Why does a child in a wagon seem to fall backward when you give the wagon a shag/ 2/s3kadb-yr xrb 8ppzja*gme r j-u23h 17lrp puy8ku3jza2-mp g 2arhxrg1rl d/b j-3b*7/s e pll forward?

A box rests on the (fr;6u/pc5 6bg cgl6cqv ll5qi1lictionless) bed of a truck. The truck driver starts the truck and a5bg ql 6l cq ;vgu6cp65ll/c1iccelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an :v36 kbfs0cj0mbo/ qhobject is zero, are no forces acting on it? Explain.

Only one force acts on aal5(95xg y eiqn object. Can the object have zero acceleration? Can it have zq 5lyaxei9(g5 ero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces ba z5v5qn)f h*rdl+hkx( ck up. (a) Is a force needed to make it bounce back up? (b) If so, what exertshlvd*(q +f5 hnk)zrx5 the force?

If you walk along a log floating on a lah+nb:jz dtip)4.q+tlke, why does the log move in the opposite directionihlz.)d +qnj:p btt4+?

Why might your foot hurt if you kick a heavy desks*)ggelu ,rr4ttd9 e. or a wall?

  When you are running and want to stop quickly, you must decelerate q +j7d5 /ab(jrf6h9inq2 ljks buickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your jar(j6 9ndfkhq 2bb5l/js7i+own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sam.zj sjj rs/ep,kp73-de thread danglr.-7 d p,j3jp/e szksjes 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.

The force of gravity ohx0 wg0pnl6b1 6 a8fdln a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall 1 80 0lb gwpn6hf6ldxafaster?

Would a spring scale carried to the Moon give accurwpth;2/una-d hj 4wd(ate results if the scale had been calibrated (a) ijt2uwd/4w; dan-ph h(n pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless 6 itl,3k pdoxk9 j6ec4table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horij4p e3x9c d6kt k6,loizontal (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 fxfr3(qzdbxto2 c1;6 ft 1 hx)worce mg exerted on it by the Earth. Yet by Newton’s third law the object exerts ant ) z(q61;1bt3f2dwxxfhrx oc 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 -0vy6l-f 6l)iwwaxq pwhen you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontx-p)w q0 f -l6ywialv6ally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tj 06qh svb3vdcskk ;4 )ngo36dug of war (Fig. 4–37) pulls with equal force on )o4dj3qvhcs;6gk n3vsk d0b6the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groc eeus3:8m17n40yef mli j/vwleries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what objecte m0f / jm1yl:usn4e78w3elvi it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, hig2 .(ys, m jj.7rdp a(zqcxt(ow large a force does the ground exert on you?d( pyrg ,q(.cxmjt .(2 aj7zis Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accwvplbe3t:* fecq .y, 3ident when the victim’s car is struck violently from the rear. Explain wh,vp.cee: *q yftbw 3l3y 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. d7 ikzdr- c8psf; k(7uWhen the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crad pdifz7 ukckr87(- ;ste to accelerate?

A block is given a push so that it slides up a ramp.6rh+r2hrzsc yn3i ns+:v(l o* After the block reaches its highest point, it slides back down but the magni+rr:6znil*3 ss( oc2yhr+ nhvtude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on enrbmnyg) zt4 *vv;43 an inclined plane? Assume the mechanism furznmyv *t)g4vb ;n4e3nctions properly, even at an angle.

  What force is needed to accelerate a child on a sled;+7c- l24ulhrkf2jv yrz k tx*emc)x4 at 1.25m/s$^2$?   

