Why does a child in a wagon seem to fall backward when you give the wagon a sc95yick) c* soharp pull fcycs9k* 5)io corward?

A box rests on the (frictionless) bed of a truck. The truck driver starc7tc8 jw oer n6:(x:bf:k l4sbts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the trubc lfkxtw e s 8o7:n46:b(jrc:ck and (b) by Chris who is riding on the truck

If the acceleration of an object kz9q9m6bpd9, t)px kzis zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelecu:(5 r.xgos-tqs4 ynm-yj 78lgf4 wrration? Can it have zero velocit:-mr(f-no t8 .qx 5s7ycsr4gy 4wjguly? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a fo,br9yp1 krsp3k,x)ai v2 fv3krce needed to make it bounce back up? (b) Irkkr,vvb 29ka3,x sppy i)13 ff so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposi(n y+vit;ey ob3jwb:8te(:weboj3vyi b+ t8 n;y direction?

Why might your foot hurt if you kick a heavy desk or a walov r0,hsk i;7ll?

  When you are running adrgoe2m7mrnj68*r r+6dv2gb nd 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 own experience) the maximum rate of deceleratio2m 2mr rb8r*n eg d+76vog6jrdn 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 section of thix.- pvibr m) ech),6.oc n(xwe 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 a x)i,-x.bm ) .wh(rovpcnie6cbove it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is to/ f32f*zwmg dwice as great as that on a 1-kg rock. Why then doesn’t the heavier rock m2 dffzo/*g w3fall faster?

Would a spring scale carried to the Moon givedi.xd)cu m:*ygfn:w 8w4x jc) accurate results if the scale had been cald*. w xyc4gnxji w ::)ucf8)mdibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictij a./2lw( z mib q8c*)hh+lszz+seetv 0en0v4onless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on)sn+z0je*be (lh scz 2e mq8/vith+z4wa0vl . 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 net qw toggnu0 ei 2i92cfw* 7:zq+force mg exerted on it by the Ear7uen:t wc*zof2w i0 igg+qq 92th. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object wheh:tm p4w0d -q5/+ odmavkmj d/n you are on the Moon with the force needed to lif +qvw5/ md4djmtha0-/d:m kopt it on Earth. 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 (Fig. 4–3e ; ra*jb*+1z 8im:cv ezjxeg,7) pulls with equal force on the other team. What, then, determinesza;g bj xc,:e 1+8 em*v*ejizr which team will win?

A person exerts an upward force of 41ysz1r ;i-hdm0 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by s hisz;-y11d rmtating (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 the ground, how large a force does the g6m5 c0tzib kx9d)-l vnround exert on you? Why doesn’t thi xcm0z5i -dvbtlk 96n)s force make you rise up into the air?

Whiplash sometimes results from an automobile accida03:v7 8rrna)k5 ylrjan mz f tu86g5jent when the victim’s car is struck violently from the rear. Explain why the head of tht8may3 n7r8aujr j6nl vakz 5g5f):r 0e victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerat, zh859h,jjxa f2ws 9h 8sgzbtes, the crate remains where izjjh btshz8xs2f8h, g5w,9 9a t 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. After the blkv 3/ l8p(syxkock reaches its highest point, it slides back down but the magnitude of itsyp x/sk kvl(38 acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclifs8;p 42fkyry ned plane? A kr 4yf2sfy8;pssume the mechanism functions properly, even at an angle.

  What force is needed to accelerate 7qja yihlbjl; .nor/ )) 1sqr-a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rid4tv28pj/a , tx :wteqmlv5t4 jer at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a far 1o/qi2n8ww/oq(- z p l7ew 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of y:wvgtku 03 q8* wul,qc,fth7a $76-\mathrm{kg}$ 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 r j7+bzbyu2e+ntr6dl49 un+ wuequired to stop an 1100-kg car in 8.0 s if the car is traveling at 95rnnjwdb++u u+ 4lyztb 2ue697 km/h? -  

