Why does a child in a wagon s2 h6x- 97 a/oqbizolzxeem to fall backward when you give the wagon a sharp pul b 9oqi6zlaz-x h/xo27l forward?

A box rests on the (frictionless) bed of a truck. The trffs.iif)zya t r 80gs8989yr nuck 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 la9 yfs)yizff8n0gr9at.8s ri8ws, 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 a*elm, /: djlmmcting on it? Explain.

Only one force acts on an objecxzufi 9 b,1vja up1mk4c2jcsjwak- i*.*1 o *mt. Can the object have zero acceleration? Can it have zero velo1os1u w41 pa*jcv9bj*ma i*. ij2c -ufxk mz,kcity? Explain.

When a golf ball is d 4 c2hcsfl-6vpropped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back us42h -lcpv6 cfp? (b) If so, what exerts the force?

If you walk along a log fl-zom tw61xld *oating on a lake, why does the log move in the opposite dl 6toxw* dm-z1irection?

Why might your foot hurt if you kick a heavy desk or a wal:wn/+le j: qvwi6g0 sj:dng5xl?

  When you are running and want to stop quickly, yous;do xq3,:y eg must decelerate quickly. (a) What is th,: dqe y3gxso;e origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fia5km /ez: g*i3wb;zn kne thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fikez ; knb:mgi*wz5 a3/g. 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 on a 2-kg rock is twice as great as that on a 1-kg rock. Wps.hm2w8lne 2 hy then doesn’t the heavier rock falhl2smen .pw28 l faster?

Would a spring scale carried to the Moo afkdbe3.-0hht l,1vrn give accurate results if the scale had been calib0 l-1ra kfdv,.3h etbhrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attac :-t+kvm cnb9zhed 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 th m:-v kn9zctb+e acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influenx3xg.v n dy64rd0:nchce of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s thirdg:v0r 3 yxhx6n.nc4dd law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force)e11iqimcp l.qu;* k4h needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to tkimq1*.iu;pe4q h1 lchrow a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war ( oq3h)t0fuj3r. mw6y tg6kh6c/mk 4xoFig. 4–37) pulls with equal force on the other team. What, then, determines whichko q) xtmom3wc4t6 3k/fhhuy.6 6rg0j team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe tb +xywb 3v*uv(i0*zm s y sw6f:v2m1lche “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 obje0u wlv+iyxv2(m vs6w1:* bf sbmc *3yzct it is exerted.

When you stand still ok371fs:ypzvr)ft+dn )8y h1 v q0 ojahn the ground, how large a force does the ground exert on you? Why dok 1ta8yojfhv:0 1q+ny 3) svr7pzf)hd esn’t this force make you rise up into the air?

Whiplash sometimes resulze, d1iz zll6rgv64s*lk v +6lts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head osi rl6*zl6ev, +klv 4lzz1gd6 f the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bedxdu7( w0ho8l k of a flatbed truck. When the truck accelerates, the crate remains where it ilxd78h uwko0(s on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so t6t 5t)p25qdal+db ;qudxne )yhat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on t ttd n2x )a55dy)qq;du+6ebplhe descent than on the ascent. Why?