  A net force of 265 N accelerates a b.muh1q0 ga h1qike 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(a*;bwyqgj0 2icd,lsh 0fba 9 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 bu;nkjet /lng-*-hx8.f l* yb $76-\mathrm{kg}$ 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 r scnr12;17 kwculq7e* nw(brbequired to stop an 1100-kg car in 8.0 s if the car is travrn 7erc17(k1ub*;wl qws b 2cneling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelc+h o xpdshd12ds-d ,nny)04slet from rest to 125m/s over a distance of 1)ds+2 4 phnds0, cs-dy nohdx0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water wite 9i4)*r aosau8wur8xh an acceleration of 2.*xs iur)re8w84u 9aao 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 coy+ s(w56me8ikpm ff-g ver 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 bvp+0*y1g) vwrgax 8gee designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forceswg)ep xg y+1vga*rv80 the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevat6c/jfv8vy(g 4b .cz2wgfds,fnv s-o(or begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the di/cyf(8.vfo 6jwg4zsc -dgsf2 v,vn(b rection of acceleration.     ----待选择----downupward 

  The cable supporting a 21z6rp8*x2up+wzec yt -25-kg elevator has a maximum strength of 21,750 N. What maximum upward accezpx2tp y+6*ru8we-zcleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg itf9 btuya :u6 sx+vfa)vm4* p4ncluding parachute) when the upward force of air resistance is equal to on) tfx +*puv4:4fu 9my6absvate-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 3mns(ypjd9i6qs qq 6q4u 53 i/v.9-m high. 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 /iq9dy4v3 jmin5p 6qq q(su s6torso (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 No2nspf1 bonv 1k/q (,+l9t wkzgu 8a*d rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40 pl,*wgdo/z at1o(f+qunv9b1n2 8sk k). 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 pl(7z j m .s.krh(cqxs)wayer
(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 baseball (a) at0907k xgk cggr the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outc0kkg09gr7g x field.

A 650-N force acts in a northwesterly direction. A second 650-N for 7bzdz:yxk9la-9us9qw (/ipy ce must be exerted in what direction so that the resultant of the two forces poiwzd : a(szpx97iybl/uq9 ky9-nts westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildings8q )+ikaxgsgefe -r1a 7e85at 10.0 m apart. The sag in the-agxqk1f7 tg8air85e+ a see) rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord frvs.(l*rt oyzv/k+0q vom 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 14.0n t76mjonin+ 6$-\mathrm{kg}$ 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 a tlgi:n 2cc98at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of thl8cc ni ga2:9te 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.,9 gf* e4ol:2rko/-tvqtb kv5b pqao6 4-47 . Determine the ratio of the tension in the coupling between tho-vp 5ka9fg e/:v *4qq2,ltkrbto b6 oe 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 buckrr2:ka uhcbsfr6 ;g*7n7o5l (u/ui eket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speeh 5 7 of7surbiu(ru6c/2neagk:kr*l ;d?   
(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 beutr/)gtb c;j 4px3ua8gan, 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 g82 h-rlrsvapz64*n v (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are i*t/o1ijs5 nt whuf f..zac w/7n contact with each other, as show t/az1.ws5jtcuw7.f/ i* onhfn 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 iiyg 48h t(cpep-e.c0tnitially 1.80 m above 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 mtc e.c p-8 (tieh0y4pgass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionz ,i: 9smucd7cless 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 zmdui 9c, 7c:sin 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 f i fyjf)kt:jut2e:3,ariction 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 required8x6 j+pxzq oldx( q1/v to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. ko6k7v yvk j:-What minimum coefficient of static friction must exist between your feet and the floor if yo:7 6okv-kvk yju are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stati1q ouf/n3 gwm93 xkms9c friction between the t uos9g3n/ 3wxq1f9m kmires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal streen-:day/ nb0ay(usw kv8sq 75ht pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked? nbwv n usyd0 /7:-ah(8kyaqs5  $^{/circ}$

  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 at apklw,alfif1/ 8 9b3z-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 aibbj)/ed.uc +hu 0;ua rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high cobi.. kz t2x6crefficient of static frictici b.ktr.62xzon.

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 kine9jx xwy1t /vydgx8z ,g 5k iz:l7r,hw;tic 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 (Example 4 4.u497hohr1nehm vl u-20) how large a mass would box A have to have to prevent any motion from 1luh94unhrm o.he 47voccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will /t tvcltqm; 19it go, given that the coefficient of kinetic friction is 0.20 and tvlttm1 q;/9cthe push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizont+bz r/ qhrlcl;ptych) 8/ny4 (al/ry+q 8)lzt;cybl4pch(nr/ h surface (Fig. 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 coefficient of e 3+ p-h7wwbdqcuhl55 static 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 s5+ebh p uw 5cql-wh3d7lide against the cab of the truck?   

