Why does a child in a wagon seem to falg. l89 fp y3)y;dytjfml backward when you give the wagon a sharp pull forwar gm yy ft3.8jdy9)f;lpd?

A box rests on the (frictionless)xey40 5u-3twd0 6b9lm,ozdt xhjv7 zi 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 4z3muw0djit,hxel7 b zvytox9-d506standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of ana5e cs2dj ;ru2wx.pmr,p yj+5 object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zerohpo-fn.f4t:o2k li1w acceleration? Can it have zer4l12h pfk wioo.-:ftn o velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a)w5s f3z*ik6v8,kl lfz 2ps( kkm2mo:1 djf xd force nd2wp,fj zik 1zv s: fkd *6klmx32k8fs 5l)mo(eeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on avaexpd v3:d4t *6 byz5 lake, why does the log move in the opposite directi batx 36v4dzyvd*e:p 5on?

Why might your foot hurt,cmzgvm kf( i:8h-qzacb 1w uo/+l6 b. if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (f:0mlv ,b1 ljmv8z ry+a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of mvll fmv0j+y :br ,81zdeceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thr)0e dn7v szb 40x: igdsl)di6wead from the ceiling, and a section of the same thread dangles from the bottom of the stonesd)0 sb:4dxi ed wl0 vgzi67n) (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.

The force of gravity 6u.yzh 7f.6sseap db;on a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall ; fzyp duhs6e .7a.s6bfaster?

Would a spring scale carried to the Moon give accurate results if the ex czd6ywwn6i i0j+urv(c- kh7xv42/ scale had been calibrated (a) in pound (vn jr+ivh40u i-ew26dxz6/xkyc7cw s, or (b) in kilograms?

You pull a box with a constant force across a frictmqxuv(qx 2;z.usyj1p:q) / ezionless table using an attached rope held horiz qxm(:u p).2x ;qe zvsqy/1zjuontally. 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? Explain.

When an object falls freely un(kif/:eh6vs9 uzm c;ader the influence of gravity there is a net force mg exerted on it by the E 9c:izahfuvkm(se/6; arth. 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 when you are on tim atvng/.6r3kzvhh* b,l(y,he Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-k,vrigyab(zh* , m/kln3t6h.v g object horizontally with a given speed on the Moon and on Earth.

According to Newton’s th1 y,cf4i)yspmx57 vnqatt(2om 5 qn9mird law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determits5mq2acmi9o x p7 q4nmy fyn()1 tv,5nes which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe them4 ).utr -s3emz a6kaw “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object w 4) mtra.sm 6e3z-uakit is exerted.

When you stand still on the ground, how large a force does the grounqzxk.z,k-j -g1a(nqn .( ewefd exert on you? Why doesn’t this zw 1g(a- .ez., kexn-njqk(fqforce make you rise up into the air?

Whiplash sometimes results from an auto c.j r:i0ca0ikqw+wb;o9+mlhmobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situationik9+cb0wl+ajr;0qoh:.ci wm . Is it really?

A heavy crate rests on the bed of a flatbed truck. Wte45xye+jl tuzup0jslm* x c cp)b.-:4i 5p:xhen the truck accelerates, the crate remains where it is on the truck, so it, too, accelerasjyxee)l:bx40m4 z*5+cpuptp:l ju5xc-. ti tes. What force causes the crate to accelerate?

A block is given a push so thai77h h+ ;bntlkt it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration isk nbli7+h7ht; less on the descent than on the ascent. Why?

What would your bathroom scale read if you wei:zdyim lt6ha(i .fr)6ghed yourself on an inclined plane? Assume the mechanism functions proper6im6 a )(yz ti:hdlrf.ly, even at an angle.

  What force is needed to accelerate a child on a sled - r2.zee*d+d *ptiuf te+wvw. s-ia7d at 1.25m/s$^2$?   

