Why does a child in a wagon s,mz4h8b d0ys 0evp4useem to fall backward when you give the wagon a shar408 yhubdves p0m4z, sp pull forward?

A box rests on the (frictionless4q8gf6*(h b( mcirm lk) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide 4kg(8*m lqbr h( 6icmftoward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no force*0-vq3(rvqmz cd;q m ixm( ho1s acting on it? Explain.

Only one force acts 1p26 4ezld -z bcaf/ luirtc67on an object. Can the object have zero acceleration? Can it have zero velocity? d- l4r6bf 6epcc/ 2a uziz7t1lExplain.

When a golf ball is dropped tv *jczw 0 * olg;r.yhbu3wd90.rq,:gngqk:gxo the pavement, it bounces back up. (a) Is a force neede*39nxgg,0w;0rgdb yr. zhqu*kq v: jwoc:g .l d to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the n6h3-a7k bp *h-ylmo55djfjklog move in the opposite do 6npblj5j *d - hfhkk3y-57amirection?

Why might your foot hurt if yo.iir x:1q v aune-(3d ;ew971rlrjjad(e/phv u kick a heavy desk or a wall?

  When you are running and want to stopl5ypq 3x1ew,i quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience1ypw5i e, xq3l) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread f/uno, o9b,at from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the/nft bouo,9,a 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 r7zp7o3o zjnu2bsz,*kock. Why then doesn’t the3zsbk* 77p jn uoz,z2o heavier rock fall faster?

Would a spring scale carried to the Moon t; z8yr4;f vjzsars8; q w4w2chop,7 pgive accurate results if the scale had been calibrated (a) in pounds, or (2z,; twfcyq8r84rvs s 7;j;w4pazh opb) in kilograms?

You pull a box with a constant force across a fr(0ur lv,) t y,ithm*ndictionless 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) remain the same, ((dntlity* )0 vu,h ,mrb) increase, or (c) decrease? Explain.

When an object falls freely qe2l:c na4c 2h;z) t7 rsmopw:under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the p)cztr w7e2h a:2oqscn:;l 4m Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg obje)nu n pj/f/aklot9x.1v03zl0/yuf irct when you are on the Moon with the force needed t.j 10luo0//nrlfy/ iv tnu3z) xp9kafo lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law,8exnwz)j q)z, s f/;oe each team in a tug of war (Fig. 4–37) pulls with equal force on the otzexe sj/q;no) z) f,w8her team. What, then, determines which team will win?

A person exerts an upwar t ydtxt,ys0ar).u;u6 d force of 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 what object it is exerted, and (d) by what object it is exert 6tuy)y.astxr;,tud 0ed.

When you stand still on the ground, how large a force does the grbnhnpz 2p7 h7y-5s+ez ound exert on you? Why doesn’t 7 + 5hn72nppzheb-yzsthis force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the c1am9;w*o*sp5ab k) p t)tp 4 ebnwio0victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in thi9t5p bnkop*)mw4 )eo i1bpsaa 0;tcw*s situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, c 1 pp5,i0fzt+ntdvy*the crate r1vfidp5p zn ,t*+0tcyemains where 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 slides up a ramp. After the block hk qp,k(5 nisxznj8tdg; u*2d u51:iquq05nnreaches its highest point, it slides back down but the magnitude of its acceleratio 5kn0qg15 ,5qdd spnutz h qnnu8(jk;ix:*iu2n is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighlz6+uw r vw4v/ed yourself on an inclined plane? Assume the mechanism functions pro6 vu r+wzw/4vlperly, even at an angle.

  What force is needed to accelerate a child on a sled at ec:.8sg*i .+wg- 2 je9t 7s;ophwf 9zgvapomk1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ri(,vuspr w8zyn2all * uq38: xbo,vx j3der at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension musttv:m vg9nt 26n a rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of b/qakat3/ly;qt (dp 65t o- bua $76-\mathrm{kg}$ 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 isoi9 md+1ie2)vx(qzjp required to stop an 1100-kg car in 8.0 s if the car is travelingjxov q 9dp(2+ e1miiz) at 95km/h? -  

