Why does a child in t3 )jw2 snp,x:bq37hkfomyb.2i ky, ua wagon seem to fall backward when you give the wagon a sharp pull f)p,tow,xij3qu:7.nh 2fkb3s mk y2byorward?

A box rests on the (f2xojfpk6 )r(h rictionless) bed 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 theof kh 2pj)6(xr motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? E3nvwd*bl12rjrhz0 : axplain.

Only one force acts on an object. Canygyoc824qn (u mwn5d e)0vla:3usy *v the object have zero acceleration? Can it have zero) uyv0(532swny yc8u n :g4mvdo l*eaq velocity? Explain.

When a golf ball is dropped to the pavemo;ab r.of g3r:ent, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If sooof r;:gb a.r3, what exerts the force?

If you walk along a log floating on a lake, w4+ 6tmd47poq s j )fs)96cn3confh zebhy does the log move in the opposite cbn7onze39)mjdho c t6 s)+f4qfs6p 4direction?

Why might your foot +oq ,oe8dom-k hurt if you kick a heavy desk or a wall?

  When you are running and waayk +2+acsa: ant to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes cys+aka 2+ a:ayou to stop? (b) Estimate (using your 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 threa2y sxx,eq:ny 2d from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or abovx :s2,y 2qxneye 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*l8 h7dwwcx n0g rock. Why then doesn’t7w80cd wnhlx* the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale o6b4niil*+(np we1gpl, bl s5had been calibrated (a) ipgs4llbpn 6, (1n5+lw *eibio n pounds, or (b) in kilograms?

You pull a box with a constant force i/l 7io7ve5 pbzjj;v -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 the acceleration of theb7l;viz jo5 7 pevj/i- box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of: zo9b7gmsjug+ 0vw5t,g 6z9 . jpyfr3qsnxp9 gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Eartz u9:pz ojg06r gn by,f x+g .57smts3qj9v9pwh. Why doesn’t the Earth move?

Compare the effort (or force) needed fasd8 gnd2+an.1l+d. j zpjm7np* ro5 to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force need fao7+dp. 2 zlmr nj1+.*sdn gna58pjded 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 (Fig.x,l.:d.i0 v x/ovydg r 4–37) pulls with equal force on thegovl.:0,vy.ix d /d rx other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to holzdtewg.1e:z *d 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, andezdwz*gte.:1 (d) by what object it is exerted.

When you stand still on the ground,m5zh,qo /9 yntq vvzjd(6t0+a how large a force does the ground exert on you? Why doesn’t this force make you rise umqz6+vqjt,ad n(90yh/zt v 5o p into the air?

Whiplash sometimes results from psjwcfrc4ui,8, .z+p an automobile accident when the victim’s car is struck violently from thuz 4w8 pfr,c+spcji ,.e rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerat br 8bj1pzk;2iwz-t(,k :0xeaz4 bg d9oz0gbzes, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate tob,4z;a9bx0 iz2rp b k8z- bkj1ggow0e:tzdz( accelerate?

A block is given a pielge uiumg78z54vmiz/2 a0 9ush so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent thanegzz 40i iua/mul52gv9e8im7 on the ascent. Why?

What would your bathroom scale read if you wei),/3fumu ufv 9ucs5; lgsy;otghed yourself on an inclined plane? Assume the mechanism functions pv;sufg f ;,9 smyu)ul 35utoc/roperly, even at an angle.

  What force is needed to accelerateo x3/m,x1w hn-webx2 /ak2q6 2 vzzkon a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bik jtr; /nuzs9u5e 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 withstanlen ;:(zls0f sd 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 -r:3og-cr-/zn oov+idyfb * l $76-\mathrm{kg}$ 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 0 .rkyt)fhu) -ai3zoq car is traveling at )0 k.a-3qz )oryufhi t95km/h? -  

  What average force is needed to accelerate a 7zo03(vfvrp 8 a.00-gram pellet from rest to 125m/s over a distance of 0.800 m alonap 3rf(vzvo 80g the barrel of a rifle?   

