Why does a child in a wagon seem to fall back4w a 88mm1 as: l3udjwyt-/zkkward when you give the wagon a sharp 4amw1d yw8z -/k8m ajt:3 ulskpull forward?

A box rests on the (frictionle,k,br61er q 7nqfe2yfss) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (1 r7fb 2e,6,k nyerqqfa) 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? E-g6hfazi nhxt n7a9 ( iv*ho1.xplain.

Only one force acts on an object. vtzzi6fhp69 fd 7h3/lCan the object have zero acceleration? Can it have zero velocity? if6tfvh67h9/zzd3p l Explain.

When a golf ball is dropped dy(fe*9grj c) to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the fcy 9g*rj() deforce?

If you walk along a log floating on a lak+ cv5:vm(,qgpkowbe87s8nwx fc rv8 0e, why does the log move in the opposite direction:pvox0b,wc 8fq vwc8e 8 v+rg(7m5ks n?

Why might your foot hurt if you kick a heavy d+(s iau:5rj98xoxhjr. vqf i6 esk or a wall?

  When you are running and wa k/, nr1wo9gmynt 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 deceleration of a person running at top speed to come to nk/ wrmyo9g1 ,rest.    m/s$^2$

A stone hangs by a fine thread from thefwe28pw 5fc.vmr5hj6 ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a ep65 hf8wf.2 mcrw vj5slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg uztfedy*7 *6) kd4aogrock. Why then4t d)*f7*zag 6uyd eok doesn’t the heavier rock fall faster?

Would a spring scale carxs(0kodyxr (dc 5 mke(0p) :syried to the Moon give accurate results if the scale had beedpo dy(x k)0y5csex:k(s( 0 mrn calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless tab(y7 (22ecgo0hdrt nw wle using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal twne2c7hr(y2od 0 (wg(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 under the influence of gravity there is a net f.v lkzxe,- 6lts8ltw 1orce mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite x ,vztwk8ll 6.1-telsforce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are onf(slw0:574hfn- y jhwav9mfy the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and o5m0j (:lwfa h-yfy 4nfsv9w7h n Earth.

According to Newton’s third law, each team in a tuge92c4 .m gawjo of war (Fig. 4–37) pulls with equal force on the other team. What, then, det 2eog4c.9jwam ermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Descibny t4)8fy2 zribe the “reaction” 2n4 ybi zty8)fforce (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground,o5u7r v es6 9u6u5khlodp3to-nnvxf-bl 2/ * s how large a force does the ground exert on you? Why doesn’t this force make you rise up into the ail5fv- u6x-5 p2 erhs ukbo/n679v ou3lst*dnor?

Whiplash sometimes results from an automobile accident when the victim’s csfs8 4 jmh8m)ucqyzw,o +57zoar is struck violently from the rear. Explain why the head of the victim seems to be throwj 4 o,5mczs8)s8ufqwy 7mz+hon backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelera,/ xtr.0 ou(gm:dg) avt q xmvom,s74ftes, the crate remains where it is on the truck, so it, too, accelerates oaxo:/)4gg 7mm vtd qu,, r0tmvx(.fs. What force causes the crate to accelerate?

A block is given a push so that iig7:k352r4 z2 bxso t9vsnewwt slides up a ramp. After the block reaches its highest point, it sszgxsiw:32nw4tr e2k7vo59 b lides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathuv1qse4f ::ijroom scale read if you weighed yourself on an inclined plane? Assume the mechanu j 4v:sife:q1ism functions properly, even at an angle.

  What force is needed t9 w9k8cfyefz/ 4,ayhg o accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accel8/oz 8c)d 0utta ,uymeerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 96chzuchk4lx0jwy cd)06w92 vj 7i5 h5 p0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a 4azg nz +*b.au$76-\mathrm{kg}$ 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 re s0.+yvofcwb+23h lykquired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h?oyvbc3 .ks2hf+y wl0+ -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 1 )w4h lqfy(+nf25m/s oveq 4h) f(n+fylwr a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertical7c k oy-zghsy3a 7 ag;0n.rc.kly out of the water with an acceleration of 2.5y .cgo7acghkzs;0 r3-.7any k $\mathrm{~m} / \mathrm{s}^{2}$ 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 qurwd*xi nv)gf *zu- 110b:urw(cs 5u zuarter-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 acceler-k 3ix;pt/daworxds*j4 a1:z0cl ur )mfj(9p ation is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max xmx(lf p3k1* i a)wt jr4daos:p9/cj0d;rzu -=    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 elevatxm*28qeyr,bjz ni w(9 or. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, b8*jmirx29zqyew n ( ,and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a y fndh3tk* x9j)3smmekr 9k6/ 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give mkme 9*dh3k3 j)9ytfn6rsx k/ the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallingn7;3a vyu: lyg sky divers (mass 132 kg including parachute) when the upward force of air gla;7: vy3n uyresistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the gnkdqnm 0k.*qyrz7d -*round below, he bends his knees so that his torso decelerates over kr.m -* dn qkz07q*ydnan 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 verticallyuyo(.ra/r,g 1, amkay upward over a pulley and a weight is hung from the other en 1ra.mgrko,ayu(y,a / d (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 forkm7sk snkm 9.*( j2u-m3fkhdm 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 dia rabu.uvc mk44:y4s o1gram of a baseball (a) at the moment it is hit by the bat, and a4.4oa c mkys ubuvr4:1gain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A zfd*3g.f4m7yg k x27 gu5k isnsecond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector k 4xnimdg5g. 273*s7kuzfyf gdiagram.

