Why does a child in a wagon seem to fall backward when you give the b 1*ba84u y xa/4wn) a(3hnlnc enfr(hwagon a sharp pull f wb3r)n(c8ua hnal *(fn4/ ahb4nyxe1orward?

A box rests on the (frictionless) bed of a truck. The truch gszx,.9 pj4-h6i-lad f dfn3k driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in tei6 faj-hn,x4 3f d dspgz.h9l-rms 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 ofu4romze,trm +k9,6dy6nfk o , an object is zero, are no forces acting on it? Explain.

Only one force acts on an objemw, 7f1q6z azo-ke ;loct. Can the object have zero acceleration? Can it have zero veloci wk;7q1ez zm 6a,lo-foty? Explain.

When a golf ball is dropped to the pavement, it bou oy 2-w0ejg*n4.xklx knces back up. (a) Is a force needed to make it bounce back up? (b) xl k4 n.0ek*o-jxgy2w If so, what exerts the force?

If you walk along a log fl2ztom -4m/z1e 9td(uuq f 1ls/gkopb0 oating on a lake, why does the log move in the opposite di1tuzo2fz/bm/ 04sgq91 -t lepmd uok( rection?

Why might your foot hurtfi1d97pie7l-1 f+ft lo kkzv. if you kick a heavy desk or a wall?

  When you are running and want to stop qe5*)rfeg e ,,h-z *.sub2zx 1nqa mzjkuickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own expeq 5k.e2feg zrna,m*x*sz1b)u-z,j herience) 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 -c+2wpwvd,nfceiling, and a section of the same thread dangles dw2- wfp+ ,vncfrom the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg roc y5c fx9.nxj+6w ,i q 9segpy0sk,ugi0k is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fallyx0,xngiqi6ps909 e5 jf y,k+ .sgc wu faster?

Would a spring scale carried to the M.appw 7u0 b ny-mnh-z0oon give accurate results if the scale had been cay0-pw-zbnp.7au0 h nmlibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table )ex uomyzw24 g2t2pf+ 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, or (c)wu oy 22)gz+mf xpe2t4 decrease? Explain.

When an object falls freely unyy;4)6sd cspnder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts nsdp; yc)y 4s6an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg ulhk;j: / vko1 yfs2r)0e1dypr0w 0u jobject when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objek0;y fjyluor0 vdujh sk 0p1/ e)rw1:2ct horizontally with a given speed on the Moon and on Earth.

According to Newton’s thbftgh;2c*p c w3)kmf+ird law, each team in a tug of war (Fig. 4–37) pulls with equal f3ch)wt ;gm*+pf2bf kcorce 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 groceries. Desuu8r12u0oycd;mk1 fa cribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) oc0;yuamru1 u d8 fok21n what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force doezh-o+v*4gm q fs the ground exert on you? Why doesn’t this force make you rise up ingv*qzm+fh 4-o to the air?

Whiplash sometimes results frm *:(gek)p; wlb.hsvsii y;fkw 8(u3i om an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be te.gk:vms(i38*k(wh ;;l p )b siwfuyihrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed aav(:z /ta*+lema5ot truck. When the truck accelerates, the crate remains wheoamt*eaa5 :v a (lt+/zre it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the bg*uc2vxdv /jt 0i;r 4block reaches its highestg;vxi2 d /4tuvbr j*0c point, it slides back down but 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 on an inclined pg*,-5xfwf;ura my )xplane? Assume the mechanism functions properly, ;) g 5a*pyu,mfwrx-xfeven at an angle.

  What force is needed to accelerate a child o n6m v xvag/c-3x0nrf+n a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates awizdk42+ohkp s(36 q 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 6dj9 resbi4v4withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oom8 9z0tpr :b8hgtjw(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 tr9j,2 bykds 9go stop an 1100-kg car in 8.0 s if the car is tragb9k 2,dsjry9veling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fry b2k cn x2lqcu+o)5l2om rest to 125m/s over a distance of 0.800 m alongl 2xn yl c2)obk+c2q5u the barrel of a rifle?   