  A net force of 265 N accelerates a boigr2m4 fqp :+aa)6l.ms.ibd ike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to acq*:07y obpd* e8 wqsez)z9tzdmyc s *,celerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ouff(gt(+ oem a,wc ;.if a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg cae4 ax5p gxv, 3 ti prgfhyn1,mbb969e5r in 8.0 s if the car is traveling ag4y g9p6m1b 5a epie5,xx,f39trhbnvt 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125m/.b qgw.- shn4ds over a distance of 0.800 m along the babs. -w.dg 4hqnrrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerar r49/3hzowbo(,g)jdlt (pe h oc 6ml9tion of 2.d) ,/e3z ( thj4 g6lwopo rmb9(colrh95 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cana(f*u g9tasx ;u5qx h9 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 ) iv* j.k wh3nlf9s to be designed so that the maximum acceleration is 0.0680 g . What are the3kn l.9fjv* wh 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 3pp2 6uel : dzt2m8nrzdsr6r/scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Csp6l:2mz d6 t d rzn/r3e8pu2ralculate 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 nq,aobb d,5l. N. What maximum upward acceleration caa,.,bqdnbo 5l n it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleratij3apklv,: 53 fcqyb d6on of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equallqa5y 6vjfbd,kpc33 : 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 the grounmy0y m 27g+n; w1:wo6cvhlr4z /mz hgrd below, he bends m0 g1/hnmo7r;+lywcrh v6w4: gz 2zymhis 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, 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 tabld 43pa/9 mok)wwxu0dbdxemw.e fy98 .e. A rope tied 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 du fpw9/0md 3wy8x4xe)a ewb.o 9md.ktable 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 forjldg6o m3-2oi)bw- aew 0v h:w 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 momentq u 3(xtn52t) 6sm gexvl1h3dt it is hit by the bat, and again (b) a s l3x2u6(tth) dnq35mtxe g1vfter it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mu.,hq d.pij(ei1xd ljsz.6-jpst be exerted in what direction so that the resultant of the two forces points we6-l.hpdjz. d ( x. eijj1qip,sstward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a y ;k/tyr90v jip3-r+sd 2 iwrw"high wire" strung horizontally between two buildings 10.0 r d0r -i+ytrk2y; wisw3 /v9pjm 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 buckz-mrs6)f :(hwrisx 5tet is hanging 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.(i(ym otm7vaql 4j2*n0$-\mathrm{kg}$ 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 locatio,5jxrk,:2kz* nf t(yisofg o: .hr*zzn at McMurdo Base, Antarctica, as shown in Fig. 4-46. Thezrk zy x. ,i *,jsoo:zg(rftnhk:52*f 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 pulln8+hm mih9d5)wkma 32:skph l ing two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in9kh 2 h:ndampmlm 38+ikwhs )5 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 :h 1v:asyvmm pz:r*( cherself upward using the bucket-pulley apparatus shown in Fig. 4-48. (*m( ah 1cv prz:::msvya) 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 ududf (jd-s51z. qja+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 (massv1myz)d1rd0s7kp 9 i5b whjud g1m6 /m $ 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 hos5i6h+3jq tm nrizontal surface are in contact with each other, as shown in Fig.5tji q3s+m6hn 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 eaci k. gesh)adcrc( (j* y/-e-jyh initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of ).-cj*rds/j iegaeykhy -(c (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 conv*dcdfky( 4 l3nected by a heavy cord of mass 1.0 kg . Calculavc*dkldy4f3( te the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction betwee o1y (*,uiwpwun 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 rw:,fey5,bvzg 6v6 av l5(p.8crsamt 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 standi+wil- 8rgh9 f2u6coudng on a train accelerating at 0.20g. What minimum coefficiendiuo gl2 -uwfhc 689r+t of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a ca*vre0) c.j;of -z3 kyiqv)jkvr can undergo if the coefficient of static friction between the tires and the ground i qk )r;0j yvk.)3icf-e*ozv jvs 0.80?   

  The coefficient of static friction between hard rubber and normal streex*ocxhw:x- m af wp; v:c2nb90eym8z/t pavement is about 0.8. On h 0x :e2/ nayc8xc*v-wph:xom9bz ;mfw ow 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 a+,5nn0/vvds che+ dj st -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rwosda 7s2- qb ll7c:obg06fg 4ough 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 con )c0jtxdow8ux: nx4y 5tact with an asphalt surface have a very high coefficient of y0x odn)4 w8xxuc:j5t static friction.

