Why does a child in a wago dutjgc8* xbxo*gy) vgu:q(13n seem to fall backward when you give the wagon a sharp pull 1gxcdq:( )ouv3gbj8*yg ut* x forward?

A box rests on the (frictionless) bed of a truck. The truck driver starroy5aoe; y3opjzu1d 5w( 9-s qts the truck and accelerates forward. The box immediately starts to slide toward the rear of t ;w ypz o91uo5o5a-rdq(js e3yhe truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting ont x4gxf w77o 7h-;hxyv+p yja6 it? Explain.

Only one force acts on an object. Can the ol7.bklv+q ts 1bject have zero acceleration? Can it have zero velocity? E.sqbtl7+ v1lkxplain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is kd2t)w +ozta14h. d;sgfga5i 6 3wscya force needed to make it bounce back up? (b) If so, what exerts the forcs)go .yc ish23;tgw5 df6ad1akw4 z+te?

If you walk along a log floa2v :fldpa.m z,ting on a lake, why does the log move in the opposite direc2.,fvadz l:pmtion?

Why might your foot hurt if you kick a heavy dk on5l62k/n vuqg /.olesk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (nhun7q yp7t .i:-dao9a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) o.i qp7:an7 tdhy9-nuthe maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section 9ful5yj368h 2q hs jhfof 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? Explainfj35 hu lj9f2y8qh6h s your answers.

The force of gravity on a 2-kg roce (0dfhf- w0tvagy * 7d8flegj47se-fk is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rog sv8 jfl7fy 00dw74h-de -egfe*a(ftck fall faster?

Would a spring scale carried to the Moon give accurate results if the sc*0fnl)axgw/+j khb g8 ale had been calibrated (a) in pounds, or (b) in kilogramxwg) hlf8b0+ /*akjgn s?

You pull a box with a constant forceox wdb/9o8 0gk across a frictionless table using an attached rope held horizog k0x/ w9bood8ntally. 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) decrease? Explain.

When an object falls freely under the influence of gravity there is a net for9hf;.ykgr;y tce mg exerted on it by the Eyyt;9fkrh; g. arth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on 6 m-lq m0xw-xkv*lni+the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizonxwlil-qm6 xm*-+0v n ktally with a given speed on the Moon and on Earth.

According to Newton’s tb+y/ezz h( w7r :q4vfhhird law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determin yrhvz+:h f(4e/zb7w qes which team will win?

A person exerts an upward force of 40 N to hovek)vdc2f0 tx1;p3gd ,i7glrld 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 exerted, and (d) by what object it is e,)c1vvgle7i0; 3p t kdgr dfx2xerted.

When you stand still on the ground, how large a force do3udh(gjg/h z0vb4l) uhn:sn) es the ground exert on you? Why doesn’t this force make you rise ubh4hd uz0n3uns/hl(v ) g:gj)p into the air?

Whiplash sometimes results from an automobile accident when sp3 jdat-8wkd v)bt//nqf/ d4a* jts9the victim’s car is stws//a9ddas8pndfjkt - /t4 qbv)* j 3truck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. W c0y4w*g8pzoz5kbfdb vp+- /8 vr-q ehhen the truck accelerates, the crate remains where it is on the truck, so it, too, a f/z0 -h8cegpvydrbzo5 w k*48-pv+bqccelerates. What force causes the crate to accelerate?

A block is given a push so t8v rl 1ywh,x2jrebzuxyv 2s u( rk65(;hat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less, evuvy2;65 zyuxk 8h(lxwjr1 rsr2( b on the descent than on the ascent. Why?

What would your bathl) iu,imkor-: room scale read if you weighed yourself on an inclined plane? Assume the mechanism functions prop u)ri:ilk -o,merly, even at an angle.

  What force is needed to accelerate a child on a sled kb h 4up3bi phk*0aw.y(y3 5sm at 1.25m/s$^2$?   

