Why does a child in a wagon seem un;j5hixcgx3ma8 2) kto fall backward when you give the wagon a sharp pulca;8x) hjk xgmn52u3 il forward?

A box rests on the (frictionless) bed of a truck. The truck drivei8lf) w x4*tier 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)8ifxt el)* i4w by Chris who is riding on the truck

If the acceleration of an object is zero, areum33u wtaw/ su*e qjjp18;mq 4 no forces acting on it? Explain.

Only one force acts on an object. rl7 xx7q nb54gCan the object have zero acceleration? Can it have zerx7 bnl7 rgqx54o velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a f stp5*m4zeps 4txe;j 1orce needed to make it bounce back up? (b) x4p;4 s5z*est1 emtjp If so, what exerts the force?

If you walk along a log floating on a lake, why does the lo9(tz n 6j)wr*d3npfeu falx ;/sjds/4g move in the opposite nxz/sn6 j)ewt(/su f3dr j 9*f 4ap;lddirection?

Why might your foot :lu1.e n4 aqc1 haf)ochurt if you kick a heavy desk or a wall?

  When you are running and want to sto;tt71)nmtdagj ac*2y p quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own ;7) ycj*mantt 1td2a gexperience) 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 f(knp kom y-de k)i-: gag4)uf/rom the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull onkukeg-k-m o4d:)ya f (p)g n/i 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 rdnv9) rusm*d1 ock is twice as great as that on a 1-kg rock. Why then doesn’t m91 vu)*ndsrdthe heavier rock fall faster?

Would a spring scale carried dv9me6 7oc,zsw13a dc)bom,pl(fq 5 ato the Moon give accurate results if the scale had beebo,q c7omma3c9e(v)z1dwa 5 pd, slf6n calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant fo 6t.3ew. su+mc*yfkfjub,jinp;h 3eh;w-7 eerce 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 accele,7; fwk.hei3 +b;jn 6.p*jtufem he 3cu eyw-sration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity the v( wlp+z-ep3lre is a net force mg exerted on it by the Earth. Yet by Newton’s third (+3pp lz-lwve 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 lif r1hltqu4uk 9 6z0tp5tt a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed tk p t94 rq5u6t10htlzuo throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each tea k: ;pu.s3coggm in a tug of war (Fig. 4–37) pulls with equal force on the3:u pcgo.ksg ; other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descrik ;n o*7zxg(ecbe the “reaction” force (Newton’s third law) by stating z(gon7k *;exc(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 grok7o1q 6dbtzd) und, how large a force does the ground exert on you? Why doesn’t this force make you rise up into th)1bqz o6dkt7d e air?

Whiplash sometimes results from an au srks4a0emnp qr7h s.7va 2*w7tomobile 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 rean7sq47sh rmeka 2p0 v7w*sra .lly?

A heavy crate rests on the bed of a flatbed truck. When th).)npm3uc7hi n5 7sa j+wgv rle truck accelerates, the crate remains where it is on the truck, so it, too, accj.hpvn7a sr g lmu7n5i)+3 wc)elerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaqt : 7.zmaa z/bn)qlv5ches its highest point, it slides back down but the magnitude /bzz tma )n. v:q7lq5aof its acceleration is less on the descent than on the ascent. Why?

What would your bathroom i+h v9s h,y)pbscale read if you weighed yourself on an inclined plane? Assum, +yh hvps9)ibe the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled a(aup*zu1a(e+oey : ed+( x rsit 1.25m/s$^2$?   

  A net force of 265 N accelerates 915rs2 u nwwf bye9vguo5/b:ih- j1p t-2dgcg a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerag6j+9yhhjur ,-wy ea-r /b*8l;gnq jote a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a f mtq :q2m k8p/g6d(wz $76-\mathrm{kg}$ 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 is tru l+ :: v, 6ci5qnqcw;jjp1vteaveling at ew puj+6 :ticcjq;5: l,q vnv1 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellets2k gk p)6hg-z from rest to 125m/s over a distance of 0.800 m along the bak)hg 2pgz-s 6krrel of a rifle?   

