Why does a child in a wagon seem to fall backward whenyd u)hnya7smw.)ejcj( p6*ceyc.* 9 x you give the wagon a sharp c.u)*)p hyjx nycw j6a9(y7d*ec. em spull forward?

A box rests on the (frictionless) bed of a truck. The truck driver start5 -vw deo+3 jtow6ck/zs the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside j+z3t-/ wv5ok6dco w ethe truck and (b) by Chris who is riding on the truck

If the acceleration of an object is9v+)w 3ogjj zd zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can ixv jn 0ma3c8 lm)ap-h6t have zero velocita)x3a-p8 j cnh lmmv06y? Explain.

When a golf ball is dropped to the pavement, it bouncemdmcj,7cfx3 vkx,gbj y o,0sr-g ,4 u;s back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the fo rs xv,mcg;jkj,xd4ou,, 7 m30cbyg f-rce?

If you walk along a log floating on a lake, why does thel fjl2a-mi 5y3/w-ije log move in the opposite dirjfiyw35-il ae-/2lj m ection?

Why might your foot hum3a2 s43k muxqrt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quica)yvrd(day3,9 o sn3kd9+lj f kly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your ow(9jl dy ks3+rn,dd)ayv3 of9 an 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 sectiotr fp m-hr9 lq)7af(p4n 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? Wp4t ahr f7q-9(fl mp)rhat if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock.wsz p :c9g+ip4 Why then doesn’t ts4+9pzw c: pgihe heavier rock fall faster?

Would a spring scale carried to the x.l h86 zuc;t5x 7ddenMoon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kiloue5 78dh6 x x.ctdnlz;grams?

You pull a box with a constant force across a frictionless table usxtdlw8 k *eiy.7/1l niing 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 acceler1yx 8nldtwkiei7.l* /ation of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence o2by9y guc smjeh06 7b8pw- ue7f 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 Earth. Why doesn’pu es6cbw20y9j m 7gby8eh7-ut the Earth move?

Compare the effort (or force) needed to lift a 10-kg- qvs z-2dmw8q 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 tw-dq- vmz8 s2qhe Moon and on Earth.

According to Newton’s third law, eachc0ps a6/ .zaztnu0gfidm-n89 team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team.sn0/ umnta gp80zd f69zc-ai will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Def- (b1uj6hll0ni- xg escribe 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 e1 jn6b0 l(-gelihx u-fxerted.

When you stand still on the ground, how large a force does the ground exert)cx)7:z c crny on you? Why doesn’t this force make yoznrc:7cxc) y) u rise up into the air?

Whiplash sometimes results from an aut2v*wrq ,ws vp5omobile accident when the victim’s car is struck violently from the rear. Explain why the head of the vicvqvr ,w25w s*ptim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelze b:4 f12hjyp2ia,xoe-2 kqw5h+gaierates, the crate remains where it is on the truck, so it, too, accelerates. What fo24 h: gk2by1jqa 5ozx 2e+hw,i-ipeafrce causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itwzr9,xk: 1rg tfg p9n,s highest point, it st ,n1kr x9p z9,fgr:wglides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathrhhm ml 0hht9;*oom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an ahm09hh;ltm * hngle.

  What force is needed to accelerate a child on a fnfyb,.(s7lhw l,e 5zsled at 1.25m/s$^2$?   

  A net force of 265 N a(,n6)s9 szlc uch 20 g)vzkuw6dsgx-vccelerates a bike 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 y9pj- +b ibgc4m7ix m7 .1qymoto accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o a;(kfbqte ,hb5p1)qze)wwj +f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an cfpy o :rm-61,fi1tsh 1100-kg car in 8.0 s if the car is travefm:,- h tpo 1sf6y1ricling at 95km/h? -  

