Why does a child in a wagon seem to fall backward when you give3zn*hl :,(of epk8 mpq the wagon a shar*e f:mn p(oz3 8lkqph,p pull forward?

A box rests on the (frictionless4n)qg)7d cpb x) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck d gqc 4n7b))xp

If the acceleration of an object is zero, are no forces acting on it? Ex z las+ j*(a(,,i/e.8;mdquxwxbpwjrplain.

Only one force acts on an object. Can t9+ighijf/0k ahe object have zero acceleration? Can it havig +jhki0/a9fe zero velocity? Explain.

When a golf ball is dropped to the pavemen;6kuj:v5x uqnonm(pv:d pss1 q8,w8 n1y unb5 t, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, wh8 yu:n npqbud,;5(1 vmpn5j 1sn skuo8vw:q6xat exerts the force?

If you walk along a log floating on ct)4oc5wwd h5a lake, why does the log move in the opposite direction?dw ch5 w45c)ot

Why might your foot hurt if yo70ylo aj) ik0vwfl*xkto*q. 1u kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) pd:xf7nptm7; );jlca c y6ik iovr3.:What is the origin of the force that causes you tvfxmi co;:dick3yr7 lpp):j a7n.;6to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same thro 05/ l6l9.pzy uytqszj)5 hglead dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull o.y lt zj59h5/ syuz lg6)pl0qon 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 g2d0od l6* i4 scjs 2mq0x 3*oryw/zbnas great as that on a 1-kg rock. Whyrslzxj* g0c6 o qbyodd3mn*s /w402 i2 then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the p t nmk m*lo+q6i85- pvei3z9ascale had been calibrated 8vqk3z i-9+* opipem 5mal6tn (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an ath y yjc93ng2 u4m;6ipxtached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Expg2p 9nih jux6y 3c4;ymlain.

When an object falls freely under the influence of gravity theez 5zf0r 4id/ere 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 Ear frd5zez04/i eth move?

Compare the effort (or force) needed to lift a 10-kg objelxve 2yxtdyox 24-e 0va0y5 7ict when you are on the Moon with the force needed to lift 2o7v0xyyde5x0t x vye2l i-a4it 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 o p6; f8 h nz-9ccd16pajwvpell/+x(o team in a tug of war (Fig. 4–37) pulls with - l c+;fop6v1 zpwa98nocpx ( d/lejh6equal force on the other team. What, then, determines which team will win?

A person exerts an upward forcz/l:aaqo+kj:k/dv/ u e of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnl/kov+a:/ uq/z j ak:ditude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large art4xax-9 q(woe wn4h327wzcy force does the ground exert on you? Why doesn’t this force make wq3wt4xx a4y7co h2z9w-n (reyou rise up into the air?

Whiplash sometimes results fcm1( ;uzx ot6wrom an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown z6m(wou c1; txbackward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When thej1 9v3fw h3sft truck accelerates, the crate remains where it is on the truck, st fj3w13fv9sho it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so 0cq b6lptqi35u-mm,a xts: g/that it slides up a ramp. After the block reaches its highest point, it slides back down but tc lm0 qxigs uabq:mt,63t/ 5p-he magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pl7a c(avhxt. +d:ov0oxane? Assume the mechanism functions pcav vx ht:(ox+.o0d7a roperly, even at an angle.

  What force is needed to accelerate a child on a sled 3 rae;uvleuebo*buka: 5 f96; at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridt*d6a.m : ocwmr8e5be er at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope i- aal, q:mmar9o0 f,pwithstand 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 am hgol8o5 p ;jm.rc5+l $76-\mathrm{kg}$ 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 i 6f9mf rg,0bqe-no3lhs required to stop an 1100-kg car in 8.0 s if the car is traveling abhfgo-m, 9e0lrqn 6 f3t 95km/h? -  

  What average force is needed to accelerate a 7.00-gram peller*v w8.w :2n(vz vouvqwi+s)d rda 2,jt from rest to 125m/s over a distance of 0.800 m along the barrel ofdrwoq,. i 2rn)+vz va(*wv8 w:d ju2vs a rifle?   

