Why does a child in a wagon seem to fall backward when you give the w78 e,yeviz 5d4paruu 6agon a sharp pull forward56 4,peuvdiy7z ruae 8?

A box rests on the (frictionless) bed of ayc9n* qy ih)9n 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, as seen (a) by Mary sta) n9cqiy9 *yhnnding 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 aacdjf v(vt9d/2.g *jacting on it? Explain.

Only one force acts on an object. Can the object have zero accelersdea.y) rho8vv5bi)4f+ c v f;ation? Can it have zero velocitbadi) h frv8fvo5yc;)s ve.4 +y? Explain.

When a golf ball is dropped to the pavement, it bounces back upb*sf7;b pd*jj. (a) Is a force needed to make it bounce back up? (b) If so, what exerjp7;b*jb d* sfts the force?

If you walk along a log floating on a lake, whtbvl/fondv3.4k3 m9 u y does the log move in the opposite dir 4f3dtmb luok9.v3vn/ection?

Why might your foot hurt if you ki b r drgnrd429;a)bx-nck a heavy desk or a wall?

  When you are running and want to stop quickly, you mul) 7alf6 xw3ql osjd28st decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a p7 j23wsf8qdal6lx o)l erson running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, andn-kjxqj bu9 d;.6 q7qb a section of 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 likely to break: below the stone or above it? What if the person gives a slow bnj bkd79;qq-xu.j6qand steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock.elzi18zcce2 9 Why then doesn’t the heavier1e8i e9cc z2zl rock fall faster?

Would a spring scale carried to the Moon give accurate results if the ca4i3rd h pyc*xa9b ;7e8msc9scale had been calibrated (a) in pounds, or (b) in ki;9dy7i 4sre 8hm3a x*9ba ccpclograms?

You pull a box with a constant force across a frictionless table using *.,9 0 znq c/qpos x*o8lwquidan attached rope held horizontally. If you now cn9 uqp.0*z*x/wqsliqod8,o 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 gravity thcyx:7pk.f kn5,q68- d g zxqyq3bsfx8ere is a net force mg exerted on it by the Ecp f 6-knq,3:xbyqxs8 k z7ygd 5fx.8qarth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) ne)hvqs5 io,g3(cq4m0n)xe ug ; rsg0jgeded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the forc;gq 0i3oe,qsggx5rc4 (nvh0ug j)ms )e needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of wpqpqx uy;9fs5hn-3 ,war (Fig. 4–37) pulls with equal force on the other team. What, then, determin p5xfp3q,w9h;nuq-sy es which team will win?

A person exerts an upward force of 40 N to hold a bag of groceriekk .wkh3 mlmm59 0jh.b .fmx.rs. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its dimmfmr3 .hxk.j5m90 .bkkl w.hrection, (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 gr ihtd)7l/v yi/ound exert on you? Why doesn’t this force mak )tvyi dl7i//he you rise up into the air?

Whiplash sometimes results from an automobile accidl; apf+r(m ab- x5b7rfent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in rb fax+f-l a(r7;m p5bthis situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, l7+f +ig rp,/iz w0w atfc(xl8the crate remains where it is on the truck,pllcta 7+f +80riwgi (zw,fx / so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaccl+r k-s24hfl hes itsk l4fr-l 2hs+c highest point, it 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 you weighed yourself on an inclined plvp35h 9lyk/d 2 */ahncvbt. mgane? Assume / *cvhyn92pk3a.gmbd/t v l5hthe mechanism functions properly, even at an angle.

  What force is needed to ac2iqywn nx 4r.v)g57m, adiu6.r 2 1brveckt9mcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acgjx.ywz 5vpc+u i; :ab19x( zscelerates 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 iskmfv(myb 2 *7t+lha 9u 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 d)gqmf5ht .h7 $76-\mathrm{kg}$ 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 kf(38gml, 8s s;fj 5drkayrib+ta6h; 1100-kg car in 8.0 s if the car is travelij 3; kr;y,ts ff 68kr(h d+bs5magal8ing at 95km/h? -  

  What average force is needed to accelerate a 7.00-bdvvdpz 2eclo .9fx/ /(0- dllgram pellet from rest to 125m/s over a distance of 0.800 m along the barrel ofl cd d.d xvv-2/l(p9/bzof0le a rifle?   

