Why does a child in a wagon seem to fall backward when you give the wagon a ky us5gs5spqeum2s, e)6 ;i ud*e. bk6sharp pulk5d6u) i,u uq s.bg5;pkems6 y es*s2el forward?

A box rests on the (frictionless) bed of a truck. The truck dri2h23of +wqe xpver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of thpowe 2h+ 2x3fqe 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 an9 s0 hvcfldz97 object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can w 8jgerc j)kt5(s(w:tjm by5+d8r4w x the object have zero acceleration? Can it have zero velocity? E (wj ) kj g eds8+t(bx5c5mrwrwj4t:y8xplain.

When a golf ball is dropped to the peq./ m7 tyv)(lx6ae8wrt g *+rof:v pyavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, eqfyv7/eamrr)8: tlo(+v py6x *w gt .what exerts the force?

If you walk along a ljujg*9,wu, skog floating on a lake, why does the log move in the opposite directi, 9 uukjjwgs,*on?

Why might your foot hurt if you kick s6p-gc 6tz;)ed.z thwa heavy desk or a wall?

  When you are running and want to stop quickly, you mus8b53h2z ttpl wauig3:if; s6tt decelerate quickly. (a) What is the origin of the force thhui:sftt5w6 3p8za b3gt;i2l at 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, and a section of the same pih r7/ ewdun18985cwfrzd7mthread dangles from the bottom of tdw n88 u 17 fh/5rcmriz79ewdphe stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that onxaqc:t ai*pq +6xdx92 a 1-kg rock. Why then doesn’t the heavier rop *idq+6x: 9xaqax2tcck fall faster?

Would a spring scalemb/ly6qw x,b 3 carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in ki w3mylqxb6 ,b/lograms?

You pull a box with a coxxfm3n 3p 6nta+/ 4epajl ))ywnstant force 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 tab lwx+3)n3/ yja t4m pxnepa6f)le), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the iqxipd a(8p/ 6po* ru5mnfluence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an o 5ra mipxd6/8up p(q*equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) e; a;f-uoai.g1dzac3needed to lift a 10-kg object when you are on the Moon wita3i a1edu;;.gocza -fh 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 Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Figl uz4t jolr:0m;50gb o. 4–37) pulls with equal force r40;tmoloj05ul:gz b on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hol3 /:ls qovi7j0yp*1r 9xbhntmd a bag of groceries. Describe the “reaction” force (Newton’s third law) by s ixh/9r: yptojls3 * 1qbn7mv0tating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the p8 jq1 kb+dlzd8.) j5 jg:epojground, how large a force does the ground exert on you? Why doesn’t this force make).k 8:q8lb5jpj1o jddzpgj+ e you rise up into the air?

Whiplash sometimes results from an automobile accl68 w pmitvl7;ident when the victim’s car is struck violently from the ;ltw6 p8 mlvi7rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When tv: a/5v)jaiv ghe truck accelerates, the crate remains where it is on the tru/ aaj:vgviv5)ck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so th b99a6eqqphz 4at it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitu9ha pbq64e9z qde of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you we9gvgo+d i;h)8i: z rrqg 17mtzighed yourself on an inclined plane? Assumeg:g i h18+t9ivzz) qgm7o;dr r the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1ie2bfom5 ksbhnt2j,y9 rt) .) m/*bg a.25m/s${}^2$?   

  A net force of 265 N accelerates a bigcc x; - nbit* lgl6(1z oxu*yb1.ys6hke and rider at 2.30$\mathrm{m}/{\mathrm{s}}^2$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 0n2,xu., xucq8 ao twf 960$-\mathrm{kg}$ car horizontally along a frictionless surface at 1.20 $\mathrm{m}/{\mathrm{s}}^2$ ?   

  What is the weight of a 5m5m(4z ngmsn$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $(g=1.7\mathrm{m}/{\mathrm{s}}^2)$ ,   
(c) on Mars $(g=3.7\mathrm{m}/{\mathrm{s}}^2)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop anh*mkl*9nbp ,pk* jw rb(6b2ue 1100-kg car in 8.0 s if the car is traveling at 95km/hk9 h*pepk2bn6j,b*b wmu (r *l? -  

