Why does a child in a wagon seem to fall bac g6/dq tpgbp(eg:-l9e fdos 69kward when you give the wagon a sharp pull6/ldo9pqbee(pg : sfg9-t 6 dg forward?

A box rests on the (frictionlg:4nye+ux 0ec4tiw 1 kess) bed of a truck. The truck driver starts the truck and accelerates forwar xe:iyt n41wk+0uc ge4d. 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 who is riding on the truck

If the acceleration of ;ho i isd+wu n.((rkw(an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Cz ull;cbg j- /)az4v2fan the object have zero acceleration? Can it have zero velocity? Exp /zagl4zbu)jc2l;v- f lain.

When a golf ball is dropped to the pc60vik/s igu 3avement, it bounces back up. (a) Is a force needed to make it bounce uc3vsi0/gi k 6back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log m *wa lw1rd3o0a 38zdovove in the opposit13 3vdwoaw *l0 8oazrde direction?

Why might your foot hurt if you kick a heavy desk or a wall ydwl eifba8k+p, s7x;8/nw8m?

  When you are running and want to stop quickly, you must dece4w .3ty gwgul)cf k:w2lerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estim.:wgg )wtck3fwlyu 42 ate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sa8 kwl18bsu9b xme thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull?wb1b 8sku98 lx Explain your answers.

The force of gravity on a 2-kg rock irjq -1;fp5/fyjj*wb es twice as great as that on a 1-kg rock. Why then doesn’t the hepef*b 5w/ qrjj1fy ;-javier rock fall faster?

Would a spring scale carried tsw6 +bjkutca7 2gj88v o the Moon give accurate results if the scale had been calibrated (a) in po8gb +w cj7v2uts8jak6 unds, or (b) in kilograms?

You pull a box with a constant force across a fric.ke5.d:xhq js: q0 kjytionless table using an attached rope held horizontally. If you now pull the rope with the same force at an anglk y.j.k: d e05jqxq:hse 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 f0 d8o3o1jnqh8xjarrv .i 60v:o3p p jxreely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equr.orvhpjo x61jq8a d j3ni0 3:v8po0xal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg ob 2 9sqtsi1/ uuv2 nd*tkhrs v1y-+g2tuject 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 ann tur *s29tq1kt/1s2-u+dvyu hsig2v d on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37 q.bq7tqb7gc4k5p1 ib) pulls with equal force on the other team. Whaq 54tpkqgbq.bb1i c77 t, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Dy (;0 meq3kawuescribe 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 obje kw3emu q(ya0;ct it is exerted.

When you stand still on the ground, hogfkmc)h7o9o 7 2v fgb5k+rd- hw large a force does the ground exert on you? Why doesn’t this force make you rise up into the a+v f9dkh7) -2hfg kbr5 oocmg7ir?

Whiplash sometimes results from an au;t .k0jfa/x. bbg2qlstomobile 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 abb;sx2 jkgf.l/t.q0situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acph1(fw/r daabx n16q+celerates, the crate remains where itx a/1(w 6b dnh1rafqp+ is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reacfzm w/yl;t.:whes its highest point, it slides back down but the magnitude of its af.mzy;/ w tl:wcceleration is less on the descent than on the ascent. Why?