A fisherman yanks a fish verticalmn6;i1 3m e7 h ;vf9pfgyqp9-zoi4joely out of the water with an acceleration of 2.p3f eo7mo9yn9 zmqi6 h4;e1iv f-g;j p5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 (4usu; d;/c-o c8gv3taz02 $\mathrm{~m}$) 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 that the maximum a:: -gi0w5fhvyrp0tu w cceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cablergt 5- hf0wyv0 :pu:iw? max =    min =   

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

  A person stands on a bathroom scale in a motionless el*hmha.jz4 hevtp s .55 ,u;xjsevator. When the elevator begins to move*x.u s; ,pjhzveh ht5m.45sja, 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 212 gwsp/:o2a( 8cf 4 2 ctw-,tlreikcyq65-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it g4e/qpy(r:f t,wa2 c-l6c cws i kt2go8ive the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling ;4/sq4tt lpknk/vdsaw-0 m,msky divers (mass 132 kg including parachute) when the upward force of air resistanceq0t4t, va /m pk /;kldw4nssm- 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 v00 2yoc*+h*ijwout roof of a house 3.9-m high. When he strikes the ground below, he bends his know0 yzv+uh** i2 cojt0ees 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 table. A rope tied to the box za s0/ 5d1 ;qxtlyyc/ow. icb2runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table e2w ;dao1t cl/5sybq/0 iczyx. xerts 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 diageg,1xplj :c(m ram for 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 the moment it ixlm;ju1 bi69 bs hit by the bat, and ag16bbj i xl9m;uain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A ho6d,bwbp ,i;second 650-N force must be exerted in what direction so tho 6;, whpbb,diat the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontalvgq o4 r.xfjg 8(nafr25y5d1wly between two buildings 10.0 ma8xjf1rgr wqvf4 o52.g dn( y5 apart. The 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 hanging bv30 vy c ,/,qnjql5mjty 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 1 (ujz )/shybj*0-urhb4.0$-\mathrm{kg}$ 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 location at McMurdo Base, Antarcticuc-3cgg*7)d o thncx 8a, as shown in Fig.3hgn 87)xctccgu*- d o 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 sf o(of9zg0h;e9z6edpk dl+xb)oa 9 6lpk;g p5ame mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and klolzpz (g66o;d p;9o99p0+ xfhka5dbegf)e 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 apparatutkdm8 8 ,f)dsrs shown in Fig. 4-48) ,d kdfrt8sm8. (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 be4i:j8fsy0v9 pxun3 n+d-ylm fgan, 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 (maa91 be:vxx ww7ss $ 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 frictid sk 4yoh)cb49onless horizontal surface are in contact with each other, as shown in Figcdo hy44ks) 9b. 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 initiall5dtaghe z rfq j6qx1e3k 5c-94y 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Astchzq4r af 3 xeqjg1-dk65e95sume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are conn mess(o* 2y5ja+rm0zfected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension5 0fj szasmrm(2yo*e+ at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction betweenw1 pbqho lz/ppb5 vq(xlg)t;)y9h1 8g 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 is4 sdhtu9i.:tg required to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at q ul lu60a5qu zv72lo;0.20g. What minimum coefficient of static friction must exist between your feet and the fll6 7uol5luvq qu0;za2 oor if you are not to slide?   

  What is the maximum acmt.u u:ocv+5mceleration a car can undergo if the coefficient of static friction between the tires and the ground i+ tumm.oc :uv5s 0.80?   

