Why does a child in a wagon seem to fall backward when you gi*e1i:oas1k(8sza gr p ve the wagon a sharp pulls: a* e(8a zgr1si1pko forward?

A box rests on the (frictionless) bed of a truck. The truck drivn7l u v+u--,1 4 kqqclbklv acjw2qv)/er 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 truck and qlu qvn41lck/7-q -)2kvwlv u+bj, ac(b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forykz sa k4t zi64z5y(8uces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration?0v.wkxo9 nsh(kiu+ zv*r0yfx )k*ag- Can it have zero velocity? Explain.s0in*(kruk - fox +yv0.9khawv g*z)x

When a golf ball is dropped to the pavement, it bounces back up. (ade58p wr-;oz l) Is a force needed to make it bounce back up? (b) If so, what exerts the fzp dlre8o-5 ;worce?

If you walk along a log floating onq6kysijq;aera 8rg 9qefc5fs:;. ;e 9 a lake, why does the log move in the opposite direqr; 8 5agri s9;k;eqfascjqf96y.:eection?

Why might your foot hurt gv6:+kfjjoks)6 u ej82q 4dw*2coqyg if you kick a heavy desk or a wall?

  When you are running and want to stop 10msb( qf.z w0kfpj+0t qf3oaquickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a persontf az mj031wsfp.qqo(kf0+b 0 running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section ofjmd6u tcoouj;8b3e ,4ps 4uf 0 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 theomsu44j6,u bd tpfu8e0o j;3c 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 asatzm08+.ux7lcw4in l )ql ei - great as that on a 1-kg rock. Why then doesn’t the heavier r7nqelltc i+4az i.w8 )x- mu0lock fall faster?

Would a spring scale carried to(cjvcll 4, mv)fc 4+dw the Moon give accurate results if the scale had been calibrated c,jv( 4vw4 )l+flmc cd(a) in pounds, or (b) in kilograms?

You pull a box with a constant force acros;*agevada0* h s 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 fd;ag0* veah* alat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freel,-oaizh blh/5l-h 9 ovy under the influence of 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 Earth. Why doesn’lho -b,h-oi5hzav/ 9l t the Earth move?

Compare the effort (or fovoai5y) 25-zm; ykh wbn/0pj n; ue*mjrce) 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 needed to throw a 2-kg objec-a5u)iob*0 ;nvyw jz;nj5hp/ 2kymemt 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. 4–37) pulls ws1ckd 01 tov)oith eqo11d 0) sokvtcual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Dp7imt+ x0c yw( fg,i4tw: 2lyqescribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on wh icp0 (m q74y+wt lx2wyf:gi,tat object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground zg*tgoxy) 8.. x76z* uidlwwe k;lwg/exert on you? Why doesn’t this force make you rise up tl8we; )*g.wg67dw/u *xyz.oi klzg xinto the air?

Whiplash sometimes results from an automobile accid c4*vnxard4 px05ql8 zent when the victim’s car is struck violently from the rexq 0p4d8v5nxc*arl z4ar. 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 oyk3 hs- pupy)0f a flatbed truck. When the truck accelerates, the crate remains wheruyph-3ksp y )0e it is on the truck, 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 reach2xr 82twor uru0hd il 58llx,0es its highest point, it slides back down but the magnitude of its acceleration is less wd 5l o0rxlu2r , tu8rx820lhion the descent than on the ascent. Why?

What would your bathroom scale read if you wo z- zwj*,sbi09wfx.)b;i 1bdrge- vieighed yourself on an inclined plane? Assume the mechanism functions properd wbrf;jb--i zo. 1s0vgbz9i), x*wiely, even at an angle.