A fisherman yanks a fish ver 8f3izn06*1 jg gynujytically out of the water with an acceleration of 2.5 yu*j80zyn3g6j gf1n i $\mathrm{~m} / \mathrm{s}^{2}$ 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 quarx1 p/owu5p m30icoom+ ter-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 designed so that the maximum accelob) )sein j)jy c9mnh w2wrfy4 69jf..eration is 0.0680 g . What anjfnw hjyr 9 m ) e9..62ib)jcfw4osy)re the 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 bathroopjqgw* g7l 92gm scale in 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 the elevator, and finl2w9 * pg7ggqjd the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum stre93olerw0j(m28o/( fkvlgik :3 rn(5k kscidg ngth of 21,750 N. What maximum upward acceleration can it give the elevator wjgkl/ i kklmsrfnv528 (:d0ogc3((o reki 93without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including2jsc q2gl3*h h parachute) when the u*jql 2gsh ch23pward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from th t.(pbw4 pjp+bccmhav,*5htbw () i8v e roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates otv(4ha+*itp w.pjcbh cb pv(5 mbw8),ver 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 tiz 8a vw, /mitwshp:b3if3 qs+0ed to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that tw3 ps hwt ii,sf0q3:/b8avm z+he 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 basketjus,fy(4u2x udwhi; 6 ,x4bixball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body d 1(3 jb3etg4zq, psmg(-vmwb miagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it ha -(14mb3btse, q gpm3(wmvjgzs left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterl8:3+tu2 ea3sh9p y abywd3gpzy direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vecto8dztae39hw u3 3pygayp+ s2:br diagram.

  Arlene is to walk across a "high wire" s 1ks:ceqe a ds0v.i5f6trung horizontally between two buildings 10.0 m apart. The sag in the rope when she is ataidkq0c1 . sfe 56v:se 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 bucketw5a f rkw )w/bn p3+roybx,0(q is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1ch9p2yuuv ccm96b-c0 4.0$-\mathrm{kg}$ 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 McMurdo9z(j0xym8h.r-xofqlr)t: mb Base, Antarctica, as shownlj-:.rbytr (zxohq)m fm9x 0 8 in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two credsr3v)h)avn1c 7y6y/h.7nzl* qubars of the same mass behind it, Fig. 4-47 . Dhshe )3q7y /1 uv 7av.cnyn)dlzr br6*etermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus s+6jt*jvgvk s 7hown in Fig. 4-48.s+6v*vk g tj7j (a) How 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 began, 63omakoq:e i26j b udg .*qi6wa 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a bl ev())bik wxno2d- j7uock (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 frictio5si 4s-*ls,+z w(jpviqc 8j vynless horizontal surface are in contact with each other, as - *v+j5siqyils jvpwc ,8sz 4(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 abov5( k pjpqe:jf pds*r7y2 2d2pme the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its dfs*pj d2q2:5 epyjkrm7 (p2pvelocity 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 connectedwk+1bmlz, u04-0 bgtdu l,lz r by a heavy cord of mass 1.0 kg . Calculate the acceleration of em0zb+k-bz4l1 gt r,lud ,w0luach box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic v 5-og42zgfk2h(xje x friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a / /yxpj lezm7:5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. Whato5u., nwy 1nl pi z;k+mr6sx3l minimum coefficient of static friction must exist between your feet and nzi yp531l, k rn+ x6ows;m.luthe floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if thewdqw5ttd x.g8b8 (ey , coefficient of static friction between thd5twwt ,ebxq8(dy.g 8e tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and nbhkwxy0bf7kd2,n eq1l6 x8h * ormal street pavement is about 0.8. On how steep a hill (8bk26h*wbqfy7,dh kl 0xn xe1maximum 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 ay*ktm3j 31yv3 zh(jjym s4*ifn* h;eft -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 rest on a rp5a,e;5x9zl z/q9 n0 onn ujzpough 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 coefficientmae2.-osy m1d of static friction1. -mmyso2dae.

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 k/p3gj(pt l3fm os3pzms 3q7x 79ngpd 3inetic 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 (Exampld53e p 3twrq.r/w y(bke 4-20) how large a mass would box A have to have to prevent any motiontpw5kb r (3.dqrwe3 /y from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fag3mmtlcol4 0n;7 y+m gr will it go, given that the coefficiem4to l7lgmgc n3;y 0+mnt 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 k 2r mjygcau1ua3w+,9 qg , are in contact and at rest on a horizontal surface (Fig. 4-54). +29auqmc1y jg r3aw,uA 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 staticcn q*;lcs0*ch friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slidqclh s*0nc* c;e against the cab of the truck?   

