Why does a child in a wagon seem to fall backward when you give the wagon i36b wy+khd 39rd5zuqa sharp pull fordwd+i9 z yq336 5rkhbuward?

A box rests on the (frbtwjcm7v2y 1co -2t 0rictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of thec o t0b1t- wcj2ymv7r2 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 (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Explaix9bfptb8s/j*z yq4j l/zm7q/n.

Only one force acts on an object. Can the object hav gu/nuk-/:o1u*mz1o fx-ma xze zero acceleration? Can it have zero velocity? E1- x u xoazmuk*zf/1moug-n/ :xplain.

When a golf ball is dropped to the pavement j *zzu g7m52ynq(*xvt /uyd5vjyix7,, it bounces back up. (a) Is a force needed to make it bounce backu*2gj7t/vz7mzny ,uy qxx5(5 viyd *j up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in o+ikpmyimls g)(i3 6:the opposite direc)3 lpg(my+ksi6miio :tion?

Why might your foot hurt i )myfh2 akyv3*0 vb(sj0t-sb xf you kick a heavy desk or a wall?

  When you are running and wbjor axob4afq mrx.7 n5yl.ql 2/)c) 4ant to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your ownlqb )yfo 54qjo7m.xna24r.ba) rl/ xc 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 fintqao+ 8 +e 57* bz5c,psp. x(kmklktwue thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person kp atu5kw,p 7(*+o8bexc.qk5 slmt+zgives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a agh.3 tkyemu8d gez(pv/ zcx.9s,0+a1-kg rock. Why then u9(g,zyev03e z x / shkdta8pcg+a..m doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon tb zg/8i4vw 7egc0 v5ggive accurate results if the scale had been calibrated (a) in pounds, or (b) iw/gz 8c evtg0v4i7gb 5n kilograms?

You pull a box with a constant force acro/6 wfw7 tp f(/5hbrwnoss a frictionless table using an attached rope held horizontally. If you now pull the rope withwb/nw tow5 /r7pf6( fh the same 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 a i/sy(soy4) rfreely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the o)(syys/i 4oarbject exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object pfu-dqi2r- sip /cw/4when 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 r i2c/- ud/s4fpi-p qwthe Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) 6b(ycdo; qfj7 pulls with equal force on the ;yqdbj7(c6of other team. What, then, determines which team will win?

A person exerts an up m9sndc7+ tdl6ward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by wh+c 9 67ltdsmndat object it is exerted.

When you stand still on the ground, how lar01-ng* q fxpqgge a force does the ground exert on y*qgf npq01 gx-ou? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results2 jdnin;kc:9ip .9iln from an automobile accident when the victim’s car is struck violently from the rear. Explain why thek i9djc.p; n inn:2l9i head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbe*ik3yp*n6 hiym c(sy d-,vx3xd truck. When the truck accelerates, the crate remains where itxys, vn(hc3x * yk6i -ipdy*3m is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slidek/7k9sm 78z jfmy)kj ms up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its)kmy/ mfk8j9 7zj7kms acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined jt-hc8:abr03;gse 4; m c tdmwxeieq 3;x)i2a plane? Assume the mechanism functions properly, even at an anglx idrmi hawc 2 tm:)4ejqtc;3xa30-sgb ee;8;e.

  What force is needed to accelerate a child on a sled a ) n/tp*tpuet1t 1.25m/s$^2$?   

  A net force of 265 N ac:rmi6 zdpa/a04bqm 1 scelerates 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 rope withstand if it ia;c:gld3x b 05zz/u 7 lwjwh9ms 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 n8k;qkk:.,z; qfex tgv : 9al4*cmhjk$76-\mathrm{kg}$ 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 ce8a hjez5 2j+5 t +fdgea1(arnar is traveling 82a+e+aar5 (tjfgz neh 15dje at 95km/h? -  

  What average force is needed 5at6mvgq: 8bu7ymb7 ra7(hqxto accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 mua:7 q5 r(bva7xmtmg6 qh b78y along the barrel of a rifle?   