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

  The coefficient of kinetic frict934t mirm1u8 mhkg y1zion 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 larxjmru v i4y.1;zt,;eo3y 3tdyge a mass would box A have to have to prevent any motioz ,;djyxty v 3o1.e3 m4;rituyn from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so ) b ivndq.ggvu a,y*4lfm1f +:that it slides across the floor. How far will it go, given that the coefficient of kinetic frict,n4uay:+ib l g fqfmdv)*g.v1ion is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 k ae oqx-uve-)kg;1 i5kj ymg1s6.,wrmg and 110 kg , are in contact and at rest on a horizontal surfac6g.- 1j-yurmx1 ks 5mka; q)evgeo,wie (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 carm95:y8v l6s8e0;mvaxh,ryy q xuk6zbrying a heavy crate. The coefficient of static friction between t x0yxml8syv e;h zb,ru6k589 avy6mq: he 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 cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which hasp.q 0ualc:/7o y bwxvl74i0t o an iwip l xqt 47.7voobyaul/c 00:ncline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 2l+ zqbtgj7seoao,8: 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted ap 6/ dzkdukqi8iv*;f :t an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed owrr53 rwv-7 r 6jawsk7f 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 reaches the c 0ru7mij -j1ptop 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 on i xs2v lwh k5.-;yh.pxnt with a force directed upward at vlx;h5-kpy sh 2.wnx.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 pr,fieq q1/g 9crojectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of q/q i9c e,f1rg$ 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 xo62+x 9yv 3xvban pn4c3*qr lstopping distance for an automobile traveling at speed v oxp l3rb6c4xvn 2y9a n+*xqv3 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 forward on the dase) he)1d*9ev a pr*iszh when the driver decelerate) v*ez)s*eear d1 9iphs 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 w/ n2x.ap if.dgiven 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 conveyor belt from where they are filled to the pacbo 5y4 *+wwsspking 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 is the minimum t*w4yb5+ opss wransit 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 fricti ;sjrbuu wj8(xkai* 2sy80cq:on 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 coast douyjpokhw3-l g-7 pn **wn 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 mammalidot2dwnif-x,ib xl9 ,g.e0:man heart, at each pulse approximately 20i.d dx ,wb 9gm0-nti,l:2fe ox 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 reasomjmn vu 13qg*ge s zz2)mrd268nable chance of surviving an automobile crash if the deceleration is no more than 30 " g 8) gm vnqsdu jm6mzr122ze*3 g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if annb vmyb8xz( dd+v:t0 h/ -b9ns object is going to "ho8b0ybsnmhn ( 9v zt:dx- v/db+ld its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two cars, m7nz: iqc3zl;.x4x el1vmrp0 beasure 72-m-long skid marks of one of the cars, which nearly came to a stop bezl cmzr0xle7q;x p1v:b.n4 i3 fore 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 1-in-4 hill () xxvga 9ygce 1;s(a7g1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Igno7g(gc1gxx a)9 e;vysare friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of t,r,pd z.ea2tbx a3o ng:3yq+ nhe Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average 2 3on yabgzdpqr3tn+,x.,ae : force of air resistance?   

  A cyclist is coasting at a ste4eueaij hxb j 3p).c+*ady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch withoutub4x ecji3a +e.h *)pj having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion 3 .fxv zhh9qtk365yoab*z,idof a city. An important consideration is how steep the roads can be so that even low-powered cars can get up thehvtz*9k fzh3y,.i6 aq bxd53o 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 piec:o/ 9kabetv tit (2lr5e of string while the jetliner she is in takes off from JFK Airport (Fig. r 5lbe (tt/vi9:ak ot24-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several rampfjtzl2 zhtqm 26g 35.gs connecting different partsg.fjmg zzttq653lh 2 2 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 to lift the piano (mass Mfxu9;ayu+i3ecm: l9 l ) using the pulley apparatus shown inl+meu;fuc x:l 9i3a 9y

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 3.5 dx,1bloelwtg+s g* .)$\mathrm{~m} / \mathrm{s}^{2}$ 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 c aah* 1vd l) bk;7km0thzhu31swg0cr5onsiders the following set o3ug0w1ta;cmb57) zh0hdrhkl1 *skvaf conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass-tj v4v1k0wp zq3vxe6 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, Bill and Karen, use safety ropes of similar length. Kareniy(zcu8r; -y b d-bdv4'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 andu diby-r8b -d;c z4(yv then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-vdc)oc + a83xc1 $\mathrm{~b}$ 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 talf(rx 1xny4+o a-4ygz bl building 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 pdv; :jnayq+ cyxd4-- are roped together are ascending an ice field inclin-4p javy-n:q; xdd+yc ed 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.