Why does a child in a wagon seem to fwaz+k fkn+q 3z6-dn .hdi)h)i all backward when you give the wagon a sharp.zw d-nfkha6)iizh )+q kd+n3 pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the t8el m8v+jad+g+0 6r buye h 7,tbyz2wlruck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on h2 z0yuab,j+by+lr ewl86v7ed+g 8mtthe truck

If the acceleration of wn 5 .t*ux(dzy1z jup:q(ugyd / )tj/fan object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelera (mht 3avuniek n, 8/bomv3/f4tion? Can it have zero velociti3kbhm n/(uao8 4e /v,fnt v3my? Explain.

When a golf ball is dropped to the pavement, it bounces back db4n )b2 plnv9up. (a) Is a force needed to make it bounce back p4dl bn n)9b2vup? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in thel5;qfi m fx1ep(,kzq( opposite directi (p qze5(;flmx1,fiq kon?

Why might your foot hurt if you kick a heavy dwul1vna-w7j 8m uf(; iesk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) +dqui7 5 .sw+z2cv ixuWhat is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running atsi 2+dz7u.wi qv +5xcu top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section ofk .xc)jq*n6c 3i) hdof the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likeqx*h.ki6j)cndfc )3 o ly 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 1-kg rockp:.bx m2(9evi i3mj xa:ddd 4w. Why then doesn’t the heavier rock f :e4.xi :ibdv3d(dja9mw xm p2all faster?

Would a spring scale carriqq u26js ur/+ned to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in k n6sq/2+jqur uilograms?

You pull a box with a cons vzv*ugt;n nm3-y4nx,tant force across a frictionless table using an attached rope held horizontally. If ;4vnntyv m xun-g3,*zyou now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of s1*g *-e-w,bhgm bwblyx+b y3gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t thewsb-yb1,** hb-gbl3w+ xm gey Earth move?

Compare the effort (or force) needed to lift a 10-kg object wheesw 82v (ju* 6dhi4kyan you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object h6h* v(sid j82ykue 4aworizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37)i (y0bf-8c,+gjj y +wy eum yhuz9g1j* pulls with equal fwf jy i8yg(+cju*b0- 1 jzh9y, y+emguorce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to holdz jndszdbr6/5n55h fv+h8 bg5 a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its/+r dg55 dz 65bhfsnh znv85bj 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 ground exert onc4;a5yz-a m .r:bxkrx you? Why doesn’t th4mkz. abc-rr y; a:x5xis force make you rise up into the air?

Whiplash sometimes results from an automobile accideg. z2b. zeqj2jnt when the victim’s car is struck violently from the rear. Explain why the head of the vi2gj .j e.qzz2bctim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed e blt s/wq+bo5smpy.(,3vlh; truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes tml5.bs3/y vwt+ho;(be,p qsl he crate to accelerate?

A block is given a push so )3can c+emht ie4y;3 bthat it slides up a ramp. After the block reaches its highest point, i4ehb;3 cma3tn c+iye )t slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if yx(01. apgi1*xxxz+i6bf ayf jou weighed yourself on an inclined plane? Assume the mechanism functions properly, even at .*10xz(j gff1ibp+xa ix6a xyan angle.

  What force is needed to accelerate a ch8trr)vl;jd 4fild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerateszqhyek 1 )9a1owm2z5r 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 is used to accelerate fnt nb u- ruo s)v3:8ufz-+/iha 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of ,tfew)( 0qz/f+ ohh yfa $76-\mathrm{kg}$ 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 ca2jeyc*4djblih9whg8) zh m 9vlx; x7,r is traveling at d8j lh;i,vly w c g)h7b*xhmzx492e9j 95km/h? -  

  What average force is needed to acc2n 3/cqpgu8d celerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alonggd/ pnc8cqu2 3 the barrel of a rifle?   

