Why does a child in a wagon seem to fall backward when you gigh8d9 qtra(3;o7sn j ive the wagon a sharp puqriton7 8h;d3g(9ajs ll forward?

A box rests on the (frictionless) bed 97rfk/lr 8)p 1 eapupjof a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slid j ar7elup9r1)/fp8kpe 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 the truck

If the acceleration of an1v jra+tkt- ;d object is zero, are no forces acting on it? Explain.

Only one force acts on an objectufrxhi**)6b )yboh o.(m rbd). Can the object have zero acceleration? Can it have zero velocity? Explarob*u)) rhb(x*i)ofy.m 6 hdbin.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a for(-jz:md,; tgltsxws ) ce needed to make it bounce back up? (b) If z,xst;g)wm:jlt- sd(so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in then5t t+ ;skwub.rsq;6j a3e7 dl opposite dire t;skus6rl.n5a b +tedqw;7j3ction?

Why might your foot hurt if you kick a heavy desk or m +owq/; h uu+lut,:cea wall?

  When you are running and want to stop quickly, you must decelerate q.ff3a3pg vcx;hac) g n--ol/muickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rah.; 3/faagf-3cpx og mc)nv-lte of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sect,h zn w1(o o:9ebrqtp0ion 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? Whah(or:wbotq ep,n1 90zt 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 asb1karc4 8 9uj;1dvz lkk(ir+tckv.f4 that on a 1-kg rock. Why vrd k+kak(k v1t9 4uz8f.c;1bic4lr jthen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate zzcu9j7/n z;,ond )szvs* ql/results if the scale had been calibrated (a) in pounds, or (b) i;cv )jn/d/nl*7s,szu z9zozqn kilograms?

You pull a box with a constant force across a frictionless tab5pl r96.hgtjcqyq (+h,zvd- u le using an attached rope held horizontally. If you now pull the rope with tuc(t.5 -vqr,9gzyp jdl qhh+6 he 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 freely5 ;absp fj6:x- hon*zc under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by New;cbx*j f-s:a5 p 6nhzoton’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) needed to lift a 10-kg 4s3+bafbc2efaom /d 9l*hc ;gie)nu(object when you are on the Moon with the force needed to lift it on Eart9faa;l3b f/sg(ohc c+ ei *m b24dune)h. Compare the force 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 war 4 .mijhfme2 2j(Fig. 4–37) pulls with equal force on the other teamfjemi2mj 2.h4 . What, then, determines which team will win?

A person exerts an upward folze ygv;(.cm 4rce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by whatg(v ;4 mlzyce. object it is exerted.

When you stand still on the ground, how large a force doesu b 3nv-q7vm,t the ground exert on you? Why doesn’t this force make you rise un -vu7tbqm,3 vp into the air?

Whiplash sometimes resultseij ;r3pvj(+hh- ort* from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situatjv+ j(heot r-;p*3 hriion. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck aqff/g,z 5 2j8: ubouwcccelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acqou52 :cfw/g 8f,juzbcelerate?

A block is given a puna 0g,; rjk/pbsh so that it slides up a ramp. After the block reaches its hinjp;k, 0ra bg/ghest 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 pl:w *i 3*ezcp d1mye:acane? Assume the mechanism functions properly, even at acea1y:p*wec:d 3*mi zn angle.

  What force is needed to accelerate a child on a sled am) )6fl 6olzz9j9.8dzhx wou at 1.25m/s$^2$?   

