Why does a child in a wagon seem to fall bac2dgyq xe 2w, fs;1i3urkward when you give the wagon a sharp pull fo,g;3fi2 dwxr1usyqe 2 rward?

A box rests on the (frictionless) be6 je2c- ;qv/f mxahx/ y)gj)twd of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, avw//) cfjem;qxt2)yg j6h -ax s 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 f s8/pix 3z 6/mifzwe:no forces acting on it? Explain.

Only one force acts on an object. Can the obyp-gg jl3q 64da-r f:gject have zero acceleration? Can it have zero velocity? E3j gr fpq :yg-6g4dl-axplain.

When a golf ball is dropped to the pavement, it bounce) ag6xhn ,zji0s back up. (a) Is a force needed to make it bounce back u0a x,)gh6 ijznp? (b) If so, what exerts the force?

If you walk along a log floating on a lakex5-3jbkfoxp5 2 qj5w n b(tl:e/iql* u, why does the log move in the opposite dkq wxji55*luebfl53bp t -x2(/:qjonirection?

Why might your foot hurt if you kick a heavy desk or a 4zivwpr3pif gy/v3cg:omsi ;( ( )d w:sem6 *swall?

  When you are runningr , gs-yre:9kcb f;z:e and want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience gr e-rscz:9: y,kf;be) 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 thre 3 ;di:jlt+xcs.l3qwuvvc46 jad from the ceiling, and a section of the same threa ;4 3djixlvq.cc w6uj3v+ :ltsd 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? 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 jr m jws46x3gid g2)thj.;7eogreat as that on a 1-kg rock. Why then doesn’t the heavies.ej ;omjihd t63ggx2w74 )r jr rock fall faster?

Would a spring scale carried to the Moon give accurate results if thvhimkayj *ee3 /164jre scale had been calibrated (a) in pyhj 3 r64*kemj /ieva1ounds, or (b) in kilograms?

You pull a box with a constant force hkqjnjgcn0bq 7m . : kd6rr104across 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 17nkr j 64.k0bmjgq0r nchqd:flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freevv/1 p.v m)0tlwd*xas9eir/at( bc)dly under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the objecdli*a( bemvvst9 x0/p r cw.)1vtda/)t 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 when you ax2bdax3k.jp 67q8gumyy 9nm2 re 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 on9yy 2.m37ax 2 mxqb8gpudk jn6 the Moon and on Earth.

According to Newton’s third law, eaci cpvaqj8(u58ikld-( co )-dl h team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team wa )p-ld8 (cd-ikol58uivjc( q ill win?

A person exerts an upward force of 40 N x) x;mgopb d*+ule7 mt:)iha3 to hold a bag of groceries. Describe the “reaction” force (Newton’s thi*hxa 7) x+ mb3 p;eu:)tgdmiolrd 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 the grh1(zounj/ ydn 38(iry ound exert on you? Why doesn’t this force make you izn y 3o8nh(1d (ru/yjrise up into the air?

Whiplash sometimes results from an automobi2l.;:bk)de nu pcaw kddoh991le accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backw.oa :d19n9dbdchk ul 2e;pk)ward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,(sjg3hbxu g7;rd- s(1xyvyjhxq3 *+oie + x6k the crate remains where it is on th7r-k* yg x q16xe+3 byh s ;gud(svxoxi(+jh3je truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that p h4(xp( 6fbmhit slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less(pp hxb h(m6f4 on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incliwz-oxs1 *k g)-hth6g tt*zyjh:.q:t b ned plane? Assume- h z :qsttozkg)gb:w t yh.*-jt*x61h the mechanism functions properly, even at an angle.

  What force is needed to t45f,,hzhyr9 r1jb3kpf j8d daccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike an/lfel2t5 :1qu8 l cxrsd 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 is used to accey2x-zg7t7 lgy9 h j4 e2jndn)xlerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a31fkt qv 7zl/ ;o3, oml*r7 likdw8pgc $76-\mathrm{kg}$ 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 requiredpct)6,9 *jcwt+w eycurfqc 28ly v -8d to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? ,eyq*8tj c)8v 6-lrfwtcdcc pw2 +9uy -  

  What average force is neq rut4j;7xh)52em cyzeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alorcx qz2;h)met 7j 54yung the barrel of a rifle?   