  What average force is needed to acceleratxpd)htd* cz):viikxp6 b4 , 5ue a 7.00-gram pellet from rest to 125m/s over a diskc p,)i vp4h6 xxb )dzdui*:t5tance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratio t3gplpkedj;i*q43q ho3o4 v)n of 2.q)pge 3kdtl3 4vopo4 ;jhi* 3q5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter- .v xohwel+i0m)3;xlimile 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 485 db (p4eu(dsr8eweaq:i- i ,8a0 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forcp(id48 sewea8:d b,(q -u riaees 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 motionless elevator. When the ele;0axilm(r* i 3so -ufuvator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the o*0 3; axui(slm-furiacceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength ob8kb : le.5 qxmfd):uxf 21,750 N. What maximum upward acceleratk x:fle 8mbx5bdu.: q)ion can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleratio v,ev3e-fiph;vsk;a4w k5hn5 n of two falling sky divers (mass 132 kg including parachute) when the upward force okps4h ;nv whav-e3;f k i5ve,5f 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 groubxzepm1sg w3 1 q500ltnd below, he bends his knees so that his5gzw3ebq01 pl1 mtsx 0 torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs verticallye:,tn+ i kbn2jeu-lv8 upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that tk8,tn ueeib+j2 :vnl -he 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 basketball *vspjsx4xr p/8,g0vu player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit .)e-m0ymkd o2uw(lugby the bat, and again (b) after it has left the bat and is flying-d.0olu(gykmmue) w 2 toward the outfield.

A 650-N force acts in a northwesterly direction. A second c ti;i:f7f(vp 650-N force must be exerted in what direction so that the resultant of thi ( :;cifv7ptfe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizo,by95ggo k ia90w xea*ntally between two buildings 10.0 m apart. The sag in the rope y iga *5 9,obkawxe0g9when 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 han 1fg.jhmi+ 4houx-bgkzt* , j3ging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14pha pdzj5d z .jej3+47yg:f e5.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new locatsg0ll (8jmf 7cion at McMurdo Base, Antarctica, as shown in Fig. 4-46.lc 8l7fsjg(0m 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. b;cdy:af1fd- 4-47 . Defc:bdyf1d -;a termine the ratio of the tension 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 buckqqyk -6)istb0e wt1b-hm9 2htet-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herseltw60qq1 byhbsih-tek29 - t m)f 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 began8 ryzaaf9sd 87- .6iasdnrn b4, 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 80hw wl6 ljsbt eu9qh+/4bf( wblock (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 contact with each othe86a6ofdbhvz 67 czd,mr, as shafzmb,8c 7odh 6 d6zv6own 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 eae)q irk4 (ip4vch initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maxp4ke viiq(4)r imum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionlessdgy+ gc68u )elj mwy z-:8x)gg table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the freeg+zgw: y-xg6g eyu8 8)jldm)c -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 frics( jy h;s5*muytion 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 requir0* j (oea w xt5gyc53gaq+v5jled 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 r5kj pn2)v0tw standing on a train accelerating at 0.20g. What minimum coefficient j2)tn0rp kwv5of static friction must 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 s -o 1trsizu;pf. k-e e8s4ezv0tatic friction between the tires and rfv z -t1p oezees8-.;iu0s4 kthe ground is 0.80?   

  The coefficient of static friction between hard rub+y59 9+wy8pc zmbyqbo ber and normal street pavement is about 0.8. On how steep a 9z5+y8 y+om9 c bwbpqyhill (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 -48n re4 piyn7)l.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 rough q) jbq,k ,kffd*s 44p ds2drq0mk+s;az)xuh8 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 havef3ax:/+ sis(z w eebh* a very high coefficient of static fricw:b/e+(i3fehs sxza* tion.

