Why does a child in a wagon seem to fal:24bbgv cvd18jatpuep4zkzv7 r s 8-2l backward when you give the wagon a sharp pull forward?b4p t1:jev p-8k r24s8vzbv cgz7 dua2

A box rests on the (frictionless) bed of a truck. The truck driver starti q-)wjox,z f+s 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 groiwf-,x+qoz j)und 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 3rynw7a9 k0db (ruobpnn /;f+it? Explain.

Only one force acts on anjg+b:db t:pj+ object. Can the object have zero acceleration? Can it have zero velo t+j :dbb:jp+gcity? Explain.

When a golf ball is dropp hct0kvnfm+ 1rd/ qhidc8;2z8 ed to the pavement, it bounces back up. (a) Is a force needed to make it bounce back hc0d2t zh8 i/fnq1kc8v+ ;rmdup? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why doe3ir;)d9ax /ck+p a jjuz3c n+qs the log move in the opposite direction?+3+r /dz p3acnxq;kjju 9i)ca

Why might your foot hurt if you zkpj133z a2.5ro gwqr zkv07m kick a heavy desk or a wall?

  When you are running and want to stop quickly,8/ee2hrme -zadx +v g. you must decelerate quickly. (a) What is the origin of the forxm ha 8v+e2-.egzr/edce that causes you 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 thread from the ceiling, and a section of the samgxtj j(qs+7.r e 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 above it? Wh7(rt qjxj+g .sat if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice z* av+5 t owto1g0dh5yas great as that on a 1-kg rock. Why then doesn’t yo55 01vzd otwgha+* tthe heavier rock fall faster?

Would a spring scale carried to the Moon give accurate r9hh:++a( fzsmg v8qqzesults if the scale had been calibrated (a) in pounds, or (b) in ki:a9 vhzq8(qhmg +fzs+lograms?

You pull a box with a constant force across a frictionless .,/feogwnbmlvfs( e()wa, .c table using an attached rope held horizontally. If you now pull the rope with the same nflw(cs .wo,).afm/v ,eebg( force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influeznh9 c(xx 5a9l+qvt)gnce 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 Eanx c( zal)x995g h+vqtrth. Why doesn’t the Earth move?

Compare the effort (or force) needed to9 4t9 )p mjc,fgjg3gm3tuc-lw 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 object horizontally with a given speed on the Moon and mj)g,j t gcg-t 9m f4w33pl9ucon Earth.

According to Newton’s third law, each team int+nfgi/w,d7*i.5hgx st tgn2(z j e3d2jj -km a tug of war (Fig. 4–37) pulls with equal force on itn.i f*j5mjdh(gx2zjt/g +nw7 , edt32k-sg 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. Dei8bg x(vqem9.scribe the.b8e9i (qvm gx “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does theklk -6ze9wl9x 5+2,cmnp1 rt gzpyj 9r ground exert on you? Why doesn’t this force make you rise up into the ai+ gz9pn1lj9xek59myr,l2-ktp rw6 z c r?

Whiplash sometimes results from an automobile accident when tuhlnr7i;c9k/ he victim’s car is struck violently fromn7/l;uh c9kri 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 flatbed truck. When thy72ar9ek i 9i 8q8kach*h0voz6l ,xg: e fxi4pe truck accelerates, the crate remains where it is *84q,i9fxhli2:x e ea gkzpvic06 ha89kryo7on 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 blox pukw/-os w s07 o;hj 4k7stwpn))rn8ck reaches its highest point, it slides back do8p wuokk-wptwnj7nho0s7)4 sxr) s/;wn but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you ee xa1+sq;ftvm9l2d: weighed yourself on an inclined plane? Assume the mechanix9qf de:l et1s2+vam;sm functions properly, even at an angle.

  What force is needed to acc -2i yhcbcq5is 60mob+elerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N ac2e;mnauvjqvw w;u gh95dhd0*9ib2 h 7 celerates 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 a ropml) (quyc+vr 7e 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 oxd,ii1e;y as: f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in(u1tiz+ 7dqfu l :c+j4t7 dvwo 8.0 s if the car is traveling at 9514fi+u u :dvqot+ d7wcjl( z7tkm/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to ;z;f lk hv5to/ -crdr;125m/s over a distance of 0.800 m along the barrel of a rivz -rtd hrk;5o/fc;l ;fle?   

