Why does a child in a wagon seem to fall backau22rr i7-s/6 frqxfbward when you give the wagon a sharp pull forwai-uffr a2x2r6b rsq/7rd?

A box rests on the (frictionless) bed of a truck. The truck drivermbtq-o5-t 6c aj;bx5x 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 ;-tjx-qt5ca xo mb56b, 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, are no forces act)e il7ghgfj. 7ing on it? Explain.

Only one force acts on an object. Can the objectemdo x083sd6y have zero acceleration? Can it have ze s0dyx 3em6o8dro velocity? Explain.

When a golf ball is dropped to the k2 5fikev:xx hzc:od5/hjtpn 0 a 46i(pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the fd:2 5/ hkho vii:( 6 pzkejc0a4xfxtn5orce?

If you walk along a log floating o3 xum wswc3ct (yihu,cyhth/55h o63cl,w7z3 n a lake, why does the log move in the opposite dir,33u,53l7 ihcyz3hts ohc(cyc6wmux h w/w t5ection?

Why might your foot hurt if you 3- v4bn5pdgjwdlew.+e g,)ax kick a heavy desk or a wall?

  When you are running and want to stop quickanfpp3u ugxj2/; 6et +ly, 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 epu ntu/gf 6+2a3 jxp;come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of vi9pm o 9d58/yfjwm.kr ,l2gn the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.n5m8r9m.dl2, v/jiwgo9pf yk

The force of gravity on a 2-kg rock is twice as great as thatpt9s hsj-.qk( on a 1-kg rock. Whytps- 9kq s.(jh then doesn’t the heavier rock fall faster?

Would a spring scale 6+ ypsxkp)a 1f3qqb,c carried to the Moon give accurate results if the scale had been calibrated (a) ib, q3sx) +1a6pfc pkqyn pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionlesz8 ksw1suy cfdir.(7g )+0cios table using an attached 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) w frk7s du 0(so1y+czici.g8)remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there z m7zecnm793wg y2xw:is a net force mg exertng 3xw z2:wcey97zmm7ed 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 lift a 10-kg object whe5x y* dcovfm d/xn;5-an you are on the Moon 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 mafynxx-5c/d *dov 5;Moon and on Earth.

According to Newton’s m66j0s1erg0h5 ci vjb third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. Whatcimges 6r 0bv0jj65 h1, then, determines which team will win?

A person exerts an upward force ofns1 93-subd0:d dhlij 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on wns9d0ui-lj1:d 3b shd hat object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force doe*(vekfg 8jo l*s the ground exert on you? Why doesn’t thi8*vjg*e of l(ks force make you rise up into the air?

Whiplash sometimes results from an automobile accident when 4bergji x7i*c-c 7ae/the victim’s car is struck violently from the rear. Explain why the 4ecibr /*ix c-e7a7gjhead of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accel35ws 6 cf8rtetyri6*gerates, the crate remains wherwygt*3f 8t65c rr6ise e it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slidefhdw6igfg1r8.-sm4hs mq (; h s up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascq1ws mf . (mhd4ghhif6r;-s8gent. Why?

What would your bathroom scale read if you weighed your8 fx 2vb./csomg dccx7k.st isc(-83aself on an inclined plane? Assume the mec7s8-2k.8sos3 c( gxambvti f xc.c /cdhanism functions properly, even at an angle.

  What force is needed to accelerate a child on+(bb7x9ts6qbgaa,kqq u2x.n/r 1 s jj a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2. ss y0rwelx4-5ga77zxp0p*tqro 8xysae,f; :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 accelerate a 960gw+l th74y7yf $-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a,* e,nct3 ltaq-wltx. * k c+wzi;4god $76-\mathrm{kg}$ 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 re1w)q,f dji2z ib)8sfkquired to stop an 1100-kg car in 8.0 s if the car is travelinz8i1),)ijqk 2wffd sb g at 95km/h? -  

  What average force is needed uexvwv 2j1/ 2qx6cf6jvt /vn16eypt4to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rix6px u 2jv6jv qye6tv21wf1c etv/4 /nfle?   