  What force is needed to accelerate a chipv h/ n-rxy-,wld on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelera f(r3hhw1v/rls )ef t6tes a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must ai(n aibvzvw5 5 9c4au5 rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a vctp;2e2k xw3$76-\mathrm{kg}$ 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 cpej -q0uyi adg h4-58mrqo -x(ar in 8.0 s if the car is traveling at j u q r-8-4(qgo -iehd5axp0ym 95km/h? -  

  What average force is needed to accelerate a 7.00-gramsj(rukxdc /dlh6ie0, hnt8 2t5zk 44f pellet from rest to 125m/s over a distance of 0.800 m 4uhz,t r5flxec(h46dkd jk02s/ni8 talong the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleyf:*wd 4 o3v,dxr:ta0f)5zz 8cspulnration of 2.: *ldzufow cd 4v :z8) a5rn03sx,yfpt5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 el8yjl s+kmw/.f2 cq )$\mathrm{~m}$) 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 designenvd8 w3qa6z7u+p3 fty d so that the maximum acceleration is 0.0680 g . What are the maximum and minipn3fa z6y7tqwduv 38+ mum 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 motionlessdzq.5wpt 4* rb elevator. When the elevator begins to move, the scale q.rz4 t*dpwb5 briefly 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 haqi(-a -lcmn(e s a maximum strength of 21,750 N. What maximum upward acceleration can it give -(a (qecminl- the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky tr6xm2 u*ni o6s o8avbvgg.d-v*/(zn divers (mass 132 kg including parach-8zvnsxr6*b(i n v/v mg2tuooag6 d.*ute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the ror+ gkm-jk(,v) kqiij2s 31dpczi 4 4wcof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over a k cskv-ki)m1rii jwpq24j ( 3+c4dzg,n 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 s:b;fv 0(mc6menhj +z table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end szhe0c(mb;+6 : f nvjm(Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball plaw*w x79, t0o,buxocooyer
(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 q(n*ddv meyh7+6gu x;the moment it is hit by the bat, and again (b) after yghumdv*n 7q;e( x+6dit has left the bat and is flying toward the outfield.

A 650-N force acts in a northwest bh2fiod/ 1fc5srzf 6*q( a;ssf47ie rerly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vssb2 4f*5eozf;q6/(fh ir asi7r1df cector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two q g)iib a6;ge8,a)jud,f a gt9buildings 10.0 m apart. The sag in the rope when she is at thq,g6ega;)a ft,) ij8di gb9u ae 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 hangi yiv/h q/k7fd.ng 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 14.0xrxwnx )/f,l3fup qvpqul,;ry /,:9q$-\mathrm{kg}$ 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 locationed)yy4 f nzj4vz0q 1s( at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum o1 fyzv4z n04sqdy (ej)f 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 ofx0 wd63oou:d o the same mass behind it, Fig. 4-47 . Determine the ow3oox:u6dd 0 ratio of the tension in 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-pup 6czzl 2ix0mgdgpjb4r-9 n3*d a(1ifue+ i-ylley apparatus shown in Ff016cilid p 2m94*je -nigr db-uzp(g3xa+ yz ig. 4-48. (a) How 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 rac(dc uzq0 :il3je began, 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 tgv v6bg0u )ohkcy1 2;block (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++a my.vmk,10f 0 blk53cmmsi xbx zb6 surface are in contact with each other, as shown in Fig. 4-51. A fm06 3b.is b 5fm v,ycxbmzk+k1ml xa+0orce $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the grounk*; yl3g0swbb d, and the massless frictionless pulley is 4.8 m above the ground. Whaylk; b wb*3gs0t 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. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a hei9q+/san,pg q*v twd ;avy cord of mass 1.0 kg . Calculate the *sn aq +/iwtv;g,9 pdqacceleration 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 of kinetic friction ol srll- 0o(g2thg4 *rbetween 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 stausjcf;hsh:g m j .x1vo 3+y8/crt 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 t+)+k toa-3gg.x omdqirain accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are-k oa.qggo3 i)dmxt++ not to slide?   