A fisherman yanks a fish vertically out of the u7z;jbb 8,y, wl i0ckbwater with an acceleration of 2.5ybulz j,0bicbw 8,7;k $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (402 /87.y;iak 2hilb uksh$\mathrm{~m}$) 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 desdcin5 8)us1hc d hv),apfl(o3y0j/k gigned so that the maximum acceleration is 0.0680 g 5 nfdv(/pl)1h, k) 03jcdgsc8ho u aiy. What 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 scale pq5(u 1rd,oqo oj5ie s- 36aygin a motionless elevator. When the elevator begins tiu o-r1sqd3jy5ap,6 q( og5eoo 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 streng.b2wy8*; qivq1 li+ ,fvikwssth of 21,750 N. What maximum upward acceleration can it give the elevator without bresfkl*qw, iywbs18ivi+q;2v .aking?    ( two decimal places)

  (a) What is the accelera:y te(tir h p4rj5w)q.tion of two falling sky divers (mass 132 kg including parachute) when the upward force of air resis5w phrte:ij)(q. ytr4tance 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 roof of a house 3.9-m high. When he strikes the ground bfo+ez vp:txy19-g dq0 elow, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is0vtp zox+g:q-dfy e1 9 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 vxct k7 2ljt*8o8lz,gno+,chto 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 exerts on the boxoghotcv j ,nk+lc l8 ,t2z8x7* 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 pla hlc5sb-dhu(7ke b,b.yer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the bf9w sd8 4f t/wnkgvbjg:g8 (:cat, and agwk v9:g/4b :8f(8t ngd fgcsjwain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dirucg. 3 nyw:a)qection. A second 650-N force must be exerted in what direction so that qcayn)3w gu.:the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" stru zt ad8f89no 8tm:me9fng horizontally between two buildings 10.0 m apart. The sag in t:t9 e8odtfm9a fzn 8m8he 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 ham0a;. 7. veaxpmkc ly4nging 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 14.0 s2nci ar::j0;chpol(g 5a4de $-\mathrm{kg}$ 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 housinr( .y)3 zlki*e)qt qi2dxu/lwg unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces ke*lu i () z.2q3 wxlqdtiyr/) $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 sam0 d dpd)pre5;2pz jhg:bis+ pyy .i,0ee mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotivebje+ps ) d ypieg0r 5d;zp:0 ,iph.d2y 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 apparato4q9j rebfnapz9 -b.(f+v4ylus shown in Fig. 4-48. (a) Howjfqy9 9f4pbl bvz+(e-na r.4o 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 /ivjm 7:z ,h);l:rikgtb5t nw65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass k(nz*48*7;pll hwu -uambxjh $ 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 frictiq7/ou yw+ my*vonless horizontal surface are in contact with each other, as shown mywv/ u7y+ oq*in 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 grounbq*wme / vu4y;2*jgri 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 acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "y;42* r wvemq/u*bigj launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a friction(r/mjo p. c mi*gq,k2kless table are connected by a heavy cord of mass 1.0 kg . Calculate the accm(j. ki,2 *org/ckqpmeleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic fric ci8(g5bp 4bkjtion 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 a ea wb/a) ev/3du tfu)cj/5p(a5.0$-\mathrm{kg}$ 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*gw2+ +gswcth on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and thesw gt2*hcw g++ floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stati1 50tk( v qctbtgwc-:qc friction between the tires and the ground is 0.kct1q:v q c-(wt5tg b080?   

  The coefficient of static friction between6oirld ad qk/es+:h9 gafxl30+ cs7a0 hard rubber and normal street pavement i0dk73s9idl hrxso:a+ 0lqaf g/6a+ces about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate hw4 atrana6s8qxqo1p v6mq+g8 z;) 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 v77 i;ny uf;(qgk iz9*8hgarm on a 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 very high coefficient xt ou986qsc1v of static friction.sx6vc9 t81 qou

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 f uk;t6huy wi3;or 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 (Example 4-20) how large a ma9j a 7oaz7xor--obnc3ss would box A have to haveox 7a9o a-3zb-cjrn7o to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Hownd dzkrz wl,ad8 )58(b1x/ 4gnanz0 ob far will it go, given that the coefficient of kinetic friction is 0.20 andb 1/nr(d 4 waz)lo,z0 b 8ddxgz85nkan the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact adm0na zga;y.3nd at rest on a horizontal surface (Fi.y3m0dz aang ;g. 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 stati f3x)m. vh)u) (veqipyc friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab)).yuqx ep3vv)him(f of the truck?   

