Why does a child in a wagon seem to fall backward when you give the wagon a tizbua(8eg/s l)5a4h sharbu/la(g) i se 8a5ht4zp pull forward?

A box rests on the (frictionless) bed of a truck. The trucks,iqe:8p 1swbdiy)8;covu c2 driver starts the truck and accelerates forward. The box immediatcsi voqi;8,yc bspw 1du)e:82 ely starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an )bdu 9ynka-50fmkxv *object is zero, are no forces acting on it? Explain.

Only one force acts on an object. q ,jl1s4s sofgqmli8dicn32r2v 1y3y2 yxo50Can the object have zero acceleration? Can it havisx 1f1ycyoqlds3,y 405 j l28ir n go23mqsv2e zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forcwa4zpwqn:0 8gdyb /x7e gq:nw8 4dpb y /wa0xz7needed 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 tho vlnx a-t),t- 1u.snulh)+*oo4mj eqm1 y)cxe log move in the opposite dho,u)jxot4lvo*.1n)snq--axc1e y) u mt m+ lirection?

Why might your foot hurt if you kick a heavy degx2:n fg7/r/yq vdmk ef:h3z5sk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) v/y-ogj.p li.What i-lj/ .yvgop. is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling-m :,+(lkezo 8qiwj5runs ty0, 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 thrtr (5-zusqle o8jm0ky : ,wi+nead 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 :xon648xpm b;8amceg on a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier roce 8o8 4b cpn;mxgam6x:k fall faster?

Would a spring scale carried to the Moon give accurate resul(5( ;ckj,vb bh.zvww 6blwi8yts if the scale had been calibrated (a) in pounds, or (wwlyjiz, bc; (bh .v6w8kb5( vb) in kilograms?

You pull a box with a constant f jjxyh*clam0-ww.c 1r1. w qi 25kz8iporce across a frictionless 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, (b) increase,rak0 phl-zwi qcxy512w8c.mwij .*j1 or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a ne-2 4 7nihxe*rr wsx/0;rsqb lat force mg e nxb 02 xr se4*arq-si/7;lhwrxerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 1oe+g doagt- a510owy-0-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moo- 01w5e-ada ggoot yo+n and on Earth.

According to Newton’s tc8f,90cv(rh y/rbb pmhird law, each team in a tug of war (Fig. 4–37) pulls with equal for,/fb(r 9 hrpc v0mb8ycce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of q(ut gvfv (. bmy,y./5wvd3 8p7dsha mgroceries. 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 vywbg qdv smy t/ 3u.,d(v5mfp87(ah.it is exerted.

When you stand still on the ground, how large a force does the ground m fd dmjx df)5z3,ummcx0,7h(exert on you? Why doesn’t this force ,07h 3),f5mzxfdjmm( cddxu mmake you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s* x1y-st qjxiqz(.p v3 car is struck violently from the rear. Explain why the head of tqtsjy- * pzx 3xi.(1qvhe victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on theb3 z (ck *cl*df4rfm;t bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force cau cz*fk 3flc(rd;mtb4*ses the crate to accelerate?

A block is given a push so24 6ypmo fye2q that it slides up a ramp. After the block reaches its highest point, it slides back down m2p yfq26 oey4but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself otzf36q+e8n;pii b8ycn an inclined plane? Assume the mechanism functions properly, even at an angz q8y;e3fi +6tn8 bciple.

  What force is needed to accelerate a child on a sled at 1.2cg)fc y1m 738oldfo 8o5m/s$^2$?   

  A net force of 265 N accelerates a bikg:jtw top8, /ay)bl9ie 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):hljc qs4cz 8b* )flg 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 a cu t0hl /-*sig lz(b2u $76-\mathrm{kg}$ 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 to8zc ,(x/ika jr stop an 1100-kg car in 8.0 s if the car is traveling at 98( /akiz,jcxr 5km/h? -  

