Why does a child in a wagon seem to fall backward when you give the wagon a sha j r5da+n3(zy*g9x rtprp pull ford3r g+yj5* t9a(p zrxnward?

A box rests on the (frictionless) bed/i 6rks34zbz u of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the mkuz r3/b sz4i6otion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no foio(p,k tg+j(rrces acting on it? Explain.

Only one force acts on an object. Can the obj 70dboj ipw7z6ect have zero acceleration? Can it have zero0d b7o 76wzijp velocity? Explain.

When a golf ball is dropped 2s; a)qz/:w1rbbwdtgu 0x 9h vto the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so9 wb;b1q2x)s razgvwu:h /d0t , what exerts the force?

If you walk along a log floating on a l,so wf.ot.uj8)geib2 ake, why does the log move in the opposite directiow 2 u 8jsbfte,ig)o.o.n?

Why might your foot hurt if you kick a heavy desk orq,n9 +uaa.k uv a wall?

  When you are running and want to stopm l(b:d 1ygk)unbo9 j7 quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience):)(y dmkgn bo7u jbl19 the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a finr .0d(0hmw 4io yefj3kf/nl2be thread from the ceiling, and a section of the same thread dangles from the bottom of thef k 4mlj 3. /oeiy(dfnw0bh0r2 stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that onhra7mvf()f5s q 4igtx +q+p4t a 1-kg rock. Why then doesn’t the hfht4qfsar+ vgmp +5( qi7)4txeavier rock fall faster?

Would a spring scale carried to the Moon give accurate results/pi:biz9 9y6wlkb ez60- -um;npzrru1wxg l 9 if the scale had been calibrated (a) in pounds, or (b) inn0 ub/--lipk;i6uyzw zp9 mgwr:xr 1b69z9el kilograms?

You pull a box with a constant force *hugz3n1 aqra8 dn2h)across a frictionless 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 the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decreqnr2n)h18dgzaa3 u h* ase? Explain.

When an object falls freely under the influence of gravity hjuh z44fy k q-+a)y0rthere is a net force mg exerted on it by the Earth. Yet 4)rj qay-fyzh4u kh0+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 when you are9g3i zy1b6ujw n5*fzq on the wingub39516j f*qzzy 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 the Moon and on Earth.

According to Newton’s th6-gnj ) c9bqrvr ln sf.9v we(kn.:;vrird law, each team in a tug of war (Fig. 4–37) pulls with equal k9(l vnvb ;) es9jf-wrcqn:6r.nvg.r force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groce8k d4 qntp hz6cq8.gz;ries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exertehg;c 86 ztq4qdzk .p8nd.

When you stand still on the ground, how large a force dogc+s(2kfdec6zpet(0 o9 x 9us es the ground exert on you? Why doesnoc6s(est2c e(+ pkd g0zux9f9’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’ 7ede1tvkhrwz4:t 0n 0s car is struck violently from the rear. Explain why the head of the victim seems to be throwhwkr e1v4:z07ed0 tt nn backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck.lf- ml hd)9ptev i733lb; giv)ezr+4d When the truck accelerates, the crate remains where it 7er9t+zldih3 gf v4ep l)ibm 3lv-d;)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 -ck5,ro0ljy y(lanx 8up a ramp. After the block reaches its highest point, it slides back down but the magnitude o,-la5cr0 xy ky(l 8onjf its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if mff; xch*n q,l9xv3a; you weighed yourself on an inclined plane? Asxm;*flvf9, ;xq 3ahn csume the mechanism functions properly, even at an angle.

  What force is needed to accelera0cg/ .rz gfplqgn476d te a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a b1ke 5js7vedsx 84 l :o0umq jpa3eq0d4ike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension mus)g knu:24: ivw, rufc 5ybrnl:t a rope 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 inwq5t r3cy(auag4*ghj:6z8 +s6 i mc$76-\mathrm{kg}$ 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 the car i4y;cj h /k4umnppl.*ts traveling at 94lun/py mtj ;* khc4p.5km/h? -  