  The coefficient of static friction between hard rubber and normal street pa0ov, gq y gpp.f-si-i-rd.a;fvement is about 0.8. On how steep a hill (maximum angle) can you leave a car-q i-gy;.go- ,fpfrv.d0ai ps 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 oyr*x4;q n.x n3mgau. 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 dldb3 0io;if78m6ty ga 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 wit1xzso-qs( f3cr 2 onvt3j0l1lh an asphalt surface have a very high coefficient of stxqo31v 3 c2lozst rjl(-01 fnsatic 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 cnm. u31crvz)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 (Example 4-20) how large a mass would box A havtnl3v85+ hmzux 9-j pye to have to prevent any motion from occzlv8x5 htny m39p+-juurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wipl24gzz4 8hlbll it go, given that the coefficie 4g428zplblhznt of kinetic friction is 0.20 and 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 and at 4/yt belq+ hhq )k),obvg28r lrest on a horizontal surface (Figek/qh ,8))+ h ro2 bby4tllgvq. 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 o0epxz(pph1 7j + ajz;wf static friction between thz 0+z p;j7apwjxe (p1he crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking youg. 0n p-hw f6p9jyrshstws7 d/,rq6(g r car in your driveway, which has an incline oy thn0ssf hdpqwsr/96 -gw( 6r7gp. j,f 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 3i1x4ehggrzxp*1wm i/ih :i8a 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 oj4ndptt ftq e8),4,nd n 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 speed ov3fta sp;:(uw r6b7u23vze q of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 6.x2yd -lq8;t lgpu+xxqv+gm2 (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 ag ;m2yrj(i**e zq8gy)illf r 5vainst a rough wall by someone pushing on it with a force directed ir*(8)e;izvg *jyql mf2 yrl5 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 dc cutz)ggx3; 9angerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch oz9gx; )gc3t cuf $ 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 automobile trav:4k6; dea-m 7*vv keq t4husafeling at speed v 47m v*4uv6de-aftk shq ;k a:e 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 fokbrr750w)vobxy 3 +bqrward on the dash when the driver decelerates from 45bk7wx)vrr+qyob0 b5 3 $\mathrm{~km} / \mathrm{h}$ 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 initial yqynme4nvqj, /()dd4 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 packio lffpl*d) z39ng 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 coefficient of static friction between a box and t flz*l )3fd9pohe belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kineticq -k+5qy .mmv9i3 nedi,x5qvu 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 down a 6o 8j lqo/:ybm n+d4c2v.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 qt5) p3zps2buv7l6l jheart, at each pulse approximately 20 g of blood is ac) lp73luq bzv6s2tj5pcelerated 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 cr sulbovr xa.ub20*,;nash if the deceleration is no more than 30 " g 's." Calcu r,ub2uob;ls vxa*0. nlate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced l-b0w t5e6kgchgq;z (by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with thezg6c- 5 l0wt;h(bqkge 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 l0a /o2yf znpch4zs2*the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came t cl pz*2 azo24hfny/s0o 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 hill (1s:/cpm . g2,.hne kwwzwxn8(s-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) Ignorepnsm( ge8kxw,2sw/ ..znwc : h 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 Towerd0ean)d-z7j9 z s slx+cou09y of Pisa and falls 55 m before reaching the ground with a speed of Wz 7sxod) j0a9e9s -n y+u0lzdchat was the average force of air resistance?   

  A cyclist is coasting at a steajlu h ,puqf *2,xrg7i-6dc3zy.e ytx: dy speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?3egj ry t ucd*f,ixyzlpuh2 x,-7.q: 6   

  A city planner is working on the redesi;6 :l+y evc d(j3yvyvlgn of a hilly portion of a city. An importantv y3: vclj+ldy(v 6;ey 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 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, dangles her watch from a thin piece) 4 rpmf cph -a3weu ks:hb9w,ojzn.5) of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that t wpa)5)uhb.kj9 3 :moeh,wnp 4zrfs-c he 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 supers azdd: x36;qrmarket, there are to be several ramps connecting different parts of aq6:3zsrdx ;dthe 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 vrc6i ldc42wg2 c3u+ a/g)preis needed to lift the piano (mass M ) using the pulley apparatus shown in 622vrwui cc4)e+crgg /lpa3 d

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 accelera qrlq;5wy c )5pyy5b3pting 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 chilygv i2l v0 0f(1zek4pld-restraint chair, an engineer considers the folp4i lk0 l2gey( vf1vz0lowing 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 mass of 660 metric tons (660.xci,vq 8f9+xow8j q a,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, umr,grm qx0 52 ,kfxvx1ls9pp bp6l:6 e v9pv/ase safety ropes of similar length. Karen's rope is more elastic, called a dy,l65mpf:g1plq9 p v/vrkx p b xsav629rmx ,0enamic 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 climber is more likely to be hurt?

A fisherman in a boa(eet. .i*rnuw t is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is alloiou;* hgbi* )adp r/s74 wbdd9x/bk- iwed 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 climbersiu6vga qhj5 9( who are roped together are ascending an ice field inclined at 21.06v jhuaqi g95($^{\circ}$ 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.