Why does a child in a *io89rb6v-8tc0/tn)lkfeucl h9 ky t dlx2 b6wagon seem to fall backward when you give the wagon a sharp pull fot6hv)e8l/ryn9ob x6 cl*df 8k92 uc k0 -tltibrward?

A box rests on the (frictionless) bed b3-ssd4wu tr8 k(ylm- of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the y dsrtl mk3bw(8-s-u4truck and (b) by Chris who is riding on the truck

If the acceleration of an objecm2pz uay 0h--st is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleji,3lj 1 2oowx+se)gz ration? Can it have zero velocity?z3g1 w e +ljoj)x,2soi Explain.

When a golf ball is dropped to the paxqu tukogle-6bb ;;98 vement, it bounces back up. (a) Is a force needed to make6ebuqu lxot ; b-9;gk8 it bounce back up? (b) If so, what exerts the force?

If you walk along a log fl6y j+jsk+xni)oating on a lake, why does the log move in the opposite disj6xy+ knj) +irection?

Why might your foot hurt if you kick a heavy desk or a walso:u: n0 g .2r;zkwgnkl?

  When you are running and want to stop quickly, you mu )c*re ttir0mds-h)g+st decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experie-hei0mtc)rd )+tg *rsnce) 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 same thqp-zm ry0f6gx+k4l7+b u im q0read dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on txg07q fz 6lipqru4k0m+m +-ybhe dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg r 61nuedsl mr7* 25kj3t fns:fdock. Why3j l 6rde57fsk nntduf*ms2:1 then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moo4jr: 4b 6e/xv( tx rxtdzhx;)sn give accurate results if the scale had been ca6x;):vb(r hd4/rjt4xxetsx zlibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant k;26/w tsbgzt 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 (with the box remaining flat on the table), does tb2w gkstz ;6/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 forc,doa izt x1559s )nrgbe mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Eags1tba o55 z dn9,)rixrth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-k+bt ;g;asvje2/jva q3 g object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizonts3 ;t vja;ba/2 qje+gvally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of w7ne8nex*j lxx)5.erq ar (Fig. 4–37) pulls with eeln8.)*e7xxej 5q xn rqual force on the other team. What, then, determines which team will win?

A person exerts an uq/ bw;og+s4kw/h 8gnnpward force of 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 exerted, and (d) bogqwg 8 wsnb/4;h/ k+ny what object it is exerted.

When you stand still on cti6x 8bx.bjv , 9.t5g,(l-zu i qkq)8cdbngdthe ground, how large a force does the ground exert on you? Why doesn’t this force kxq,.lcb8d i c5n. -u(xjtz)v6 ,b qit8gd9bgmake you rise up into the air?

Whiplash sometimes results from an automo44wet qt 72 r dhu:;y*xtdxr9e;ubez. bile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backwattet9q; zby2:w*7xduudr x r. h ee4;4rd in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,wnywx ykf0o2 iy;/e 78pimn5 * the crate remains where it is on the truck,8 x mye0yw2 i f/ny;*owp5in7k 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 rev-lo3u)f l 2l:h5p allaches its highest point, it slides back down but tllva5: 23oh)ul p-f llhe magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighe-k ogtqh+h ;d/1lp3nn yao9w*d yourself on an inclined plane? Assume the mechanism functions properly,wd-p;/1aqth3hoog* + ky9n nl even at an angle.

  What force is needed to accelerate a child on 0gnaorckb1 k 5dz 5,amr/,j8ra sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike an4rb.-e*+6 ha zyezd( oh ps7jtd 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 -hz: 4 vgl7e ;5jjasslto accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ov,vnf6j i5. pryc mu0(f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the car izx80,n -pxa nf qh;am:s traveling at 95km/hhanqznp:,x a-fm 0 8x;? -  

  What average force is needed to accelerate a 7.0jf av,0swufu )q -6(lrp/i9e s0-gram pellet from rest to 125m/s over a distance of 0.800 m along the barsrlv90s/( up uj,6)eiqf a -fwrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration r/u),d5akcmxk h hy: 6of 2.5 yk/ :u,c xda rhmk6h5)$\mathrm{~m} / \mathrm{s}^{2}$ 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-m1 wva,wr-) s,rhd-uyj ile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum a gz. mm6fl4; lygvw7yyshfz-+;ou0m 6cceleration is 0.0680 g . What are the maximum and minimufg4 y06-ylvzu whglmz6 o+. 7myf;sm;m 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 sc ,ma5qsb ub :okyz.:l)ale in a motionless elevator. When the elevator begins to move, the scale briyk )bo:s l5b,q :u.mazefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. x q bkt: r a/7axn(.pvy:boju8yo/53q What maximum upward acceleration can it give the elevator witub// x r87:vqt.ap o:3xojk(yay5 bnq hout breaking?    ( two decimal places)