  What average force is n9c0t;)sdr fh ha,2kzc eeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m,h c ar )kt;0zcd2f9hs along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of */s xfqa:nmk,ca:c7twc8w.v lgl9sxj 58q7t 2. *::, w8vfx7wj7 a s 5g9.q stcltmckx/8caqln5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-/b6kacgxk+t * i x x; s8r90xz5ejdhy/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 tom ,bup3xh8qg 1 be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor bqm, hg381pxushould 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 motionles a: p w;cabv/8 pv)-joyyhbk*+s elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of thec;ypj*h-a8p:v kb/w by o)av+ elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2:,sd4h)j ux kg125-kg elevator has a maximum strength of 21,750 N. What maximum upward accelerationk:x ,ush4gjd) can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (m75k p ngpz.c.fass 132 kg including parachute) when the upward c..p5 p7gzfknforce of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When scftt 4dfl+i0gr7.;ahe strikes the ground below, he bends his knees so that his torso decelerates over an approximaicdfaltt; 7 +0s4 gfr.te 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 Nojvqvlxp4;).sfu 2 e0qk(7 kb rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other siek .q v) lq4x;70jkuv(bs2pfo de of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagr*un*vbbuz897 yem6 aqam 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 di -u* 8biy g62zs-rdlfaagram of a baseball (a) at the moment it is hit by the bat, and again (b) after itgfb8url 6*daizy s2- - has left the bat and is flying toward the outfield.