  What average force is needed to accelerate a 7.ox eum48lg4ugo3 (-etg do1 x;00-gram pellet from rest to 125m/s over a diso(t1d8 e3lxxggo4 g4;-u meuo tance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish ver+c+1b ifvy 7ztm(;tlfmcp.i 9 tically out of the water with an acceleration of 2.5 bizv myi9l ; +t.c+(f1fpt7mc $\mathrm{~m} / \mathrm{s}^{2}$ 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 qc 57tk ui+boz.uarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to bedb ii6q-tc41cfm1kg w:e ;h t7 designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should-7;it61wih e4g1 mcd:tf qkcb exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevatopd )g89ztzj0dr begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction o0gzdj)8 9 zptdf acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750eapnsv1s.lb7ksox uy (85f(u 7ws1 8j N. What maximum upward acceleration n18.lspyfj x7 1es a(sw5uvs k8o7 b(ucan it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceler 9gsc xfnjsnrqjy41( xr:l io,f8* 4t3ation of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance 4(yojs 4l*xfcg 91j8 sfq t:n3 ri,nxris 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 hounzjk07:a.g wvfw t0o74 hbkq4 se 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torsokg44h 0nzo:jww7bq07f vtak . (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 vertica*(dawbaa2d gigfr - *v;6t h7olly 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 if the weight hanging on the other si; d*tg(6g7 rvd-2wha*ai fbaode of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for e jzkydr+9o ;fu pnpeird 0bw;q:*( 1,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 mome6j6e ue)l vjs8nt it is hit by the ba)8jue6 se6jvlt, and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northg-*jepq-n: t owesterly direction. A second 650-N force must be exerted in what ejq :o- p*ntg-direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung z21)x t/rxtl1 bd1uqwhorizontally between two buildings 10.0 m apart. The sag in x)u1/ ttz121rbxd qlw the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging /r2 ce y7gigu8+ic .sjj:i6a kby 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 149jbitx(t 1+d o.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 -oi6h1rpg ti;qj7ax n,b:eb ,h0 avn2 unit to a new location at McMurdo Base, Antarctica, as show6aj0 i-h:to; xpg7i2b ran ,n,bh1qven 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 h6ehy 93d4qqd behind it, Fig. 4-47 . Determh4e63 dqqdyh 9ine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-l qw;dz z-x+xd++2 teigx),za pulley apparatus shown in Fig. 4-48. (a) How hard must she zax+dl x-q+x,;g2 ie+zzd) wtpull 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 65z9z f+yxiyufrjc3 55 4$-\mathrm{kg}$ 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 blocdqkx9 fb.mvp1+/ ml: hk (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 *s4c lwyoi; cck7 e5vq8t, ub2horizontal surface are in contact with each other7 cvkc4lyos*2;5w ctube8,qi, as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 ares:5tndfl2h d emw4w-m)a7wa: 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 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 mdhm l)tw52esfn w: a-:47awd hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tdno xwox6k1ux)*g j/1able are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each eno1*61xj)xud/k ox gw nd 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 kinetic4u vzy)s2i1pi8hq9n a 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 requ weq1x3j/82 fa.:+p7a wp2eqa kr j,)ccuc osrired 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)xdl9 jrg861wwh*zkohj;9 6 fnt.l xy nimum coefficient of static friction must exist between your feet and the floor if you are not to s xd9*9zy.;rf6jtlw h6)81w n hoxkgljlide?   

  What is the maximum acceleration a car can undergo if t65jc3lvahva -mi xc* a y5xd25he coefficient of static friction between the tires an6x55xc hvjamac*vy 5-l a d2i3d the ground is 0.80?   

  The coefficient of statp.w; *rv4 njf,u 9pghx6 yo-yyic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angrnyp jyv*u;. wpy4h gx9-6,o fle) 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 -c0wmohllxay*ca3 m*8 jt) 4 -y4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ronp)aq/r,ik s)w , bm4vugh 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 ub4*xdf dh3j j1k+b7/j8o ip bwith an asphalt surface have a very high coefficient of sta+b8 3k7d b4uj/o1ipjxhjfdb *tic friction.

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

  The coefficient of kinetic frictio0 0qt 5pnw.zsocai1c;n 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 ;w-yngj-ihcwn /)xvei uv4( pv m0z50large a mass would box A have to have to prevent any motion from occur-xpg0um en)wz hjvv( /0cw;iiny5v4- ring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across 3x afpj)s;jer 6 qqqy53dq9 *7v,o uuxthe floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the a*qxjdeoqu5,)3r7;9q 3 6uxfqy jp svpush imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact 97v5c-rfixnfch3 -5k)p yi)jnupe .o and at rest on a horizontalo h9uxp) c-n.ikcpj ery)fiv3f5n 75- surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy cranne j:t5bf1d xnt quq1t.w 7072lgp+hte. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate sl5.g71 fn0b 2e thlpnutwt 1x q7j+:qndide against the cab of the truck?   

