Why does a child in a wa/is2 )zcs6guo ,lej0p gon seem to fall backward when you give the wagon a sharp pull f)o/supj eiz,0sc lg62orward?

A box rests on the (frictionless) bed of a truck. The truck driv 1.nmi8iwt+mf4 w, xdber starts the truck and accelerates forward. The box imm tmbifd14w,i8. n mxw+ediately 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 truck and (b) by Chris who is riding on the truck

If the acceleration of an objectu+ol 04podx)2k enax + is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the objec ngu ,2*s(;gn3qcybaxt have zero acceleration? Can it have zero velocityy;g(un3qb sa ,2xc* ng? Explain.

When a golf ball is dropp9 6n ifs81p,-alagp pced to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, c8p6a1, pn s9afglpi- what exerts the force?

If you walk along a log floatingjf 0 9c n0zgt*xa9b ugs- le-x-g1bx3o on a lake, why does the log move in the oppositxx gc- 9-ujzeo0*3 lfa1tnbbxs9g0 -ge direction?

Why might your foot hurt if you kih)(rttfbqc05. 7 idvwu(gki; ck a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerat,u0-k yuue mxuwi2 ylj(w213xe quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate wu1yuuk-y2wj0 3(xi2lux , em (using your own 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 ceiling, and a section of the same threa rz5iy 4i;yx(zt.jhe:ze z3o6d 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 st4oz:yh( rez5.jx6;zz3 ei yt ione or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twicerk -odiy*3;3hdlww6 i as great as that on a 1-kg rock. Why then doesn’t the hea*diyiw ;3h6r kd3w lo-vier rock fall faster?

Would a spring scale carried to the Moon give accuran0jy(a :-duyjl1u n7s+/f nyngw)n /mte results if the scale had been calibrated (a) in pouyn0f -wun/7/ysmn+ :()lna njy gu1jdnds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an ;7iyezg srm2gk uny2 ,qfh2+ 7attached ropem+zhg rs fg y7k2,ne7y22i;qu held horizontally. If you 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 n*q/9kx d3zl no2tr wy0et force mg exerted on it by the Earth. Ye9z/rwny*lo3 xdt 0kq2t 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) neu b/c / ml2+88 hljov(iya.igeeded to lift a 10-kg object when you are on the Moon with the force needed to lg o2l(y.ji +mhc/8i8bea/uvl ift 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. 4–37) pulls (;k9 xw hym af:gkh1 o5 (vn2a(kfs1nbwith equal force on the other team. What, then, determines which team wikvhx9s wnf2 y ho1(;km(f nkag51:a (bll win?

A person exerts an upward force of 40 N mz 44m8kp ynq8tbbkaa24/x2 gk6p) drto hold a bag of groceries. Describe the “reaction” force (Newton’s third4mbk22 rb naat84kp4gd ) pkyqzxm/86 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 the ground,ve /qo+6bv *pq how large a force does the ground exert on you? Why doesn’t this force make you risebv+po eq/6 *qv up into the air?

Whiplash sometimes results fyi)b ;yg f+l4from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it f)lfy4 ;ib y+greally?

A heavy crate rests on the bed of a fhu(u- bo+vl0z* njqv7t f:xz 2latbed truck. When the truck accelerates, the crate rel7h nzz-u2xb :(vq+ uo0* jvftmains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a pudd:.u p g8kxkoqd. tt*8q a26msh so that it slides up a ramp. After the block reaches its highest point8.2dm td:t oukp.kaq86q*gxd, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathbrgdjk-/cc+td * 9vs6room scale read if you weighed yourself on an inclined plane? Asd/c-9*k vdtcr gjb +6ssume the mechanism functions properly, even at an angle.