  A net force of 265 Nngqx 8+jj,f;b yv4yn/ accelerates 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 mustmv4ed kadird q93c0-if,+*nr a rope withstand 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 of a yt4 tm ab6i6;lt o,0z r+rwm0.fuvv5a$76-\mathrm{kg}$ 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-kg car in 8.0 s if the carnhxdwr v4;p 8k /ddts-e+4*rz is travelinv es-4* +d;r8p /rkhd dzwx4tng at 95km/h? -  

  What average force is needed to accelerh tsk-q6bg1m3fh p 1/oate a 7.00-gram pellet from rest to 125m/s os1bt -kmh3f p/q1h6ogver a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratobc3ok 3)u;gw g4x )wluq3o i a/3gc1hion of 2.w14go3o3lw 3bxciuo g3 ) q/;gucakh )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 ca8hdha;t:v6ja4+:sx4acd q nh n cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so *cmsa.e. noe1 that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert c*ao. .nm1es eon the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. Whentf0pvxh5 it lmc rl3 au ;iv;7,vp)j)+ the elevator begins to move, the scale briefly reads onllv)upl;xv+a i ;f i, mt5pjhrv) 07c3ty 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 haspmkosk/.-klf n )pum5np 0 g-) a maximum strength of 21,750 N. What maximuuo-n k )mmp/pfsn.kgk)-0 lp5 m upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceler gz)8aclxloh4 x:ht)j)ii;* qation of two falling sky divers (mass 132 kg including parachute)4oaxqlc) i :h)h lj;tx*i8z) g when the upward 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 the roof of a house 3.9-m hhe 4ro,ijjd c/v 08ovi4bkk(5igh. When he strikes 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 ,b /(ovrj45j 8vh ik0eo4cidk(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 k9(f; )+t5uc/7q0buy p1nbrhn oo ogztable. A rope tied to the box runs vertically upward over a+ t qn9u p)f;7og1b05uh cnoyb(/zo rk 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 diagrswc(qg9 s+,znam for a basketball 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 *f2onfr( thg* ty 3sy6baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfield.3hys*t2tnofyf* r6g(

A 650-N force acts in a northwesterly direction. A secz2xwukvjf27 db8n(k r5 6ls1b: xca- bond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diafx k(jlba 2d1r5xvzwbunc8s b-267:k gram.

  Arlene is to walk across a "highvo- wkc( skbfq2)u5 p- wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at theb 5k(cuvo-q2) f -wpks 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 masslessm (hx tkx 8eay6ekz;x;bo(r-0 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..euqc6is g2lw * 9sv2rd2 ok8w25rsvc0$-\mathrm{kg}$ 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, Ant0wxy+e8 mg 0rdbx3iz0 *vq hgwf72 cf2arctica, as show q32 7m0+wxv2f wygizh0reb fcg*xd08n 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 cars of the same mass behind it,l) qkmh8qyw ;wa- 8.bj Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car8ykw;l.q hm qa8j-w b) $\left(F_{\mathrm{T} 1}\right)$ , 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 shown7*0pyqh tay(u in Fig. 4-48. (a) How hard must she pull downwarq uy7tpyh* 0(ad 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, p-8v dn/2fr8(hm1unrakwn p, 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 (mass .)ledrxk y otvb:61- p$ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact witt+ :bcfc:d+dy h each other,+:c+bt :ddcf y as 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 ground, ancky)8vp5 9*r ox2zk aid 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 "launch" speed.k*vpa 29y)i8kx5 zco r Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionles93k rbrt ong96j6 /r4a tka)rqs table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. As ortrta39kg46 bk96nr /ajqr)sume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 laoqnzr-scd3h;0s 5mcl+() z 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 e): ippyq./b-azwmv82vdcnd) . x xi0to 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 0.2hm r0 x xol*(3at9bp,e0g. What minimum coefficient of static friction must exist between your lmt03xx, ep(r9ab oh*feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient ofozr,noz6 olvl;h :o99 static friction between the tireoln h;l o o9:,96ovzzrs and the ground is 0.80?   