  What average force is needed to accelerajedl.g0l/1 ujte a 7.00-gram pellet from rest to 125m/s over a distllj1 ue.g/ j0dance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceler3i ve xb0*t)lz k96didation of 2.)tixdi39lezk v 0b 6d*5 $\mathrm{m}/{\mathrm{s}}^2$ 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 covdhjvj5fo9: : cpl*/wsx1;di qw l6ku6er 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 t4) zu p5s-rmwwo be designed so that the maximum acceleration is 0.0680 g . What are the )4sz m5wuprw-maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in:x)bplyly ;xf 8272bxi qwso7sy sll-y 88+ to a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of thbs x2w2:pl 8yl -slqi7xtby;fy oyo lsx8+7)8e elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of y.z y+ n9s ms(8t+(omuztre;g21,750 N. What maximum upz( yt8sr.; ym+ne z9ugstm+(oward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky 1/h5tiyd3cua divers (mass 132 kg including parachute) when the upward force of air resis1ua ti h/yc53dtance 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 house 3.9-m high. When hu 2*s8 hpbb17lsdza dx6,oe2xe strikes the ground below, he bends his knees so that his torso decelerates ovep28axu*ddb7x 162sl , s ohezbr 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 r7lcndbs82 r .guns vertically upward over a pulley and a weight is hung from the other end g7dl2scnr b8.(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 p97vv4rfj9no z, 7pxdnbb d9ams07;jv layer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram0wj1(at4 q s-sw jb3w ;wce6qk of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is 1c0(wast q6-jsq ww4 3w;k ebjflying toward the outfield.

A 650-N force acts in a northwesterly dire yq3vmby)*:h3lf th x1ction. A second 650-N force must be exlh*h b3f qxyy:t3m1v)erted in what 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" sta*a l1 4eucmpm8rv/)yrung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint myaelpu8a r)m /c1v*4is 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 by a massless glf -2tpa.4y mcord 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./e)dftv .kj + r gcxq/lm )t7shmv;k*.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 loca: g)pf6sn 7i5g td+doy2f/az mtion at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the 7/g6gy) 5 dt f foisn:pmz+2adforces ${\overrightarrow{\mathbf{F}}}_{\mathrm{A}}$ 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 t du(h 8 yd.kmo9nll:1/po :ywsame mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the olmk py/d 9:.(:yt8lwnho1dufirst 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-pulley9o oyutsk 68 as9zdb89 apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowls8 zukot 9o699y8sbady at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race b l8onz rbdjw3-,fn l))v6dw p5r2vbgieg(a + 7egan, 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 (maal e4m:b8tjg0w9n pa7 ss $m_1$ ) 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 cmkw4 tv1tg:(y ontact with each other, as shown in Ftktmgv(y w41 :ig. 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 i;t ygaz )a7+ uzed8avvb8(k :sn Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What may88g:avd(k tb+ a7szu a) ;vzeximum 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 hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a fricttf fz+1w w2cp9wu9z+1a tr-ceionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagram1cw9fa+ 9 wu1cwp re+tzt-z 2fs shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0\mathrm{N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic flx xowp2zk.;nb4 .v )olcp9uf -l-9ekriction 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 requi 7qs z3,er,tjored 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 7orrv8k+m 1ztstanding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are tvr8 +1m7ozkrnot to slide?   

  What is the maximum accvpal y:cv)rr1+7 po+v9ji2 wdeleration a car can undergo if the coefficient of static friction between the tires ar7:iv9+ )+ycdvvwa o ppl1 r2jnd the ground is 0.80?   

  The coefficient of sek/,q 54rrr0 vjtu(bytatic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle4reuq ,( rb vkr/t05yj) 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 deceleratem1 9tk /lkz-z: cpch4njb+gp1 at -4.80 $\mathrm{m}/{\mathrm{s}}^2$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13${}^{\circ }$ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest8*lgmoww6sdgx+ g f40w6 l dy8 on a rough 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 vgg1p:l glj/efz743hg2b3 6vwyx qq 6uery high coefficient of static g 6x1g y4q/6 vjzhllwfqg ug3 3pb2e7: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 ftw1g;(udgr w91rzm k. riction 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 (fqyq+wlsn uw 6;2a/s/ :uor whave to hswfy;uqs l 2n:w(r q//+6auow ave to prevent any motion from occurring? Assume ${\mu }_{\mathrm{s}}=0.30$ .   

