Why does a child in a wagon seem to fall backward when you give the wag: 95 arrpqnu5n*u y1nc 4hrg,bon a sharp pul ,pgr cbn un5qh9415any *r:url forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts- s xhgnkr/qmgm;a :b9a4 e;j: the truck and accelerates forward. The b amj9km- xgga bhr ;4qn:s/;e:ox 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 an object is zero, are no forces acting on it? Explaint q qcf5y6)4 fv+,phh9ka)fcr.

Only one force acts on an object. Can the object have zero acceleration? Can it t0a, 7(z8-okjaqk +z/dxipxnhavedqt -p0aijzk7,z8xno /a(x k+ zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces bacbl;qbh:eho- c0;p s r xi-iz22k up. (a) Is a force needed to make it bounce back up? (b) If so, wha;bs-zbr ;:l o0hxecipi2- qh 2t exerts the force?

If you walk along a log floating on a lake2) 3mci stk,4ov-npg a1:nuwz, why does the log move in the opposite directiokt2a vuong),i 3 zwcm4-ps1n :n?

Why might your foot hurt if you kick a heavyklayg(e j2; 5o desk or a wall?

  When you are running 6ss*d 3 mwii4do*x5 tfand want to stop 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 deceleratiosdtimo x*4 6sfwi d3*5n 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 .ig::fo:o bhf a section of the 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? Explf g.i:hfo::bo ain your answers.

The force of gravity on a 2-kg rock is twice as great as88r7 ygtjwev* w* ax*3vgi pl3 that on a 1-kg rock. Why then dlev*r83w37j* y8a gpg*tv xwioesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resu kk2 nw+bq4fji3br 2+ jtqyf-3lts if the scale had been calibrated (a) ny-qjt 4wk b23jb q+ ff+2r3ikin pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionlew)oecfjdls f:/60 u)zss table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) 6/:w0c)fdes ozfj ) uldecrease? Explain.

When an object falls freely under the influenpq:1 l w+/;rp m/u,wj)jagqecs8oks6ce of gravity there is a net force mg exerted on it bye juk/l,w18/;jqqsas: o) p+g rmc6 wp the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when- o 1-47s dwlxpgzi;nx you are on the Moon with the fin gxl -sox;4w1d7p z-orce 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 Earth.

According to Newton’s third law, each team b*ml4*qks vli ;pbphi514x* e in a tug of war (Fig. 4–37) pulls with equalelp* k4bbh ;5v14l* p xis*qmi force on the other team. What, then, determines which team will win?

A person exerts an upward force ofqf0:4y f dpn3ic3c6bt 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what objefbti6nq 30:f ypdc34c ct it is exerted.

When you stand still on the ground, how large a force do22h34 2sacjjyx:ajat es the ground exert on you? Why doesnht 2c3sja 2:yj42aja x’t this force make you rise up into the air?

Whiplash sometimes results from an automob, o3fwsic/r5)6 pat) l-omzpuile accident when the victim’s car is struck violc3is)/ -mp,lrf5z p6ou)ato w ently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acceleraa*4c y8k*sd ea0vn-xa 3r6b cxw*g1 metes, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acceler- c1y3 c 80r nxaae4wavsg*xb *ekmd*6ate?

A block is given a push so that it slides up a ramp. After 6gbba71fwdp .the block reaches its highest point, it slides bawg1.bd6f7a pbck down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wein/x1ad ltlzfu3*z )k 4ghed yourself on an inclined plane? Assume the mec k1du*zfa)x4 z3tll/ nhanism functions properly, even at an angle.

  What force is needed to accelerate a chp jpw8sz;xs8yc lj+ jqin*4j /-h3t4lild on a sled at 1.25m/s$^2$?   