  The coefficient of static friction between hard rubber anjs;;rqc9lpau v6 5 1xh7pmhlgkhn1 +8d normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leav5h j96pu7l;h + gl 8sk 1cpahxq;rmn1ve 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 deceleratepa3 h uj0cn5z: at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest 918j xfwr tpf5on 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 b/gbdp:i fp9h cp:+d,very high coefficient of statpc: ih,:+gfpd d/b p9bic 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 f dw-xh;nxav4d13 ,vc zor 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 aesa;9vhp 1 a+of )lpp1 mass would box A have to haveo+v91falap1e pps ;)h to prevent 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 n im*hr+7xrdn ((j3u cwhr.a2 go, giv7uwmcnr h 2 .nih+*r(jdx( ra3en that the coefficient 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 omlo hd:.d8d8dv89 ahd5b7 4 hr))lik il7vzl110 kg , are in contact and at rest on a horizontal surface (F k9dh v)ho dilhm47lab58lrd7zol)8v8:di d.ig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficiencvwe395j9/: k z ppoiot of static friction between the crate and theo/o9v3ip9: p cz5 ekjw 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 carnj:qr/ ew+unuw.km0(gj9t.dh 3v m+g in your driveway, which has an incline ou:m .j(ukw.thnwn+q 9jegv r /md3g0 +f 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 slizvh /6da*pn l*l 5szi0de 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 ti z58f2;iz: qf fob cnaq.87uvclted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial,pztmu0 ,whusb 7 (x(m7 2omgj 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 4sa0 g2d7w mmpsteepest 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 someonv wp421 tlhaf9m,2grd e pushing on it with a force directed upward at 2 drhgfawvt9lm ,241p28$^{\circ}$ 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 dangao +zd3eq t cb3imy77.erous projectiles as they melt. Consider 7m deq+cyzi3at3o . b7a 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 forhua 7 ghowi2d:yuy,+6 an automobile traveling at speed v is yuh+y72gi6dou : h,w aequal 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 forw5.wx;)vt39vmsl *)ztp ugnu w)bbtc 3ard on the dash when the driver decelerates from 45 )t bbvsvp5 3m g)u 3l t;wctx*zwun9.)$\mathrm{~km} / \mathrm{h}$ 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 initiba5+ po)v dw j/:y,y)v ;qhftial 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 filled to the packing:mk v)jzp://bxu7zt n station 11.0 m away. The beltz:j:u)z// 7 kbt vxnmp 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 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 coefficien1-njae 06 ,npb r7xsbu 5t;nmpt 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 65v dum9p 13+pp 1m(fugc kg (including 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( wm3p/so.5 hunrm ,dp, at each pulse approximately 20 g of blood is pmnpmhd u,3r .ws/(o5accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crashl0 bz2rq d1sj6bj4kv: if the deceleration is no more than 30 " g 's." 0j1q6j4bsvdr b :2klzCalculate 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 ajo.w gxxu 2 o).:;(ghwz; hwptn earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with ttgwog)hw(2.o;jz.: uxp; xh whe ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two carspgbc zw1-;er560 nt e1itk brjbg 6. e:j6-mnt, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before collidiwgee: bc6t05n p66-nki -zj1;rb ejbt.g 1 rtmng. 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 hilpt slihy z07wc6v.vo3i;*ke6l (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches theev6vzi0 p yi lk76 *;.3wctsoh 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 pc -r*7gn l1ecthe top of the Leaning Tower of Pisa and falls 55 m before reaching the ground crn1e- g7lc*p with a speed of What was the average force of air resistance?   

  A cyclist is coastinz0j0/ji 7;pxw(wo 4v+ vndprgg at a 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 witho v(0;njg4v0r wjzpw7px/i d+ out having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working ev-l5 7hwi vx 9re/phlm;vq;* on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on-x;el 7lv5rhpvm;* hw /vqi 9e 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, dangk z(bs-f* xfmr* ak68lles her watch from a thin piece of string while the jetliner she is in takes ofzla68 x*f-kmrf*k sb( f 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 supermarksof 4 jf 4*3*ibwk v8 6olbt0ax.f+jrdet, there are to be several ramps connecting different par4tjf84ow *d3j6r xalkv i*o .0+bsb ffts 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 (mass M ) gcn v)4zhg-e bza b753using the pulley apparatus shown in zvg ebac)g7h b4-5n3z

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 acce+xs*h )g jmcf1lerating 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 chair, an engineer considers the fol8x029qqt3o ke. ljd fe,cof;j leqjq,ojo;lk308 .c2d x tfe9fowing 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 mam yx/,de8xb6lss 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 Ka;bn) aw4+o,fxnot; pbren, use 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 constant, how large a force she will feel from the rope. (Express the resubnf b+4oxa) p;,n ;twolt 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 t5yyn7ko9q. 4jd ahq+ -k )ad1a8vbur" 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 isxhz2d l/ 8k29c5zltx 2t sv pu8n:mbp3 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 an ice field (b8oeu2s dc44ae5bpninclined e( p4anc82d54ubso b eat 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.