A fisherman yanks a fish vertically out of the waj3 5s qyuv71scter with an acceleration of 2.c 5js3qu7v1ys5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 aec 8 aqb( hma28v-)sde quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) i po/-y5fm zse0s to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportin -py/s5 0mfoezg cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When thed8xno4ivudc-q6e 9h 0 elevator begins4q8vc9x deihnu o6- 0d to move, the scale 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 has a maximum strength of 21,750+rfc(2*,gixv9 r gkhn 1g3a ru N. What maximum upward acceleration can it give the elevator without g 1u nc2v3xg(f ghk,ra+rr i*9breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including pa p7h )cvg)n95vx;zew mrachute x)p7w5m)enz v9c;vgh) 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 ro5lm7 lncq3fj0 of of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his to fmq 35jc0l7nlrso (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 box run(d i-s 85 jbsocwbvz-3s 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 z (- b5ss-jc3dw8viboif 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 bask:t z- / wvz * kjz9nzzco2/l7y;y;yjly3: rsyketball 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 jom(m uiq )m-zi/oc+(the moment it is hit by the bat, and again (b) after it has left the bat and is f)cji- qmi(m o+ umo/(zlying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be e:eaf .vf : zjs6pi0pu5xerted in what direction so that the espi05v6fzja f::up. 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 building 15k vufg8 )wc5.j cdzwc,x ndo3i9wa.s 10.0 m apart. The sag in the ropza5cn )j1wv9fk o d5 c dw.xc8iguw.,3e 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 massle9 r7cajrtw5f6 wcax3zacp+/6ss 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 14.5wt,t /yunxj h:hch2/0$-\mathrm{kg}$ 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 lo v wrg+rl3bdx7hithzui 0 q76+3 mq/*gcation at McMurdo Base, Antarctica, as shown in Fig. 4-46. Thehghqti6lir 7r 0zug m/d+7x b*33vqw+ 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 pullirvuae: 8 x i07z86b ff( cslticzk*.5fng two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firri8kfzuf.0x f l :8i se(6ccbav5z*7tst 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 ap/d4esy+flkoa5 +m)2dt r q c/vparatus shown in Fig. 4-48. (a) How hard must she pull downward to rq2d a+5)sr+o4lvc/ km yd/t efaise 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 bj- swq-iunfy3( (rwbq/h 72 xkegan, 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 (mav :i9ul-0e/ t+txhx7 u*1bn 2nxukpnoss $ 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 xrfb u1z/2br33 u yrn0kmj )xi 3yw19ahorizontal surface are in contact with each other, as shown in Fig.uam 3 rj9w /21u 3yxzxn)r30rbyi1fkb 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 abg;o hj1v63;6k w qpu ae2ndna5ove 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 pne2uv6 kqgw;hajoa 1n6;d5 3hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionlessrn)f0*w+ w*md4a;ya g mv.esh table are connected by a heavy cord of mass 1.0 kg . Calculate the acceavame)g4wfd; *0nwm.ry+ *s h leration 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 fhg 6loxh;h;2kinetic 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 requirebrpfavu8xo80zyk. f ( 5ou1(o d to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing olpadt ng/tn 0;o p y/fb-xbzr 2/;:zt6n a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and /zd n/btnz6/; fg0- ;:poyl2pr xb tatthe floor if you are not to slide?   

  What is the maximum acf - e:me43 fsf 1th:;gygbetz0ctbc0 9celeration a car can undergo if the coefficient of static friction betwee0;: e gmby fc401tfegb t-ehz:t9cfs3n the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pave3,qqqiln)k)+q*pbuz 0yr.yq ment is about 0.8. On how steep a hill (maximum angle) can you leave a ca 03zlq) ,bi)yqu*+y. q rqqnkpr parked?   $^{/circ}$

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

  A car can decelerate at -4.80smw8qene6, f 1 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough 30mkn. x 6jhfk37 5jz;xd$^{\circ}$ 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 surfacep+p4o*ehf; 7 kk5y khy6ps .tt have a very high coefficient of static frictio+6kpe*7o5; s tk hhp.4k fpyytn.