A fisherman yanks a fish vertically out of the water with an acceleration ofy h.37ep33yobdfk xw. 2.5kbdy 37.w3 x.h e3opfy $\mathrm{~m} / \mathrm{s}^{2}$ 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 cover a quarter-mpik961 b2 1nwdavv.btile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleration vhnm8zpn eh 3 oh3y0r4gl5s-4is 0.0680 g . What are the maximum and minimum forcvh0on gpre544h ysm33nlz8-h es 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 batp+y9hj +,8dz n jx6ijahroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Cajjh+x a96j,yzd n8 i+plculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximt0uvql(cdv8: um strength of 21,750 N. What maximum upward acceleration can it give the elevator without vq: c(l vtu08dbreaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dive2wbw239p sd7nqmxi:u rs (mass 132 kg including parachute) when the upward force of air resistance is equal t9qm 2bi3 xn2up dw:7wso 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 the gu.3 yvmu 9.gelround below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 um.3gu9 .vl yem. 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 wu/+i(l ,yvctv n9*9qi-rnl e2aunw, wma,/r to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box ifnwmw/a99, vwn-av*lytr (,lei/2cu i u n q+,r 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 kh24n pnrv -5*tgd0l/n-y iwd 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 the b5n*b j;cg, hd.qhmw4tat, and again (b) after it has left the bat and is flyim,4q5;gbht hdn* w.c jng toward the outfield.

A 650-N force acts i/73:w,fuevz*h th wh hv9 vrk1n a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate hwv3u hkwvv:r1 zte7f9*, /hh your answer with a vector diagram.

  Arlene is to walk across a "high wire"h6l7b :et oh9lp;tz/ p strung horizontally between two buildings 10.0 m apart. The sag in the rope when she i:e h9o/ p tl7ph;6ztbls 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 hanginga q08t(-bnh sl by 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.f76,q+ux/ u c a4lgnal7pbhf*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 unit to a new location at McMurdo Bpd( jffj g+4q)n k:.ydase, Antarctica, asdq4j)y fdj+fnk: (p.g shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 . ih+fmydf6)r) , 4q imeDetermine the ratio of the tension in the coupling between the loc,ymf+ )d ri6qf)i m4ehomotive 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-pull +b:hgu2 1cb8nebrvjycx. y* elg170rey apparatus shown in Fig. 4-48. (a) How hard must she pull downward to c8 1l eyg0b:. y 1xjvu+7*bnbh 2recgrraise 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 b)gm)e/7dgg ,ej l;xe iegan, 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 mw,mlpi i3* o/04ouhd (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 horwd6).ofidgl f 3z ,h-d:(bcitr gp--a izontal surface are in contact with each other, as shown in F )di dbgz(wit -pfa.3c- rd:go-6,l hfig. 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 above the ground, ai fxxv1xxv,)2d;as -cnd the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the xxv;1 a x,fixc )sv2d-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 arew71e0 wt 9m)uj agzygsw8k;s6 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 thyg9 zaw jk71t6sw e;)wm u80sge 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 d;gn ;q gyz,fz,9 nh5ukinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a gd+f( pfms4;z 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 0.20tvi:h/; kn 3vdg. What minimum coefficient of static friction must ekvi/d v3h;t:nxist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the codl 3rz4mz9xcoevr41/7 , mcjkefficient of static friction between the tires and the gro/rr9zxl k vo, j7 c3medcmz441und is 0.80?   

  The coefficient of statii1 jwn bspnnkp09h-h8 7u4w q4c friction between hard rubber and normal street pavement is about 0.8. On 0 kjpnhshpw-4 u1 4q8n9 iw7bnhow steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80 o+jdy( +ql qh cak+7wfaq8+8j$\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough sj6y (luf(yr,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 conta 1l: idpn9weit:go; o+ct with an asphalt surface have a very high coefficient of static frictioitipn+og9o:w d; 1e:ln.

