Why does a child in a wagon seem to fall backy;z.vr 6baidh 9 i(+ wdc8go;jward when you give the wagon a sharp pull fojd 8 c(gdw9+;. i6zhv;aryobi rward?

A box rests on the (frictionless) bed of a truckv8rq9g q f2kn7. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the mo 7fqq 9rv82gkntion 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 qasq s3/g*g(sno forces acting on it? Explain.

Only one force acts on ane41-p5hm e6sz)9 dp1 uzhkwaw4rjx 3d object. Can the object have zero acceleration? Can it have zero velocity? Ew31p4h1d6 ma5ke4rx )ez-jsdwhz pu9xplain.

When a golf ball is dropped to the pavement, it bounces b2ks9y6y x 8qkojy j.(vack up. (a) Is a force needed to make it bounce back uykj96 8.2 o(q ykxvjsyp? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the ftd1 )q(8kutat)w8w 6x4ess rlog move in the opposite directkdt1 88at s )que4(xrs wt)fw6ion?

Why might your foot hurt if you kick a heavy desk or a walle:0;5koq5hyk: fjkpq ?

  When you are running and want to st uile;kq 3g*yycm;m*8op quickly, you must 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 person running gmy8i3ue*;y*m cqk; lat top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from thev2c f+lmwhe 9*s;gsp.v-:l h:p ujpl: ceiling, and 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 abovew *sv:; 2hj-mpsp:gl.lcu+9v:phf l e it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg lz14o* zty ( ;spfefv,rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall faster? t4 ffzzp(,v;eo*sy1 l

Would a spring scale carried to the Moon give acnhw,se :- 9+uw.fgewopqpjzm p g)7..curate results if the scale had been calibrated (a) in + hww.p .-9mwepqg):s f.pg,u7jze nopounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an att +/zoy4* ggxvmached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the *y mg+gx/vo4 zbox 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 neteyjt9 logl.17 force mg exerted on it by the Earth. Yet by Newton’e1j lg7. 9lytos 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 object when qw8:kjc uze)o:;6jy ayou are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on th aojju:8;:e6q)kzc wye Moon and on Earth.

According to Newton’s third law, each 0c6)th v;hu iyj,-bn ateam in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team ayjvuhb6n) t0h,i c;- will win?

A person exerts an ub6zp-rnl -iji 8 pq4t4pward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s thl4-8-zrt 6pni4qp bjiird law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on tht2 dvix ilre48nv:8noy q312we ground, how large a force does the ground exert on you? Why doesn 13qy4nvtd : iwlex828 nv2iro’t this force make you rise up into the air?

Whiplash sometimes resultmubukhz 1+r4 ;s from an automobile accident when the victim’s car is struck violently from the rear. Explain why the zk;1u +hbm ru4head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a fla4wj 6 dlphx4zpj; ww-1tbed truck. When the truck accelerates, the crate remains where it is j6hlwx44p pzj; ww1 -don the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so t4ycw0c s*a6)r1x kp9zk i2)8ds obvzbhat it slides up a ramp. After the block reaches its highest point, i 4c9vwa 2ki1b0zo) y)6*kxrzpsdc 8b st slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom,xpb8 tn9j9l8sx8 c rt scale read if you weighed yourself on an inclined plane? Assume the mechanism functs l8cr9ptt89nxj8x, bions properly, even at an angle.

  What force is needed to pg)l-llju:u ,d -2z*7 fznc o0tsp 1ddaccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratesxwd4 nbl9w1 6md1 z,pd 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 fz7 z m8k4ts3znwh yo+q+8k lxi17qu/withstand if it is 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 w lvb-4u2sd,q - 0,sep xfj9es $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-nwwkuwv/90rb lo /(9p kg car in 8.0 s if the car is traveling at /rwl9u0/kob w(n pvw 995km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet)i9x9 e7aqvbt from rest to 125m/s over a distance of 0.800 m along 9xbtev qi97) athe barrel of a rifle?   