What would your bathroom scale read if you weighed 3vpk q8 zb1j t +m9u3xxloj3v*yourself on an inclined plane? Assume the mechanism functions properly,qjx1 po83+xtv*jl k9z 3vb m3u even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/so,js y9:ffc(ua:p -h:s vpe v+$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.3l -)csn p+h)52c zpldb0$ \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 13kc18jnm9s uesft x4accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of ak ,p;5xnve s5i 8otoj0bi3 rz3 $76-\mathrm{kg}$ 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 stoplt5emw(cp,.vcy+o 8ad 5pt m: an 1100-kg car in 8.0 s if the car is traveling a(twp5+ 8d.yca:vo,lctmpm e5 t 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fmlj2t3 8c( purrom rest to 125m/s over a distance 3c(p8urmtjl 2 of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vecc 1l,zo q-+ jjk,gmde98u b/irtically out of the water with an acceleration of 2.i1q m,,9 ebojjzklc- gduc+/ 85 $\mathrm{~m} / \mathrm{s}^{2}$ 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 covgnaj l*b-20v xp8 ej,xer 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 to3e: 8m zf1nkazcl 0s3ke:qgi/ be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? maxm0q:cnekk/ : 3 lf1sz8gzeai3 =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elev0t-3 / adgxvsgpo 88zvgmyb05ator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accelerati ggdv8pb0-z soyt8gm3 x0va5/on 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 21,7505x 2o) hsp(dsu N. What maximum upushopxs (d) 52ward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (massub pjmya)qp,fyc*l;3 :p4-av 132 kg including parachutf* ulbyvpam-q)4: ;p3j p ,ayce) 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 hous/(st kzzv5x;d 4vh5ore 3.9-m high. When he strikes the ground below, he bezs;ro 5 (4kv5hvtx/ dznds his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertic,pwbi ca7-u e-ally upward over a pulley and a weight is hung from the other end (bcpwaei , u--7Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pl*,,fcx te)+vdm b;5o1 xvhkf jayer
(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) e/x l .7yal2 man9ffo8at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the ou fe/xfl.oya 8a2mn9l 7tfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mu6gnl:rq r1vs)h: *fg 3rw+ey bst be exerted in what direction bw)g g1q 3 r:lre:yrh* 6+svfnso that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high 6kfmvbfu sr(8wur:e81quy8u1 00r rp wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope wheuk01r6br8qu88 0: vm yefruwp s 1(furn 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 buckkh6mf8mw3j( t et 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 14wjl v+r,ff(e3.0$-\mathrm{kg}$ 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 Base, n0d03 wsnnrr+Antarctica, as shown in Fig. 4-46. The suwn+0 d03snrrn m 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 sam7e x 9pwa o*h3k23a:yza7 otwue mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the loco7o3o wpkt7 ezhxy 9*2a ua:a3wmotive 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 pullsjwh3 0bz6q id3 herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself sjh3zb03qw 6di lowly 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 rachi y0pu(p 3+mue began, 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 bl)hd13-+1l cfu l sngffsl15 ewock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact w 3 9osuqmfqpz9ee1+ *with each other, as shown in Figmqp*9ew u ofq e+913zs. 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- ot+l.s 60ztx8 m)bzgs52 are each 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 0.tx6mg slts) zo 8zb+reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of masszuxo 90 .-, 1dzeokbs9+gn(lb r i*hug 1.0 kg . Calculate the acceleration of each box and the tension at each endzed 90, .rioog1u-xs hnu*b bl9+(zgk 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 kineticd 5ey) tlg8fi*qyx8ndb 5(od/ 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 isx dcb*ue( )jtg2.f j/,rf-ncy required to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What mi, vqu4kzp8m5jnimum coeup4q85,vz mkjfficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo 9h (pr3t d:eusif the coefficient of static friction between the tirer( he9t3sup: ds and the ground is 0.80?   

  The coefficient of static friction between hard rubber.l5 f)vat.z(znvpx 8h and normal street pavement )8hl(atf. zz5vn.pv xis about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -46:0i ugceke e4a m7a4h 73mbmc.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 rux*s jc i7mz)*ough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very 8b-g t9klpvndv4e xja60 a.,zhigh coefficient of st60eavvkn,- xgpbd8 49jz .tla atic 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 frictim7lokb af:3iz: k:c a3on 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 A hav gmas h ad(4.t8ulh40ee to have to p lhm480tahed sg.4a( urevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor.v tn2z,vf1r7-h.aunz h; e3ag How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts t3;fhhnza,un r -1gvve7z.2aan initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are p:uj)1;(g dvrelh *-gf; mzqbin contact and at rest on a horizontal surface (Fig. 4-54).ug1dfhm:ezgb;- q)prj ;*v (l 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 of gvx7rmq . t*2j2wxn34-e zu, vpdt(d fstatic 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 cratfjx,end2t- 4 g7d (trq3wv*xvu 2 mz.pe slide against the cab of the truck?   