On an icy day, you worry ab) 2x40ss h7 sq8bjmnurout parking your car in your driveway, which has an incline of 12 2 rm4b0js7s n)hs8uxq$^{\circ}$ . 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 slid2n(9hsc p( fup b+jvvqpe4/b9 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. 4-55 lies cn utf0 /tef,7-j/z- ryj roj(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 initial9 qu;c- w0fo:nh iam)f 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 tot+gk fn3 oi, l :/qyytgx/80eap of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by b z+anhbnoz sjj : wkblp,5,.-4eds/. someone pushing on it with a force directed upward at ,-j.ld /pb. sj,ke4z:wn5bnsazob +h 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 dan5er2n1tx2/i911m uypaexe oygerous projectiles as they melt. Consid1 t5/xe m1 pu29ry21ayenioexer a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an auto) zh*:xsj 11/lukjqivnxst+* mobile traveling at speed v is eq1lu/ni **tjz1s+ vs j xqxkh:)ual 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 dashboah8rx,qv(m04lplw : (nj3 vh fm5s-pdird of a car slides forward on the dash when the driver decelerates fr:3vm8l hxpv(l,h-5sm0d i rfq j4pn( wom 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 ini4l:oxx f *,ocz(stsl mlj2+tg c *:x.stial 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 whe hdrxdru05 id g(p6(wd*b .h-yre they are filled to the packing station 11.0 m away. The belt is initially sta6h du5b- pdr(r*.0hxyg d idw(tionary 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 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 coefficien yqvpzf:-.ku+ t of 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 bicycle) canz2ia 9b.vnsm b66b9ui 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 a87 )aly9g y-pnmbe7hheart, at each pulse approximately 20 g of blood is accelerated from y e7)alhy nab98pmg-70.25 $\mathrm{~m} / \mathrm{s}$ 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 anga nfk+w 8 )oavb7g.s2y(1k qp automobile crash if the deceleration is no more than 30 " g 's." Calcnkg(qv+ 7o) b1agyfw2pk a s.8ulate 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 ears.r2hl i(* txytw enb9 1pi*m w4*rmq1thquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the grons*t*mwi prq9*( hex.twbyr421 l 1miund 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 ant *g(lj7k g2xnyo1 u5t accident involving two 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 initial speed of that car assuming a level 7 uynxt*o2gtj g1kl5( road.   

  A car starts rolling down a,nw,dj v3u1 vk;+ xbmu 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going whe v,;v b,wnuud+j3kmx1n it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower ofd/w uc9: i2kwk Pisa and falls 55 m before reaching the ground with a speed of What was the :wuc diwk/9 k2average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretchrqusz99rsukwy/77e t ra,i 8 6)tubh6 where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for ) qtsb6u e,w86u9/ur97r zahi7 st kry11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion o :b/qgw4r(on vf a city. An important consideration is how steep the roads can be so that even low-powered cars can get upnwo /g(4v:b rq 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 likes physics experiments, dangles her watch from a thin pie/gqa5 qb +fnvb-u/5bwui/ /iwce of string while the jetlinf//bubvq iu5 wib+naw q-5 g//er 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 supermarketpyw7 8wpx 5dazy;i3.gsz uj;-0ejj5e, there are to be several ramps connecting different par7;5 j8x ; zajep0y3yuw5- egpsdz.wj its 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 in gp,u- .xq/0t i0wu4patkja6s needed to lift the piano (mass M ) using the pulley w0 ,tkai gux4u.ap-06/ qptnjapparatus 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 accelerating at 3.5 3qqg kn*qye04$\mathrm{~m} / \mathrm{s}^{2}$ 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 engineer coo+2w5yu 6v h:nkm(aounsiders the fol2w(u5+hamvuk6 on: yo lowing 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-carqakn 07f r,lr4 Italian train has 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?   

Two rock climbers, Bill and Karen, use safety ropev )rlj(*p td eh9mpomf9 hw.r6bb6)4ns of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a stati* h6v9r p nrod6 mef)wb)b49mpt.jh (lc 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 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 cs :*v v)yq-yd$\mathrm{~b}$ 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 b61ja6c5 jw yneuilding 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 ascending , i4bdp1ft3puan ice field inclined at 21p,fi1 pb4dt3u .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.