Why does a child in a wagon seem to fall backward when you give the wagon1vard4m:ivq 3 wv4aubfklz* :,tu1/h a sharp pull fo, zikvtrv:31mq 4ubaw1ulv/ f4d:a*hrward?

A box rests on the (frictionless) bed of a truck. The truck driver stf l3qs/ s7o( n:;hv9zhn;waqt8 9sid xarts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of savh79dost xlnh q;z(8q :s /;ni3w f9the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zefrfc c*(o,hkm4f4 wsd 4 -p0qoro, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zerok:zicr s sbr-n3 we277q;lov . acceleration? Can it have zero3wsq.r v2 sor;7l ci:k-ze7nb velocity? Explain.

When a golf ball is dropped to the pavement, ibp ,te:ackr;m y)o);yt bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts th; akbrmyey o,)p; )c:te force?

If you walk along a log floating on a lake, why does the log move in the o6e4 xl m;p:qf 2zm,sh29cffrn pposite direction?mm,pfcl69hx4 s qz: e22 ff;nr

Why might your foot hurt 2ye orlp)s 9 jp2i7 jxj uv8gdb7.nx7,if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly)4ixcab9+d)oy o:kpsox k6e 1. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a peropoxa6ky4)9so c+) ide b1kx:son running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceilin;(ob ijts +.qng, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers;(+jqio.bt ns.

The force of gravity on a 2-kg rock is twice as great as that onq/x)3y5iatk lsx5h5n *fa*hb a 1-kg rock. Why t3 n5kx*5/xbaiqf 5ah*s htl) yhen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon gi3hsgm.. l f,,s,1/c6lhmw kdoc*skxzve accurate results if the scale had been s/cx1 .d,lmswc.3gom hl *6 ,zsfkhk,calibrated (a) in pounds, or (b) in kilograms?

You pull a box with knol w( cq4-/va constant 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 4 cq-k/lw(o vn(with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely unders(blm 0dz:cdt;u;fkz */s * qr the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Ear0 s*fzub;lct/(s*zk:qdd;r m th. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you ar v;*0el tkqmt)e 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 spmtl; e)0vtk* qeed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pf5l9t5c*icpwhu /:c tulls with equuf p5 hcl:t9w /5ictc*al force on the other team. What, then, determines which team will win?

A person exerts an upward force y*xyxhy +:6ul e1h2 giof 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exert*+1ilxh:u26e xyh gyyed, and (d) by what object it is exerted.

When you stand still on the ground, how large a force dol )/jjmut9q6yes the ground exert on you? Why doesn’t this force ma/q yj)j6mlu9t ke you rise up into the air?

Whiplash sometimes reszoh7j g t,3kp9ults from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of g 793zhjpt,kothe victim 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 accelj ,9f2n(gejzgerates, the crateezjj,gf n(2g9 remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches its9ajk fc,px x32)4y xsa highest point, it slides back down but the maj4,xsc f2 ka9 3)xypxagnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if yo-k. 5icoj1; o4ig mziypjb v;(u weighed yourself on an inclined plane? Assume the mechanism functionj gmpo ii4zib-cjv ;15o.;yk (s properly, even at an angle.

  What force is needed to accelerate a child on a sl7xh yo j4j0mx(+qdli;i9 hj1oed at 1.25m/s$^2$?   