A fisherman yanks a fish vertically out of the water with an accel.m6gl a/gn;4aomb tn)eration of 2./a tb .na6m;o 4ggmln)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 cadi.8w+)4p)a v/4cwb pwjrdu fr can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that w o*z w8ztd6rebtw;p-*6 df.ithe maximum acceleration is 0.0680 g . What are the maximum and minz *dt-b.wo rzw;i86 tdepf6w*imum 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 idek1s f1il*6pxkf*tdy9n* 3;cz: vj hj8n i5elevator. When the elevator begin 9dn vk1n*cfsk*ejf5itip:xj;ydh6z i3l *1 8s to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximumypgsoow 422+i strength of 21,750 N. What maximum upward acceleration can it give the elevagwiyo 22sp4 o+tor without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclhyc/6a. wgwh c qn(n19uding paracqn w6h.(9hcw yn gac/1hute) when the upward force of air resistance is equal 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 house 3.9-m high. When he strikes thfxa,b.f qw3n+hv s2 3ee ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If thesfewnfaq+,v 3.3 h2bx 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 table2u t,-tpfnj ,k) yxd;t. A rope tied to the box runs vertically upward o2jykft)px-d; ,nt u ,tver a pulley 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 dia0r 71svdo sg:1qitk 9ngram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment itrce3; b7 ondjhu30x5e e j;l0p is hit by the bat, and again (b) after it has left the bat and is flying tow;e0dh0 rj3u;jen73 xcpboe5 lard the outfield.

A 650-N force acts in a northwg 7dr.m+verla3:2)ktm w kv np8qo :2yesterly direction. A second 650-N force must be exerted in what dirv 38mryw 2mvrnld2).qeag :kpk +to:7ection so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acros xs4j 5t0q)zrhs a "high wire" strung horizontally between two buildings 10.0 x )j 05qzsrt4hm 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 bebm+/7n/yf qmj( viuca23.bhy a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14+pa*q pbj2 ,fz.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 housing58 epbt 0pv4 f.jihi/x unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The su8h/5vj4 itp0p.fx eibm of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same nvi4)ed 8:tvro87qy nmass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locom)rtn48v8 vndiqe :yo7otive 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 thgfvqwkv,:a irx ; m79uqg9 2p2e bucket-pulley apparatus shown in Fig. , gfrqqvg9ap9w2ivu7m2 x:;k4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a s.z8msr sd:s-u/ v -oc 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 39cbzjx d-lvlev+ : /iblock (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 ax(kt7k5nv fp .re in contact with each other, a 7pkf(k5v.xnts shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above4xz-h jb3z2 ra the ground, and the massle xz2arh3jz4- bss frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionick-3 s 1ny(mkk .o4p02f rpprless table are 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 nk21 rp-ksr0k4pyf .oi3 mc(p 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 fri dx4 s,j,5g)gx jig4bp ),mwyuction 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 requires z2e6. z/ofbfdy+v 0ud 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 onek8px v0v y 0wsy1t7lfn(*,nn a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if yo0tnv *vsnn 1(8wfy,kyex pl07u are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of staxgj* w dm/kbae((42ixtic friction between the tires and the gr24wdk (m xje*/(xbigaound is 0.80?   

  The coefficient of static friction ez)m/; eqd;xr between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you dzmr)qe/e; x;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 4q4q )qj:gav;8 ncdgm -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 restp uw uj 45l4)i0x (n.pawmj3rrt)9 ycq on 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 ira17qmbs f ic/05v *qsurface have a very high coefficient of static f qcf5av7bs *10irm i/qriction.

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 for a +v:f3u pn0nqa4heew lf9)zin+. cz9d$ 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 have +/ypc8j yj 0xg)aed u)to have to prevent any motiy j) )cp dg/eyu8+xa0jon from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far w h2de/hnnfz; 9 qto60mill it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initiazt;9nnqf6md20 e/ hhol speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contfrj6g(qj 9 w5dr,l+s ract and at rest on a horizontal surface (Fig. 4-5dr6 rrgjfw, ls9(qj+5 4). 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 cra59.0 5*ccoleig yt wcqte. 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 against the catq occe50gl wy*i. c59b of the truck?   