A fisherman yanks a fish vesrcsdp-8n v ej34vf zamrd (0 qq)c,-.rtically out of the water with an acceleration of 2.5 0j8q4n3,(r-sv zdscdqm a rf)- pevc.$\mathrm{~m} / \mathrm{s}^{2}$ 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 quar.vtc . hu a-oe/qulq47ter-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 ) is to be designed so thk5 :w76lm.yo*o y;c pbp3c xixat the maximum acceleration is 0.0680 g . Whaw 7blpckox.c3xy ;p5 *omy6i:t are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scaleg mw oba*c34h52wk *mhv g+run8 0fc2z in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Camc+ gawc *8hmubg2vk r fo53hnz20*4wlculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator hhy(jqz .7j2a zas a maximum strength of 21,750 N. What maximum jzz2h( qj 7ya.upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sdh6z/ 1w9 ix9rkt rtv5ky divers (mass 132 kg including parachute) whe1 9hvi6rt9wdx kztr/ 5n 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 thez -urvg311ch8uz(0 /z h mykaw roof of a house 3.9-m high. When he strikes the ground below, he bends (/z8g hw1-mazkhc301zuu yr v 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 oc - oxdx(k/-zbv0n,urests on a 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). Determine the force that the table exe0k(-xd n,- ozvbux/corts 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 player 8v 6lspiv;q(v5 vp h4t
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it x6 +/eq1nxnntis hit by the bat, and again (b) after it has left the bat ande 6nxtq1 xnn/+ is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be hmtoth0 )3xh-vq ,yf)exerted i) ,xthh0oh)m- qvtf3yn what direction so that the 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 buildings. sbof *u0irf2 10.0 m apart. The ofrs*ibu 20 f.sag 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 is-v hl;n(bg ooq+,lk8 p 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 14.01uo22bl03ggd im zp+ e$-\mathrm{kg}$ 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 all-h9)t *p7nygyw ey0 new location at McMurdo Base, Antarctica, asyl9ngy y)p l he0t*w-7 shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-4o 6i5f:.jnpyb 7 . Determine the ratio of the te5j i.yn ofp6:bnsion 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-pulley a s()*vq+ryp6v g5oootw 7, aelpparatus shown in Fig. 4-48p) +oqve a5l t7(or,o*6 ygsvw. (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 race began, a v 6j,.x wtpvf/*z2 vns65$-\mathrm{kg}$ 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 bloc0mn0py sdf4mpmp j, )*k (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in co ujtilm :k1n9opin)j s(;( f3lntact with each other, as shown imln3p1iits:ul9on)(f ;k( jjn Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the groun f6sbcx0j(nog bz6w zeo6/;f;d, 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 acceleratie;zc nbwf;06(6o 6g zsbjxfo /on 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 frictimgz*iw ::vcv9r gl u9r.60ggkonless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tensimu:wvg 6 ggivc9l *r:gr 90kz.on 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 of7)8b ssrf:q rl 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 sta szyweit 44e7zo *k-0brt 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 train accelerating ;u ,vu*vnq vm;09 eh,vvz)tfhiss-r 6at 0.20g. What minimum coeffic,f vzesn6-qr;vuhiu0) v;sv v, h9t* mient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sl ,wv0/ xf8zxdtatic friction between the tires and the gro8zwxx/d,fl 0 vund is 0.80?   

