Why does a child in a wagon seem to fa 5nztm0mr5 f+q.ijlih-oa:bb/xj (8mll backward when you give the wagon a sharp pull fo-.xm:j z5l iaon ibqh8tjr (mmf0+ 5b/rward?

A box rests on the (frictionless) bed of a truck. The truckev*s5yykam5x2j( d /2 vy 9 twenz/.nh 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 besj 5 (/vvxednaznys2/y .2h5e*9kytmw ide the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zeroc 5g/mlg8y) udsu, ,ok, are no forces acting on it? Explain.

Only one force acts on an object. Can the object ha v 4jjw)h1xpq0x1 iv4xve zero acceleration? Can it hjp4i1xwh x4x) 0vj1vqave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back eaft *0k se0 aln 74(fzp3v18 aap+iuvup. (a) Is a force needed to make it bounce bavapl* 7 peav0a su+n84tfza3ekif 01 (ck up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the *jrg2:ig 5bl;uakk * nlog move in the opposite u5i*gb*gal nk rj2k:; direction?

Why might your foot hurt if you kick a heavy desk or a wallcbd ld+ (wqq/smll-.l4(xe9 c2 g5kqa?

  When you are running and want to stop quic-w3nwi:hstn 0f u:b3i kly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the mawui::nnst w033 h-bfiximum 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 threiepqq4ids:g k,m1-8 vp* arba:.bsi5 ad dangles from the bot5ase.ib iamri pv4 bd q*s81,qpk::g-tom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-k)frw06ol0mm i e pm:0kg rock. Why then doesn’t the heavier rock fallmf0:0rme l6)pmw io0k faster?

Would a spring scale carrieqt*f zh.v)h-vh7cb 9q.ssyj8 d to the Moon give accurate results if the scale had been calif8q.j-b q v)hhsz*h79tsv .cy brated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a friction2p a vff7m1coh. shl:3less 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 the accpl :fo s1hc2hmv7f a.3eleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity 7-ws ;4x ur:m c9i1hpzx5 lwi.0oqbmxthere is a net force mg exerted on it by the Earth. Yet by p9 xmiwxihmbc:1ou5; xz. s7 q4rl-w0 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 forcej d:ch8c7c lqqi)9 8by) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force neededhc8 :7l q ibycd8)qj9c to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (F6b1 t:grl vse9z 1v:vaig. 4–37) pulls with equal force on the other team. What, then, detv:1ta1rzsbev 9l g:6 vermines which team will win?

A person exerts an upwar 4n/o8eji/a9zbnn 1prd 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 b/r9ni/jo1 zn 4 pea8nis exerted, and (d) by what object it is exerted.

When you stand stilly )n)9ng x l+)1zxqv;jxtvu g* on the ground, how large a force does the ground exert on you? Why doen )g nxjvtzy+ xxl ))*gquv19;sn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the v-aqo.pzb2 qq-w.sz p:d gx(/victim’s car is struck vpqs.-z-g.vzp d2bo: qq w /ax(iolently 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 flatc4dq t.el ,kzc r26w/nbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate tol,dkc/4r2 .e6ztn qc w accelerate?

A block is given a push so that it slides u h)k++ +r onql1s ssms-,aweuqcah,07p a ramp. After the block reaches its highest point, it slides back down but the magnitude ofhecs ,q ah,7om+)ua-1 +kssrl qw0ns+ its acceleration is less on the descent than on the ascent. Why?

What would your bathroom r33 )jzf /tk2/gdy z.- tsp7y)mefpss scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even.s)jtmd/p 23k ygr fe/s z3y 7)ts-zfp at an angle.

  What force is needed to accelerate a child on a sledbbka,nl* +g1qivw -(oju r(k7 at 1.25m/s$^2$?   

  A net force of 265 N accelerates a nggu;pe otibl).6 pk/l48w5o bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand ifemu gdj:p+tc:e;w;1d p/ck8 s 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 as6t8xd huwab+d 32sa9 $76-\mathrm{kg}$ 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 o;d beb0grg:j :pf()hs if the car is traveling at)b:dg:pe; jbgo 0fr(h 95km/h? -  

  What average force is needed to ox m50a tcmzs:x7m /tuofvn4 3,a;vw1 accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a riflem m tof5;w atoxac:x,4n30s1v m/ uzv7?   