A fisherman yanks a fish vertically out of thenclc7l4 0/e k;jj7kru water with an acceleration of 2.5jc0jkk; cu/lnl e7r 47 $\mathrm{~m} / \mathrm{s}^{2}$ 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 (n2l6vvbo)nm r6*.jw 0vqorc ; *0wt-zwqkq.k 402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designnr/0jpz5 *zg -vw (xqied so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suppor*pz0vqxjw5 rz / g-(niting 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 motionltz *.gf2- exfk rmhj-t,z0m.m g7k3bt ess elevator. When the elevator begins to move, the scale briefly xfg. zr ,g2-0tte. hfz 3tkm7-*jkmmbreads 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 q.ll qk erc*y7vj,.2x a 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleratiol 2k.erl7y . vc*jq,xqn can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg in3npk*(x*r0-obna( uo0+ b nmtmf .rxhcluding parachute) when the upward force of air resistance is equal to one-fourth of t-o 0*nupxr3x+htb aok.mr mn(0 f n*b(heir 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. Whenyay,y/ 97z95/k-xrspjwjcn 6l jx i6e he strikes the ground below, he i6jeyxy c-wsy7zl/9p k 56rj,xajn/ 9bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a xu81 px2mimvd21 c q ma,tqx z7nucx07p;,z9v table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Dete m1axxt12qmu7z cdi vu8 qz;0pncp2 x79mx,, vrmine 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 f:g*rp1o ii 1z7eceyk:or a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at tb .nlupz n616the moment it is hit by the bat, and again (b) after it has left the banz.1bn6l u pt6t and is flying toward the outfield.

A 650-N force acts in a northwesterly direx .fa7oyxhf48 mx 1 b)wtrou)3ction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwa 3 f 7m))fxarwo841ohyxx.tb urd? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between tw8 ed02rjaulax +o( /eko buildings 10.0 m apart. The sa(k oae xrul 8d+0/2eajg in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket kfohma4gfqr1m6 e *:8 3 xl9fris hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14qst43a1 k;1xn5gdwp/ ;j nidc.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 loca7);pf qjmovl6 tion at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forclv)f m jqpo76;es $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass be2 ll(oqylx o4/hind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between thly lo 24/qo(lxe locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus sh f3dh5sbj +: eq6y6kgmax,s +xown in Fig. 4-48. (a) How hard must she pull downward to rx+ 6yfds jq3m5ex,kh+gas:b 6 aise 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 begankg7h*z5lp wj 3, 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 (massw czpp4ps0 q96 $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in cont*2 s6 o;t i0dnku/-bk ,tq0(e mpzs4kez .sixzact with each other, as shown in Fig. 4-51- q(u; dbn exit.tszz6zo4e2sp0kkm/* s,k0i. 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 x r7ok)ytfwr(0vq7. :m skd q)1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the ())k :yw.xd0strovr 7qkm7 fq 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 kkcxth99yp)8 w,g ip/qhv i5 9heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-5pkcvti px5kg9,h/q y9i 8)w h93. 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 os ,gbv);+oi fff kinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start bbfi-htb( ;.b wohe45a 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 xi+l+bd-*c b+ygswc 47sdo 7utrain accelerating at 0.20g. What minimum coefficient of static friction must exist betwe*cbx gs7b7 oc4d w-+ld us++yien your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coi2gzj :ui 4:,tfyc:ye efficient of static friction between the tires and the ground is ,ji 24cfy::: tiyzegu0.80?   

  The coefficient of static friction betw w.diy* h ns2x.dy (t3aagy/4heen hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you(h *ayx ng2yw4da.3yshd i/t . 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 )(ovl-z dgk*o at -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 robncea03bo )7n ugh 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 g2 b5vom.-nvo a very high coefficient of static fricob.g-o v5n2vm tion.