  The coefficient of static fr q 1a,qodvt;z l/0;thj t.ju*liction between hard rubber and normal street pavement is about 0.8. On.u,t q /;1vaql z0jl o;tdtjh* 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 477 jg3 nqxdxnov +er8c,s:ky 4fb,jd 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 advt1rca*p1eu 7g pn03nc 4,ro rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very3.nx 7k8gbqtu5nyd t 3 high coefficient of stattk5t yq n.3dub73x ng8ic 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 friction for ; 8u .eq9 gbvcb(efc1*)wbm sla $ 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 (salx7cuyr6+q gbmba o:5c +63 Example 4-20) how large a mass would box A have to have to prevent any motion frcb: mu yg5a r+6s+oxlb73ca6q om occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it s 3wg1wgfkp85d*kfhrc t-;4 6 d)rmjhulides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push g1;5u 6dt48* rmfrhfpjck-)hwgd 3 kwimparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on acty- vj m )*7qr;vz rns10nv6e horizontal svj;eq)v7 r60nm- r n1yszcvt*urface (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 ;pj y,6c6zwpk;.2lwcm,mjn n coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum6n 6 w;. n;zyc,mjcpw m,2lpjk 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, wha7s-r 2w sv (47h tg2*r;h k(jcuemps0gqnka9ich has an im 4kavs*k(h7rcpg qe ausj922-0 7rnws g t;h(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 with a qjn, jj:v 7 ev*q7c/-qncb5ws 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 d:,vw/djt6 rv4/qjn qFig. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spewga) /or 1a3xwrl(pjh )9a9m8 gqzg ,fed 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 hiltsz(h6;q ncwc k-ae 51l 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 plac4w *5vuu ok(rt3jlc*v e against a rough wall by someone pushing on it with a force directed upwaok(*r4 t 5ulc3*v wvujrd 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 sli . ls6t:rra33qxs u)+rss x mix7je52y2p8q vlppery roofs can become dangerous projectiles as they melt. Consider a chunk 8 rs qx rq:tx.j6lrl5yv+xum2saei7 )sp332sof snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimumbfm (2iqhx( .u stopping distance for an automobile traveling at speed v ximq2h fu.(( b 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 slides forward on the dash when the driv:wn-zuw.f;l 6 xbb9q uer decelerates from . uq 6w bzf:9wnulb-x;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 mas-r1e cfn;vfuy,njsr fn)-r *7 s 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 the packing stow8lcjl1-nq*/ wwc s ,dh94n mation 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is thq hwl8 c91jw mnc/on-dsw*4 ,le 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 coefficiebaxg) 9qqi*6j+kzd23n ajska77n.jh nt of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast dtw 2e. ) gsdxucj3/io7own 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 each pulse approximatelma)mazb: q14 cy 20 g of :qa4 )bcmam1zblood 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 ij/6wie,yy tx bluqem1-2qh/a.q f6 )surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the formeq -iwxay6/f hu,i qel1.tqy/j62b)ce 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 producedg*c+on6lawxe/8w p s 81mbvr. by an earthquake is a , and if an object is going tw w/sa 8oe xr1l8.pmcvg+ nb*6o "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 th 6hlz,e2 kem n)su2l:oe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearlns 2ezem hkl6,)uol :2y 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 level road.   

  A car starts rolling down a 1-in-4 hil;,9wf7-3 ae :+co aocjgwewail (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 frico9ac;awicw -j+3eo ag 7e ,f:wtion.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the wfa9 o7iop9o (Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average 9(wp9oio 7fa oforce of air resistance?   

  A cyclist is coasting at a steady speed of 126s*tcb(+ l*x v.bxu,9ilb qn cm/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for*b bxl( cqxvlt9s*+i.6,uc bn 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An impyl -6b t 2dyt36v:ccpbortant 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 a6 c6l-cpyt 3byt:vb2dccelerate 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 uyv)h)z- qblm nykn54i3)o9wm ybt;2 experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Jz5n))-n;qv t kub2h9 w4ly y)mb3iymo FK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, thereoiz ,jejj. f+pa.na e2h3h7/o are to be several ramps connecting different parts ,ohap.i3. efaej 7nzo jj/2h+ 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 nk8zfaa7 u vsbs /,-u/reeded to lift the piano (mass M ) using the pulley apparatus shown inuarsvs- //z f7au8k,b

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 acceleratingx ;ousjy-o69 ui-da/x 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 chilnko2o7y 0lo.fd-restraint chair, an engineer considers the followilo k70o.ofn2 yng set 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 Italian train has a masso;8ee ha; jv6g 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 sim0wp6*g eat8nailar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the 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 clinw g6*apet80 amber is more likely to be hurt?

A fisherman in a boat is usin14y kxn:kldq5(v-l nc 3 wgvz6g 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 ry7n8tw zit 0f9each 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 arzvn4-v. ,ohoxp6+ 6nvt s xx2ie roped together are ascending an ice field inclinedi-4, xo v.2tno6s 6pxhnvx+vz at 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.