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 nk;a :w0i(( *atk 6uhq sdpec.for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box At1tu )nwjd 0r2 have to hau1t)2tn0jwdr ve to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, po4.o 1ko*qcm given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed q .pookmo*4c 1of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rex iz s/aud+ba0a9m3,5ovi i 2 j.rr;zist on a horizontal surface (Fig. 4-54).5bi. ij3uzrorzis+9v0ixa2ad , a;/ m 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 oiq9.dhfg4; gt eu(s7h f static friction between the crate and the bed of the truck is 0.75. Wdi4qgsetg;u h(7 f .h9hat is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway,63g/(lg5 epgxrd2npozlv7 v6 which has an incline of gx 66g 3lzvve5gnlpo rp/2d (7 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 l*eb t)y9p- ur,hd+vdwith a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a pa7*.p8l e7tz6ui+qvnxl8d lq lane 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 s+c g28r9jio aspeed 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 reachesk5sjjgw x arfs :p3,qud4*w3) 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 pprb0+hjntn,dm 3sx,s 49q.aplace against a rough wall by someone pushing on it with a force directed upwa mht p,nd9sqxnb3ap ,0+r.4sj rd 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 dangerou ,1(bxc trh 3utdwle72s projectiles as they melt. Consider a chunk d, (xtbr uct3e7h2lw1 of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum sto lggd-3;5s- x8 ayik91. zsdg:iwnrzmpping distance for an automobile traveling at speed vgiwm18d;i.:k-lgsryax -nzd93 5gz s 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 dax5 z8f0rzz*z cshboard of a car slides forward on the dash when the driver decelerates fr85 xr zfczzz*0om 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 inj drvansk br0bd48win;r2(+ 2itial 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 packic)oik flsmr( 8y ()e4tng 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 t)lm t r4(eoks8i(fy)c he 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 ofyhfr4abe3 c2jn .wjgv.a+ 2 ;/l6wvuu kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) cu/nrp/t+y- g(a-athpf4j o:)b y ee* ian 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 of2dl9ka5mbsscf bfa5 s5 74-hp a mammalian heart, at each pulse approximately 20m -b2hf5ca ak5bps5ss47d9 fl 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 if2i 7thd -mihk*lku- u+ the deceleration is no more than 30 " g 's." i 2ht7*iudl +--uhkmkCalculate 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 an vd i+xjkt)3: o 5bnt2wobject is going to "hold its place" on the ground, show that the)+ v wx35kdo jbi2ntt: 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 thecw4g 5zh4b5 ye scene of an accident involving two cars, measure 72-m-long skid marks of one of the carsc5w4ez4 yg5b h, 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 level road.   

  A car starts rolling down a 3j e2/lpsllxz5v;z4a3-djj u1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation4z2 3j l5 jxsl va;juldz3p/-e 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 top of 2fnh 1uvcy)hvv:6v 3 ethe Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air reshh)v23v1v 6ceunv yf:istance?   

  A cyclist is coasting at a steady speed of sa)b 7 iplg12n12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from n2p b1gsia )l7the 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 portio5 f3ke4dp zgx-n of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills-3xg e5pzkdf4 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+.8qba hocij3 physics 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 string m8j3b+oacihq . akes 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, vu2zy1 yqx3j2there are to be several ramps connecting different parts y qz1x2vj2uy3 of the 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 force F is needed te 4 (s8y/hjbbbo lift the piano (mass M ) using the pulley apparaj8h4bybe ( /sbtus 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.b 0y,hhbe ;ed a3ai)x 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, ndfcb9qxc (zt9*zgu74 ,/u cc an engineer considers the following set of conditionsxu9 7zu/fc*(c c,z9ngd qtcb4:
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 tra5n1yo-+rm ev tb8fkr+ in has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bic8e/4:sp i wodhnd;nt9 f* -mall 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 re/4wm:oph fd9nie-8sndt *c;a sult in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " ebs- s/ow3hv+ 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 allow7ljl2fc/ +de.pfuh+aeuf,p z 5/gxlj(b) 0gaed 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 climber;v9tn xi,- uie y*dsl) -xzdh 7,*htjrs who are roped together are ascending an ice field inclined 7; i vuyhid*e-xtz ,s*x-n ,lrd9 jth)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.