  A net force of 265 N aft(if k2qqh ztdm )/49ccelerates 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 topfu.l8.2oa e lro8 l j73/0w hdqkln1t accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a ;z2t n vchs0r2ik2li z;om45t$76-\mathrm{kg}$ 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 1100-kgls ok*;v7 0lpis5do9c car in 8.0 s if the car is traveling at 95kmlk9c7 l*spo; s0d5 ivo/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rezmc 0 9x)kt ishp9j3**gxn2abst to 125m/s over a distance of 0.800 m along the barrel of amsa* ihc*0n 3x 2z)bt pj99xgk rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of r2 uq df5*.pb hepujpg1nm r2*6,4sg t2. u4 .,hpgp2tjre1ds5rm*u2 qpb fg n6*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 cover a quarter-mile track x5 ovw) lelpe t761ma6 (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 accelerjc* fvb(,1d scation is 0.0680 g . What are the maximum and m f( jbdccs1v,*inimum 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 scabrok-ky73,rtga 02pp le in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the20k rpr ,t bp7k-ag3oy 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 strength of 21,750 N. Wh)kwir/x/m; igat maximum upward accelerag/rm) ;ik/ xiwtion can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 k1vne n g2 vafb v3-ua69m4kx,ng including parachute) when the upward forgaavmkbn 9ve 64fv1u,n23 nx-ce 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 the roof of a house 3.9-m high. When he strikd n +a trm427re)ykkm.es the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding4)m+rn7.e2 tmrday kk 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 tbsys7 ig8*2vnhe box runs vertically upward over a s87s*vyn b2igpulley 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 basketball pla uup/d5ji 8eb u- to)w) *-2+rhskvntpyer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagramwg-bluo)3cv eu zvx24h:9 2yc of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the baubz)xoy9evh-ccv 2 :l24w3ugt and is flying toward the outfield.

A 650-N force acts in a northwesterly a,0qgmf hu+z:zuz88k /kg zm- direction. A second 650-N force must be exerted in what direction so that the:zqkmh+ uzm fu,8g0z ka8z-/g resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" sgq4) ti dz1d4utrung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is q4 igz)d d14ut 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 cz 0aw7 t (k,yomcn,9uuord 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 1t h jf.idd+w5 on86zz-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 McMurdo Base, Antarcb mi ap .myycp,:5a+6 z81bywmtica, as shown in mwzmc +,b5iyy 1b.ypma8:ap6 Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 . a1g 5 ivd4im/6ipj,+gpk vb4nDetermine the ratio of the tension in the coupling between the locomotive and ivppig,d546 +m/ k1iagjv4bnthe 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 sho/o yi/d+ u)kfjwn in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constantk)oiy/ud +/fj 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 lx yqr 8m509mpn oj+,pbegan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (ma,/ .ffqfc zg(ns h.d0j /ll v0*modc9yss $ 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 z8-8w2+pz9d (ekfhw. apupo s)n(o evhorizontal surface are in contact with each other, as shown)w s (o .9kzpzo f(2pehaudenpv -88+w 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 grou5va0a y:i0 ki2n7onls8mn v0bnd, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its 7oksian8mlyi20vvbn0a0 : 5n"launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by ap8 t +sztdne68 heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the 88zt6pn +dts efree-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 friction betw 0fkz ),rr*paaeen 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 5.0nbnz3udy:1+; v )zh2mm3crq g$-\mathrm{kg}$ 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 accel0+6 6v hgsfaaterating at 0.20g. What minimum coefficient of static friction must exiftgh 0av+6 sa6st between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car h9f cxso1r7;y can undergo if the coefficient of static friction between the tires an;c97h oy1xf srd the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal,rpjpe6p,7a 9 xpvr p;ar +lt3 street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a9;p, ep7,v6alpxr r pj+rtp a3 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 s b (:f.rfj( enwu/8rqat -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 rough 3m+gvxk 7 fsgkpsf; -*-0$^{\circ}$ 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 aspn-q*a-fbaz(tnv. nj gkj7/i-halt surface have a very high coefficient of static friction.an7a/-n. ji (j tn-bqzf*-g kv

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 f3lb. h9pstnea xzl v4(ic4p 9ss9 9b:zriction 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 havjv4eey h.0m8fe to have to prevent any motion from occh0mj ef8y.e v4urring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far mjm3d zqs p vi(m./3k 7a,x5prioeu52 will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed isra,p3i .mvm(/qmxu kz2po7d5 je53 of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg e9v:d)24 garynliq:p and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). 9n edl iyga :2)rqv4p:A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of stsix y/jogik g 26qd;;9atic 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 slide k/ ;sgxiy9giq o62d;jagainst the cab of the truck?   