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 friction for a p o (am7j650xsm n1udah*ixu(- epv8hx,dsu- $ 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 ha3n) 0dxcvy)z -ilcu6pve to have to prevent3c- y6)uxz pvid0 )cln any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it jv 1r;vdtc8c,j 8l k-nslides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speedktjl;v8d, j1-8cvrn c of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 g 6olw4i i8u+k5r .a/li-r:fypqhu0 ukg and 110 kg , are in contact and at rest on a horizontalrr 6gh/4fupl+i5 uoky w li-u:ai.80q surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fr za(vr+tlox7.iction 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 cab of the trvor.lxat( +7 zuck?   

On an icy day, you worry about parking yondmsz8u y8 .z+m2 (c2f:ca xlpur car in your driveway, which has an iczd8:2+ma f(2sc nxlypz um 8.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 sliqasxu*gn+)5 54 f4pv6mkbywavrc; .sde with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted ak61gw)fs e7smt 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 3+fr2y py.8t kdxqo(zj9 -sgj(.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 6.0.1 x,n590o w ogq/ f j.btmfqobq7rs3o$ \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 x4e gm 3dm b(t7h:6rllrough wall by someone pushing on it with a f bem(lgml d:643h rtx7orce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become 77ywdmbihr3 :dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof7 :i37bmdyrw h 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 stopfo a b5f67er3 fql s*0:b2llnkping distance for an automobile traveling at speed v is equal to l qr: 3b*a0ffsbenlok56f 7 2l $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 da g pwk* itq4jyboywunzg4-s93(;;) tqsh when the driver decelerate s;gw3tn)b4oyi u*qwj; -(pzkgt4q9y s 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 inobf-jn0 kxk 1c1r ir61itial 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 bt;:etqp7 ) hn e/we4.tmnd v4felt from where they are filled to the packing station 11.0 m away. The belt is inip)wefth/nv4 e . ;:q ment7dt4tially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of ktih9aw 6tv5s : y0.rhmtl:wi4,upye ;inetic 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 (including the bicycle) can cie l( :bqta,dv0vy7d: oast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian hew*e..uhdo 2 bfart, at each pulse approximately 20 gd *f..wu h2oeb of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an1nxzl x)be- hqco; 0 zz*3luzo6uw9v7 automobile crash if the deceleration is no more than 30 " g 's." Calculate th07z 9 6h-) *zczxnl3lv ;1uxbowuzeoqe 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 ifoh*s)5uo o.j8lvei ou l me592 an object is going to "hold its place" on the ground, show that tjo 98. eo *2)hm5 lu5seluooivhe 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, examininvm0yc .v.nph7zc*ml, g the scene 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 initial speed of that car assuming a levm0hpcvmc z7 .,yvln.* el road.   

  A car starts rolling down a 1-in-4 hillwly 2jx1:;dj2ds 4)xz6y gru::psohw (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) Ignore frictionxd 1s yj: )wd;p6z:gr: o2s j2uxhywl4.   
(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 and falls 5d3 v4vw1-xtz z5 m before reaching the g-zwv 1txdv34zround with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steadybg 3y4ja42w 7to7*g.6rrw- sx uutno l 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 sn4 g3yw 6tt47b xwuu-o saljrro* .7g2tretch 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 ao8g,v) v s5oelop1m0 j hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg ,vsevo15 8lpg,mo0)oj 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 experimv2bc2n0ry9y( f;noio zhjs ou8 ls4/4 ents, 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 ma84r2suzf0osjl / vob;yiyh(on429n c kes 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 diffe8:w5( fhqii-d oo+l0lr ghhl-rent par dhloh5l(8friw qo+l0-h ig -:ts 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 pcl:ty+ d2 56kwa ujtz2ulley apparatus shownkcja2w+zuy6 2 t:ld5t 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 acceleratint,jlmat. )jp e,mt f8.g 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 chilis7f-- -w w+h o 1ashvz/ttdk;d-restraint chair, an engineer considers the following set-/-wzvw;-ih+d h1ks7f st ato of conditions:
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 Itar7tyxa96ow 5 52a yhpalian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of sim9um e)jn7zx9jdkf (f;fxm+ -milar 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). (zk)9n-fe; ( m jfuxmx jfd+9m7a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is usinq +-c/wn.px mh-qa)xpg 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 r9h9t+ah rz *cjfo2dr3 each 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 are roped toger+ qeq0o8pvio t 5p.e3ther are ascending an ice field inclined tpo.e3+o e5vr0qq8piat 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.