  What force is needed tqe,2a .yo g 7/aun6x)r/.yp q(irr)mg*l d mrro accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider axid 9vuo3*6y l/ yplm*t 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand xuwv*w z:c4t( 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 ofqnq9bd dq2v9/m(3pmum- m8ug a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if t,1h)rehsspl 0 he car is traveling asr hel0s)p1,ht 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest tontco4 x09vu w/ 125m/s over a distance of 0.800 m along the t0 nxovwu49c/barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration16l y3fxg6slf of 2.gslf3f616 yl x5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile track c3 dk+qr3gf +uxd1qslur(qso/.5)b z (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that thi 5uyml) *fz mqcr5bje7 h)22euv(o4 ve maximum acceleration is 7)uuc2jehbezvf iyo*rvm 4 )l 5(m52q0.0680 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 i* )7qb g,f,nan vpyls*n a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of theqnyl,*fgv, p7 )ab*sn person’s regular 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 strength of 21,750 N. Whatuepfhwc; wtu: s3.,2f maximum upward acceleration can it give the elevator p3the fwwsu;f ,uc2 :.without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includin21/i6cs:zlp5xl wh*x jk,wct g parachute)/pz sj5 *x,l khlcx w:1ti2wc6 when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof.x3 dv hyr,a0nyb2l: x of a house 3.9-m high. When he strikes the ground belox0dhyva2r b:xl 3,y n.w, 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
(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 ti+b :o4.tbyobgh3zyc3rm p8 *he box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40*yo g.3bh3zt: m4 8cbbyoirp +). Determine the force 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 diagrade5ada5v4(8 q vzzh9d+y ru4y m for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body (n+y fwqg.d*jj7t5 tudiagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying tow w7fjnq.tj(5d t+guy*ard the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forcvd4t24*xtc iie must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagra c2vit4x*dit4 m.

  Arlene is to walk across a "high wire" strung horizontally between two qy) 1y9qj)2bqh wm9(yerx q1k buildings 10.0 m apart. The sag in the rope when she is ax )e(1 myyh)q qyqq991 w2rkjbt the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from ano.t(9epbof7s p5/2u f jtnt,* qxjbs7pther 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 1cmou 84cl3 xy.4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base,dd/ *cyxj b;ifbb)::zx 1go s3 Antarctica, as shown f b 1i);sxgbo:z3 djyb:/c*dx 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 samem lus1an8sph2+ f-6bs mass behind it, Fig. 4-47 . Determine the ra8+ auhf2n s 6sl1sbpm-tio 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 bucket-pulley apparatg ;1q x9y4jxcc6l zx:fd6qf;tus shown in Fig. 4-48. (a) How hard must she pull dow46qxq ft;6 9y ;z:dlcfjxgc 1xnward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 70qzrfcadve6) na . c6l5tvz( 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 (massq 5e6yl-btgs*0cr)oeamcd/ : $ 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 exuoe** -lrvk:y7bu w5ach other, as showkoe:yr5*b-vl w7x *uun 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 areg7vixr91ax15 0 bowim 9 dxst; 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 the lighter mass and then i d0gb swa9 x;xi51 v1moxr7t9its 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 connectedjfe.z, ev pa:1 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 free-body diagrams shown in Fig. 4-53. A,epja1zfv: e.ssume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 frict,sf1w s4d3tytion 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 requirxne,2ev w,i0z 6 :qupwed to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g5ryq 2e y7zn* s-umowp.bs:+ q. What minimum coefficient of static friction must exist between your feet and the floor if you are n7b2p*:ur m5 -zyy qs.qe +ownsot to slide?   

  What is the maximum accel md**qr sp.p:rctud. *eration a car can undergo if the coefficient of static friction between tq tdup :*.* *rprds.mche tires and the ground is 0.80?   