  A net force of 265 N ag)q b7daje2sah )lx4+ ccelerates 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 aea 0c-7q0k.xrst wii0ccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o+23toi1 dl/c 0 qlixe9y ur1pgf a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required 7.zay61s diprm9 a s,eto stop an 1100-kg car in 8.0 s if the car is traveling at 95km/hd.ia, zpr69 am1sse y7? -  

  What average force is needed to accelerate a 7m/ t,xq9t-o nku;p.dj.00-gram pellet from rest to 125m/s over a distance of 0-x mt,o;.kpnj /td9qu.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertica u6h c1;:um r4ab imtpj82yj0illy out of the water with an acceleration of 2.5 1jt80 r2i:uupybj6h;4cmi ma$\mathrm{~m} / \mathrm{s}^{2}$ 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 quart7, 4 hea;n hgyg6(jnn2 beew:wer-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 that the max0kaxj. a7b3 fmimum acceleration is 0.0680 g . What are the maximum and minimum forces the motor aa 7kx.jmbf03 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 in a motionless7uhh ogix3 9wil+1s(wnsoy7v - r i y3zd.l.q* elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Co*3 7 yw(qo .+srsllzih1wu 7inyd gh3 9.xiv-alculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator ha .fz/afn 1q(tts a maximum strength of 21,750 N. What maxim 1fa(ttnq/. fzum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dive sy3k0fldo1j9rs (mass 132 kg including parachuteofsd1j 903l yk) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the grr1.-:tm)kofo wegk h3ound below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the masgrwh .e t-:o 1kf3mk)os 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 res8 klxk1j; 8z:wo *v)lxlzkb,ets 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 exerts on the box if the weight hanging o 8e*x1bzlk jlz;,kko: xwl)8vn the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram ffge0umm9ys 6kz d v17f*:9u fvor 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 .5 qw(z g dq7(sy0)egmkd.bbgbaseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is fly)bmggz(.g ed0s .7 qy dq(bk5wing toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must bc 4j pzk):r-lqc 2pzh1e exerted in what direction so that the resultant of t1-j p4kh)cp 2:cqlzrzhe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two 9lsix))w ;doqbuildings 10.0 m apart. The sag in the rols) )iq odw;x9pe when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from another vm x2hu+qq:3jlp, h7f 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 14v)3q r3rac8gz ix qpp2*v2l n/.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 ho8eja .ettqs( 1using unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of tha1. (e 8tqtejse 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 thet;6 q -zimo w-hm,;b+co rfm6k same mass behind it, Fig. 4-47 . Determine the ratio of the tension in t6;;hf,cr -m +mwt6oobkq zmi-he 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 buck;ve 89,f 6(lpwpi5q htjacq*q et-pulley apparatus shown in Fig. 4-48. (a) (tqf i,pw a5cqpl v;8hje q96*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 650qo/;e oe f8gd+ssw q7$-\mathrm{kg}$ 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 li;57(ktxi ovyk+px. (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 c 3xys2. q3un6*gbpryyontact with each other, as shouy*3 p 6bqyxr 2sgy.n3wn 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 the8y ) ie.-tpfry 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? [yi-)y pte. fr8Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table arj bjdn x(48guljn, ;a/e connected by a heavy cord of mass 1.0 kg . Calculate the xl;(4bjng8nu/, aj j dacceleration 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 frictio h r-oywz,m,n(n 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 start1icbc2h bt24kc g hx;- 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 0.20g. Whath2vkks;y*. 2 elk,lfh minimum coeffisleh2kv;f ,*yk2k. l hcient 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; ;biwjugj(r 1 undergo if the coefficient of static friction between the tires and the ground is gj urji(1;bw;0.80?   

  The coefficient of static friction between hard rubber and normal street 2z n(+olu en-z; gzf-tzo00jx pavement is about 0.8. Ozzjt lnzxo ugn o02f+- (-ze;0n 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 at()pkdy etang a;4, 5ps -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rougf6 5jan;ky/ frh 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 surfp6wl+vm .;qkzt2qm: r;mqvz4 ace have a very high coefficient of static friction;t : m;+zpwlqrvm46q 2 qkvm.z.

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 kinehcw3a eta . fgn,-2vfpnj(8w8tic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Figkt+3 3+pu s v+vwn,iic. 4-32 (Example 4-20) how large a mass would box A have to have to prevent any w,kut+ +ivcip+ns 33v motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it gmiofab-qi4h* f2 ,su .o, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0bs42u.*ofhi ,a fqi-m $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on oq1 )fvkb2qjq 7a,h5x a horizontal surface (Fig.a7qoj,)vh1q kx2fq5b 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 .bcygm- 1aww2:w8dfr a heavy crate. The coefficient of static 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 c-cb rw2f.1 8wamw d:ygrate slide against the cab of the truck?   