On an icy day, you worry aboutk.w e1*q0oi37vbtdjz parking your car in your driveway, which has an incline o1vzk7t*jiwe o. d 03bqf 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 d d12 cn b k;:plrebj)q;f/wp728$^{\circ}$ 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 at an an hvfzj/ .uf(b; *kxt9hgle $\theta=22.0^{\circ}$ 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 initia wpt s2hs7tb83 ;d-ksjl speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepe0 vw0d 4jceo:3+xsp rist 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 it with bsyy8z-93mrin6:kb + jbrc;l7cmp /d a force directed upwa-dzy8mlp/c7 +;ym j9in3kbcr b br6: srd 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 slipp59pmy3* 9sn7nw4supm f qiew(ery roofs can become dangerous projectiles as they melt. Consider a pp(u 9y 9mmiq4s3ne s5nf7ww* chunk 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 stopping distance for an automobile travelon uzoj tbap7s8yr+s*8u36 *iing at speed 3ia o8o7u6*+*trp bs yz8s nju v 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 dashboarx aha14ab7c k+w.wl:d d of a car slides forward on the dash when the driver decelerb4l a1+cakxa7.dw :hw ates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given aj .u ndb;9xq07csd+akn 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 fr)tfznjfjzmm 9k-*26 i om where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a b* )j9tf mf6i2mnzzk- jox 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 kinet )4+uqf ycxymw*vj41y ic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 6.0q)acgm ttmyqzo8 w/q,w*. 0 (uir :fm1$^{\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 ma:bhui sni2u7k r)ah,4mmalian heart, at each pulse approximately 20 g of blood is ac nh:iaush)i,rb2k74 ucelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the e 10y-fpvxmv9gzt;c.deceleration is no more than 30 " g 's." Calculate the tf 9vcp.g; mz01e-xv yforce 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 es2(wo4vs( x)szy w3 vhj7z3lu arthquake is a , and if an object is going to "howw3v slso2)3vz7y ((huxzj 4sld 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 carhhl/zypg89b97-l vyps r3, ev td8d; rs, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The c ,rpdlb/r98- ;lgzhs9h7edtyv38 pvyoefficient 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-in-4 means that for eac lvh5 kuklvtmwqf1/izd:-i u-6nnv h8/c.)d 4h 4 m traveled along the road, the elevation 5idvd/ :w8l6n ) h1 .mt-4uiz hkun v/-kvlcqfchange 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 the L-+4: 8 c6*vn ckjvp yea/xfolheaning Tower of Pisa and falls 55 m before reaching the ground with a scpk n/ j8evflcvha y-4o6*+x:peed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy soz.lga ,z*v3t)7v3t giv+tl- fl bq,atretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal a)vvla,.,3*- ll7zoigg t ft+qzb 3t vif the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working-:- x8jeifwm b on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without --:wxf imj be8slowing 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.4s w- 3ns/zv0sqc wbi a thin piece of string while the jetline0zw4w/ - iqncsb 3s.vsr she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be severaleq;+.- nmnc-bfti x2 o ramps connecting different parts of thee 2b mo.i f+;xnntc--q 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 lifb6itr h *xm( x5f.xh:et the piano (mass M ) using the pulley appaefxh( .6x *ihr 5bt:mxratus 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 accelek1, wls.m4nu trating 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 chaiyt;)1ja:kdv wr, an engineer considers the following set of condi;w )k:jtvd 1yations:
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 metric3dt(3vkqqnxeuow+r7b(u- 93j q fid) 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 a yj)- 67 gfy ypmrwd s:(scm2d2n(abv/nd 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 my2:d/(snf w6gmj 7p2 )sb(cvyy da-rthe 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 " 10-1 es79lpf7cw/rvq1hi 8 f ef6y 0n/9svj$\mathrm{~b}$ 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 buildc3qs:clu k3ds i7,f d9ing is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped toge -,/rgrxw g+r6 htm ds.5eqea 2rx-kc+ther are ascending an ice field inclined at xa6qkd 2ees.5rtcr- r/hw+-x+mrg, g 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.