Why does a child in a wagon seem to falla 6p*0g8rtjqk backward when you give the wagon a sharp pulq a860 jgtkr*pl forward?

A box rests on the (frictionless) b28 q;*4n mycu2nkfq qqed 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 motion of the box, in terms of Newton’s laws, as seen (a) by Mary stq2 ny*8cq uqqm4n2;fkanding on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an obk9m;sd (ptihyh- h /w/ject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the objk tqh3 jhsm5u tit34:nr17(uiect have zero acceleration? Can it have zero velocity? Explain.4kh(t 1jir h 7t33mi:nqt5u su

When a golf ball is dropped to the pavement, it bounces back up. (a +d5sc5 ndp6jh) Is a force needed to make it bounce badpd +55nsc6hjck up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in o)amtued-.4 b m-nuh:the opposite )bdmem4tha-: uu.o- ndirection?

Why might your foot hurt if you kick a heavy desk oz0nf:7 rjraj5(fcw gk x7w44g r a wall?

  When you are running and want to seqx9 t:dx5ut6 top quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a pertxt 9xud5q :e6son running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sectiommsmu)zs(;y 6z 1)es sn of the same thread s(6zm s;)se yu)s mzm1dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or 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 on a 1-kg t1u r ejtmg9uh*f 8w4-rock. Why then doesn’t the he-trfghew 8 1ujt94*mu avier rock fall faster?

Would a spring scale carried to the Moon give cme8*b m4xy 3iaccurate results if the scale had been calibrated (a) i*b3m8m4yx ic en pounds, or (b) in kilograms?

You pull a box with a constant force ac zi kctlix7,0or)zo41ross 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 remainingizcolix74 ktz) 0,o 1r 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 influegcxwasm* jz3/)f8yf. nce of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Ear3fymj*az .w )g/fcx 8sth. Why doesn’t the Earth move?

Compare the effort (or force) nee d8( b*c6ulay-9b* yq4 +qsl.uhjcnk sded to lift a 10-kg object when you are on the 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 qbhl6b sl8n c* *u(yj.9-yda+c qusk4Earth.

According to Newton’s third law, each team in a tuanb:j.ij l 3.ua o4w-xg of war (Fig. 4–37) pulls with equal force on the other team. What, then, det.4a.bx:u olw ji -nj3aermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desc6ph;k-x;r vx iribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its directioihk-6v;;px xrn, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the gro d k0h0xs9xxf azj+,;vund exert on you? Why doesn’t this fo0 hjvxksa;x0+d,x9 zfrce make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car oa5 )kcrum,f8w r (ma,wr:+3 6diqn rwis struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it re ua3(qn8d ,)rkma+:6 crmworiwr 5,fwally?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,);hw)sniw+lzsb7 f9e the crate remains where it is on the truck, so it, too, accelerates. What for;7hiew )nlb)9s +fwzsce causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Afgap *yjo iu5+:qtu3j( ter the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent th3uj+y*g:jut (i 5qpaoan on the ascent. Why?

What would your bathroom scale read if you weig0r2nbdsq 19z gp 33zsghed yourself on an inclined plane? Assume the mechanism sg31 z3d brnqpz9g 0s2functions properly, even at an angle.

