Why does a child in a wagon seem to fall backward whenn63iu8b.jt 1- u*rv*-w s dozrro)obh you give the wagon a sharnho -rdu3*jziw ut-*)ors.1bb8vro6p pull forward?

A box rests on the (frictionless) bedb (g zkhq0,z4m 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. Discg 4z(bh, qmkz0uss 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 an object is zero, are no fo8wm63pjdu74 cs9b n ltrces acting on it? Explain.

Only one force acts 1 3yqyk l7lcxt-nad68 ss ;zv)on an object. Can the object have zero acceleration? Can it have zero velocity? Expla6nsz7s ldy xc3a1)y v8t- lqk;in.

When a golf ball is dro/g41 8glo 4xbsy2oek5m wz.c dpped to the pavement, it bounces back up. (a) Is a force needed to make it bounce bac/5z14gc s.4wodyxoe k2lg b8mk up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the .4x +o kf2q 2/m vxeeqewq(s)s6yqvh1opposite direc1e qw v.(qxsmef22k6)qo x/ esyv4 +hqtion?

Why might your foot hurt if you cpu)k wx.-c 9ii,nyy: kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceleratew3df 82u2b.8w6euj zckgs*z b quickly. (a) What is the origin of the force that causes you to bjuwz23 fbgdw8 .ek2us*8 c6zstop? (b) Estimate (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 taz7 z 7tz h.s(z4yo(bcpctq4- he same 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? Exp-c 4a hstq.p7zo z7b(z (tzc4ylain your answers.

The force of gravity on a 2-kg r3-rbufp ,wtc2 ock is twice as great as that on a 1-kg rock. Why then doesn’ct3fp,- rbw2ut the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale h)1ds l -eoy.tt3eb cl/ad been calibra )3 l/ye ob1t.lce-stdted (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a friction6 9mi 0x/v -hnbn-ymfuh 8(gc;srk f)xu2f2pjless table using an attached rope held horizontally. If you now pull the rope with x )c9hi;hf(fm6p-yuu rvk2b/0-2n fg s jn8mx the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely ug+vcf4oe4xy1+c wk: ender the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law gc:x+ yc14v f4 kowe+ethe object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are w qja6 0u 1g1sunqm9x8*5ppz ton 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 speedmqsuzx1 195w*6 apu8g0p jntq on the Moon and on Earth.

According to Newton’s third law, each team;9 gnlwssu4 mk gz9h4/ in a tug of war (Fig. 4–37) pulls with equal force on t z4s; wk4uglm h/n9s9ghe other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag ocs0g 0vbm hoy31n(m ybhz6b-/q4+sj k f groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (dqhbybhog y/6v0 mms(- js3 0+kb1cnz4 ) by what object it is exerted.

When you stand still on the ground, how larh70mml2lw*gb56mx fj ge a force does the ground exert on you? Why doesn’t this force make you rise up into theb0 mf5lj6xm h*7 mgwl2 air?

Whiplash sometimes results from an aut ,gqzaugn);9ssad28dd: .erep: q;qorsy:4 lomobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be throwqe)d9d,2ueysz:lg 8qr rn:ogp s qadsa; :4;. n backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelersmyxt l)*5iu) 4yx jl:ates, the crate remains where it is on the truck, so it, too, acceleratyt:)l)xj y4ui*lsx 5 mes. What force causes the crate to accelerate?

A block is given a push so that it slides up a rampw8fof vn2r/ o9lwapt 3.lbb r *rt69v/. After the block reaches its highest point, itvfr9w /2l 8b .v/*p9wtbora6nltf 3o r slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you9l9; qfzsto )i weighed yourself on an inclined plane? As os9 9i;tflqz)sume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a w9wck7,:2yqq hx7ry:v fh ,sxchild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike andjj( wn5 g5(bxhbgx)n, 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 withm5 zz0a/ pe9m nnie9,fstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a *j.j7,pde(wuy iy)ou $76-\mathrm{kg}$ 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 st+g *x0 *xvygjtop an 1100-kg car in 8.0 s if the car is traveling ax0g+ v *tygxj*t 95km/h? -  

  What average force is neededq5y jf ma3b-c7tf,8 2fqvkjz , to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a jftyf ma,v3cqq78,5zkf b2j -rifle?   

