Why does a child in a wav oerdj;.;qt )-ibzb6gon seem to fall backward when you give the wagon a sharp pul;bezjb. -)dvo ;6q rtil forward?

A box rests on the (frictionless) bed of a truck. The trv.g:/ x)wnncfuck driver starts 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 truck and (b) by Chris wh.xwg c/:)vnfno is riding on the truck

If the acceleration of an object is zero, are no forces ac 3 oleda 4)(e,acum8zuting on it? Explain.

Only one force acts on an object. Can the-q 0 myp19tv1fpfhz )a object have zero acceleration? Can it have zero velocity? a9- pmp)tzqf1h1 0yfvExplain.

When a golf ball is d3 /jmhqp5fx, p* h.rjkropped to the pavement, it bounces back up. (a) Is a force needed to make it bounce kh/ q3ppfx j5j.h m,*rback up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in theubt zogn6x1h87.j)z 4wye*tp opposit7wjyztut zh1. nb4og)p8 e* x6e direction?

Why might your foot hurt if you kak-5nmbj s+ 2zick a heavy desk or a wall?

  When you are running)*qzdhgfx 3ex*9:dn(b 5g yry and want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (**rbqhg x) d39 :exf(z5nyygdusing 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, am*6p4-h pda uznd a section of the same thread dangles from the bottom of the stone (Fig. 4–36). 4ph*p z-a 6umdIf 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 ros.xqxm+z4q lf vn rg4 .e;.3b+7dx9dg hb:cw uck is twice as great as that on a 1-kg rock. Why then doesn’t l9x s:r4fzb4 qcm+.dgn .g;u.q whex3bd+7xvthe heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the 0 7nywk :ug.q2fbq;g(o4wng mscale had bee:ok0y(w gq g7fw.g4b; q nu2mnn calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across nb 6dkum 7.ne2a frictionless table using an attached rope held horiz.u b27kdnm ne6ontally. 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 th)wnx6a*- lkqc p0hzes jz,an .;th(s6ere is a net force mg exerteq6 - tlnzwjk)sex nhc6z;spha *a (,.0d on it by the Earth. 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) neededcpttk2 -tg ho 5d5(l9b to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare th2b(t 5cplokt tg- d9h5e 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, e3 pyamm 8/ca-fach team in a tug of war (Fig. 4–37) pulls with equal force on the other teammfa 3y- c8am/p. What, then, determines which team will win?

A person exerts an upward force of 4-m*rkb)wt 8kpaafv)9 n0 tlu- pun5y-0 N to hold a bag of groceries. 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 i- t) mf 8*9tr -- 0pbvpwa5yknkuna)lus exerted.

When you stand still on the ground, how la 02m8p5gtggkui6) l- tt*pfgo4yzt7 nrge a force does the ground exert on you? Why doesn’t this force make you rise up into the t4* l-t0g5tkiu2g8 )ggmp pnf6to 7zyair?

Whiplash sometimes results from an automobile .gibafw ;p i26x1l 9qsuyea( .accident when the victim’s car is struck violently from the rear. Explain why the head of the (gpyf; ax.2.qasue6 bw i1l9i 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 accelaqof)9v yr8e0ie5kqq-m)* f t erates, the crate ret)fi0a)f9m5 *q -keqevq8oy rmains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a p3ylnb5 .ke1)mdzq-pmush so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descenepm1qb .3 k-n)yldm 5zt than on the ascent. Why?

What would your bathroom scale read if youb2-xkq yrc i-zgzhwdmu m)z+6+1/ad6 weighed yourself on an inclined plane? Assume the mechanism fb2zry x 1-q+gmdck)dihza /mwu-z+66unctions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25mdmxz msws 1.)31 v6cdo eekbf8m e *g1xndm0-+/s$^2$?   

  A net force of 265 N accelerates a 7gvx gn3 (,0jki (lqury;axu.bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand/rza06jfk0yn/q,j: yxv hci) xanz dn6p 2,)i 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 yhl jrr*8 bd9bwmqm,*;.o) jq $76-\mathrm{kg}$ 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 h zmtt*com7;0( kiqy -is travelz cmh i 0*kto(-tmqy7;ing at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelle5l9x-vjt k .5.pg u3 w ycjdh8;so.x3swe gig3t from rest to 125m/s over a distance wssp9v3 ; j8x kj edwclxuiot5 g3-h.5y..3ggof 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelera j j+omgjiw+hf p2e-d:r76/q etion of 2.52d -ojer+6ijfmq h+j/e :wgp 7 $\mathrm{~m} / \mathrm{s}^{2}$ 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 fa rpd peu4+8/can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that(o5sb6o.x a:q*1wqzwxaj be;)s(bt l the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the qbxot(e b.bawszx:w )j*5ao ;q6(s 1 lmotor 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 w p.gdm.g2(xh m5ls:it35t iq motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of li5dxtq(3hsgmi 2:.g. 5 mtwpacceleration.     ----待选择----downupward 