What would your bathroom f4vn2 7wzr 7zwscale read if you weighed yourself on an inclined plane? Assume t4nfzv7wwz7 r2he mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25s eted t*kzro34bn8,l cu ks8;i)u5e4m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2h/qd c*gc5wwdjn, gvu (c1l+,.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 acckimav4 .dy v4by(y i9-elerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight omikrip)cl d- ikjm, 3ax9x)+6f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the car is traqt1cw73j59 5pawk*y1yby( jjdh0h itvelinbpaw itwjc 5ht yd9(j j1qyh5y 7k3*10g at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 126a6 cv;h7yvzt8c/ wdj5m/s over a 6ydc;6av 8/ whcztj7 vdistance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verti/yq/* ny 8 2ienpwg r0kce i-g0/l2wbvcally out of the water with an acceleration of 2.5k08/i/0nnwbe2y* rggli/qe y w 2v-pc $\mathrm{~m} / \mathrm{s}^{2}$ 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 quarterml)pk3pu5ou04a r cijaz92n+ -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 the maximum accele-u( irp(bm1w d8 x5ydqration is 0.0680 g . What are the maximum and minimum forces the motor 8md yb (5rxqpuid1(-w 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 bath) aoq3qd ,2,:;foqqn ooca8exroom scale in a motionless elevator. When the elevator begins to move, t,) ad 8 qn:o3;eaqxcqoo2, fqohe scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength .9s8gfu :f-(j 4 dcqwktp1va vxtv u,)of 21,750 N. What maximum upward acceleratioq(8vdg-j fvs tu9t :fx,)vu4k.1wpac n can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclukdn/obc;sa x2*3lw( vding parachute) when the upward force of air resistance is equal to one-fourth of the 2c v3wsdbno l;*k/x(air 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 housebwd gafdi);oqp . wzq/.a://s 3.9-m high. When he strikes the ground below, he bends his knees so that his tfd: soa qi wg//dz..abw q/);porso 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 ro.er*i )6ep zywpe tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on thy)p wr eez*i.6e 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 basketbal31 wgih v/whi6l 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 baseball (a) at the moment it is hit by the*;vxzs h07i+tj ghu1 z bat, and again (b) after it has left the bat and is flying toward the outfield.z +0ith ;su7hxjvz* 1g

A 650-N force acts in a northwesterly direction. A second 650-N force msnh jafzc/ (6( i2p23gmwvc+o ust be exerted in what direction so that the resultant of the two forces i zp vwg(ca6on 2jfc3hm2(+/s points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildy7 :m,zs+jrqw ings 10.0 m apart. The sag in the ro yw:j 7,s+rzmqpe 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 zj1krj 73)z4 j6p4hlaz ul/k ,a jcu1i3.2$-\mathrm{kg}$ 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 145j;tyg llqq(bk -4oa /.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 loca* rrs)9e09iurlddnro 161h3 es.y kx xtion at McMurdo Base, Antarctica, as s9ord 9dur)ir1n1r6xs0 xselh y.3 k*ehown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling ,6x(8csucj kz4mr9e- abo9+ hgjqp4ltwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tensiz-ajm6ub+9( 4cs4r e pogqx9 8kl,cjhon 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-pshl.9u b anv88zz:o/x ulley apparatus shown in Fig. 4-48. (a) How hard must s/xz8: on9 uhvz. sabl8he 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 begkmr)2l r3t3tarir m ((an, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (massu rt.9g(:bbh r $ 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 s 5v6l*e8 yue4 -oasklin contact with each other, as shown in Fig. 4yl8* -es6lkou5sv4ae-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 vfuazzq34-(4o ug 0 gvin Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does thezvq 4uz43-a(uggov0 f 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 arem0 )5fhfg.j0fkg) c di connected by a heavy cord of mass 1.00f hf)jidfg g) .50cmk 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 $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 kineticgw)q/gwt xu+ 7 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 starar9a,x4v6qgw6jk 1t.irasw)t 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 try: +v;:x h))6 y ,vbmavlm 1vudsrcd8bain accelerating at 0.20g. What minimum coefficient of stati,vydv8v xrybu m )1l;mc+6svad: hb:)c friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum accely198,;3uoo0k yamlextx e;z o v49npgeration a car can undergo if the coefficient of static friction between the tires and the ground is t 10uln89oyapoz;4,vye9; e komg3xx0.80?   

  The coefficient of static friction betwee *91--nyb bu1 eq6 wuvk 6)xouuwuw6ehn hard rubber and normal street pavement iewukwub h nv*b6e--uu6 u1 6oqy)1wx9s about 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 qub z;as0.rpo.+-id opv p;k3-4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest onl;n2n 0 x0brar 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 swp7u )ji) eaqkcpnr*nxea2v0b,;k +- ly(b3i urface have a very high coefficient of static friction.02q ,a(b uric+na l* bxey3nek-ip;7jv )kwp)

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 for z-hx:i*j9gkl p -f lp,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 woulyez pw4yp.r t 1km9yh ,dx4:h-*s s06,pkbdppd box A have to hay6hk 4:,p4tp-b.yp kdrmzw xsp*hs d 01,pye 9ve to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Ho 5amoios;p 2o zgu34d(w far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spe5og3m oi2u(apz ds;4oed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horiz6u 8 t1pt8ypjzontal surface (Fig. 4-54). Atp88tjy61p uz 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient ofeo8(e+x wvnd r ).z,ji 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 crate slide against the cab of the tro i.j rn+d v(8)ewxez,uck?   