  The coefficient of static friction between hartlbz pm l3xc-23+3d izd rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can ymil+p3bz z3-lx2t 3cdou 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 s) +ac5ffx/o. d.nu oyat -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a r zy*6khe* ncc1ough 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 lpsk.9 og .47kda96hww:i qfxcoefficient of stat.slqw9g ko p 9kh6x4wad.i:f7ic 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 kinewk * -ib5nd/oni 4x:go,yk5sctic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A (pbgq+ bfa 1wbq2c 6(phave to have to prevent any motion fromac( +wfbg1 26bbq(pq p occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How jn0jfhv ) 75ycfar will it go, given that the coefficient of k5c7f 0ynj)jv hinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a hgu)pj1 xt8ngj87 llzty8e) t*orizontal surface (Figz7) jn8*uey gg 1x8jttp8ll)t . 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of /b*5xlx-ev+6e h aario 2y.afstatic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate so2eh fe 5ri*y- bvax 6lax+/a.lide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which1:8m+zm fym zj 4h)btl has an iz:1b l)fmj4y zm+m h8tncline 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 yhw) ;w ycxm2+hc-eo+ 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.;pcc u np0:p4 g9ei0tj 4-55 lies 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 initp*g0o .ftro:mial 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 speew wqhn9- 8yfpjm a0cr2.eg0p 1d 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 push:ggs/*fmyqjj24 hdb05921vs hj hd pbing on it with a force direc4dj1j g/h*92 ms5bghfyjps qd 02:bh vted 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 slipj**foje :7pobj w.-ii pery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitchi.*e :jjobp oi7w*jf - 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 5ygwm/,.vsrgw:o v0 f*w+sa o distance for an automobile traveling at speed v wgv,5so/f .o sywwm*+rgva0: is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dashf2(gce0ekof9qeb s, + when the driver deceler+o s2e(fbcgefe09q,k ates 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 initiai5+dbefjl fo; :) i6w b:b*clul speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the p0 -tra.xwku jtxg b,72br)1r4pbt5 mbacking statiob k4rr-x )jx.t atgbu251tb7w0,mrpb n 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is 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 bet*gt j75 uz;ikbween $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) gmy4c f;6-dr zru:6mgcan 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 eacs d8n6qc x,jm;h pulse approximately 20 g of blood is accelxc; n6,jmsd8qerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crashivivjcl, ,ms)f)8 )4,x poe it if the deceleration is no more than 30 " g 's." Calcula 4vjfiost),x)cmp,l v ,eii 8)te 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 z rd(zk/lu -9c b;oj av./oljn44e2w pan object is going to "hold its place" on the grounwudo49 onc.krvla l;24j(p-bjzz//e d, 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 vjw5h*j b h1 l+jmw1)fcars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. hfjm1w+wvb5hl *jj 1) 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 n*b4j hq4v9budt// mit rz7qyrjj)+4a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is jjr 9 zq /dbv+*r/ijntuq7y)4mb4t4h 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 jm b1oh*rhz:u dno-0q; -nv2ytop of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of *h v- dqnmj0u h2o1z;:nbr-oyWhat was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch whe9j koy qo*n9l,re the effective coefficient of friction is 0.60. Will the cyclist emer* yojnl,q99o kge 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 redesign of k5+2fsf1n j vaa hilly portion of a city. An important consi 1n5s2afvjk+ fderation is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from*4kbn3 p2/ 6f;qhfgssz47fm i cnyht 0)jkem: a thin piece of string while the jetliner she b7*fpshkcq ;ezj4i2 4n6/k :m )0 gnmht3sfyfis 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 t89*ze ef ort)*blw(h ro be several ramps connecting different h fl zwr98te**)rob( eparts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano 01 ddr;bk2vch (mass M ) using the pulley apparatus sc1hd2v0;drkb hown 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 acceleratip2dg(e/m;za7kag:d;c:h g9:ypbl gw ng 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 en7mcpw4 r1t,m-hkf jwm0kq 81agineer considers the follow8 mm,hw rwtfj pmq4711 cakk0-ing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a z+ecvec q(4fx,pfz ghp,p 15ron9w k 8tfw9+2mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar length. ava 9m6iac tm3b. q;h7Karen'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 (9;iabm.3t q7avc 6 mhaFig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using-6ow4 y 20di 0vptpnlz a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall buil;nc2bj8p y+6:qrpm 3wxw l:r)yv0f0 rmfnnd2ding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending k:ri8 q8l)2e uaz6:hnyb qse0 an ice field inclined at 21.z)u:a6 qleryq8 8eins 0h b2:k0$^{\circ}$ 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.