  The cable supporting a 2125- 0b8y dyprg xy).j:*cnkg elevator has a maximum strength of 21,750 N. What maximum uydj.yb p:c*n8ygx r)0 pward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accelerati2, /s ihboj une/t*to7dy vp.+on of two falling sky divers (mass 132 kg including parachute) w+hs /*7yb . oup,ovneidt t/2jhen 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 of a house 3.97f fwv*kjlmr p;5:zns (bp58z-m high. When he strikes the ground below, he bends his knees so that hisl8b7( *m 5vrwzk; :ns pjzffp5 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 tiep/e.3bkcy3oja;5eyo 6owi p 5d to the box runs vertically upward over a pulley andk/ee.y6 opp3ybja ;35i5owo c 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 side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskeqvw;anqnjdjw)s*fe) ;p ( 7q8tball 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 ag ht 24i12chlv3t-ocz baseball (a) at the moment it is hit by the bat, and again (b) after it has left the-tcth1g v3 4 2hoic2lz bat and is flying toward the outfield.

A 650-N force acts in a northwmvvml3t7arw i-cz( 14esterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwcaz i(lv 4mt r7m3-1wvard? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally bfmbv3egzh0 gh:c.m :8p)ch;w etween two buildings 1 hgzmphc8.gbw30:m; eh):fc v0.0 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from another 3. /pte-wy10q-n+,zky sy/ afc d2$-\mathrm{kg}$ 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 15rvt5zh;i5 tb8 8cmntvs,q i 04.0$-\mathrm{kg}$ 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 toh-f1ek1 d go4g a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the for4 gdk1 h1fego-ces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 carsfgxd8a ,yvi;kj ,5 n bn5i-pm: of the same mass behind it, Fig. 4-47 . Determine the r; in5nvxk- gdb,i jaf8mp:,5yatio 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 apparatus shown in ib ti39jgv okoyvdx5s.;9 zk) /r(3 ncFig. 4-48. (a) How hard must she pu 5k33zikgyod 9nbsc 9xv(ijt;/ .r) ovll downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6f f 8.kuqx.i/q5$-\mathrm{kg}$ 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 (mgi0e1i n1 wt2fn(h(5bhfp *ut ass $ 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 wiebn ld bkhe.nxv1r6j89h +5c6aug, 4 hth each other6x1b5l ndcr+,h 9b6jeh 4 eg hn.k8vau, as shown 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 each initially 1.80 m above the ground, 0o m 8mqwjt:dgx .:4btand the massless frictionless pulley is 4.8 m above the ground. What maximum height djg x8bo0mt :: tq4.mdwoes 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 frictionless table are mzn+:69wd bla1be9reconnected by a heavy cord of mass 1.0 kg . Calculate the accz1 anm6 d+ew9b:b9lr eeleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between 9t4m/zbyi 8+yro ome,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 ,otqm4qzx6+wun . mg0w0ipe,x5 ape: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 i bocu.3j 30u0wup(gw a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your f(p uoju ucg00b.3iww 3eet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stue)g.sz/ksg sh z1-lub6y..* uqqy,)ixtie0atic friction between the tires6s)sks yg-il1).*hiux.qz eequ uzt,.yb /g 0 and the ground is 0.80?   

  The coefficient of static friction between hr( llyhxj1x )gf*a+jgbb5 zu,4m c9q- ard rubber and normal street pavement is abo(cmraxgbj ,b 5y gu4* -l9)q+x hl1zjfut 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4+u4)hj g hmhq1.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 restqn*3wj:-os np 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 with an 4bu7v mxlm0i )rsu0d d71k2qpasphalt surface have a very high coefficient of statib4m 2uskm di)plr7x107udqv0c 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 kineti)p( cn7tj.rr .6cdidic 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 would1;6bkk(xj- b) xsan9uo; p idl box A have to have to prevent any motion from occurring? Assuax)1bd skxp;b l(n ;j69k o-iume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far willdx m ,snu;t6ig9p*0:v7s rs kv it go, given that the coefficient of kinetic friction is 0.2v9gkisxpdu ;07,s6s* m :rvn t0 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 r4ef/cfv n9z7best on a horizontal surface (bf9 /zvef47cnFig. 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 coeffj;f(mgdp7 i;mh3, idx icient of static friction betwe3gxhij;7(,;ifm d pdmen 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 slide against the cab of the truck?   

