Why does a child in a tk+9- nkr;p o0vbbk5e wagon seem to fall backward when you give the wagon a sharp p kktbo5kp;+ r9 b-ven0ull forward?

A box rests on the (frictionless) bed oct0 dm(nr /ucu:23 guuf a truck. The truck driver starts the truck and accelerates forward. The box immediately starts ugr uccutm03:n (u/2dto 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 the truck

If the acceleration of an object is zero, are no forces actza)zfw4 (,o8wic5f c 9 s:cjshing on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Caq jnr/(; owvbucz 7-4vvg0 xr-g.w;gd n it have zero vebqnrgorw;gg-0/xv4 -j 7dzu (.wv v;clocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up.1 wr-2ixcgyy2.y7 ygbe(d rc ; (a) Is a force needed to make it bounce back u gcbd.ry-1i;2yerc x 7 ywy2g(p? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in .;hv gyy,o2oq sh3ss9 the opposite direction?s 239 ;y.,hygosohsq v

Why might your foot hurt if you kick a heavy deng zp6 4*o,1kd d7vmsdghx5 b.sk or a wall?

  When you are running anr2)t n8s,t,gp v qw9amd want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your ownvpr s,w)n m,2atg 9qt8 experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the cd b3xrb7yu(-ztx7 ea4 eiling, and a section of the same thread dangles from the brdbb- (ua47x3y7xet z ottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock5*nhl thb/ rh2 is twice as great as that on a 1-kg rock. Why then doesn’t the heavier hrh/n2h l5tb* rock fall faster?

Would a spring scale carried to the Moon give accurate results if the *1ohqs sd-zv 1ltgi42scale had been cat* zv1q s-1oi42l hsgdlibrated (a) in pounds, or (b) in kilograms?

You pull a box with acg t5imge u72i*b u:d/ constant force across a frictionless table using an attached rope held horizontally. If yi*i g7:e5 ct/bd m2uguou 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 gravity there is a +.z 02z 3l9oebudg msgnet force mg exerted on it by the Earth. Yet s3e2g.m0+zg ld9bo uzby 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 f 9,zo6(zbi2ccj j 9fm/yejy1 jorce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally wit 9 ey9mc1,(zz cj2jj/6bijfoy h a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fi8plsy* -lwli*8 xdata.2d u+ bwf+a5og. 4–37) pulls with equal force on the other team. What, then, determines which te8 i2tbxw l+w8pdalas.of-y+d lau* 5*am will win?

A person exerts an upward force of 40 N to hold a bag of grocerqcv5j,a*cv i6z8fs9 aies. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object ic *qiv59 8j6 azvafcs,t is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how 9e o* ovs.d52 uv:yzcdlarge a force does the ground exert on you? Why doesn’t this foue5 o :vcsodvz29d*. yrce make you rise up into the air?

Whiplash sometimes results from an automobile a/ p(cfk6cyxw. ccident when the victim’s car is struck violently wx c6c.pf/yk (from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on tca i(pawht.):txru:-he bed of a flatbed truck. When the truck accelerates, the crate rema:ih.-cx)pt:(r tw au ains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp :l2k d8vjpu5ss1aep* . After the block reaches its highest poin1 ps:jd8a puslke25* vt, 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 weighetxcs0ds ews/m gkl7 lcmn7:5:h c,k.;d yourself on an inclined plane? Assume tn5ks,;c 7ss :mll 7:tc x 0/h.kwmgcedhe mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.2d6jqe g/b9uu,t 09 lq6ji3 inw5m/s$^2$?   