  What force is needed to accelerate a child on a sledbw lg1mi 5zd- 5dpsu55 at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at ctbs +, c:dx-t/alq3o 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a ro )9t misl5pnj0pe 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 aev;(j+ 59iw hq:korzq $76-\mathrm{kg}$ 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 rq1pdmua8/,w r,, * b/qpc ghapequired to stop an 1100-kg car in 8.0 s if the car is travelinmw 8, ,dpra1c,/qbqu/ap ph*gg at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram peljq*6hda*./qaqmk:lh let from rest to 125m/s over : .qaj6h/maldh*qq*k a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verticalbm j-)m.jp(bhly out of the water with an acceleration of 2.5 bjhj m-)(b.m p$\mathrm{~m} / \mathrm{s}^{2}$ 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 (4(sfw7 st;ka -q02 $\mathrm{~m}$) 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 desig ;mp ffmqek 851xed7.gjf)rxu5po 5 2pned so that the maximum acceleration is kfd)5fp5x;75mmgjpq 21perex . 8fuo 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a 4y nevc lrarqx/hm39 99gos-h98+ gs zbathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleraev 99y hgm93o8+ r nqgc azxhrs-l/94stion of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevat+ak lw lgz; 7ux9+esv:up* /l8jbmno 9or has a maximum strength of 21,750 N. What maximum upward acceleration can it give toa* ml9 nz9e8kbug w7+p:xls jlu; +/vhe elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky)ik3 gwp+a*k f divers (mass 132 kg including parachute) when tap+kf3 )gk*wihe 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 3.9-m high. When he strik:/izjh*lp ,hvgpnz zvqg,52 2 es the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the masspizv2z h ,*2 5znp/ghlg, :vqj 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 verticall -iq t9v9v b*lq3ptl:p*k m(rwy 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 box9tiv pq-*w lbk3 rlqmtp9*:v( 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 forz 5xjm .gl7s ayx//-ur 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 diagram of a baseballoe6x d h9s (h s*5 u;xi6ls/tf0)kfkrf (a) at the moment it is hit by the bat, and again (b) after it has left th5()e0r osu66*f9;s iflfxkd /h kht sxe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be(w 2la17ox ar7ma 6x8sqzlff/ exerted in what direction so that the resultant of the two forces points westward? Illust21l/sxq om7(aw6 fz7a x lfra8rate your answer with a vector diagram.

  Arlene is to walk acrosw(ki;3chb, x ts a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in th w3;,hxikbct(e 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 bh/5m1(z-sy b mf+ msx3j efgt;y 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 14 nmuoi7; 0h*yp :pirc,.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Bzj27r+adv6 d1zv e0op ase, Antarctica, as shown in Fig. 4-46. The sum of th7zvro a16vd2d+0zepje forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 qgsud y5b to*uhgf+ **-v/s0z. Determine the ratio of the tension in the coupling between the lo/o*ugf-gyz 5s+d h0* tqsuv* bcomotive 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 bu4 gvj1mj6/7pxsfm k+ztk2q y7cket-pulley apparatus shown in Fig. 4-48. (a) Ho/ygp71ks kt7mv q jjf2m +z4x6w hard must she pull 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 g bd.1r s7.z6 4c-izlj,lbncz 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 bloc8obx ,2h2nj )6uayh fpk (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 frictionle b*c1 igzfi:h4+8qmp tn 4wx9rss horizontal surface are in contact with each otherm h*94r 4iziwqf8:1+ gbptncx, 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 eacuw- j un-v f5ehe7g .2yrfr)o het0**ih initially 1.80 m above the ground, and the mass ti0-r7weu )5h2oevfh*f-ne ujy* . grless 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 pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of mass :o chb+;uo*el 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume u;e cb+lh:oo* $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 gjtv y0lls+y/wf9d 2x jt/+n (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 require4dsvl j9q 7+iqd to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train ai hd05rs .1lxm64ih eqccelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slideq4ix 1l5 ihm .dsr60he?   

  What is the maximum accelerati6/-q26euwi tb rc6e ioon a car can undergo if the coefficient of static friction between the tires and the ground is 0.80? t6o i2irwqe66c- /ube   

  The coefficient of static friction between hard rubber and normal syvlhzj9(3mn42hs1 l e*5slmuj37t i ltreet pavement is about 0.8. On how steep a hill (maximum angle) can you leav lm7j2zs1u(e 9 il5*hls4lh33tj mynve 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 al(,5/lsd (sv:)x bsypclv7r h t -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 res*noj( x5) l ggen u24auyp-a,at 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 asphalt surface have a very high coefficqo7q tp n 6zzi3qp)(e;i3q2 wjient of sta zq qt7pqwi3;) i jq3o2(np6eztic 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 friction forqhw h.o1v40bo xw+ht9g c5/ai 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 (Examkp4e:zbs5 hz0-2a kkwple 4-20) how large a mass would box A have to have to prevent any mok s:e-khb0pkzw4 a5z2tion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the f02ura6i0 qiy3q sl4hst2r7 zlloor. How far will it go, given that the coefficient of kinet37i rl0ushst2za i q2yrl6q40 ic 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 ah7;* l(od3u y:mwdhi rnd at rest on a horizontal surface (Fig. 4-54). A diy(7h*l3dhw mru:;o 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 coeffiob/5 f5bq 8 r8/hpzzj bb20ezjcient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the cra80ezrb jhqb/2bzjfz85p5b /ote slide against the cab of the truck?   