  A net force of 265 N aclahxjy 4 pc p.57l6mk0celerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is use2o1v. mfzc j;sd 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 ae ylt/3-0f qpv $76-\mathrm{kg}$ 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 a8xozh)fx h k/(*ui x.tn 1100-kg car in 8.0 s if the car is traveling at 95kx*8h)xiozh/t(xk .u fm/h? -  

  What average force is needed to accelerl+2s*u( aep)7 ksioy xate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle? o2 i(asy xl7e)p+kus*  

A fisherman yanks a fish vertically out of the water with an 66h;4hqi+zxf je -)gow9pem cacceleration of 2.5 f- );+jwgmei9 ph66zhoe4qx c $\mathrm{~m} / \mathrm{s}^{2}$ 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 quarter5t/sbka-,jmxo mq y z/wxh,94-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 48mv b p+(s:.nvk50 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are vv:b+s.m(npk 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 bathroom scale in a motionless elevator. When the eleva jt.9jw(y2s-p0 )ae d3whecqctor begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration. 02 - j qeyw .j(pw9eac3scdh)t    ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 2kawu p0iq0+-ta j is(-1,750 N. What maximum upward acceleration can it give the elevator w(0a k iia0w+sj -t-puqithout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclu;,+ o t6c*faqxy 6od7 gpnuc( tn(5kapding parachute) when the upward force of air resistance is equal to oneyf po7; *anct n o gx6,6+dp5(qtack(u-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 strikes the oxbk 7vc*-2l p w(aas(ground below, he bends his knees so that hwp 2cxob(7(sk*avl -ais torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vg2xd9( la lpy3/o,iql ertically upward over a pulley and a weight is hlo xl/3,a2igd y(p9q lung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playerm v+49g yai-kn.x x.jgxw9/fg
(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 baseba yy.0eh8en:m ymxj-kcvu 47a*ll (a) at the moment it is hit by the bat, and again (b) after it hau eyjaxm.cenyy04 8:m-*7k hvs left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 65g 2yq vwg6r0d iu5/qwxu,5 c:m- r(ckv0-N force must be exerted in what direction so that the resultant of th6c,xv0(/-i5qw gdgqwrm:5cyu 2vkr u e two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acghpcngrq ,. 2:hw29 luross a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she i.p9n,2h: rhwqc u2ggls 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 froyo7jpqwmclc653 *.fs m 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 14zn:ymouv):w*wuf 5m4 .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 locati*gok4 p2-g9me aufm)y6t;so von at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum o *eggsu) -o42 toak;fvpm6ym9f the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same massgf4zony8 yyw9vd xdgez d .0i70:tp:udn +*e: behind it, Fig. 4-47 . Determ+yo d z*dgypv.d8x d04yu7: n:0tni9gefw: zeine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the9 2mc ipdmvo brc 5iv0o3(d7i) bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowlv5(oob)c 70 i23mv9ii rdcmd py 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)jbqdnp: 7)e2g yr4 xl, 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 u4qt 8us5c1 qe(mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in 8jg k11 a,yn +zwaza2k-apw0w contact with each other, as shown in Fig. 4-51. A for+anzajg 8w w y02wa- k1,a1kpzce $\overrightarrow{\mathbf{F}}$ 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. ise ,vdd3ak(rd8(o ,f 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 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. o8fv( (,k,s adedd3ri Assume it doesn't hit the pulley.]   

Suppose two boxes on a fricw pzk ygc q8*ua 5tc9if9zw;7/tionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acc7kgw9;f 5 z9*i8/tauyzcwqp celeration 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 kineticry eff/ 8 vhxh7u 881(fcc)ie:dtlbb 4 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 requ1u r zn2qlw)r uu)d)tt *98nnuired 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 0.20g. What minimum c 9 k3ag89do:usnr, wufoefficient of static frictir o fk:9g 8s9uwud,3naon must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a ca b9dg,v huo8hgg.e/ p5r can undergo if the coefficient of static friction betwee,v o 5b89d.hge g/phugn the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber ao ; (l23qioh2ox) om ; hk)j6wwjq8gycnd normal street pavement is about 0.8. On how s)h2w(o jxoq8;o;mg2qky6 li ocj w )h3teep 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 jk9c :m1bbs)fd6u-s pn7p ;irat -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 rm6sa9 uf t o,2otwb/**ulla6 4x+tbg oough 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 avl0rfci- j h./ ;)* ig-fplyfasphalt surface have a very high coefficient of static frf -l* /a-pfl.;r ivg0 ihcjf)yiction.