A fisherman yanks a pxz1k25fr7hl 7n6u xav 0h( ekfish vertically out of the water with an acceleration of 2.5 x2(l1x e n65kv77zh u0karfp h$\mathrm{~m} / \mathrm{s}^{2}$ 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 (402 u1zayiu:5h3 y $\mathrm{~m}$) 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 481auc .m;ac 8mk50 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maxm8a.u1;k cmca imum and minimum 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 scale in a motionless elz .vjv kr dczti1j5*11evator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regulac z1 i1kvt* 51dvrzj.jr weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevatorsbn zmaq)6+6 i has a maximum strength of 21,750 N. What maxi+mbna)izs 6q 6mum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two f0g7yrf 9o2lv+ (bdxjgalling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal9 02+rgoxvd7(yjl fbg 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. (b;azy ry )d4xWhen he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding ladx (y4;bzy r)egs) 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 box runs verticam7() l)dld f.ebj-e8ireze e8lly upward over a pulley and a weight is hung from the other end (e ()z. bjre)dm8 eielf 7l-8edFig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskeh 1-q/sl*xfti(e a,sdfa,ng0tball 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 moment it is hit by .zpwa/zj6 a g5dt:/wic:bpr vx- v,2vthe bat, and again (b) after i:-d .6v caz5pr2ixvgj:/ z bwtpw,/vat has left the bat and is flying toward the outfield.

A 650-N force acts in a northwester(-(e:6t2dgh5lk2ktlb i lxhfly direction. A second 650-N force must be exerted in what direction so that thl g i65(kxtll(2th2:bhfek -de resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildin91c,0w0 himn 8ool d .hiu56kq oje+fhtn34r vgs 10.0 m apart. The sag in the 0 93etocqkv85+jno6h,f.w 1rdolmih 0u4 hi nrope 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 hangkj xnyk- 1i a8+c,6a;pl v6wxaing 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 14vyn7 qv-*qe v o6:zxa8.0$-\mathrm{kg}$ 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 lddf+qj*sm+pmp3 r3p1j(r q +lsx ezef /m2(p*ocation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of tm(j p+3m+pp m f3q sze e+rjd*p dlr2qfs*(1x/he 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 masjn2ld4bg54docs glk4vv9x 0 ab6 ((jwra b0 l4s behind it, Fig. 4-47 . Determine the ratio of the tension in thewcb2 dl04jksdg9vna a5 6orb0xjv l(b 4g l44( 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 pullscj):baf4*muo qfnw* 7 herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How :7n4ao jqcwb)fuf*m* hard must she pull 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 bevh.iut+w11 gjbu qyu.3y7 )z.yg( jbw gan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass :z7o ,4zsl uwo ph;se5$ 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 fricti+k 8i)whbqr(wonless horizontal surface are in contact with each other, as shown in qb8 )rk iww(h+Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abovhwx nc;s-u/e0 fre* 4te 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 heavier one hits the ground. This is its "launch" speed.ws/; n4u-ec* frhet0x Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected byttxicbuw r0sba++*tzn k; o i cn ,;y0k2(t:/k a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the s/t2 t;kk+kzbi(b0rwyn :*ttaoi0n, cu;cx+ 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 of kinetic friction be( -s z.,ouczsq +a4 (vjavby0itween a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5g8spu(la4p u9;z- z chx eid vks-k9/1.0$-\mathrm{kg}$ 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 traiwjtkb.s7-m /n+1l dksn accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor .nmtk-+1 sj7 kws/dbl if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coef swv2oj )f jdo-i)y3j*ficient of static frictiv2 i)3 sowjj)y fdo*-jon between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber a98j/ptytwfo80dz- c 8y3 oaz nnd normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leav93nz aywo c-0ftyjt 8 /8p8odze 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 atye(sm:wt i2,mir 6wg s 9dyk-h8;0ved -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 y/v(cnv5* gx hj8 h-qwrough 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 veb* rsazx9c 3e:ry high coefficient of static frict*cera:b zx s93ion.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic frictioprapui m4 9s3sc8d1 7en 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 (Ebgr72rz j gkxubt.044xample 4-20) how large a mass would box A have to have to prevent any motion from occurrinrxbzj 42 k47rb0u g.gtg? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push ns vq*3 / 2k0x:y,qkdm3zrk mims4)fmso that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impartq sin4qvdkr3m/) f, z:skm2m* x30mkys an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in cuwyrv ) x*q)v*p sab:-ontact and at rest on a horizontal surface (Fig. 4-54). yxrpas: )u)v* v*- bwqA 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 sta3 *,n5skht.mpi00t csazb;x rtic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the ca s * z.nc3thmk5ra;x,st0b 0ipb of the truck?   