A fisherman yanks a fish vertically out of the water with an accelerf.tr ew2u q 34y/wird1ation of 2.5 r w/fr .d i3t2quwe41y$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (4 lai ;xu9lf-0yp)4unu02 $\mathrm{~m}$) 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 accelerati nw0hswc zu/,nuc7,/kon is 0.0680 g . What are the maximum and minimum forces the motor should exert onnc/hu s ww70,/,czkn u 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 n,37co7(jv andxdh4tin a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regulax37n (t acdd47hjnov,r 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)v 83xptpa i-dc3;pst a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking c8;p)ix-pttv3sd 3ap ?    ( two decimal places)

  (a) What is the acceleration oesvp(4sx5 c3r 4ofmz (f two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weightp4m45oef zx s rcs(v3(?   
(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 strike)*25 hb4 o0uxey+dyxngwg 8tas the ground below, he bends his knees so tha+4y 8o5ht)2*0by eg gunxxawdt his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the bodeue 52 ,h.ewzg/cl3 s)gosb.x runs vertically upward over a 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 weighsc3, .5 2)bdeglwge ous /.ezsh
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for z9 ct)xa:z)6j)v lydda 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 baseball (a) at the mom+n4.w rnayc nu,/i b3rent it is hit by the bat,, n 3 ./4nirbna+wcury and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mu-z( m xtcxa)ol;9dpkili: 7/vst be exerted in what direction so that the resultant of the two forces points wes t)(p-7 oxa;i:ci zdvl/x9ml ktward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung yuy67g2,36 (/v hotjj0d/t .vhwnqn rflj wh)horizontally between two buildings 10.0 m apart. The sag in0vyj6 tq,hv g(j 6jt /2uw7n y.r/h)hwl fod3n the 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 masslessr n.yl,p,tcfaeqk 385lxw85;kv9 yk +8q jdmp 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 14ufe ; 1w:x.xgj)a i8t o9a(huy.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, :qn8w x .jo1wm iarv,5ley1+fAntarctica, as shown in Fig. 4-mq.f1:1j +ny ,vawr5xi8leow46. 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 mar-xh3i uzyn1 ez-8ug9ss behind it, Fig. 4-47 . Determine the ratio of the tension in gzyr9 8z -ue3nh-x1 uithe coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley appz 2pusk jtmv55fp1eux.h i4.(aratus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at conzj52fm5(p u1 te.h.pvxsuki 4stant 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 653 8agi i4v4aeh$-\mathrm{kg}$ 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 blo:6jsgk;6idyjt, w ibcx; my84w*0u jnck (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 in contact -4mp,ej gh 6zhwith each other, as shown in Fig. 4-51. A forhm,4hze6j- gpce $\overrightarrow{\mathbf{F}}$ 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.9zjluzu3u 1dpw( 4: bq 4-52 are each initially 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 velocity at the moment the heavierj : lu dzbwqp1(uu49z3 one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a hsh8 vp,ihkvsm f 0.+g/6ai+:w2l n gx;s ,qugpeavy cord of mass 1.0 kg . m.vgw i8ki, ;x,h/vgf:g2 +lq + n0pauph sss6Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient orp+6sv sp: e 25qz.a/1aal qqcf kinetic 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 cvm -f py*i,-qto 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 trainbptxu99i0hl s4 fwio9 x /l,8tz ,.ksg accelerating at 0.20g. What minimum coefficient of static friction mustl.9hz,9x,4t9 kiupbw l/gx 0 ossif8t exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeff r.z;v* ltxc)d wxh5/micient of static friction between the tiv hxc m d/;z*)l.5xtrwres and the ground is 0.80?   