  A net force of 265 N ac(unwn -1 u+sobcelerates 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 uvq92vfo u,h3 a hd4 7h(bzdse-fc0(ttsed 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 3u-ib4 7)g8 g lxosqd /w.knat$76-\mathrm{kg}$ 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 requirlg8p:k: 4q,y.pz z lqned to stop an 1100-kg car in 8.0 s if the car is travelingp.z ,:4lq8 kpqgln :zy at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from q t+ok89b rl (1*el-,rrnmhc gktt:7tr nl+v)rest to 125m/s over arkch g rle:r-lkqo7+n+tm19*8brt)(ln t,vt distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelera4lrdj/ ;t7x hation of 2.lhxdj;r 74a /t5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 qu 0tkpb-hiv 8h/arter-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 pech9idzt ),;:i r0m 9 hvbby() is to be designed so that the maximum acceleration is 0.068p v,c d0rm:)(9bb i;yie zh9ht0 g . 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 in a motihv )rn x-okl t:)jshja0)h91v onless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s r k shnj1)hvv ))0-:xr lh9otjaegular 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 stre; mvf5 ai 5(o3qg5 qvso)ykx8xngth of 21,750 N. What maximum upward acceleration can it give the elek)axv;i5s5o q g5ox8fv qm3y(vator without breaking?    ( two decimal places)

  (a) What is the acceleration of twbwm*e /5x -jdpo falling sky divers (mass 132 kg including parachute) when the upward force of/p*we-xj bd5m 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 strik,n*,(cb4s qf fz o)sstes the ground below, he bends his knees so that his torso on fs *4)ssfz,qbct, (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 runs ver57o.;f i d.mf0wguje q0bj*kmy o4f2mtically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the forcee. ;7imd20 kuf0 *mj.jo5q4o gm ffwby that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbaxii5g )x,vw :*quq;c xll 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)o6t78 x iz wes)9ubs)s at the moment it is hit by the bat, and again (b) after it has left the bat ss)9zb) s 8wiox tue67and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A secoetix(gb* .9l9z w en5ynd 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer wit nzigb(ytl e9 5.e*x9wh a vector diagram.

  Arlene is to walk across a "high wire" t1mf0v :eju;5asv uq* strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoinfe0 5aus; mj*tuq1:vvt 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 mqi-qi:ohz+ q:t t km34oxs)-zassless 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.obe ,f4 alw.1m0$-\mathrm{kg}$ 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, Antarctica,qiac jn o8x5+jj-j4g) asgjcj)-qi 4jaj5x 8on+ shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4- bk/mefe y yqcm40 d(k()fjk8547 . Determine the ratio of the tensbkj/08qe) kcydymefm5( fk4(ion in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pullby;5bx*gxb y 9,6k 7rloyp9f oey apparatus shown in Fig. 4-48. (a) How hard must she pull*xbgl 7ro,xb659 p;9y fybkyo 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, r vy(5w4ch 6sogwja7ri;t3k . 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 63js+ *2*gamz xhky/h zupt4t(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 horin85 ry7:8htmwt/8nh apta x7 c.gdry, zontal surface are in contact with each other, as shown in7,7cat:ga8 h x /m8rnt 8rydnyw 5tp.h 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 gropi- j;q5gvjec;/ 3p1 qxw c-vl (wqxi4und, 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 "lauxwxci ip v35;1 4cq- (qqgjwep;/v-ljnch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a hedi wj6f(.s o1navy cord of mass 1.0 kf6 di 1(oj.snwg . Calculate the acceleration 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 k/xd 5tvbgm8 /g-)o - lusovn./oyb-okinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.0)rf w5,j t1 blzm/ds8q$-\mathrm{kg}$ 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. What minimum9a:w4 ftwqfo ) r bzi95he2.8egyera( coefficient of static friction must exist between your feet and a5g.yo:e (we4az)ieb rff9h9 q2t w8r the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of statvx4, 4mv iiksg ( 3)u4zgy-hnuox 6op8kmja81ic friction between ti(oax 6 ku,8p o4uhynm4ms1 g j4vg vki)-8z3xhe tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street plc4u mqfa ,al j)6d* gf8sg:p+avement is about 0.8. On hojsug*q+ 6,d8f: )4cgaplf amlw 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 -4b, v zsqxu5s0/.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 r lv/uf hts:.mm0c p)4uough 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 asp*5fqwjz3d gl9 halt surface have a very high coefficient of stati9 dw3fgq 5*lzjc 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 fr1qbhly) 3 v: 0jxwiu 0mc3(uxiiction 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 bofhlk8*;dun)dc fpcv0:xiv5; ih- fsc x-2 u)c x A have to have to prevent any moti x8 )2h h )dcucvpcvn-;0sidfl :*ucfxfk-i;5on from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wi og(5w9k.gpcpi-r +csl)2lkb ll it go, given that th2si + c(r w-b9kp kglo.plgc)5e coefficient 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 dd*oc)w-yty; in contact and at rest on a horizontal surface (Fig. 4-54). A 6t-;yd*w c d)yo20$-\mathrm{N}$ 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 carryincmdc:u hjc2f;botv) hy 0cydb4macw7++7j ,1g 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 avoid0yhoy:b7b af;j 4cw+1 2th cu)v+, 7dmdjccmc having the crate slide against the cab of the truck?   