On an icy day, you worry about parkind oe5(d12rsz;. s1icoimqkz-g your car in your driveway, which has an inclinedro z(25sicq - ;11d.eoszmki 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 a +e:jagf7id6 me3y zh) po:: gz 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 tv 1:e+j e:a:5dnp;xv.qd ryk 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 3pc0;5m.pbm /pq. xnwn .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 kw rt(h4vd thk;e-x*jw41*i n;tfg)pa 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 ro a5vye3zh :+* aytb+zs33y ibrugh wall by someone pushing on it with a force divbr5+3*3 +ysybyea ih3 atz:zrected 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 dangerous projectiles as they melt. 888ric v1gj,+wszv dyConsider a chun8gd8zivv,y18 cj+ srwk 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 anejrlkd4b o)hd)n; d 0+ automobile traveling at speed v is equal t0lon d;dkrdbh+4)j)e o $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 dashboardqv1z j)p/fiaxzrn -9 6 of a car slides forward on the dash when the driver arxz1)f p6n 9 -iqj/vzdecelerates 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 m is given an inb,4scuy kxeta,kq,;1 itial 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 wheg+px383qcb:ot m; abare they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates f 3t obcxamq: +a83gpb;or 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 coefficientdg *r rdexv9 n.e,a2a8 of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (in e5og(x1le 0d2hse x6tcluding 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 mammali cikvk+4gq;f ;l--nupk( js 4jan heart, at each pulse approximately 20 g offjkc u(4vk+p;qnlk --si;4gj 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 surviving an :0)d qq6kl0v +ldj lukautomobile crash if the deceleration is nlk+qk0v:dqll)u6 d0j o 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 earthquo6/yxs2h k4rbd.wr*gv ( 4* vq3ffpdt ake is a , and if an object is going to "hol/ kyq tb. rsg*(v orpdfh 4x*v2w6d34fd 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 w2-2 tr7gbt edinvolving 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 rubber and the pavement is about 0.80. Estimate the initial speed of that car assumd22t-wgre 7tb ing a level road.   

  A car starts rolling down a 1-inotoi*p6tc/ h5 -4 hill (1-in-4 means that for each 4 m traveled along the road, ptoht5co/ *6 ithe elevation change is 1 m). How fast is it going when 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 (z ka1qxg7ra l,*)jsx Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistanj,)l1k gz xqs(*a7x race?   

  A cyclist is coasting at a sv9+zv q vqnaz p;1l3r.teady speed of 12m/s but enters a muddy stretch where the effective coefficient of fv 9azv3nlqrvq+1 .;pzriction 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 porr6,d njorc :hg/ .s m9oro,7qrtion of a city. An important consideration is how steep the roads can be so that even low-ph c,:97,6/rr.j gdoo rrosnmqowered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experimeij s0k w9 y)78hqp8gzknts, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an ang87 kji)zkhg09sq 8ypwle 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 diff;lz*oqa.v f1 7tcpq) ferent part ca;of) zvqp.q*t7l1f s of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the puybth r5pg3+o/ojgon l8;t+- slley apparatuysbrp+ o3ojggotht -n ;5/8l+s 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 accelera12-km i2ckvk,d)sqv mting 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 procesve 1(21h 3k j jrlrxexq,0rt5ns for a child-restraint chair, an engineer considers the following set of con xq3jl50re,envh1 t2x1rr (kj ditions:
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 metrick4v9a a k0dms870sgms) u 2i8azmc5ug 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 , -lj m8eu6ljx:dp0eg of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rgpu8l:0 6je-mdlxj , eope. (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 use/ca/mbklojfv tp1a;k+k*+ ; ing 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 ow;z nj devmq9koe *6e3-(i m;pf 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 ice0 4tss*w*2 :rl rfdxof field inclined afwxl0s4tro*2drf *s :t 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.