On an icy day, you worry about parking your car in y6flv 3o vm7ye;n.7bkgour driveway, which has an incline of6 fbok3v7 nl.v;m 7gey 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 with a 28otc i2we8v(t6wf qb-q,g g n28$^{\circ}$ 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 Fekgi4 0-stw,g2i (mt da da4j3ig. 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 initial speed of 3.0 7xa l3,m,iocb $\mathrm{~m} / \mathrm{s}$ 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 steev1byepy30qt7 )nt+ q*kq c*mkpest 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 agaiw:v w, 6s 2yfcnrqtjvy )0rc:+nst a rough wall by someone pushing on it with a force directed upward cs f0wvrvjt:w:c+q, n 6 2yy)rat 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they m t .;wyj65f1z7us8 ppk siheh:elt. Consider a chunk of snow at the ridge of a rowpsf t6psz;8hiyu: 5e.17jkh of 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 di0lwy*m8 (fd3)gneg rrvv-l*e stance for an automobile traveling at speed v is equal*egy vrr3 le8)m fw-0lv(ndg* 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 qq3)gb bt(ul qr4 p.x5of a car slides forward on the dash when the driver g 53)xb4. lruq(qq ptbdecelerates 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 fr j5bo,r ,c0:z7gdf eis given an 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 from where they are filled to the packing(m4mpq 9gsn le:6(b cr station 11.0 m away. The belt is initially stationary6gm 4c(sbmqpr9 (e:ln 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 q;neu: bxy-9 en.gkspp / /vv5between $m_{1}$ 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 6 sfxejn(x 6*e;5 kg (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 model88v pn4cef4d+ oo9ar o:afms::)ccq p of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.c4 +:d 9q f)ocf mvo::a8pra8ecnso p425 $\mathrm{~m} / \mathrm{s}$ 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 sum:m gx)(loe5eh 6 p5(5wne wvzrviving an automobile crash if the deceleration is no more than 30 " g 's." 6hxme5ev 5 5w)ln( o:gmz e(pwCalculate 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 earthquaket+dw((wd . 9rp*m,8rgvvevb;hi rmq) is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictio.d,r(b pte8 g+hvwwv( 9;v *di m)qrrmn 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 involvid,9tcr3*4hvqcyatv 2 ng 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 of that car assy vt vc2cr*ht,3aq 4d9uming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each gko68r )fe qi*)vzjg3 7b(giu 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (f uk38)vo()riggq7e* i 6gjzba) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower ofg;o an-38 jjcwze g2(r Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air res;3g2( rzj8weoag-jc nistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy st ;pt)t cm0vp-zl(lr4pretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch withol vc m)rp;p(0p tlzt-4ut 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 a hilly portion of if,wjv;6pl 1(q6tr naa city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can acce6ljiq p1v;a,w( 6fr ntlerate 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 a th*8qt2 lwyai1skk3-h zin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She not8a2kstik3qz1hl w y-*ices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be sev (5g*)astoztcix*1o0 ww2i fieral ramps connecting different parts of the sttoisw1i2)f at g5*wi0c o* x(zore.
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 (mas lop9qt0t93ak s M ) using the pulley apparatus s9p3 tkl9 toa0qhown 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 accelerabp 6l aq cty02d(6*bi5nrm -8wr yr1psak7h:wting 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 cs1dnke rgkwi-5l -wh28m3rm3 hild-restraint chair, an engineer considers the following set of condi21d8kn hwskr3li -mw5emg3r -tions:
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 tr r;4tm,4ek ce)v uvca(ain 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 d :ms7gq:;n 0mb2gnrkKaren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the 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 climbdrksb g:7 0:qnm2m;n ger is more likely to be hurt?

A fisherman in a boat is 5t b5 demwvtr gw9o,vs+ zq;a(q )6)yx3amzd5using 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 building is allowed to reachdtt7 npsp6 +d9tmmg67 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 to x. qui3e(k2together are ascending an ice field inclined at 21.0o3 qt2(.iekxu$^{\circ}$ 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.