On an icy day, you worry about parkiow+m;5 )w dhy/ b,rfchx y;;lhng your car in your driveway, which has an incline o r y5mc+);;;hlw,dhhxyb o fw/f 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 sli*-0.sk:ld kwh w ymi1rde 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 plane tilted at an an1pc96ls hu- xsrtb q1*gle $\theta=22.0^{\circ}$ 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 initi05)-j+oc rcn ipo e98lbqi *zral speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 6.rp+j( + 0vcixv/ne w2d0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on it wit3x*.jv(pcb s w7 blf7eh a force directed upwcx3be 7w(7f.vj *lbpsard 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 roofs can become dangerous projectiles as they )n)okip gbhu68z,x.m melt. Consider a chunk of snow at the ridge of a rooo b.)zg)ki6hp nmu 8x,f 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 ati5ww0do :f-. zgw+jyl speed v wfo g-5w:jw iy 0dl+z. 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 dav.pn u*4(v,w wu/lac mshboard of a car slides forward on the dash when the driver decelerates frolav /v(m, unc wuw*4.pm 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 acy2eml- qo91o- jx )hpn 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 l)a b( ;n5ggrvnb -mg4from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip.n;g(vg4b 5gm r)a-l nb 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 kinet e9j4 (77dp bdu+ukeojic 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 (incrd..nt/63zt ;3 dug3bmqeqaaz6l 6cpluding 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 simplifb6.+u; 7y uhj6f9v f2rbyqhv eied model of a mammalian heart, at each pulse approximately9bfjy+vvf62ybuu7q 6 .hhr ;e 20 g of blood is accelerated 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 vokq,e(/yiv/ of surviving an automobile crash if the deceleration is no more than 30 " g 's."i/o(q,/ vky ev 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 0got5wsce9 70fuz5xd an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the 9c0 fg0s w5zt7do5u xeground 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, exwku hab nfvg8:pi ms;( :(/ )h-+kg(j: moekamamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level ro ifmnewk :j+pb(( mamo(gu: g;hk k:)h8/v-asad.   

  A car starts rolling down a 1-in- 3f0rxb(+h-qy7wqu er 6 mgm0h4 hill (1-in-4 means that for each 4 m traveled along txgw-mmh r q00(7eryb6h3fu q +he road, the elevation change is 1 m). How 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 droe pum2:-n)glf z7 kqg1pped from the top of the Leaning Tower of Pisa and falls 55 m beforg pn):u2mzg1fk -qe 7le 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;av7 qinej k 6)ao4ft* enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge qf6* ea)ikjt;o v74 nafrom the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hillq e5ii1e2 otc5y portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can gee te155 co2iiqt up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics5k ,uco 2gttj: experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 2k:oguc2j ,t5t5$^{\circ}$ 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 connecting dir 2-3 xgbu/1emqok urt1)e .nmfferent partsumo/emx kn u1bq3t1r 2-rge.) of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mas)k*pbp7b)avp1g*qe w s M ) using the pulley apparatus shown1 *)gpe pqwb)7*vabk p in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating cnx0o1 0xs; tznk+ 2xmat 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-restraintwgi 3a ,7aslh8 chair, an engineer considers the following set of conditgw3 8,aihs7 laions:
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 av-b6ir co9x 0c 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 9 rj 5+dv9b4aqox 4pfdof 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 re59d4fvbro49 p+j dxaqsult 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 ny 6rh+njn1(i using 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 za2kee fi4j .+0r svu4building 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 togdwiax y9a; 2e c3f:gh+iw(8:nm ksn,uether are ascending an ice field inclined at 2n:e ,ixu kc2w w:hfd;g9ma8iy3s +(na1.0$^{\circ}$ 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.