On an icy day, you worry about parking your c*zuk- p2w7 vy ivr1xptwg) wj6n0y.)x ar in your driveway, which has an injv xyxi 2u*rtyzp.1gn7-p0w w ))6 wkvcline 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/i rda9(m(yd a 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 nbgjzn3 m .+h8hbu+l 3at 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 initialx p99wen - uifp /x9t;a/y6uv2uya0zl 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 t47 n khp3 ec+kznoqjoc7:le;h3 o0 yg+he 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 w6d(twcj0m;r (1yg+dyk0 z o/. qvebsin place against a rough wall by someone pushing on it with a force dir06z0 ddkt+ cgewwbry(ov y .s/ q;j(m1ected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they lof lpg2xq,v4k 6:n curf4 n(cfl*) 1rmelt. Consider a c6pn24nfr)x lgocfc ,k4frq: * (vlu 1lhunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum swi. fjvzw89 sz/70f p )2koe1wp8udlmtopping distance for an automobile traveling at speed v is equal7z/. 2kfl9u08 dpfwmi) p8wv zow 1sej 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 k m14j.t en/ wgo0a7ydof a car slides forward on the dash when the driver decelerates from gjm4tw/.yn 0d ak71oe45 $\mathrm{~km} / \mathrm{h}$ 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 initiaobwa;yltkg86 51u t6 bl 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 paunwtgz u2 u.h()hq1u5cking station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accou2w)qun1h h(.zug5t umplished 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 coefficient8ug sq+m kd/w; 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 dot8-gc a/9n.f tpu w45llew )lmwn 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 simplakepj gbg2./0 js*z/d. pibl1 ified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0gi0a.1/b/e2pz* .gj pjds b kl.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 crash if thexj 5h0 h,j+46wkjmv lo deceleration is no more than 30 " g 's." Calculate the force onjk j0vjom+l4 h ,6w5xh 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 i*ood w w) j1bgvc+89an0w4rgqf an object is going to "hold its place" on the ground, show that the coefficient of static fr9bjo8wqov)+r w c0g 1dng4*a wiction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scx:/q rcr+2l vkene 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 aboutxrv r:l k+qc2/ 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each ze-72 ;)horx lw9uqbw 4 m traveled along the roa7 hburw wl2qezo9;-x) d, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppbu0(zley -+kb;m+ub s0l4ydl-ft/bb lwj/ r; ed from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Whats-lbbbe; uwytf 0(b -bkl/+/4lljyzr ;+m u0d was the average force of air resistance?   

  A cyclist is coastingxaf /w5 y-/hwkt)1didfgx*1 h0 p 4jwr at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the mudhf4ida15p-txw j/w0/wdf rh)x ky *1g dy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilp biz s+0v xea47ac:s o()8tmlly 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 masa em)b8vxs0o ias tz:c+47l p(s of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physicnex khbeh sux :0 w)(n8u06rn7s experiments, dangles her watch from a thin piece of string whilusu):ennbw xxhh60 7n0 rk e8(e the jetliner she is in takes off from JFK 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, ther;x/rmyrh nrj p;l9.u96w)l ije are to be several ramps connecting differer/ 9.l ui)hymwrl;;9njxpjr6nt parts 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 t:zyfpdpp-r(q :zi+y0o r 2j2 jo lift the piano (mass M ) using the pulley apparatus 02rzoi y-:jp jfp2( rdq :+pzyshown 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 acceler-f;yhh ucy6 iitkbhb:cuh *x,.:-2i jating 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 foref rb6b+am( 9r a child-restraint chair, an engineer considers the following set of conditiof+a rme6(br9b ns:
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-c binv;p 1 )f8-t.thpmear Italian 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 mwum vtf:- k 9.yzlr77of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro c.:w lfk9vzmtmu yr7 7-limbing. 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 climber is more likely to be hurt?

A fisherman in a boat isg:pc8 2 r9zz 9qi w:ridqw;8kb 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 bub7nhc:cix:*ss1+m kyexd 0r 4 qjrs/1 ilding 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 climberen*pyq6*3d (d2, .jb p n.8alrzccters who are roped together are ascending an ice field inclined ,n.bj 2cd*n t8 ry*d p3(6p.qezlaecrat 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.