8e zl8v0+c8 , cuwvmver 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 5iei)neo (m(k) is to be designed so that the maximum acceleration is 0.0680 g .e)m o5i(( eink What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevator3 x433fixi ,i0sqxnuv begins to move, the scale briefly read3x xfi i3squ4v,i30xns 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 6g:4y* zl dwfwN. What maximum upward acceleration can it give the elevator withow:lfg dw6y z4*ut breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg + dgt0p 8ihfkgc.i(z; including parachute) when the upward force of air resistance is equal to one-foupi ; 08zi(c.g+tgdf khrth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m hiou djq x9;dry.( 5n g6wyys):kgh. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, osg q)k ;xd.n(9dwy6ry: 5uyjfind
(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 rf 89 v,hj7.j tadpbw*1ndq da,ests on a table. A rope tied to the box runs vertically upward over a fd1j,b,vn* wq98at dh . 7japdpulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbal f :v67kmq:+idf upoj(l 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 is hit by thedi-kz5-dz1:q lg,l3zaxj ,4s -ixd 4.k mzyl r bat, and again (b) after it ha zr,-xgd--5dz,ydzjkk l m.xz i414liqa3 :sl s left the bat and is flying toward the outfield.

A 650-N force acts in a north71qq fx0bxt m/westerly direction. A second 650-N force must be exerted in what dire/ b7qt1qx0fm xction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betweergy *y a:xu1h2ah;k2 gn two buildings 10.0 m apart. The sag in the rope when she is atg;:k 21* 2graay xhuyh 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 anothe:jm h:ez(/fjt uhk;rn).h *aa r 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 14.0fnn(6vcsm ) l1$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location ace:ac0bs0ovh/ krajc 16u*k +rkb i,8t McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of th0rba0 c*61 :ibc hek, jkuko8crv/s+ae 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 them 8c2j-;zw q*ahj( epr same mass behind it, Fig. 4-47 . Determine the ratio of the tension in cj ;28 jqham-pwe(zr *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 apparatuyn/ 3-by, lklos shown in Fig. 4-48. (a) How hard must she pull dow/byl ly- no3k,nward 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 5;m ton v2 fzl+g,8rze8igy ;ebegan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (m;twwg vdf;r4 6ass $ 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 ar8 askfe/z v2phcz+ v uj/(lvgu978q3qe in contact with each other, as shown in Fig.z3 uuc2sl /a( heq7qjzv+9 v vgkf88p/ 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 1.80 m abov 5fzgmk9 x7t)qbcah 7+e the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximumzh)b5qc +amx79 gkt 7f 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 heavy cord of mass 7 zw a5do2ts2;axzg- s1.0 kg . Calculate the acceleration of each box anss7;go5ax a2-z 2tw zdd the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction be* sso 3ql:h1otsk4t z 289nzzg7rqw1ctween 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 rej, uqmrxte/ .g,fth ,.quired 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 a train accelerating at 0.20g. What+50c ,d -xkn2)uf1 bcd vdcbhc minimum coefficient of static friction must exist between your feet and the floor if you are not )+5vcnc1cd,2dh u0k bcx d- bfto slide?   

  What is the maximum acceleration a car ckchc wpc, kx;1e780u can undergo if the coefficient of static friction between the tires and the gro1;cx8ch70uepwkck c, und is 0.80?   