  What average force is needed to accelerate a 7.00-a;2i y.a8yku hgram pellet from rest to 125m/s over a distance of 0.ah2 yaiu;.k 8y800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an*xh1s;)b t(jxg y8n*zgaj * ex acceleration of 2.5 8aj* bxn*zh1 *e;xy )g tsxjg($\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (4a*:zuh4vnz .ke/gdos -m b+:y02 $\mathrm{~m}$) 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 ) w)pi6)bada 3dk6d pf8is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportdw p6pa )6ki)fabdd 38ing 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 motionlessfd 3/urr0 c3*. *mvoxcro(ztn elevator. When the elevator 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 of acz *v(tdf3x .om*nru0 or/ 3crcceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750(6u 4r fp)lbhe 5e- +ci0qnops N. Whatrfueqs)plo-b5+np (eh40 i c6 maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of2t 5w2mdu0g ri two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weig02rmw 5 diu2tght?   
(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 ground qqs48ctoxl) v39g+itbelow, he bends his knees so that his torso decelerates over an approximate distance of 0.g3 o8slqv)q9tit+c4 x70 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 run dysm38lr(ir 8x zf8l*s vertically upward over a pulley and a weight is hung 8ls*d rx l8i rmzf(38yfrom the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball p3 -oln3)*her heww v:zlayer
(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 bafae1-k oo7 .*nh k hst5w3tm6rseball (a) at the moment it is hit by the bat, and again (b) amor3 th7a-6k1kf ehns* .t5 wofter it has left the bat and is flying toward the outfield.

A 650-N force acts in ac5lm :/d -c1nnbnv3 dw northwesterly direction. A second 650-N force must be exerted in what dcm5vnnbcn3wl d-1:/ 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 horizontal-p2 qqu5pjq1nly between two buildings 10.0 m apart. The sag in the rope when she is at the - 5j12nqu qqppmidpoint 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 i7vzf t+. sv9xis 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 14.0 .evmn0;j n70adb rhtv fk14l0$-\mathrm{kg}$ 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 nteoflkg2) k+f zw-1) nm0h4n Base, Antarctica, as shown in Fig. 4-46. wnl0gk)+ -1z4f f)hknmneto2 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 xlvs c-3orrt ed3/,r *cw;e 9etwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and therree ts-3e/9vo* c3;x dr,clw 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-pulley apparatus shokcwp(rifo8 22e47sjiam9 zc; -n6x lnwn in Fig. 4-48. (a) How hard must she pull downward to raise herself slo6c4r78n 2 i joxps kw9 eimc-2;(nalfzwly 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 begaypo31 v/ emuli7zr , 1d(+3onkdzn) tun, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (ma 3gqse pf/i66yss $ 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 con/en98d0 i yf9( njbz/j 0cfrxhtact with each other, as shown in Fig. 4-51. Arcy8(n jjh0nxd9f9ib/fe0z / force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abqu+k(tnf4owy8u;5r)qp5yapw e j:4i ove the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object ryoj (wput 8+u ;p4yk)i qnwf:55a4qereach 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-3x q9sojhi+y mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams sh9 jqy3oh+ixs -own 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 between-gc 0zc lsxm6jjz/exghq :(yl0g5 97g 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 az.msv;x 7m ia:ki)ccp)f .s/ n 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 0w/j xvii f/g .pgb:a2dq7*gw-.20g. What minimum coefficient of static friction must exist between ww/i-2g/ a dgv iqbfxg.p*:7jyour feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can ytfts u:3m8532b ji txfg-r 7tundergo if the coefficient of static friction between the sttbgmu :rt5f3yj2ftix 78- 3tires and the ground is 0.80?   

  The coefficient of static friction betw d054,ba;bc ero 5+gmargzs+deen hard rubber and normal street pavement is abea45cgrrosm++ , b 5dab;dzg0out 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 -4 yig5qimom t6i30:b6r.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 roug jzsj,iy9crger-ox 29-yw/q f. wa y0:h 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 o.rum n5). vaphave a very high coefficient of aop.)m nvu 5r.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 ki60bppml9su)gw zp+.t netic friction 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 masbubos( , ij8 kb(fn)h4s would box A have to have to prev4nh)(jof, 8u (k sbbbient any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, s l d.u.g3u *dwvojj;dofiac16- 77qi given that the coefficient of kinetic fricai;3 jgof.dq* o7iv7l1wu6jc uds -.dtion is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a ho) 8j3hxrx7x3r rvjm l7rizontarv3)xr7 x jhrj73lmx8 l 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 crate. The coefficient of static frictiolb,.*u x w,ks q,y,ml;bpn6wpn between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the trubx*,,bu w,.lp,sw6mqk nl py; ck?   