On an icy day, you worry about parking your car in your dris zkbm ) n*;lul-6dz*sveway, which has an incl)l*-s*kb6 dslnuzm ; zine 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 zb r; + axm3n8oe:5eyaslide 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 Fiyuj/jg;9un t 7g. 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. yl-xq+ 6thn.xzx /schd/m ;u60 $\mathrm{~m} / \mathrm{s}$ 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 sp)xfl1i2w 4cmwg /hq)nl )jqs0eed 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 di 69bzblc.x+ rough wall by someone pushing on it with a force directed upward atb +69 db.lzcxi 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 melt.59w f0.t)i(idh riod .eja)sy Consider a chunk of snow id5ie.dfsa)0rj) hy .t9i o(w 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 g6d. lexd)/ ox rqojw+7q1c/l+a7wcuautomobile traveling at speed v i )q67da1 w/r ulo+wl/+.eo7dcqcg x xjs equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forwar8 cr dw94heh9dd on the dash when the driver decelera ehdr994w8cdhtes from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an inilz /ta7tdj4 *ntial 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 con9/e0v cr+sw vhveyor belt from where they are filled to the packing stateh/w+ r09cvvs ion 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kineticuo 5a )3yn(.yrsc3ppt:7 v(worxrpk7 friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) cao3dlxvlz6o0h3f( dl : n 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 simplifiehp4qu8ev8h7p s l+i6*6 qa;ydiav(end model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated fq8a 4 phi;yd6n 6eh +iqp78av evs(l*urom 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 if the deceled7m cn 6 *4txr6tvr*qmration is no more than 30 " g 's." Cam6n4vq r x*tcd67rt*m lculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is ol1s1iqw,l w n-nx ke/p6sb5(ly of(4a , and if an object is going to "hold its place" on the ground, show that the c( lokq-p y s4,won61 sxbe(l/nlf15i woefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident intmq ;e6icl. ux-q l809 )ujtkivolving 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 pave)-jt.eqii8kmqu6c;ut l9 0lx ment is about 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 thav:q6b nn(uabh . 35 uz0xs7thlt for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the vabbnz :l. 3(0hut5 xqshu76nbottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Totp(/2l(aq zdbwer of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air abp(( qz2/ltd resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy str.6hu9h,a fq3f f+qd caetch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having 9h.,d u qaf6chf3f+aqto 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 a city. An impo8+xp8 ill42 j 4,d ;s1m2cbhdyaflsnartant consideration is how flld8+a4jpmhs,y1ia 2 d 4 bxls8n;2c steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics ex rotskco:63ty:x+ :dwperiments, dangles her watch from a thin piece of st6+xkr:t owc3:od:ystring while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a superma lb9qsy523 xfgrket, there are to be several ramps connecting different paqgyl bf39s2x5rts 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 x (vm*zun p 1ne+kv p/),eice)to lift the piano (mass M ) using the pulley apparatus shk(zpveni*e 1/nvp) cux+ ,e)mown 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 at 3.5 s ,ev-d p*+d2qjuac.eg:i.gw $\mathrm{~m} / \mathrm{s}^{2}$ 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, an8t svrz q)qqjho603v 6 engineer considers the followi608sv o3zv) rt6qhq qjng set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian trm, hnmj,j94d iain 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 Kares:ma*-6,fp0.ny.neio w o hugh *.owgn, 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 r .nwo- f,.6ehy0 :s gug*imhpnoo.a*wope 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 climber is more likely to be hurt?

A fisherman in a boat is using a " 10-/a 9yrycj - pn4lg8/ .vhpqjr+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 re:fprjno;bqk :w (dmg9f )3ey g2v1 +goach 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 kd6 c pp *5 cnn s4170fk svgkn)9zk30p4ymtwvan ice field inclined atkws nnkkc)m0dn95sz *vp tc 7p1 4gy436pfkv0 21.0$^{\circ}$ 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.