On an icy day, you worry abmvi z;8al; vwdi xh:+ 2pq.rr2out parking your car in your driveway, which has an incliiwi.v;ar qp;h8m zxlr +dv22: 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 ponfxs+:q9() :r0;fkdsiy qhslide 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 at an aiur 1 b2*cn,xtu)9*wsi3 )wmaosyk+q wp2jx /ngle $\theta=22.0^{\circ}$ 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 ,b+nke k8ob) iwyk (s hrqm7l(u6dk*+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 (lfn/ s6+g8i.mgmd m -7bkdau l+ ksk4of 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 p /tdh gopd a/dn.0)2evlace against a rough wall by someone pushing on it with a force directed upward agt/ .andd0hp2/voe d)t 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 dangerous projemwek52c)enpjxli).gc -.8 jy ctiles as they melt. Consider a ci )ye j5)w.cg-8jlkpx .nmce 2hunk 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 dista al- pd;a6d8xv:n x1xpnce for an automobile traveling at speed v is ev lx-p:6n1;p a8dax dxqual 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 thl jy.m ,gymg,**lua;oe dash when the drive m,lglogy;m.j*au, y *r decelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mas,sct3f6. ud buevqx;3s m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are fi(3 h2scv;fexjx9v),af+sf*i dt r. 4thp qwg.lled 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 ,wvp9 hqf (g aes ri.jt.;c)2f*fh43svtdx+x and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic frictef dq+)a9sna4nu 6u8uhcurza1 6 9u9tion 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 (inclu6qmb 2k jk,i*dding 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 mammaf.atupcjk/z* ;r4t b)lian heart, at each pulse approximately 20 g of blood is accelerated from 0f /. ptur)a ctb;jzk4*.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 )(ch 0hijc5o;r r rnm)chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a noc;r mrh))hic r(0 5j70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , andf;d7gcp+jk: b if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the groub g7fjd:kcp;+nd 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 iz c, jk.lbvcdobz.x93p8 0dc py57a,k nvolving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop beforlb,0 yj .k3p.z7 a,59ck cpx8vocdbdze 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 road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means tc.(xkl8n8qy x hat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore frictiox8. c lq8nx(ykn.   
(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 of Pisa and falls o um* be zzd4tulrne904)x.a655 m before reaching the ground with a speed of What was the average force of air resistance? o)zt z44 .bm0xn*e69uledaur  

  A cyclist is coasting at d f*,xjo h*ee;*hw;jxa steady 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 to pedal if the mud lasts for 11 m? If so, what will be the speewx*o;ej x, h*h;efj*d d upon emerging?   

  A city planner is working on the redesign of a hilly porti/*( txbs .f3 v9*km qmvfex3dmon of a city. An important consideration is how steep the dmsf me3*tkq(*vx bmf93 xv./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 likes physics experiments, dangles her w4w4jmic+ d0os atch from a thin piece of string while the jetlid4 0i j+wmos4cner 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 ramqm2 - unscr-mz3h-yd)ps connecting different parts of the smcnr3)-- 2z -qhduym 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 tudn f )bw(1(ia5dmx- wofte4(o lift the piano (mass M ) using the pulley appww xam(b -f(5d d)tf(ne 4i1ouaratus 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 accew;2 z g-cpe,m6o4k2 yjrp0 kgulerating 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 7 7)f kzxqmw:tjth7/ 5hwo6q gul )7yechild-restraint chair, an engineer considers the following set 6jowmh:qz )tg7 xue7lhtwy) 7f5 q/7kof 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 trainf3ha* rnd6(k gx yd1fw/sn1/o 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 fsiqbdb qq34c)e5 n g:r;g6 f*safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constan4g) n6q*;rb:qf3bcsiq fe5 gdt, 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 ,rpl 8x :n e3uv0dhdg2a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to js) e +2w9bspkreach 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 an ice 294n gjmvs 7tb*jevx- field inclined at v-mtj x7ev2n 94jsbg* 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.