A fisherman yanks a fish veyfx isd 4vm49*rtically out of the water with an acceleration of 2.5 vdm yif4 *94xs$\mathrm{~m} / \mathrm{s}^{2}$ 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 (40p5 c2 80j fjmdjxo65;5uqwywegh(x- n46gjic2 $\mathrm{~m}$) 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 i o*eqy8omr1-00 7n8 muwtgq tacceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert ontog 1wi780oqunem-*t8 qmy0r 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 bathroo 9o(gi qqe76dm(1heml(d xy0g m scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular w71qi(degmoqg y(hm 9de6lx(0 eight. 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 maximumc)y 0gy6 0nclp strength of 21,750 N. What maximum upward acceleyp00) ccngl6 yration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky wjho;,j ;11dox fqie6divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their whf1e6jow xjdi1;o ;q ,eight?   
(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 tr-tcy0z jv4s2he roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelera-c2vys 0rjz4 ttes 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 ropr(help*x +n0g39bzo u e tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Detenb+x *rl3eu9 (ho0 gpzrmine 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 diagryvm6kbw j)gij f: :;:vam for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at th x*q1fj ,shkee)o*6xp e moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfio,hf p*jsx) e61q*xe keld.

A 650-N force acts in a northwesterly direction. A second 650cnu7j 7un1ipu a+2go4-N force must be exerted oi g4pa2+ c7nuju17nu in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across *d ;tc( e(cmmua "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope*mdmtue( ;( cc 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 ma** b4pj2y jjjvssless 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 14.0vr;a:3ozt (dw$-\mathrm{kg}$ 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 housi2m2 wg-5e3qcu w-oz+ o8kaum yng unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the force 5+g8- o2cqu-akwmy uw zoe3m2s $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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. 456 ibm+5m l;.efml gbs-47 . Determine the ratio of the tension in the coupling between the locomotive and the5 bfie mmm6sg l+bl;.5 first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus shown i u5 50zqqi,eyx.4gaqe n Fig. 4-48. (a) How hard must she pu,5q aqeux 5y4i. qegz0ll 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 race9,)kupj;2snx ms o q3 mlv;2sp began, 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 (mas6a;9o;. er.ryykrmpn0(f ctts $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in co4 ab7dvrwve: f6cza/w /j.m ;intact with each other, as shown inaw jzfi/6cr; wd .:mab7e vv/4 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.y dvxk;xh t-atyiy )a ;(6+6z/ qwl3dm 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 the lighter object reach after the system is released? [Hint: First determin+aqwyv;xyxhy)z6am / t;6 d-k (tl3die 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 f9a65 +zoa jsl gc-bbndir:+b 0rictionless table are connected by a heavy cord of mass 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 Fiba6iz -brcb l5sg++: o9dnj0a g. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction be+*uz 4pd) o,wqizrgb z9s3p)c tween 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 require )kbv/ 79mqbbzd 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 accelerating at oq5 , ;z8kuy3hj+oqur0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slideyzro5hoq8 +j,q 3;kuu?   

  What is the maximum acceleration a car can undergo e+dhj a+1ip o8if the coefficient of static friction between the tires and the grjo pa ih8ed1++ound is 0.80?   

  The coefficient of static friction between hard rubber a-+q)j tufi(yrnhw-1,xamy)ts ba0 f )nd normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parkef,m-)y+a autf) 1ixqyt )0j(wnr-b shd?   $^{/circ}$

  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-n juh0i :k:uwxcd* 8m at -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 on a rough 3 8gh -sdkygwk);)w 6qc0$^{\circ}$ 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 3-woe(d sv.p,bb.q+ p:pqbvx surface have a very high coefficient of staticvbo 3x .spv-:dpb(qe+pw, .bq 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 for (p ra5- 91r6sisl owapzu7g9b 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. 4exs+.i( ey fsnk;d/l+-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from osey(+ ns/d kf.;lie+xccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides aceri1. 6v4 i) jofvmv+gaq0)ctross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initrj)14caeiv )f.ogm6 vv0 t+iqial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at res-rq3)v*whk zdcx p1mm2 yg g58ix( l5wt on a horizontal surface (Fig. 4-54). A 620gwxg)z ck m mx3r5i*dwqvlp1y 52-8(h$-\mathrm{N}$ 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 cra3qlmn3t /httg z9w+a9te. The coefficient 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 crate slide against the cab /n+mgt9zh 339tqtalw of the truck?   