  The coefficient of static friction between hard rubber and normal streetv g1vfeb3ep wper j46ol:1fvlq)/7e/ pavement is about 0.8. On how steep a hill (1e elf)w/ev 671f4r /jo:vp qebv3g lpmaximum 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 -vgub c00u i1 d uvkg6mz 8q3*0fntp+*b4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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-;it vnt4ez(ofg1 y2m a 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 hib2m7q2r c s/c0/ vtowngh coefficient of sta/nowtcb m2 720 cvqsr/tic 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 fri+ z 492vj w.vawyncw1r,p7eqxction 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 wouldd+.ni(q-e7y wy+ l)/t xjse cl box A have to have to preven(qslwede yy i++n)xc jt/ 7l-.t any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrossv/.b+ w m+;i nq02vsz62b gqtbvq w3uxd )+tbi the floor. How far will it go, given that t/.niq w qd 3btt bu6vz22wsxiv; vb0g+ q+)m+bhe coefficient 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 conw0vlg hx+kp9k ;2l6xp tact and at rest on a horizontal x9 p;hvxk2gkl60pl+ w surface (Fig. 4-54). 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 o,320rmezdh (x gwp gw1s6yso3f static friction between the crate 2, x(m hrwsdsg3g 63pzy 0ewo1and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about9vax0:s 1uq1t fidqljzl9tb3yu05 1r parking your car in your driveway, which has an incline of 1 91q09byzdxu:u lailrvtqf 15 js 30t12$^{\circ}$ . 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 sli.rwvqatjeo x:y 9fp((te-*; y de with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fy: rzlkpw2ip+ 44u4p xig. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an i/gik *n rn9pr z2oga9n*drpmi/t8p18nitial speed 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 reacosb s0f z1zy:/hes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a r)d+rs beu 75c(5 c5tr)yun jpw/o;ut..rwyrhough wall by someone pushing on it with a force directed upward at 2/urhc t; r. c5de5try) u 7syopn)+ b5u(.wrwj8$^{\circ}$ 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 as the kdno exi.). v5ga/c*ry melt. Consider a chunk of snow at the ridge of a a)dv.n5okx/*e i rgc.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 minimu6ixs l 53ft,. wu ,,*kc2or r8bxjkjplm stopping distance for an automobile traveling at speed v j5,pb3. ukt,x,cjo6f8 * xskrl2 wlir is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides h4gpq-kj +;4 ji 5c+n*wsuyksokg,8 wforward on the dash when the driver decelk-gcy*nwq+ su+458jwp4h, s ;ji okkg erates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial sp qos(4; ,f 5:7mtbl xqy*zbt zmsc;9kceed $ 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 w ss c;,oycy2, i9cp5hsr d( .(dgrmm(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 the5 od dmypc(rs,s;9ig(r,. ccs yhm2(w 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 wx f *sxotjr(8.;bgh7 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 bicycle) can coac8rbx gs k5d*(st 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 approximatecfpas8ja8 ()*v n a*izly 20 g of blood is acceler8ap*8sa )cfvn*zij a(ated 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 crash 3 1ltl ss8va3kif the deceleration is no more than 30 " g 's." Calculate1tvll83 3sas k 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 earthquak kmu8b.); xwo*5 gwqlo9vs0jbe is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must b5 bso *vb9mk0ugl.wj );8q oxwe 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 scep+ fs+agrxurwr)e65b l 15x4n ne 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 ab6a +lu+rn 15bgxw5f4)rrxps eout 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that fo/yzqz/g 1g( wb-g :rjzh:n h+zr each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bot-z bn:h:1zgwhgj //qgyzr (+ ztom 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 tr )/zx4zzp4 ru zlq4.kop of the Leaning Tower of Pisa and falls 55 m bef zxr)l4q4ur kz .z4/pzore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed o9y u1;c 2.kuoxtrneh k/27pby3n. uxdf 12m/s but enters a muddy stretch where the effe.791p y htb;yodx2xk.nkrnc23uu /euctive coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redess :hk* m,9pzvzign 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 wit,zzh: vsm* pk9hout 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 physi3 ;oj 6jx38rl4 )f dig.vijqxqcs experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the strq4.fj3 rjo )iiqvx 3g8x;lj6ding 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, o cf 34h.dvlip/a(xhlo 6h9( pthere are to be several ramps connecting different parts of the stor/9ahi(p3h.(v4pdo6 oclflx he.
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 wt-/cic dz)x8.xshtkm. om:*M ) using the pulley apparatus hk.*w8/-smic:t xzm dco t.)xshown 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 acce:vmi;(p4zj oqn1rbuj,i + ,lns2mx 9llerating 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 chitmdd6fhc f+4tq g:k 36ld-restraint chair, an engineer considers the following set of conditionstdh4 k+dq6m3gf:t 6cf:
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 660 metric tons*5 bc/gwexir - (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of)gl8/zd6tgh2 oiu( po0sw ba 4 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.hb (64/zop08 gat usg2iwlod) (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 k wdak*du as(s2. k0bae-1y1m using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reachk* mv;/-1td89ow a*mnrny wfo a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascendin ).40dkcb/iu)uen8pm6ays q zg an ice field inclinedqz0bas.p )/)6ueyciu d n8mk4 at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.