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 a7qlvkq)hqh; 3 $ 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 mas3swcqd0rb j5r0c7q u,lw/4vq s would box A have to have to prevent any motion from occurring? qc5w wu4d 0sqb3j qvl,70rrc/Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it gl )1zj3k gr(;yd pb7pslides across the floor. How far will it go, given that the coefficient of kinetic friction is73b gg(zp)1pl jydk;r 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and -)1*ohyq yevilz b ,5)c)h tph110 kg , are in contact and at rest on a horizontab i)h-opthh,yyl z 5) 1ev*qc)l surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. T b-8pt,m*nh t(rt;- wbebvjx6he 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 ew -b r;vbjt6n( bhpt*-8x,mtof the truck?   

On an icy day, you worryr- co,9)snz mn about parking your car in your driveway, which has an incline of 12 mosnncr ),9z-$^{\circ}$ . 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 wj /0l7n mh(yzc a7t*fyith 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 angz67 pjgyld79xn.do3sq l0wd +m:a zjf,+2 rmwle $\theta=22.0^{\circ}$ 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 sp nmr14*at7p nieed 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 rea6l4y 1azfrr9iwd/n *x+zy( l qches the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someonetne 0xa99mhh7v qc u6x;6 rx/l pushing on it with a x9l vqtncu9a6h7eh; 0m6x x/rforce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slipperk9lei 5+tpd,/ewo9fny roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of9lwo ,it/ p ef59d+ekn $ 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 trzz * pi8(+tiwxaveling at speed(i8 +zpx*iwzt v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of aym9o5zd v/0zfoo1/ 0 m if:ry,badz +m car slides forward on the dash when the driver decem5m afzry1 f9o+ :,oidzby/z0o /mv0dlerates 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 giveygdp) m60ywlor0 1oc3 n an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled tk2/n;mm rqnrv*m j5dt(1q oc8o 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 di qmnr 5 8mkdjncro(mtv21 q;*/stance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction between 0(sm 4p-jru m9nh sy - /pafsmyz8+-iw $m_{1}$ 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) can coast yvh9 b:u kedk z4ke0.7down 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 ez9 :j8m ps8pqheart, at each pulse approximately p9 jp s8:mqe8z20 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 of surviving an automobilefxya,poo(y; ( crash if the deceleration is no more than 30 " g 's." Calculate the force o a,xpof(; (yyon 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 acceleratkh j6ngbkgo +i p(-j5or mi4k(rm +y12ion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coeffic1gn + gjomh2k6-+br(ry 54iko(pjk i mient 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 involvinyg j4v + i5u*n1f(lxy7dcwoxx q; 9vx5-co *rcg two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. Th5r*9lxvn1y cfuxv* (q4iygo-c j5c;7d+owxx e coefficient of kinetic friction between rubber and the pavement 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- 1gen+6i vcr;81jmywl .ol(qsin-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 bottom af 1+yerws1nc6g(j .olql 8i mv;ter traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droply 33hc(;n2 kmq 2cvreped from the top of the Leaning Tower of Pisa and falls 55 m before rl2kmr(q c3hve3 y ;c2neaching 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 -g x l,d,u*r5k ix1 cqeegx/f+enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge,*-grq,x5 u1el dek cxg+f/xi from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An imh(yb2ckw zt c0cq-5 -iportant consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from(c hqk --iwycbz t250c 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 physicsp+a qaw-p) -cs experiments, dangles her watch from a thin piece of string while the + asca )pq-w-pjetliner 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 supermarket, therel:z+)uw:co bvm56pf rwyp 30v are to be several ramps connecting different parts of the vwb +c po:u:lyr53pzv)0m6 fwstore.
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 (mass M ) using the p fm0,6qp3n calulley apparatus sa0qmpn l 3cf6,hown 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 accelerati:;z bbi./4bnx2n qt( ak(klvp8.fv e sng 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 chilhaz.3p2ik aur 2xi/oje6 vq,-d-restraint chair, an engineer considers the following x,6qa2er hva i-2u.3 j zopk/iset 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 train has a mass of 660 metric tons (6659m cqp+n:ww ksjan)30,000 $\mathrm{~kg}$) . 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, B0: 2kvwngb sv,du od:mr.h 3a5ill 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 md5 kv w:d, ga orhn:u320svb.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 " 10-1 r38gj8owl+fa y:(7(lpd ci dz$\mathrm{~b}$ 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 maximum speed of g +k(rwc, ku3u 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ice pxho: sfm2;x3field inclined a 2xs xfmhp3:;ot 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.