On an icy day, you worry about parking your car in your g. ssmv,h tn c:x+5b+usk9o0e driveway, which has an inclik9 sbc s+v+ nxt0us .eg5hm,:one 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 wy-i z4.q7r) *e u9dh ,olys*vbocmy5cith 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 tilt, -g0e7gb rbjh xacrl,1 tr:c/ed at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 s 5zng61ai0ff2314 n/ fpnse bhg/khq $\mathrm{~m} / \mathrm{s}$ 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 6fzc8,jh. wyr1n0eu6is+ a r80 a+ofmd.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 / k;ovuftw *:ta rough wall by someone pushing on it with a force directed upward at : t*fwvu;/tok 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 slipftyd85k0eh- ipery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pi ei0fd5tk-8 yhtch 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 automobij0u bji esyy4 t7.ly0dv a8j)0le traveling at speed v is 8sijue)djyb40 l0.a 7yyt0vjequal 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 forward on the dash when the drive0 -x2tdssa(kg r decelerates from k-sta2xs d g(045 $\mathrm{~km} / \mathrm{h}$ 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 initial speeyz w**vxq4 + iman7,of*p i.wfd $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to trduc eple-2 49he packing stat-lced92peu r4 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 kinee4o1(bhvk/m f tic 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 bicycg: lvn.wm -o*vle) 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 pulse approximats p;65s :ycpcy*wum(r/antmq0p2 p 1tely 20 g of blood is accelerated from 0.25 s y w6tm(t12ppq 5crm/:*c np0 usyap;$\mathrm{~m} / \mathrm{s}$ 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 p(sg9r ;obek gt7f25 mcrash if the deceleration is no more than 30 " g 'bgk(sp5 m927frtgoe; s." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquakwv4 loz8 zvx+.e is a , and if an object is going to "hold its pxzv8 oz w4vl.+lace" 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 scene of anh0n*21db ek+nvl y1y,kye ix.rw: f;rv w0r(h 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 asey;.nf(rv hyvnde klwi+0 *k :,2rr x1b0wy1hsuming a level road.   

  A car starts rolling down a 1-in68-63u sxy- bx )5rserob nxuu-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bxb)uoe x nxbr--8y5uu3 s6s6rottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppc/ 4:*tig) gmases n*bed from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forc* * :an/tiegc)4gbmss e of air resistance?   

  A cyclist is coasting at a steady 47; k8:krslvaxaou1 u2 c,sol speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 112; ,su8lo4r uax s 1koc7kv:al m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesieu4vuxr. w 7l1gn 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 slowing down. A particular small car, with a mass of 1100 kg , canx rw74 u1ulev. accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles h r.b1*,b+3yyg7jj bfwm nm *sier watch from a thin piece of string while the jetliner she is in takes off from JFK Ay31*.bjm , rn*7 bwgfymb s+jiirport (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 supermarke3d9puo as0*+oy6wbgc t, there are to be several ramps connecting different parts of the6y* c0osw uod+ga9pb3 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 bk6xmrr 5qi9jo jy:0 2)tp*lelift the piano (mass M ) using the pulley apparatus shownl5j:x9pim q * 6rbek0t yor2j) 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 x*jtzrszaazed a o **2)2t,+i 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 chairorh fabq3x)isriq6 ,2v4bh/ ., an engineer considers the following set of con3o,q4bfr haq h2r./i 6xv)i sbditions:
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 mass of 6f ypi9z8k+6hs 60 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, Bti kzav*:j(j9j+0fi-.a0 closg e jd8 ill and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (lv jejc+ -oj 8*ai0.i j9kg0sfd:atz( 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 i ra0n1)3 gkw4m1lamra " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a max4*vg emn4+qy dimum 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 roped6trmo9evvj ,:gnh(j 2 together are ascending an ice field inclined agj(:,t9 nmo e2v6hvr jt 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.