  What average force is needed to accelerate a g75(/gj b4d/uqdd jsf7.00-gram pellet from rest to 125m/s over a disduj g4gq//s(j75dd b ftance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelm6:nc:ur h)c8rr c)szeration of 2.5: u)rn)sccz8:6 rchmr $\mathrm{~m} / \mathrm{s}^{2}$ 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 quartecm-ausaf 6(5on xb(h9 r-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 be designezcl v-fy4ocyl-n9p(+9t/rs f d so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportingpv -ytlrf- ocz+fn(c yl9s49/ 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. u)rvekv c/.m7w qkp9;v:k-lzWhen the elevator begins to move, .e; 7p/)9mvrlk-: q uzv wkkcvthe scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum mjfh5*expl6/5a oza*strength of 21,750 N. What maximum upward acceleration can it give the elevator without brea ae m*fjazh*/5oxp6l5 king?    ( two decimal places)

  (a) What is the accelelz ik8lohhxtxgux8+ d6frf7 n.u,0(/ ration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal tf8giux.xfo nux/r,tl 6z kh8h(l 7d+0o one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikyz+c k8,vo7byl+gee.1wu* 8bg ) ybgoes the ground beogy.g+8)uwyz8eb1 bk b+* veco, gyl7low, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically x,p( skw;f s*bto9dt5ismi5.upward over a;ws.sb5 ti (,sodfkp 95tm ix* 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 side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketblwpg l* kl52j.all 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 ; otjic*jh- f od,;gbl+ .o3dlbaseball (a) at the moment it is hit by the bat, and again (b)ilf;jo . -3,g ht ld*bo;ojcd+ after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must +8lb(u m;xsf rbe exerted in what d;+8x sfr buml(irection 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 horizontally betwee1t1w (qj wc*9e78ykq ;*yshjfg 8ojxsn two buildings 10.*q8 wefq(w1jj oct 18sjy;x 7 sykhg*90 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless qah+xd-qd *dj/m2vs/ 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 m6varv u+h.)qc/cy2j.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarct)sxzxy* m 6w sc-vd9/yica, as shown in Fig. 4-46. Thc w-dz/x9sxvm *yy s)6e 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 ud:3u19n p.nvrd 8oajcars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car o dvuj1u 3:9dpn8.nar$\left(F_{\mathrm{T} 1}\right)$ , 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 rbwlt6 je1) d5shown in Fig. 4-48. (a) Ho5ble)d6j trw 1w hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race b/z;yztn d,b)d-px g5tegan, 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 .p9/: zuygu;-b hvzmm(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 horino *c6jtx u vmfly;r c;6/p8+pq53ck xzontal surface are in contact with each other, ac5 x+/8cn6y ; qfmlpro3tx*vc;6jup ks 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 are each initially 1.80 m above the gr( m, 8slhmjopnzl, u3*)bzoa- ound, 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:,usb ( nz)azj ollmh,8 p3-m*o 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 h:p g,g,5j ) guirx3uyceavy 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 diagrams shown in Fi yu guir35,c, gjg:)pxg. 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 ac soh(h2rq5tx 2dj+ ,n 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 re lrmug-vg :sf1ns5paz6( )h ;aquired 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 0.2fh).-lvb *ici ,qs:6lu fue :a0g. What minimum coefficient of static friction must exist between your feet f::-isbluf ,vla6 u* qe.cih) and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of static l7zw ;8lt4exa/um l l4friction between the tires and the ground is 0.4ll7/z; e8wmxtula l4 80?   

  The coefficient of static friction between hard rubber and normal a,hq k t4 -fsmb7s,p7dstreet pavement isd -sq,ptmf 74,7bkhas about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate azy2n+e5 6qe pae ,du8nt -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 rest1h.mtao7 hs s1 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 very high coeh/7f o07ocd ez9 m7talfficient of sodaf/ t07om h79z l7ectatic 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 friction forsm,l;2jf0vkr 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 4-2:e:2exewy z1b 0) how large a mass would box A have to have to preeeyx2w ze b1::vent 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 g,o(.ichz pwl.vath .8o, given that the ch,z(ith.clw. .ovpa8 oefficient 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 re hpgx.- bc-a9 8t, 1dab6bsjrnst on a horizontal surface (Fig6, b g bdjrpnbx8a19ta-.chs-. 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 carry y 1p23 np0+zhsyum/wving a heavy crate. The coefficient of static friction betwe 2p0+/ mynspuw13zvhyen 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 truck?   