On an icy day, you worry about par xl eyhw(n9+,b*uw p3r-s dzm6king your car in your driveway, which has an inclib(+w d9z u s*mn3pl,hew-yxr6ne 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 2df)llrtumg +k3 (av*ck/qv;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. 4-7 jdvq;ez4+n n55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3c/ pcklr3 7ycvnh3p3 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 top of the steepest hill with a speedk d6aws qdo4l+17, inx 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 it with/ask/(l 5gt v;rbc ma1dx.z*x a force directed upward r/tv/. c5mz(asxk gl*a dx;1 bat 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 becoz -d( ialtv4c 3q+ 42r z(fe.ey6bzduyr 2ix-ome dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of (2u( rz4ztr4ciaziybyveq-3l f 6 d+-o.e dx2$ 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 travelif2hzvr: y,*wl) wv g8bdiufk3*9ag -t ng at speed ,u -t hvlfwa9yfg*8gwvzk* d )i rb2:3v 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 dash when the dmill.b18d5x shwv i75 river decelerate7 5hl.85ilidws 1vxb ms 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 m8 iw(y4r7jiq ,hhdv u*d +axt ylk1(/i 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 -p7l mq)i8 yobltk )9hconveyor 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 tmi) b9lqo lk-h7pt 8)yhe trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic fr(x5pf o nlc; occ/:ub1iction 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 down a kgw *hqi76pl n3b3g/jb34kf gl3hq f,6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at eachvj9 lv4a bf(fpo6pyt72 6; rgd pulse approximately 20 9frvb6l7apg4(tpvd2;y f o6jg 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 c+-t j4sgkti c2rash if the deceleration is no more than 30 " g 's." Calculate thej+ s-4t 2ikgct 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 earthquakev wk+4jf+j8dw is a , and if an object is going to "hold its place" on the ground, show thajkwj+w 48 +vfdt 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, - gor .;g0x; wtvza;oxexamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, whichoxr0aw ; -z;vt.xo;gg 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 1-in-4 hill (1-i( /p aj gblu)y7)*sbtfn-4 means that for each 4 m traveled along the road, the elevation chang7)bf*y/ gl(aj bpts u)e 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 drop eyiwsx +jj:lg/ cn7*: l6;t9kfo6vfaped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was thf;*ot6:l gn xvycwijf9s 6akj7/ l+:e e average force of air resistance?   

  A cyclist is coasting at a steady speed of qt m hu0i5eg 09/az)sv7q,2 tqk2jw ea12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclihvzj22 7k9 q e q0itaw gumqe)5t,a/0sst emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly port s25k(/ahlmplswu +0v8f4qjhion of a city. An important consideration is how steep the roads can be so that even low-powered 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 ta0k( sw4ql/jv +hm2s5f8 plhu o 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 *:fj8t i. n6xneuvc; fa thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that t. vi;fe *:nnu jcx86fthe 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, twidn ux+0uwxt/k3d +) here are to be several ramps connecting different partdk+wdw tn/3u xiux+0)s 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 for ;nt rir2vo;t9t,9tkwce F is needed to lift the piano (mass M ) using the pulley apparatus shown ito9w;k2r n;t i, t9vrtn

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 acceleratinua6)n v-n nt utqdwqy9 .qgsbg .*;:6bg at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineeqkl gm7m1w. ,pr considers the following set .kqm l7g1w,p mof 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 of 660 metric tons xoa/ :n3(cbz g (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 g+t**cw-s yrr3kybg3 gpba .7 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.) (bg wg3 t37ksy*c-.ay* br+bgr p) 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/j j egnv3ss9-u5 ovk* a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allo758dmxm:ce:tik6 c v xwed 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 rope gfdg3pnw ;(awy,cre80 b-6pf d together are ascending an ice field inclined at 21;-a(pbgfr6 d0,wwe p n8yf cg3.0$^{\circ}$ 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.