A 650-N force acts in a nqt1 s*vbd6ao) orthwesterly direction. A second 650-N force must be exerted in wo6d1 t*s)bvq ahat direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buifoa4** -mr (bye6r 0fnsz m0wkp zcc)-ldings 10.0 m apart. The sag in the rope when she is at the midpc)6yzmf zm*-0c4aeof(p rbws* -r0nk oint 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 masslessw.jxl/l3: ; *gw cjokn 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.qj; ; lhm28ozt0$-\mathrm{kg}$ 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 locati0rqb kuie/52ezhb, + gon at McMurdo Base, Antarctica, as shown ink 5ei0bq,z2rgh+/e bu 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 oi.yp jg)jz n.l ;f:i 1svw:vqlu(4 g8xf the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the wijpz: gy4xq 1:l) vfi(sn 8j.v;gul .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 appara2ml;w ixav55 otus shown in Fig. 4-48. (a) How hard must she pull downward to raise hw5a;v 2l 5xmioerself 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 begzelnhzo +h+o3q / i;pjqkn0 2-an, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass a 0e5*rp z vbiqpk.vfq5230gt$ 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 ss9w7 26mko y c3gln/aa+.ln irurface are in contact with each other, as shown in Fig. 4-51. Ann s+ilk7w y3926ag/rmc.a lo force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above v0ahesa;: 1gothe 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 its velocity at the moment the heavier one hits the ground. This is its "launhe :vo 0sa;1agch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord o+f wml3 6apq:sf mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-bodyw6qf +p la:s3m 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 frictvqh0 rq8 t.ds6mm uc*5ion between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start nf cpjd5 n1x/3,jj, f.3ieuxn m+ sw+sa 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 agt) nfn-j+ 7nc train accelerating at 0.20g. What minimum coefficient of static friction must exist bt7+f jc- nng)netween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can unden1ve)l-,o2b3i tzub w8* 3-pfj sy clkrgo if the coefficient of static friction betkizu y -13tenc-f v)pjwl 2o,8*3sbl bween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal stsj: fa.jwn 9-sk8itnwu2 4cd ;ya;sw fo4nv-:reet pavement is about 0.8. On how stee u2 t;ny8wwsn;sow9j aand-4:-ik :j fv.f4csp a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80 a3(4i0f-9gh u)fl1 4da-u lxa bbikd a$\mathrm{~m} / \mathrm{s}^{2}$ 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 jsz-1edi q9;jxu 0h/s on 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 wo ; g2t 6cd,go.oizbr9ith an asphalt surface have a very high coefficient of stat ob.9,toogz2g rc d;6iic 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 fric)owecx5e5 1w lj ;widbpd63 o*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 4-2cga y*n-;)q xe0) how large a mass would box A have to have to prevent any -aq*xyn;cge) motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a pushv::4ntadpmh4k ,iwr0 so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial sakhrm,p0d44w i:vt :n peed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact zjp((( ib fvd6and at rest on a horizontal surf6bvz dj(fpi(( ace (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 carrying a heavy crate. The coefficient of static frictxui te rm*:boj08f2e n4c65ution between the crate a05: 6ui2*fjtrcb oe48utxemnnd 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 slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drivewa:f/,px* f2;g l q1x6qsoujt tvy, which has an incline of x6/,:fsutqv2pt f*q;j1xl o g 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 ov ln1y/cw- hzr4,:nk slide 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 lies on a pl 3xzrvnyv0;*ca 4hxo 4ane 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 sp zwwmoubmh-4li6(4c h(-nn4 eeed 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 reacjv5q sk-kco : hj8zg+:cc*qs8 hes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rout ) aeeli::zl)gh wall by someone pushing on it with a force directed upward at e t:zl :eil))a 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 projecti:ws9tz5eiq1 h*rhy8mtgr0jy p* 8n n( les as they melt. Consider a chunk of snow at8p *ht q :nj*0y rermz8g1t(i5ywsh 9n 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 stopping distance for an automobile traveling /ltmxpbg-r; xh7t ukyfr l0jt5;:u- 1at speed v ;u t1xg-fjlkt ux;5b ythp :7rm-0/l r 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 for3ue(yux 0 e r:e9wn(czu (n;kna3/ns bward on the dash when the driver decey 9 enke;n3u3s(( :wa(zrxcbu/ u0nn elerates 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 initi i6ezhgny 54a:9 ik07;rrymumal 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 packinq2quh a-m/t8r ca:n7thfr-i -g station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belh- qm78a/--urqithfa :rn2tc t 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 2ndnp*ze ;q1 akinetic 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 (including the bicycle) can coas5st 2a7 9tc8e4wgx * xb4wjwxat down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse aon );tucjo5d(s d/f 0opproximately 20 g of blood is acceleratou n5oj c)tsf(0 odd/;ed 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 surv vglly) xia5b0..9kx piving an automobile crash if the deceleration is. l. 5bxig)xpa90 vylk no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earta 8cfmjmz 87,2wa+sj6 o+ldnchquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mu a6m8acfl72m+zj ,dn w+s8o cjst 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 tw2tpq8 x1*j(g vt2(hejqqo*qdht*y8mo 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((v pjm1t*t22 qdhqo*tx*8 jqq8gey h speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each tkwo 9nhp8 qwqq5cs5k9t68f- 4 m traveled along the road, the elevation change is 1 m). Hq 6tnh 8qfkpq co5s5k8t9ww- 9ow fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leae,gs j/rwh 5 ic (q63ay-zgxn7ning Tower of Pisa and falls 55 m beghacn/z(ygx e w6 ,r 53s7jq-ifore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s0sxhn( ke3 xb4 but enters a muddy stretch where the effective coefficient of friction is 0bh0 xk3ens4x( .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 redesw)waj) qzt:4 cign 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 t4z wt): jaw)cqhe 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, da6ayovv - god:/) tkeohru.9w*hmj;6pngles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fi-o66 gehwj :v p.m*oh; )u /vkydorta9g. 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 areocj 1ik fidmnuq7ppto;(+1. 0 to be several ramps connecting different parts of pd 1nu1+ fo(tqi7 p;kji.omc0 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 wow0w9ug j6t 8sj2)xk to lift the piano (mass M ) using the pulley awk)xwtg w 082j6ujo9 spparatus 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 acceleratx/+ 4uipzkiq (ing 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-restr3ts(6i r xzyvjh pp192-/qwyb mm0 6ehaint chair, an engineer considers the following set of conditiohr-m0ej2xbsy(6vy1t6 z3ph q/ w9im pns:
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 Ikl-7 y :mfqen7dxhm: (talian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of simirq7x:eli*q-vx 4udexp0(; y s/e8s kilar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope0(sl x*k ;x74:pr ui- diesyq8evex/q 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 " 18 mrwlrg(kdwj +ss1mryu(7+- 0-1 $\mathrm{~b}$ 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 is0iwmn 1hg0tf;mqfh5h95gmdx +)b+df 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 an )b/(aby.ybfe r.r9 fg+btw f0ice field inclined at 21e)f 0y bgrrw.t( b9.+af/byb f.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.