On an icy day, you worry about parking your car in 4fu yu89m hlcds6t;( syour driveway, which has an incline of 12 (6tslh;df 9c4m8yuu s$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 2 o:-5wi1hkr1v orn7bna1d7z i8$^{\circ}$ 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 at an angle cxp ggzo m:.59 $\theta=22.0^{\circ}$ 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 initia dc(/w ,if(fqql 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 t0 9fv0 idghd;c ;+1:fcoimesc op of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place age)o wek5 1/a42z ypsnvainst a rough wall by someone pushing on it with a force directed upward 4eoky5 2)vs1ezn/a p wat 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 thhqp5+:h5gex k ey melt. Consider a chunk of snow at the ridge of a roof with a pitch ofhe g+:x55k pqh $ 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 anvfgl0cmxjv.k0 79 6mx5b u zn7 automobile traveling at speed v 6zxx70v9n7 j5 umbgkvl f.mc0 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 tdl-w+gbplflvoh 5 z)(m78v v6 he driverglho6pv()lb 5-lv f78+wmdv z decelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is givefle 95 zuxr q4b)fj4mi1g-j/dn 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 pafqx 46m 54cfs)tbz )sh-4hu vp2gq2tgcking 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 the belt is 0.60, what is thq chhsgvu) p24fzf56xq-4t4m bg 2) ste 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 kinetic frt..a/lpka8jlz7; g,nsu d2f biction 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 d r29rp bq f gctgyebtzi4f:59*ufu5- 7own 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 simplifzr wbkk q-z2.)ied model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated rk.) 2wz kbq-zfrom 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 automh2dep 1w k:v7rziv4kne 02ra-obile crash if the deceleration is no more than 30 " g 's."ie74k2e rv1-vd a0kwr: phnz2 Calculate 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 by an earthquakearp 6lkb9d2. ggl 3l-7npb b1u is a , and if an object is going to "hold its place" on thn 7bb g31rab .u d-llpk692gple 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 the scene of an accident in .cq+ mn)h/dahvolving 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 be/nmhd) chqa+.tween 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 (1-in-4 g hk8h (de2g+jx 1ax2bmeans that for each 4 m traveled along the roadgj2bhe kx2gax1( 8dh+, 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 dropped from the top of the Leaning Tower 2zg(o .+ql:kjld ,gld of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistd.(jl :zg,k lg+oql 2dance?   

  A cyclist is coasting at a steady spe9th1/-mfxb xgjvl5 4med of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist fh5 b4-t jlgxvmmx19 /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?   

  A city planner is working on the redt+/tj(g gtl) 1 wuaon3esign of a hilly portion of a city. An importag3l1n(u) jto+ wgtt/ant 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 phyon/, 7i)ycrp gsics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Air ,/7)i cgrnyopport (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, there are to be several ramps connecting differtjj df6 o(wz8,ent pow,d j 8zt(6fjarts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the f:c0:o7fr:aw 8cdk y fpulle rcaco:fyf :7df:kw08y apparatus shown 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 accelerating at 3b+ x,com 9:f+fsp ,mfi.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 child-restraint chairq7 ib/et)* mxr8r7p/ gj9auvz, an engineer considers the following set of conditip) qzjm/89igr77xa/e* b utvrons:
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-ca:g0e cy*f :p7 nhh.jpat(d r,vr 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 of similaiy b(oq5 -ii-cr length. Karen's rope is more e5c-oiq( b i-yilastic, 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 climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1 tp-13zddag. f $\mathrm{~b}$ 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 reach a maximum speed of9*g dfeab/eczkx 8f 35 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together aretyg mnt9gbb-op pf)d-zz hg 4*756c t(8f g6bn ascending an ice field inclined at 218tz-p7t6 mtbg9d g n 6o4(cn - p5bffzygh*bg).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.