  A box is given a push so t 2djme w6t,qli9z. l1qhat it slides across the floor. How far will it go, given that the coefficie,6iw9dzl 2qtqe.1l mjnt of kinetic friction 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*fv*w.xlkx d s-d(d*c horizontal surface (*d*.klwv (*c-x dxfsdFig. 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 cx 7lxsn6ns 2;yoefficient of static friction between the crate and the bed of the truck is 0.75. What is the maxsl7sxxn ;y26nimum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which ha ncpfrt54sa+ -s an inclinrs54+f-tp ca ne 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 slid n6*gqxenq/b -e with a 28${}^{\circ }$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4( 9cqx+ 922acu8ianbik5v bmy-55 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 m ufxsg9 u fj*k5)(-ovof 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 speed of qyf pti74b s8:t4x/dx 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 z bekscv+tui, f.li- 2+.yrp* wall by someone pushing on it with a fosr. uipcv. t+z,+eb2 *lk-yfirce 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 rl vawvp9 ,3aj-oofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with aj-w9al 3pa,vv 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 traveling at spee aph;9 .e svtz.)egub84nr1gq( ,chp cd (tg4 )cgh raes8,1nbpzeqc; . h9puv.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 dashboard of a car slides forward on the dash when the drive; 3sg*3whtv52kvp x qbr decelerates from gh2q3 vpsvk3tx wb;5*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 initipem6oe/ 4 d;rrmbu:5obw/n( bal speed $v_0$ up a ramp inclined at angle $\theta$ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where ths4(vkw :ns j95s x tqiv:3jbt,ey 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 stibnvqs 4: wjv k3:s, jt(5x9static 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 ; efk rpkwx/aeudn-o6 kn 27,;kinetic friction between $m_1$ and the plane in Fig. 4-57 is ${\mu }_{\mathrm{k}}=0.15$ , and that $m_1=m_2=2.7\mathrm{kg}$ . As $m_2$ moves down, determine the magnitude of the acceleration of $m_1$ and $m_2$ , given $\theta =25$ ?   
(b) What smallest value of ${\mu }_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycsunp7 f t;28, 5n))hbjqwx4gwirg-vlle) 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 simplified model of a mammalian heart, at each pulse app e6sz.7k;yn9j o cf+rcnr6x+g roximately 20 g of blood is kxn+;jzye 6sr9cc g f n+76or.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 *ei9y )( c5bzyog bf*pwn*tp5surviving an automobile crash if the deceleration is no more than 30 " g pno*c5ey)5fp bgi(z* t b*9yw '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 earth jozddk1 +28qcquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient +8 qcjzkd1do2of 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 two7eb w.t a)jnekui2ju0;m*1bks3 iiq 5 cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the i*u;itbmskee3). i 1juj7q05bnk2wa 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 4 m tqi p1,*uk :xom7t g42rq4/j uegk ie/praveled along the road, the elevation change is 1 m). How fast is it going when it i1gxpku /e/qier*g2: 4m,o kq7ptuj4reaches 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 thu8d (8tfhbtnery 1kmz/,i 09ve top of the Leaning Tower of Pisa and falls 55 m before reaching the ground9z 1t t0(d ihnvby8/u,m8k rfe with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady sp1 nqqgxbj3km61+s/8fi dt)rleed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Wf qi1l k)g/sq+ n3mb1t6j8 drxill 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 por6 wu:9kz5-of ldor+wj+;jd 1kheye3 j tion of a city. An important coo 9w: 5udydkk+heow3z1r6f +j ;eljj-nsideration 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 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 likesb;6td45xz.;qei e6uw9p eike physics experiments, dangles her watch from a thin piece of string while the jetlix t94i q6k b;z6u;.pwe deee5iner 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 several rampsl:fhwms;f 0stop u6m- 7qtyg*+0p ,fx connecting different parts of the s-wfm so*hy7;fq+,pm :0 tfg6xu0pstl tore.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    ${}^{\circ }$

(a) What minimum force F is needed to lift the piano (mass v2wi,1pj+tbxnoe6 iyz- ms -9..a psl M ) using the pulley apparatus show9+ iptb,.o -xami2jsy.n l1z w6-psevn in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T}1},F_{\mathrm{T}2},F_{\mathrm{T}3}$, and $F_{\mathrm{T}4}$ ,

  A jet aircraft is accelerating at 3. bl02r)zbst x: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 engiv04qy1r 8 7asylafxl-neer considers the following set of conditions: 4lxsfq- a70r1vayly 8
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 x0 pg2h.4e ydfeybp8p;zs8 zy/1f km;a mass of 660 metric tons (660,000 $\mathrm{kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{km}/\mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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