  (a) What is the accelerat1;y mg4 n1n jp3hou0epdt/ys3hnh. +jion of two falling sky divers (mass 132 kg including parachute) when thu0n eo;sh t+y y4/dphph3j1.1 jn3gnme 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 high. When he strikes the ground p2yndq ap3 -99vq3cwynf;4 lkao-6ki below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 y2nfvq9 ko p9qa3-d-ayc3 i;ln4pw k6m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the9o9gmiouv()gg43zj;82gm 2uu rusm r box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determi 93j2g2mu)msg uo 8 mgrr;izou( g94vune 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 bas-gnl/-kub+ or ketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body irsh /qk+xo m.ea- 19bdiagram of a baseball (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 +xq- ob9hs/kim.ea 1r.

A 650-N force acts in a northwesterly direction. A second 650-N forcaqw:v 5ndob gu4 o4n71e must be exerted in what d4q nbo1u g74:vwnda5 oirection so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wq ;y9spkao1q1 ire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when spa;o q119ys kqhe 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 isj io:9tuv2 )lf(y b9xz hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0uu;haqm(fm v)n8v zulo0*)-v$-\mathrm{kg}$ 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 housinp** v g/ 6ppk *o:rvkkre8dil3hd,xg2g unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sumvkx*e2rlr/k,vpk8 *dpgigdp 3ho6:* 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 behindg fek9o;l.8: 0q k fl6qjpk7uc it, Fig. 4-47 . Determine the ratio of the tension igl;7offek:qc069 k qjup8 lk.n the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-t,p0 :0leda6)s mxvp9i;blb moy lp*.pulley apparatus shown in Fig. 4-48. (a) How hard must she pulioxl,ybb. le v:9pdmptl)p*; 0s6a 0m l downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 9lrh*e *54fp(q pg r1-pgiquy 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 (mass6d 3+ mqtkx7aw -ey5atnnp)3j $ 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 cmz3hz 3(/kr:r. psfn 0yvsl/9guifu * ontact with each other,//k3 isn ( 9 ff0vuzh3rzl.:ygmps* ur 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 initiv )-sq; h s r;x5)sark5yeu vd7zkcs22ally 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 mass and then its velocityys ;z ue52qxssks ar;k)v)-vh2d7r 5c at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless t 1i7amjnhb+ cux8zjnt/j6 - r-able 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, ujix1tzbrn-j8-cn7m hjua + /6 sing the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic fr7 .q5i 8xkejubbdd2nim+n 2u6iction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to stq3d o4e qanh; crd8)0jart 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 trainonl/56kx-,uo7 df i vtz0o1 ra accelerating at 0.20g. What minimum coefficient of static friction must e0zt -iu6 ovo f xl/k5onra1,7dxist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of static ,2)n olk 4fuoj6a.t :xtbw0ccfriction between the tires and the x4fow tcajk,b. 6ou )2lt:0ncground is 0.80?   

  The coefficient of static friction between hard rubber and ns) fl- s7x2nl;yr/u6 t q7qojgormal street pavement is about 0.8. On how steep a hill (maximum angle) can youfs7 g/7l)rt ojq2l6 s;qn-yxu leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80ajo2 vkex jaqtis4 :xdue- .v0ao*64,9v , wya $\mathrm{~m} / \mathrm{s}^{2}$ 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 gj q(/.mxmx7r 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 contotp:5umym( h3s0 0bkwact with an asphalt surface have a very high coefficient of static fri5(0m:0p omkbw stuhy3 ction.