  The coefficient of static fr ,how 0b.ixap3m7. mfdiction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angl.ifmx dop h73awb.,0me) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at3xm) mg61kipi -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rouk:f mj:vyq85 axf*r7hr*e z.v gh 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 contacbtfo430 icpo aynv*p. w)) -idt with an asphalt surface have a very high coefficient ofc) taid-3f )piyn.vop*4obw 0 static 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 kinnlxx /cgx x 4vz xu*31(+vic,getic 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 4-20) how large a mass would box A haeg 466ovif ,bn*ly*y -es ymy/ve to have to prevent any motion from occurring? Assume l*y*ey-, vnofegiym/ 46syb6 $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, ga byu n wy+3g8(0czhm3iven that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 amg 3w nzu b+h3yc8(0y$\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg r8wjole.gb26 r z 6zmhp(;a*n , are in contact and at rest on a horizontal sabh*jen2 g(m.; rlpz68o 6wzrurface (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 heav9zta kc04ibxq)3 hd 0fy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What i q )0k 3i4t9fb0zchdaxs 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 car in you88 tc*lzeie 4h c2xfotfj+:7ur driveway, which has an inclin utihf +8t 4 cz*lfce28jx:eo7e of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with 2( pnj61y5 vtki;5. dpwivvqca 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. 4-53jl2 (y (eygxh.h82krmp8ykl5 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 initial speed of qxzzpb )1q7 94t2rigxlm45 ii3.0 $\mathrm{~m} / \mathrm{s}$ 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 rsn)4wag8ij/n.j g6 ,w8k7ai+ qxqdj 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 wamsm4i0yq z*wwh 07+k fll by someone pushing on it with a force directed upward a4 kw+y0 hsi7z0wqf* mmt 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 r,p wlkc3k t)e5 drl+l: aht)*xoofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with r )l 3)ex+klk,adt :wph tl*5ca 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 autom6qpe*eoa w -5acr f2i;obile traveling at speed v is eieqa2-rape; 56cw*o fqual 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 s; 0gk s5fcz5wvlides forward on the dash when the driver decele5swc 5fv;k0z grates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass vx k41 rgjhh;5 di45mfm is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled tonk sb 1 7w5ha1.;/f2w;iokg w temrf;z the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the b bwmhori;1w5a kg71 / nft2s ke;f.w;zelt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic fri v1c) vjlwwih0np w96,s) *pevction 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 (e zhiud7gx jr7l/*3lq 25lc d.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 modn8abjd2 ts// fel of a mammalian heart, at each pulse approximately 20 g of blos d/8t/f bja2nod 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 surviving an automobile crash if the dem+-l vm( 1hn(kxyxjh 3celeration is no more than 30 " g 's." Cak(lmv-ym1hxh +3( n jxlculate 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 earthquake is a , and if an obj ikp)qbw/p)wa0 c 3snwd65t,dect is going to "hold its place" on the ground, sqpsan3d) twwkci 50 ),d6/pwbhow 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 involvinz* 4 -kttg5tn9)scbtk g two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rub-ttsk)c kb9t4n g z*t5ber 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- qyvta8v ,s7n3in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignorq,n83ya vv ts7e friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the tofl0 2;sxn*pn33 tfmb vp of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was thesfx ;0fm plv3nnb2*3 t average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddoc0v ).82sqju/i8fozizris: y stretch where the effective coz0i.s svzqi28)cro fj:u o8 /iefficient 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 the redesign of a hilly portion of a citsmrf*ob + 0sn)y. 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 from rest nf)mr0o sb*+ sto 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 experimtn pyfxvm7u*;+,m. i gents, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (npi.mv mx ytfu+;*7g,Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting differu.f.o;sst mvhl8wm ;0 ent parts of thel wtsu .s;v mo0;h8fm. 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 9:.y jayoa qf0is needed to lift the piano (mass M ) using the pulley 0j 9yoa.fqya :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 accelerat 6dh7tk6e r0moing 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 ++ztclooezvcd;( q v0oe 70 :xthe following set of cond;vo q: +7clte zd0x+oz(0oevc itions:
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 (uair0y5 i5g py 2vm(s.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 K pjs5vr myh)ru0(a,/naren, 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 forc50,umvynj par)srh(/ e 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 usij80(iqjt 8 qfnvwm r85ng 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 building is allowed to reach a maximum speed ofl j /:2jatw;mgfymb9. 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 g q9beva/-h+xinclined at 9ag xe+h/b-qv 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.