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 fricx)hi u 0pyoj/)tion 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 j l23-/0 d 3edaocthv.wji,e;cd 1 aduwould box A have to have to prevent any motion from o-o .1d;aj3lc e2d etjau/w0h cidd, v3ccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, gi -w/,3uvtp -6gf ieauzven that the coefficient of kinetic friction is -3, 6puwe-zi aufg /tv0.20 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 co;;m*h30m5 oaj 4 t wff9v obxf9v8awztntact and at rest on a horizontal sur ;j*wv;mzx vo fw59ba3o9tf8af0 mht 4face (Fig. 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 carrj9u- c owa:j8vying 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 j:w 8vo- 9ujcadecelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking y (zn r.akk6nc+our car in your driveway, which has an incline of 1nknc .zk+a(6 r2$^{\circ}$ . 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 withd4v6a8 f-mo wj 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 at a 0eu.vu8b3( t+c ofwzan 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 initiaj fnyi +lwlgr**+ t ;/f6xbg5nl speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed lzv2kledwz:g9z:j)/ mg4.; p nh 7a luof 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 placm;.zg u-jlzw(0 ci ycke;mhu): (kzg,e against a rough wall by someone pushing on it with a force dirzu)z:;y0(g .mgk(ciz kl,jc he u;w-mected 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 slipperyt;kc l)r n24ppz,3wr zih7;juo/rh 6 w roofs can become dangerous projectiles as they melt. Conside pcp;7t3w rz6,/n4rulo; wh i2jzrh)kr a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stoppinrc/ / oeebkp;1px: 3fc-te;a hg distance for an automobile traveling at speed v is hece:e p-fc;o /rktp ;b/13axequal 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 the drirpq, iu0rp*zj *v4e7. b s)jlhver di4z *.eqr)0bsp* lrj7puh,jv ecelerates 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 a+t(; qt0hiy gcn 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 fn eyt)d h0zk.bmx qung my.8 7xa+4p(7rom where they are 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 distance, then decelerates for the final half of the bentp 7k(xu7 q0a4.y h +)8mznym.dxgtrip. 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 beno;z v6qu), / ,ev qwf9di/dtctween $m_{1}$ 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 kczxp igks 0(wgk8b94*g (including 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 simplified model of a mammalian he;e1o ewk z(xe:ol.br .art, at each pulse approximately 20 g of blood is accelere ol ezbox: .k;e(w1r.ated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an auto8lqjad8w( j*3/ms2w9k-ehk * eojefc mobile crash if the deceleration is no more than * klej-89ej*hjcea/(swmwo q 32f k8d30 " 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 by an earthquake is ami tpz k5,;b7f, er+q a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at leas7 k,,f rt;b+imzp ae5qt $\mu_{\mathrm{s}}=a / g$ . (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, c q, p/q m+a fz:5)ta*rbx9cjcexamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed ofx*b: mc f q/5qzapc ,9a+tr)jc that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travbtz;dbje r lp-0r6 4;ueled along the road, the elevation change is 1 m). How fast is it goi; ztlb6re pj-dbu 4r0;ng 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 thv+ m ixi50r8sh45 ga i4h(urgde top of the Leaning Tower of Pisa and falls 55 m before reagm(gu rs +45i i0 xhdi48h5rvaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretchtv3p lm .z6)jq where the effective coefficient of friction is p63.l)zj tqv m0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the re*hy a3 4rqvp y3i*6rumdesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-po6 yyqm3urhri* p4va *3wered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experimentsyj /)utvev+r* , dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the str evt+vu/ry*)jing 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 r1 z90eymrey7)+q9bs nkg q45 z /ppajqamps connecting different parts of the storeze /q5mnb a7y4g)rq9 1jz9qsp+e kyp0.
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 t) 82v1w dyfgu 1ep9xotbuy5q8 he pulley a2y wovyu81q g18)9ftbe5dux ppparatus 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 3.5r,+lbf fwk.w.u9) 0 e/fsr qtr $\mathrm{~m} / \mathrm{s}^{2}$ 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 co4 attymgjpm+e;0zz*z )0/ o hwnsiders the following sygm)/zht+p 0 wze ao0 tjzm*;4et 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 metriciqf1bg (an)nham 7,+jxdo,u ) 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, Be;bazr x+n2 ukv/ a7okn. -o8till and Karen, 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 na-x+ oub2 7ok z8kna;tr ev./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 "q- w+ r6r my(r8sgxbm(ia2 xcmj(. ik* 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 5beny evyr(+ li54ak9;3buy y3.5 $\mathrm{~m} / \mathrm{s}$ 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 a:+9d pmsm lc o9+r9uutscending an ice field inclined9or u c mp9u+:s+t9lmd at 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.