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 kin*1gq tz/,dlw betic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Ex n)ta2zyko; r/ample 4-20) how large a mass would box A have to have to prevent anr yna/z)2k ot;y motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How farqvgfp( ge;7tktj 830i will it go, given that the coefficient of kinetic friction is 0.20 and the7v (8f0etg i;g3qptjk push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 jb2uy6,leub:0b c2,*g-k qfdem m.ar kg , are in contact and at rest on a horizontal surface (Fig. 4kef bqb,ucj.mb m-g:6l2ad* y02 ,u er-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 friction bogm; o-fgg;1qbtcqk9w 4 j47 tetween the crate and the bed of the truck is 0.75. What is 4 toq79mqckj fg1 ;-w4ogb;gt the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has an ipj)6; e ezhq:1z woc,bncline p ohq1wezz b:)jc ,;e6of 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 2.d8 .:lobo(4 ccsestd 8$^{\circ}$ 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 atm b37( qxrhy 6fi,moj2 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 init 5w7 wx u-nf:0ttkz2lfial 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:u,5: l zcvt3vq6uupy the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by someone pushi 4 dpeke8(3b8xlyqwqy f:5v/ hng on it with a for/8blxhf 4:e( qvq3wy5p y8dkece 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 dangerous projectilemsoow4. tqh3 ahh75i2s as they melt. Consider a chunk of snow at hqwosi2h.t75 aom h43the 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(*-yxzh9k ufb f7u3sy automobile traveling at speed9su3 xh(*kzuy-fb f y7 v is 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 slidevke j*f01z/n7wu+us(a k3vqu s forward on the dash when the driver decelerates from 4vseku7 va0wk3 f1/ (zuuqnj*+5 $\mathrm{~km} / \mathrm{h}$ 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 mass3t 1b5unqwrk2 m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to theymu1;1uc90acak r /vs packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficien/u ;a 9r01sm 1yacuvkct 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 coefficient7 vi8o66jevhx3 zvxp4 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 65mwwks6y1e1s+ y ,usylqz6y4 : kg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at e-)juem gt. ;nys7on niaf+*.dach pulse approximately 20mi.u.nj- do at+n*ne ;gf)ys 7 g 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 an automobile cras6dn* y23efm5dxp ox2rh if the deceleration is no more than 30 " g 's." Calculate the forc35p e22y*fm6xdronx de 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 +owkh1 -g0mvu, and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the 0+mh-wvg ouk1 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, exabnr;ihwqa +l5noo +- jnm,7b2mining 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 nibwnrnb, -+2lo5mhao+7; q j that car assuming a level road.   

  A car starts rolling downnr ;hgxisd1u1 s;/2xl a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1/gs2x l1i s;;d rxnh1u 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 Tomv f1 sv.j, hi-f-v0kgwer of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of aifigv0f1.-v, jv m-shk r resistance?   

  A cyclist is coasting at a steadb+1ny k8pugl 811er2w b0oftsy speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emergeebwy208 nu rt1kg o+81lp1fbs 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 workin(3 ;yefy( w7sdc;sncqg on the redesign 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 down. A particular small car, with a mass of 1100 kg , can accelerate on a level qf(y(c ;n73;scwesd y 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 experiments, s dm9i *kzy kpzrh- :2r5hmd.3dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airporzdh 3k*5.dysr :9 mmizr-hkp 2t (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a super1q- t5ohao 8ahc4er;k6z vb-nmarket, there are to be several ramps connecting different parts of the st ; 4qnoebcoatah1 kr58-hz6-vore.
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 to2ln3uh6m 7m fc lift the piano (mass M ) using the pulley apparatus shown m7 6hc2mn lu3fin

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 accelerating -9brj:xcb 8-khssfb tv+h,2u6b7zvg 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 ch(kq -y8erinj b* 4k;spo07 hphild-restraint chair, an engineer considers the following set of conditi4bj 8p7nyh shr kp-ei(0*;kqoons:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,000qv:v i yyvou287yw 39u $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar lengthd a ;z)7rgj,3,bmg.a)gy fc: qo,sntg . 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 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 bysmd),ta3, jco.nf 7zgr,)agq; g :ghim? Which climber is more likely to be hurt?

A fisherman in a boat is ag p;9ysqdm*/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 b ucnsjz8,9)r kuilding 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 are roped together are ascending an p)m9 ce zfu*r 4qkr3y/ice field inclined 4zrmc)/*9 f3 eqpuykrat 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.