A fisherman yanks a fish verticj0 k -)ph/ a;gddt1(yx+jfk )v/gdskl ally out of the water with an acceleration of 2.5 t(1y a g dk0k )+s;x//hd-jjdgpk)lvf$\mathrm{~m} / \mathrm{s}^{2}$ 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 bg+- u w6-;2eec5f:bqeiua 3iwrg*g v (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 485 mkvch6z/4q r3bw tb* va2lr+3kn1gt50 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum andtw+tgbak/v6qbvc3r3nrk 14 l hm5* 2z 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 in a motio1mjnx;xn o98wnless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular wein 81mn ;xw9ojxght. 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 ofxlu 330 qki0,wob99j bxcso*w-d:qjl 21,750 N. What maximum upward acceleration can ikoc 0xb *i0-s dbq9, :xw 39wqlujljo3t give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclu d 1h:wc54pxwbding parachute) when the upward dww5hp4x1c : bforce 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 hejb32 ;ukxnh 8(m5/mvn1ka qxouse 3.9-m high. When he strikes the ground below, he bends his knees so that hisk8 ma/j;kn1qbmh(x2vn e3 xu 5 torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs ;hefbung7xly-: q9l+ vertically upward over a pulley and a wy9-el+:xnq lhfb7 g;u eight 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 basketball player gi+*.,e.k q hrcxwyp8gd4zn-ii 5xa,
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body dvbvlu:jhz) xi: p6q67iagram of a baseball (a) at the moment it is hit by the bat, and aglvq xuhi67:j)bv6p z :ain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a nor e,a9- rmr5ljs*+yghvthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diaa,95jhme- lg +ysv* rrgram.

  Arlene is to walk across a "high wire" strw8ta1o; dxz6n) j qbeze5)8z(gf sf1 fung horizontally between two buildings 10.0 m apart) fj dfz 1( 16;szgwq5noee8axf b8z)t. 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 bucku/a 2pcku.4csgi+vra1 . su t3et is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1 78r myzfhqm 7rt2)o8g4.0$-\mathrm{kg}$ 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 locationg68ykmny .1v) 5dfmwc at McMurdo Base, Antarctica, as shown in Fig.wkv d yg85mnf y1)m6c. 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 atfh.3lbvy l1 crdow (/0vu+5mq4g.xy.2 vox same mass behind it, Fig. 4-47 . Determine the ratio of the tension in thev+lf .d a1.g/uw.3(0 yybc v v4omo5qrhxtlx2 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 upwadelp 3f,:oqyd*cdh 9; rd using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downwd;e3lp:d ho ycdf,*9qard 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,;x4 kutd(hip ,nf)sr ( 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 b;frdv:pbrw - o; zy.bgj*9q4* xh myc-lock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surto3)v. hukc pn mr 4a31cuz()xface are in contact with each other, as shown in Fhkrtz um(3)p nxcc vuo13)4a.ig. 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 grou 9m-xdj ki0y6q m(bq0n 2ktbg7nd, 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 "launch" speed. Assume it doesn't hit the pulg (i mb-9qj n0bm20x tkkyq7d6ley.]   

Suppose two boxes on a frictionless table are connected by a auqlmg/6-x nt k3 64srheavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using tnu6kt/46rsxm 3lq g-ahe 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/s ijrv ,3ie a+yseh2 )(ba+nw friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to st(dj(y xpjoj5* art 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 accelerating9:t rxp 4aq.an-d s7ae at 0.20g. What minimum coefficietq9a: x.sapan4r d-7 ent of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stati6.a:jf 44.mtn +; mhunnyu pffc f.j+h6:m 4f.tapum4y n fnn f;uriction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavlnm9 k.kx4m. am7cyw) ement is about 0.8. On how steep a hill (maximum angle) canc n49wm )m.ma7kl kx.y 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((vl-wvk5; pgfdyljyqk -)ht 7i9p (4py6jqq -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 restq ni1e jat/gi o1w;z5aq *32yg 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 witlvs tfz1s),tu l29z5p)4zexlh an asphalt surface have a very high coefficient of static frictsvlz)l9exz z ptt4 u),fl5 s21ion.