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 kineti*fysmk5)*0y(aje+d h(jjb i cc 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. 4-3fwjf,c7bp, mt6 d47u1grzp1 r2 (Example 4-20) how large a mass would box A have to have tj z 74bd,u1t 7,cw1pfgrpfmr6o prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slideiv8(fi4yskn*va/9 z hs across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 ah/i4 kvi(s y*98fnvaznd the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and r yh19o+/bro o /eh;kggywg-+ :)yfyzat rest on a horizontal sub-h +ozry/9;) heyf+kwor/ 1oygg:ygrface (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. T c3w6a z1z+fv vt8(mhghe coefficient of static friction between the crate and the bed of the truck is 0vvz8t ga+ 1z3m6h( fcw.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 you/ m c v +:twjfu37fhhxdc*l8e;r car in your driveway, which has an incline of je l/md;chfxu* + t78 :hvw3cf12$^{\circ}$ . 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 slu6b :+hxrb a(tide 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 t1xnw 19jzg(l8uqurw17:yjg*hje.e w ilted 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 initia0v9g*9vl3aicp n)vhaaa c +8o l 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 steep;,on,zcbrycu41 il 6west 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 s/ mq/t)in;m bfasv*1pomeone pushing on it with / m/;t mavip*1fsbq) na force directed upward 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 slippery roofs can become dangq*znhrp+*tr h0z9n5tt 0y8,ysm u- zb erous projectiles as they melt. Consider a chy*y0pr r 8t q0t*h9hnsz+z um5 tbn,z-unk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling k8w-w (ezub8( aw1ksimf*8pac ij9s )at speed v is equ8zw*) aiwsb- c 9 s(j8w e1u8pkfmika(al 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 dash;ojy1) nr(*ws o2xrmp board of a car slides forward on the dash when the driver decelerates frorm21 o( *;)s yorxwnpjm 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 speewnl4e3p, :m8ulol 8 hnd $ 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 1o lojxrpawm2o6)kq24*6byt they are filled to the packing station 11.0 m away. The belt is i1r p6 o oytqa2m kx)4*o62wbjlnitially 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 coefficient of kiv-xpqzr*hcjqc 90 y prpmo6(+f s *0+snetic 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 k+n*ifyhceewj;oe9+:zxs 13 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 mam/wihbqc; pjuc+v o21.malian heart, at each pulse approximately 20 g of blood is accelera1u+c ;.i cvjb wh/op2qted 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 v vi/8zfsag(a9.v (pcan automobile crash if the deceleration /p(8 v azafgi csv(9v.is no more than 30 " g 's." 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 earthquakju xj/k1u1l3: cbxz(fmr4 i:tm)e aj/e is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction wi1ul amzt)mk juj//rexx:3fc4 j( bi:1th 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 4urpe iob5b ua1o 640uzw0-pdscene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kine poaberu b-40dp14wi 0u5u 6zotic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveds/f 60fofd2bled along the road, the elevation change is 1 m). How fast is it going whe/db6 f02d fsofn it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of*a v0+7v32m c8wtdzfeb:ab eb Pisa and falls 55 m before reaching the ground with a speed of What wa 8afw c:ev +zbb3md270*avtbes the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but xzvu0m5w; a0w 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 speed0avw wm ;x50zu upon emerging?   

  A city planner is working on the dy4g/ - /xile(p2 ixwdredesign 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 hdp x2eid-wx il4/y(g/ills 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 2ldrr u4j-6 hvz y,*pnphysics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notidl*pvzhr2,6u4yj-rn ces that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps ;m*ur 48qkxs iyncv, l d3ka(8connecting different parts of the s k*m(axlys ;ud 3c8qi8nk4v r,tore.
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 td0om r 8ys6kr1q )xfj7px f+ykg,); e.ctbj, M ) using the pulley ap0sk tgmbj)f +q6oxd 8ye) rcp1y,7 f,rk ;tx.jparatus 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 accelerath t5cv2wc1y q- )3d3(u hmg db-p;xmgying 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 chi9 35tc5 5ktnuqdpoj4kld-restraint chair, an engineer considers the following set of condit3no j5k4k d pt59cq5utions:
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 mass of 660 metric tons (66p5czmoe+4 raov1 8vs6 0,000 $\mathrm{~kg}$) . 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 dz + f:v)ibw+fzwxo) atkv*,5. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static ropeai +dx:zf b*v5,ft)vzww)k+o, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is u bwg.+)l iwr+ssing a " 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 builoqy8h/6r uyf 0ding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who ar4 a2+n)bks/vg 87 vyyeqprsy5 e roped together are ascending an ice field inclined at 21ag8 +k4rnv/ye5 y72b )q psyvs.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.