On an icy day, you worry about parking your car in your driveway, which hles-ew 6mk):a as an incline o-a:6)wekl m sef 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 28zo,es y+j/ly;hip p;h7qfel3 1ygy :1$^{\circ}$ 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 anss*z: m eta,7t 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 q,gz8h -f o+t(s0 swrsr:1icz 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 spe239k) sspbk r9dv n4hded 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 pshw8hp;z x 7(dushing on it with 8;w7h d(sxhzp a force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become daniq0ktvtj cci/./qb 96gerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a piqv09q6 /c/k.ijt tcibtch 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 minij 1e41 ;vttf d.tb9)irxzt. nxnzo2s+ mum stopping distance for an automobile traveling at speed v is equa9t12rxbjz.d; .4 zeos1 )nf+vtinxt tl 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 eg475xg-a.b l1bm8yaxm i( u.; dutnoslides forward on the dash when the driver4imgu ;1.tgxn-x loaub7 8e.my 5db(a decelerates 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 an initio.ytvx/ia7el p ml;f+rb54 1aal 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 convoa-gsrf/by bv33(uy0b lg +nz .0 8xbaeyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient olgybbrosanbx 0- /v38g f 3zu0 +aby.(f 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 friction bet1t,gv0x3 +re jp1pm/8nv p g5 lmqgic4o3r+gaween $m_{1}$ 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 bicycl x(uqn8la1uu+ e) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplq/+ xj ,j-ubd wveqcqk7; ;ezq3(qaq+ ified model of a mammalian heart, at each pulse approximately 20 g of ;7qqq-qeq;(wj,xdzuajb3 e / +cq v+k blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the o2e( czzjgu1ljy-hrp *: ow,5 deceleration is :ejo ju(y p,5c1zl*2hzrgow- no more than 30 " 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 an objrr2-5lzeo qs f40 as2nect is going se-2l4zrqn2rfo0 5sato "hold 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 t(v(ufh8u m tg19djz5dhe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The f 9h (u51dzdg u8tvmj(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-in-4 means that for each dj6; npaki9q t9-ui/v 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?v9anq6j9ikdtipu; - / (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from thea+7m o4;o td+:q hfywk p8hb:9gxkg0h top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the aveg g4df7k 0x + tq;w+mhpyb9k:o8ohah:rage force of air resistance?   

  A cyclist is coasting at p8s wlq2; ycf3a steady speed of 12m/s but enters a muddy stretch where the effective coeffy23c sl8;wqp ficient of friction is 0.60. Will the cyclist 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 portion md6pm6maz0 ,cqlr :q5of 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 dozpq0rm5m6 daq l c6m,:wn. 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 pm / blf:4yf hgmu9czts7xl4/1iece of string while the jetliner she is in takes off fm4l m z/lg:4c fx9h7tyus/ 1bfrom 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 several ramps connectiucu41;qf n-jzng differen u 4j-;z1unqfct parts 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 pe7y d;1rs 1l2m vf-sineeded to lift the piano (mass M ) using the pulley apparatu -fr2ys;1p17 i edslmvs 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 accelera8 hlpx f,xu:h+t)j /cating 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 childdq;2 ge n1sfz,(nz6y a-restraint chair, an engineer considers the following q,z zy 1g6;nsn2( afedset of 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 mnzptef7vj w 6v *h*,i:etric 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 simid(eclp( cn9+z0k ojw 0lar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm zpc 90 (w+d lkjnc0e(oonly. 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)t8 7lc l59cdzxb./sob ,ojwk-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 buildinggmd:jr8l f 24g is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascen,csih2y59r v 2hsd)lz3; :beiy gw*r vding an ice field inclined at 2c*)wyirvhelsh2 ivzd 95 r: b3 2ys,;g1.0$^{\circ}$ 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.