On an icy day, you worry about parking your car in your driveway, which has a6mae,g( w1afx;jq t ;kn incline of, gm; w6qxef;( ka1atj 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 wi)jj7; uwn2u k kol hwz.mer:;u*ubsw9( ;izb.th 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 liewku23e (:s.yxug, vyj s 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 initi,)+movoo -zu4yy;l tdemnv m8 j8w2w 5al 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 reach ,zs-67lomwqwes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing onc21 i6p uheyyzath623w2e8,g x*lqns it with a force dire83 h 1y6nsx ay2i6 22ple*geuzwcqh,t cted 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 projectilo); ph3ql*ryies as they melt. Consider a chunk of snow at the ridge of a roof with a pitchr3h)y oq*;pli 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 at sxsoqph 5wqaub6) 7mwl; tj7+;peed v is equal to hx qs qua)7w bolpj;t;m76 +w5 $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 cqjjnw,8 h.s p8 hyn//zar slides forward on the dash when the driver decelera/w phj8 ,/qnzhny8s. jtes 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 masskrosc d;*bmfy3+-q 5o m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a chi oyt6xjyj8-/u r o4kj-m0tv.zm( 4qonveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what u-vmj(yjiq-t/8y4 z hok6j 4m.r0xt ois 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 kii/o x*jkm phoxfc):+8 +obe(a netic 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 (incfhm2; .b 2uy2v16briagdy c,xluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model ow8 p/4b4 rs+tdriqk j voj)biev. ,)x9f a mammalian heart, at each pulse approximatelyri 4+.s)94v) epjbr/tb,ojv i8wd qkx 20 g of blood 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 crash if the deceler2ex/i,ui 5wjpj1fh 1b ation is no more than 30 " g 's." Caljwjb, p ie1i1u h/f25xculate 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 earthquat+4fg k,r(ek tuv p-/eke 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 be at leas(,eu4kp/g vf+tte- kr t $\mu_{\mathrm{s}}=a / g$ . (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,q y 6uu.-6s7 /qmjbrlx examining the scene 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 cajsbl-/q.q uy 6rxu6m7 r assuming a level road.   

  A car starts rolling down a 1-in-4 hi6k:40 q ytxogzll (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 reachesz0y t6 q4oxg:k 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 thmyk4-4x qtg7gn rk);tk7* hlop 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 ryh7 4)-mglkt7nq; k4ghtk x* resistance?   

  A cyclist is coasting at a ste9:yc s ft9nfam dyy)axu(myt / ppr8gl (-.j/2ady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddya-8y/y ad 9c(:slr 2 fng)f .j/xm pyy(u9mtpt 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 redesiah .57jkwu:)m6 b baqugn of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-pomuh:)wj q6k75ubb .aawered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 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 thin piece of+jzg/w6+ d)yc1sx q obixp3/t string while the jetliner she is in takes off from JFK Airport (Fiwyq z pts/ci)+ox+3g6x b/d1jg. 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 b+ 9flbwxs; dei n1jfh qe60s3/e several ramps connecting different parts of the; 0 sxj1lf9snif/ debqh6 3w+e store.
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 forcue w: ::jgf 823bz:lnzw mr2nje F is needed to lift the piano (mass M ) using the pulley appa8b nmj2 z :guzwwfn::l r:j3e2ratus 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 atz(rbu b (4je.z qw4-nd 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 ch r9og9kbe0a hnm0p7) onsiders the following set of conditih9r gpa eom 9b)h0n0k7ons:
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 (t5kxevgiu )qh 5l 2-s0mqrw/ +02urfk 660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, B*b knqmy*0 *i m5n(vabill and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. va*kmi* bymqn 0*5b n(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 " 10-1/j , meeigr;+b $\mathrm{~b}$ 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 bui zmqxwc/*9q *xr:( hksqu-u.nlding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice-.vi r3ifrx h29j. xak field inclined ahifik ..j-3a2vrr xx9t 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.