  What is the maximum acceleration a car can underofdi tmcoth 4 z.48*9zgo if the coefficient of static f44 tf9.zicz*tmhoo8driction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal stree/*zk2*offe py t pavement is about 0.8 p2ye*ff *zk/o. On how steep a hill (maximum angle) 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 at)kxa4dejl6 s9 -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 roud7r lm):qlf+7pwwde y zr 6 -(yth9mc1gh 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 asp, pcu 7yuw58. y topjre,ocvx3s,,x9xhalt surface have a very high coefficient oy xp735c,uc9. vsjrop, t,oe yw,u8x xf 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 kinetic fri)wi7mtq2a 7i bction 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.;jf w8-l6hr0lhj tq 0t 4-32 (Example 4-20) how large a mass would box A have to have to prevent any moj-rhl0 fth8t0jl;6 wq tion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that 4()sh- byhpab82 bhowzk, q6,j-v pz vit slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparth(4vqbp-b2z h6oypa ) kbh,w8-zjv , ss an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are i ja5mp(nc +hs8n contact and at rest on a horizontal surface (Fig. 4-54). A 62nap m(s +j5c8h0$-\mathrm{N}$ 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 craz4 f erp);1ydtte. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate s1df z;yr4et)p lide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whichz +x+mtsz m(e( has an i+ez+(xmt( msz ncline 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 witmdj3 8y.qe /nhft7qm *h 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 j mf;w0-zgy*w 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 initi9mv oq b6jjr a)jx(a+,al speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill wimj,r ak9mq5ae8 ;1pg ith 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 ef)hp,ma0 z a v+gcn(p, 67w:v 1p(epokpaa/yby someone pushing on it with a forcep( p+106afyp w p:7o ,kmeapanh(vzacgve),/ 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 slipperyjr.g .,+/oxh j8ktsm c roofs can become dangerous projectiles as they melt. Consider a chunk of snowgmj,k.x /r jt.os+8hc 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 automoo6 b:gxu(o,, lfv)+y(uaovy/n pl3 z hbile traveling at speed v is ) a6vp v:/blny3fhoo,,z+ oyxu(gu l(equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when thcq,;f p2mgbz wtx5/7p e driver decelep,57 x;m2gpbwzqtf /c rates 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 ggp4 7gs/ dvsj*ioab /2iven 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 to the packing st,6 ;kdpgc; g qpbn98bjation 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 finalp 6bqg bjpn;k,8 dcg9; 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 kinetic friction betweera)0r *f.ikamzb5*opn $m_{1}$ 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 (including the bicycle6u:+ip mm8g o, o9lzvkt m085cj iq0vb) 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 simpllgt2rwi5h :r- mtd d 3ol/x;h;-f( bwx/vd 3uwified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 d/3v5rh: i ut2dodwf-(gbhtmx-r wl; /wxl3;$\mathrm{~m} / \mathrm{s}$ 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 de -klhbp lssmvl+6c+6; **u lpuceleration is no more than 30 " g l +;vcp*khll *ss6+l6u -b mpu '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 *;hh,mq3o xcoi15f joj51rj .mz1wv f by an earthquake is a , and if an object is goi1hc11x5 z,*mw ovj mj; hf5 ijqorf.o3ng to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the sceszl)112so hga wcn4n 6ne 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 kinetic friction between rubber and the pavement is about 0.80. Estimate the in4 zhac11)s o6wgsln2nitial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-inr*i y /qg1rba rnw.-z).lcgu 4k 2*rsb-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) Ignor2qgzb.c r-iy4 /*bw r)n 1rrs* ukalg.e 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 Pisa vi5 d-eqx: q)pand falls 55 m befei q)-:dxpq v5ore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting atj9 j.tuvm.vnw1r **pj a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without havwm j r.jv*p1vt*u9 j.ning 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 l( mzhvw.32kaip6z3c of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing 3pk. ( iahc w623zvlzmdown. 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 expibr8an pah3/ v(x,tl4.x f/yqeriments, 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 makexr/v4 th3n8q b i(,fy. xalap/s 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 differc40jv 2iu7nv tent parts of c 0ti7 42uvvnjthe 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 e0gz)i bs0y vzc2zsmq/e44)z needed to lift the piano (mass M ) using the pulley apparatus shown in e 2z sym4ez4zvi/z0c)b0 g)q s

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 acceldy2qw ok8zg+ 0.i;nv verating 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 fob dtnh ob6sq.y0g2 lz8.gz8p 7r a child-restraint chair, an engineer considers the following set of b 6gslnh.d8q 08to zyg.b2 z7pconditions:
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 na+8 ;nou-3zf3u+ ;lcly o quxmass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Ka dn+0-c() p3xnuxfedlren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constnpn (03x xl+)e-udcd fant, 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 boa s6k1k,upi;p9c* psuct is using 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 ciq; 6z/k*alqt80lz vbuilding 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 arfwz(j m.*rjs5e roped together are ascending an ice field inclined at 21.0*j(fzrw.5ms j$^{\circ}$ 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.