On an icy day, you wtnh l)txf -d)-orry about parking your car in your driveway, which has an incli t-)tdn-x lfh)ne 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 wih4li:uo3 e s chwkj4*m-p6)luth 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 atlbebpkc ,rsw o*18 8:t 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 ini9 gur)hu vf5/grxq6*n tial 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 topp6kg ,uqiyf g74,;x:3pwcebw 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 against a rough wall by someone pushing on it 7lzv2 i-cuhu3with a force v37h-cz 2u luidirected 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 slippebwzt 6s (aj08yfv h wxd5;fd)9 5evrh6ry roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge ofrhdwfd9b 5t6 xjhvy58e;) vs6aw 0( fz a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile travel h /vxgliif009ing at speed 0hlvxf/i90ig v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides z gq3dd peq:n wtovv8 (8a43v9forward on the dash when the driver decelerates from 45 v:n e v4apz q93(d8vg3qo8tw d$\mathrm{~km} / \mathrm{h}$ 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 i rp+ (k.fc,meqnitial 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 ;z/nhly7j66 crntnz0 9tou 6i where they are filled to the packing station 11.0 m away. The 7 6/ n;9ctnz t6zln0ijyoh 6urbelt 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 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 kinetic friction betw4g ,md pm4 .7trsdxxt*een $m_{1}$ 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 bigqot/ ,dve0 (e.jh /yicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pul 5cxoa7r-abrj) c h(.mse approximately 20 g of-57rcax)ra (mcj .ohb blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of x*8 ni:)h(qqvp4/fi- cekgwgsurviving an automobile crash if the deceleration is no more thak nqie( q)cw i4*g8g-xf/vh:pn 30 " g 's." 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 ( e/dbzdf9kqa6k5km0q (ho+b by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficie5ok0k6fq mbqh9bd(/kza e d+ (nt 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 accid5 tq9b*b 9tstuent involving two cars, measure 72-m-lonst99 tbq*t5ub g skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-inp98 wehf2j hegfu .ndex) sy60ya7g;8-4 means that for each 4 m traveled along the road, the elevation change is 1 m). H 0exuah6hpn y .2;jdf)9e7esy88wfggow 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 ofzhvp;:k5 e ivb ..gi/t Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air t..ge:vk;bi /izh 5vpresistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy 264zauhw akl, stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal 4ah2lz a,kw6u if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign*7ncpd v eo/8 (xacq hn4ta2k0 of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, witde atcn2khc80av( *qp4o /7xnh 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 0n o h/hh5ka,qw.:zsd from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the s, wo.dq5:khs h/0 znahtring 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) fkava4hue4vl ;a9.u be several ramps connecting different parts of l4ea;uk a4a) u.hv9fvthe 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 neph9sd,2c t8m p;rl4dy/wa)j9k a djt- eded to lift the piano (mass M ) using the pulley apparatus s4 asdj 9/9;t- k cy ldmrtp2h,)dpwaj8hown 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 acceleratingi kt7:)azua;+sty oz h6)mj:e 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 child-restraint chair, an 8b. r -w1tfdt vj:wl-hengineer considers the following set of conditiot8j--v drw:w t lfbh1.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-car Iy,jk,g +6 q gz+kch-witalian 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, iwsg1mdyxg 7:-jlr4; use safety ropes of 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 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 resul1;7srji-lw:4g g ydmxt 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 " 2wih4*xj3 u lw 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 1 i; -,wh rtf/g)-exdxhrbq2dl+b7fa3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field incl8xcgtm2k am 6ac2/+y zined a2k8xczm /26tmcy+ gaat 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.