On an icy day, you worry az*dipel,7,3 t0egltcbout parking your car in your driveway, which has an incline ,eipl*ttg dzl, c0e3 7of 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 slide with a8ct83 lhxdov5jkgr 7) 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 m4ed5na h;f:1dduxb / lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initi-,53 1yqj aclbdxukt2 al speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a spz3ry k7jhrhu.w .8u xg,deuir93d .v ,eed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on itzxpdg6- 3os5 n h67vdq with a force directed 6 p6gv nod 5dqs-xh37zupward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slipp21fgvso 8/pbqzqq8a: 6x zkbc87k o1rery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the rxb8 cvr1k82bq7sf z 61aq/8p z:oogkqidge 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 automobici(etw0 r-1yw ek ,di:le traveling at speed v is equaley,diwr-:1e0wt k( ci to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the daidfxwt 70hfwr 6 4z:;; ct0koq*v ya9oi ;:ygbsh when the driver decelerates from ty;6z ;ifyiw7xfg o :vd: oat bcrw0q4h;90*k 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 initial 66 (com5 7hdtx0w ztsxh99lkb 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 8d jv-v6)xbpg station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished -db v6)8xpjvg 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 coefficient of kinj,3 sov nfo1oau6o 4o*ad; r/ietic 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 (includinze3e 4ti5 /tfyg the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each q, uwgehhr(n4d 9d9tvrw9 g7: pulse approximatel,9twv 9drgh4g 9 eqnhwdru(:7y 20 g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of su0i g re p8waa/jsi ew+d6/az9)+q5 kesrviving an automobile crash if the deceleration is no more than 30 " g 's." 8qe/ )pawdi+ek+6gw szjs r9a5 /0iae Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an eadta5a codq5; u ig.a9qc nm 6nfv6jqv61q01 a7rthquake is a , and if an object is ga qdat7v5q6um.f6ciqca djqav5n1 n096 o;1 going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident iiq,.fz5 y-ijp 73wsrp nvolving two cars, measure 72-m-long skid marks of one oip y zqp,sj -3.i7r5wff 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 road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means thagppv u90-hza.j3jivl+1 z i3ot 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 5pj-190 i. 3jgvpai ozulh+vz3 5 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the zke e;:tqgs 86top of the Leaning Tower of Pisa and falls 55 m before reacekt6 8eszg;: qhing the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a st14jbf;g (m3hjf i xx3xeady speed of 12m/s but enters a muddy stretch where the effective coefficient 3 m4xbjffxi g3(;jh1x 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 speed upon emerging?   

  A city planner is working on ti02g0q.kj ju0m p lo qw6wj21khe 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 a level road fropj 0g .o22m wq0jk 6uiqj10wlkm 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 akm3e , mz,:zlwp-h(+ r)xfwa/rggbt; thin piece of string while the jetliner she is in take gw(;p: lb-az+re/wmxh,gk3r) mz, t fs 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, thc)p;/v0lnf xbz8cp1 nere are to be several ramps connecting differentzvx80bcf) nnc ; p1pl/ parts 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 it, moc:bd*u) 3.mjjq1i ptg, F is needed to lift the piano (mass M ) using the pulleu,t* p.i djqimb3jo),1:g t mcy apparatus 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 acceg ec l-s/jhsdf/2(si,lerating 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 1 scm8o+ai7ut-restraint chair, an engineer considers the following set of conditionci1m7s8+ ua ots:
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 ha5mwt: -yy hb-: fud:bzs 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 ropes of similar length. 96wd.yi+ao1 q *vtmsmcorq;u6x c)q2Karen'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 result in multiples of her weight.) (b) In a similar fall, Bi2* 6mr+ 9; .qo tdqyox1qw)aiv 6cusmcll'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 " 10-1xsv29)2 i ilxyf fh50z7rf5jf $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a m:pm) pf l7td q4m.dq4iaximum 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 ascendin zi qq)dl uu5u*3s8j,jg an ice field inclined at 21 8lz3uj uq,u5i*q) sdj.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.