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 frictnzpv4t61mh ,;nn)g h bas/vd1 )wkh*sion 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 Figj0,dp/r ehz5u . 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurring? Ar5dhupz 0j ,/essume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acros; q8f6 ttf+inei4 a0 1jsaawa/o -gi/os the floor. How far will it go, given that thfa4qtnswi+aatoo i1i/6/;g ej 0a-8 fe coefficient of kinetic 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 ax 7*dllx:z3dcvaprops0 go4 4(cvw(0t rest on a horizontal surface 4vd7 3w ccgz:a*0(d4xv (xprll0sop o (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 sr f,os05a;xf crate. The coefficient of static friction between the crate and the bed of the truck is 0.75; 0 r,sffaoxs5. 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 driveway, which hs4 mr(zgws ; f:mua;rc: amj*c:xcp7px.zj , 1as an inclin4u * spxrr(z:ca m;cc mj1,;jp:xzm7:agw sf.e 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 withh h1-uw*xol3 a a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilte)9 kf(s e pxt;q2hk+cld 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 3.08ozr k86e85tu.vp jv.pvum;v $\mathrm{~m} / \mathrm{s}$ 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 spee.d)mg ;lo pg,hdf( q5zd 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 wallu60l -euf 2ila by someone pushing on it with a force dir-l2f eui ul06aected 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 slippery rol*oor lm+8 fh*ofs can become dangerous projectiles as they melt. Consider a chunk of slm l+8orhfo **now at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at spe9(f f-/dbekiy- .9nzcs-7hb.eqq ad szj5 ff *ed s -fi.q5hds-9e 9n j-(*7.fyqfc bebdz/afk z v 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 of2 q2ek j,d*w p2plltx-0qym k4 a car slides forward on the dash when the driver dt2mpp*4ed y2l-wjqk,0xk q 2l ecelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given vmpc(pieav/ s.4p, gh.+k 2ipan 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 t8v x(7tcoman 8o the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is thmct8n (vo 7xa8e 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 between n szf:5jt)aswz+(w, j$m_{1}$ 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 bicyclv2+ t fdei:rjv*7htiu - ues:*e) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pad gnu m0+d+*sf.k pd3q3nl 6zulse approximately 20 g of blood is a udk3+gd0d6. pm3q *aszfnn l+ccelerated 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 crash z(lx src388 g4xkva +jif the decelera8 zgvlc4j a8 x(kr+s3xtion is 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 prc1(yoa*bje .noduced by an earthquake is a , and if an object isjcoye. n(b *1a going to "hold its place" on the ground, 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 scenejrd-s7usa * xhm(6;mi of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about aj*m(s-ri ;6 hudsx7m 0.80. Estimate the initial 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 .rj6j/4l 7)g byt ollbsz u+,a4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottoj /b,au l jy74)6zol+rltg sb.m 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 *s8:uw s *(p+mkxhac/. q8yc d.xofwqtop of the Leaning Tower of Pisa and falls 55 kh*x ao+8fwxc(qc qp.*yd8s.wm : / usm before 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/s but enter6 ck57q m4dw dv-xk+*rez qa8js a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist em7 vm w6458jcd kkqq+dra*xz-eerge 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 rr7t7x3wr/u 0 d )mvzuy8qhma)edesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without /qm7h)y0rz u8)uwvmtx 7d ra3slowing 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 experimeohh+zvy8;lz2ug. 7y 7wu 8ysd nts, dangles her watch from a thin piece of string while the jetliner she is i7gy7uov8suhy+ d ;2 zyhz .lw8n takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecti9hc.zz l 22p.azzci.tng different cizah2.pz.c zl2t9 .z parts 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 liftw.zdkle6.8r mlag /:k the piano (mass M ) using the pulley aegz 6 ra 8mlw/kkl..:dpparatus 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 accelera+ ;z3m dszi :uai,rkc4ting 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 engin3fyhlk2 (q8xseer considers the following set of conlkh8q xfs3y(2 ditions:
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 mas /525 hm z)aa6x3gdf r y9mdph+qqtk-rs 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.llr.swwl8 g:6ln2vl9x -s ar) 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. 6n llr.-x a l2)8gsl:lw sr9wv(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 usasbtc.e e7 t. ;9 t0gz.ybte8aing 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 bu 9rvswanr4 (b)ilding 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 an ice fiei + 4l3hwdmegakw,;2 qld inclined at +wa,lgm3; w hdq e24ik21.0$^{\circ}$ 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.