A fisherman yanks a fish vertically out of sf y/q 0z21lwr+sndu:the water with an acceleration of 2.5 +1 / wnrufs2d 0qyzls:$\mathrm{~m} / \mathrm{s}^{2}$ 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*i /9en uq8pslzzl:k*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 ) is to be designed so that2j04w*rnuycckn:kjl40 u s l 3 the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting k:rnu44u 0cl *0ns3c 2kwj jlycable? 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 elevator. When the ele s o9yc.ne2de1vator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleratios2y dc.eno91e n.     ----待选择----downupward 

  The cable supportingcxtd.)/ramn zpd4 7p2 a 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acc/r. 4 xcd)at md27ppzneleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers r6s a)ro:r0xfk0 x9hx7. ux hr(mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of the :harrxufhrr.sxx0097o) x k6ir 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 grou1;ukm7ft6e / d)8 xny tobcoh.nd below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find 1tk )nmob yecd.8u ;xhotf6/7
(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 bav2 6*-b mpry7warr* 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 bvm*p-ry6b *7 arab2w rox if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pu9wv6 , voexm(layer
(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 i 8hlnmha ,hn,ygo,d;t1p f/9ss hit by the bat, and again (b) after it has left the bat and is flying toward the outfield./p;f 9hhl oynng,m h,,d8st 1a

A 650-N force acts in a northwesterly direction. A seconvj1 g.(zq yh,t1wz p0od 650-N force must be exerted in what direction so that the resultant of the gwj0zq11yz.vpt,h( o two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betw-(d;qpexwk2+ eq jh(seen two buildings 10.0 m apart. The sag in jk;qd(w qese2 x(p+-hthe 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 by a mt0cvs*ydba ,,o; e)hwhg 4 7knassless 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 14.0y5apyge(r-6 oao b3 +nv *bco,$-\mathrm{kg}$ 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 h6wj sx 1 zbau/wle,)h9ousing unit to a new location at McMurdo Base, Antarctica, as shown9s,)axjuwwz6lh e/b1 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.q;27)m0rqh, yi vic/ qkpu 6wr 4-47 . Determine the ratio of the tension in the coupling between the lq rwh,p7q/ q2uiy0 mc6k;ivr )ocomotive 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 usuev qmdo8 tvd1mjsv4: n3t- 73ing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at1sd84n3ved7j:vv 3qm t-muo t 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 oxdl0) b -y7k++:c vxenw ij*rw1v 2kvbegan, 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 blocfo1r y6t,e wn*29fcu bk (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 horizonth7u,66p hm t0d+uzgap al surface are in contact with each other, as shown in Fig. 4-51. A force mph+ g 6uhz6d0tup7 ,a $\overrightarrow{\mathbf{F}}$ 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. 4xsq( b 4q31 n;n:hry+ie fim8c-52 are each initially 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 theeni4i; r s:mc (nfq1qb 3hx8y+ 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 are connected by a heavy cord of mass n)q r*x2ihjog1vjb )j :0.a ot1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Figjh0bg)):a rv j1xo i2*no qtj.. 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 kineti8edd-emnv:zp 4 4d+6 ace-yoec 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 v :r t43 ep,n9isam; tbxee7y-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 accejcxqswel102 ) 3c leaw, f3p7clerating at 0.20g. What minimum coefficient of static friction alx103 sww)ej2q,cp ef3 l 7ccmust exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of staticka cm*:;w8jfv8 , yssw friction between the tires and the ground is 0.80s8f:k ywm;w a* ,c8vsj?   

  The coefficient of st xp)x / oe4 0o3e t5ff5f)g1h;t4ijurfog3aoratic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car )0r o4xuetx53 f5o1j/ gof34f;pihae)rgoftparked?   $^{/circ}$