On an icy day, you worry about parking your car in your driv8hzuy/wv : hlh m3ciy)az;;b. eway, which has an incline ofh z:iv.aulzmhy )w y;;3 8hcb/ 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 slidlkw4 )whj1+ yyg r/fhgs/9*twe 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. 4-55 lies on a plane tilted aeo:y53lhhdu 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 :/qgv kg 9ewbch+p k96initial 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 steepest hill with a spg1qs+ ex : pve3*w3h svpmw8g+eed 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 roug8jese wx wo9il3u044l h wall by someone pushing on it with a force directed upward at 288l3 l0o4sw uej9ix4ew$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they melt.mj6bypd kn 87/ Consider a chunk of snow at the ridge o67 8pnk/m ydbjf 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 minimumiis gl.*, a159q muwzn36iawe stopping distance for an automobile traveling at speed v is equal t iwi6.wl nmuq*eg13s aa ,iz95o $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 rkrx 04md u+mmm(gn1*qb6g.qslides forward on the dash when the driver decelerates from1 0 *k+ndgqbmx(.6r u rmmmg4q 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,2uwlaqh)abs4 bt7e ld93eq3 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 ;umgp6 fqa :b6-bsv2y conveyor 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 of static friction between a box and the belt is 0.60, what is the minimum transit time for6fvbapy62 bgq u-:;ms 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 kineti )vz7 vsnmkj t)ukk983sbv7t*c 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 (including3iv +mj:eek)o6 iog. 0grxr:a the bicycle) 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 approximatf 92 ke)og d/0yhjmdx8ely 20 g of blood is accelog8f x)d9jd2 m0 yek/herated 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 reasonablu qa7qpmbgg3:i625c-,ex to 49 gptii e chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate thet95ba pm icgtugq,4 iox-gpe3762 iq: 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 acceleg 2k8mo0 btf0zration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must b8o k0fztb0 m2ge 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 acciq(c)( )yep ),zov2w5ocjeia f dent involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. Tqpi)yoo )2c (afce w )ev,5j(zhe 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 h j qqb :o.8b1sd5sv+zj ,lkb9each 4 m traveled along the road, the elevation change is 1 m). How fast is it jsbk zq,8+5:bqoh v j9b.sl1d 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 droppedqpt ub / ).:cy5eey.ph from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air.eyyhp)tbe q:/u.p 5c resistance?   

  A cyclist is coasting at a stdw8;h a;qi 0d q(em *o75fyc wcs-nhs*eady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having toh*m-fw0 dcd;c7sqnaohwy( 8 ;qs5e*i 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 of a 9s7 mhs x7mj(rs:rq23q gfi9ncity. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a l7 r9(:s9nfmxs 3 7jqrgqi2mhsevel 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 m2)5h n(t+ntyb5 za bssw.gr*from a thin piece of string while the jetliner she is in takes ofsnwy. *r2g s5(+ tmha5 )tbnbzf 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 ramps connjcnom . t,xf, rb.9.3pzxfzf :ecting different partfxt9z. .,xo n:p.z , 3rfcmfjbs of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (m xa47;bf da,dagmzw7su 6j /+bass M ) using the pulley apdb a7/46x jusf;wz db, a+7agmparatus 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 acctpu+f bf 2h3+helerating 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*y;b+,yt t mla chair, an engineer considers the foll+t ;y,*yblma towing set 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 ma6qb6eko b;m1qss of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropez14d6milcs n u3 w*yc-wq4nu1s 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 freeln3wimd4uwc6qz - yc*4lu 11sn y 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 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*m cqlk 38)vmj $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speedx:d azi )q ;mrc89nyg- 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 as )kupv(+t8*m5se ciki cending an ice field inclined at 21st)k+cp8k*i v5iuem( .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.