  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 -4: wo2 t*,lzdrc.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 on12 eobmr ci vz0zks8*/ a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high j7l6z s; g*7nviugdga * 2x9awcoefficient ofx2*vj7 si; g7*6wgazd9naulg static 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 forwy w( r*jl:hhyc;gel1: ag6s, syu5,h 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 havemdis*k+2qz0vuug d y ;b/3kq7 to have to prevent any motioikd7q+ z ;0um3gyvkqu2s*db/ n from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it s6x4jms pqsmx lp2 d9y xz,233tlides across the floor. How far will it go, given that the coefficient of kinetic 24,p9q26ys d3ptsz3 jm xlxmxfriction 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 ,lvts)u: p(ib ha9d4rcontact and at rest on a horizontal surface (Fig. 4-54). A 620stirahdp ),bl:(4v 9u $-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fr-,i cloxmwa,fhs 1* qzt 43j3wiction between the crate and the bed of the truck is 0.75. What is the maximum rate at which t3xh3qwlw4jcz1t,,m o-fisa *he driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worrg :;/a 4n8 kmtuyhsn9py about parking your car in your driveway, which has an incugmnak;4p9s 8/t: hyn line 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 1*fk+ r)sgx xi r5ny-q.:k yanslide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 liesh,4 g8q,f f xo** mw;z,lzimqp on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.q*g8f*(vuw-(w h w z5sdi fr hfy6 *nqj-q+q.f0 $\mathrm{~m} / \mathrm{s}$ 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 s w4uiwyiq (/z)peed 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 b w1* ybf-vuta-tmsk ve*4k ff45 dh31vy someone pushing on it with a force directed upwardk3fvf * -5fwye*v v41s-u t4bt1mhkad at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as t -sdc dz/:5zpphey melt. Consider a chunk of snow at the c- 5:pzddpsz/ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile4 +cvx3rflb2gt cz+9q traveling at speed v is b r2z +3cxg4tq+fl9cv 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 d iak3y 6ped58pashboard of a car slides forward on the dash when the driver deceleratesyk5ei3p 6d a8p 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 given an initial speed,ww9r84wod4 66 (wgy ioogmln $ 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 arek.z/ 8w5 n22s fhzyhpw filled to the packing 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 dist5z/wys2p.wnf h82z khance, 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 kinekc07 w-nv3c d;po0 ,ah .0uesqagu0 zgtic 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 (inc-:1:e2 vxdg l8lu qtdyluding the bicycle) 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 simplifiu7)a-ynfb1jkk.w tna v:pn2 3ed model of a mammalian heart, at each pulse approximately 203p ju)kkf 72aab-t1 nwnnvy :. g of 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 surviving anmt4*)qtnr6 x x;awp c/ automobile crash if the deceleration is no more than 30 " *tm rnx6x4);t /wqpacg '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 by an earthquake is a , and if anew+suqv+- qfwvo cl :+q+n8sb i4;v3j object is going to "hold its place" on the grounv;vv3+i sus4w+w f 8e:+cl -jqq+o qbnd, 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 involving two d) * d67t4l1cwn sjlbecars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial 7wn* d) jlte4c6l dbs1speed of that car assuming a level road.   

  A car starts rolling down ao85 v,momym4k 1-in-4 hill (1-in-4 means that for each 4 m traveled almo km,y5 4om8vong the road, 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 tmf:yuw2d2va diqmx+k8 b. im87-pxl +op of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of py+.ud8q2l bmf d8:x7 +ii2mxkvmaw- air resistance?   

  A cyclist is coasting at a steady speed of 1my1s 0lkyi e/02m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch wiyy/el0i0m 1 ksthout 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 ,y 5diecde jvg jo+ 6,9(0os y *m9mdwsvp/ux2redesign 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 withovj5(o+ dj9ycem9i uo6 /v *mp,dwge,y0sx ds2 ut 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 p+.egtypc; i 9 w*mo;aqhysics experiments, dangles her watch from a thin piece of string while the jetl;+i*. gwocmqp;9ty aeiner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be sev4d(;i*k an thteral ramps connecting different parts of the st kd(t n;4*htiaore.
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 i0a 6brbvf8/qrfb*0n gs needed to lift the piano (mass M ) using the pulley appanvb* 6qabf0rrb/g8 f0ratus 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 accelfr7fp ono;.cb )x,s d/erating 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 engineer considers noc -np fh;ro. .0p mwt8l5ow9the following sethm .9 lt c.w;o80on5o-nfr ppw 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 4l ob ug:/knc:k+au4c 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 uy8g,i e0 (cp/b)qcep 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) Estimatuc0 p/,p y(e)8gbe cqie, 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 ows2os/5(9ue(+ztxz/ mnet r" 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 ream 3y2lxqfeb k30rd, 8,oenrh *ch a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers +n3iol+8, y zrat2bwv who are roped together are ascending an ice field inclined at 21.0ota2 ynlz, 3wi+b8r+v$^{\circ}$ 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.