  Arlene is to walk across a "high wirib0fc j(*xhe6l4xy g/: ;*kbn el cb(qe" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is anbxe/f 0b**:ceq6 ( yblk(h;xl i4gjct 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 3.6g iq8ybq 8mjfw7( ce6dc g -8ritdp(12$-\mathrm{kg}$ 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.h)6f0ah7q;)0 w) ciiensjcuv0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Basuxpyz9 a)4 tj1:ihs7ahxxy*z .rx 4n-qg5r4 ge, Antarctica, as shown in Fig. 4-4gn :y* a 5-jxg7zi 4hr)4xqxth.4z yxrup1s 9a6. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4- wbg 5,s::rf0at os/ej47 . erb,w0 5t:ao/fssjg:Determine 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 the bucket-pulley apparatus shown g47xoe ood+ -nin e- 4+nox7 godoFig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 65lty 2ude/om5x ulq6w*a) e;6j$-\mathrm{kg}$ 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 blockvqils bgo n2*/84*csb (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 c3 :ammnp9 k;xgy)hd2eontact with each other, as shown in Fig. 4-51. A)h2 :my9n xgekda;3mp 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 Fi 1.jy cn53* e9kjfko ;ud) +8;wy axhnwd7wyatg. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What mawj xd71ykhy.+9t;8o f*)ywuc 3 nj;awa5 nkedximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless te)uypr m+d40qcfp 0l+able are connected by a heavy cord of mass 1.m u ef0+yr0ppql4dc)+0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 ofk-st op :7hj+l kinetic 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 start a5du/-ckn/bv hwjm l,(m, 5rfga( 3eav 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 97hbuogyuf , (minimum coefficient of static frictg9yb 7,h(u fouion must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficie+ xae/ xjxvv:.nt of static friction between the tires and the ground is 0.80?xj. vx/e +:vax   

  The coefficient of static frictionc9ix m fx:8-hq between hard rubber and normal street pavement is h:89 mi-x qxfcabout 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 a5 yn7rf f,2yqgt -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 m- zm v1ycz7b8b i8/bqon a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeffici8d:*e2qqy uv tent of static friction. t:v qqd 2yue8*

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 frictsh sm. l 5 s)7.vrh, h2uirm+xmob*ti4ion for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) hoqkv35x d.srs+id* hg(w large a mass would box A have to have to prevenrv*dk .5( 3sighs+ xqdt any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Howkfcrrl(8 dr0 , far will it go, given that the coefficient of kinetic fricc8lrf k,r 0dr(tion is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg qbqj:s*ipun zqhj3y+g/at43hw 37t .and 110 kg , are in contact and at rest on a horizontal surface (Fhg 37/b q.hu yj334*tjw izqtps+:qnaig. 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 carryi:f7: xzl9 yw+f :vupflng a heavy crate. The coefficient of static friction bet:zuf lv:fy :wf9+xl 7pween 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 truck?   

On an icy day, you worry about parking your car in your driveway, which has anph:h9 izvz4bk 5 9*c rp8ti/we inewri/ * h9thp piz95c8: k4vzbcline 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 oazx7h4(+uu8kyjhs * *8sh ab slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at a2 e0sou,b sba 43eus6en 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 4 cjpu -e4fws(/w jng9initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches .ouzp;vcgi, ikd v-b luukq0123 :*ko vsss**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 rmi)yhwj 58/9 vi +2;j+ h 7qe,cvears7wspvd kough wall by someone pushing on it with a fs5v emi wy7vejh;rp2,a j8/w) s+97c+kivdq horce 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 slippery roofs can become dangerous prs447cy :*-klxer e uuqojectiles as they melt. Consider a chunk of snow at the ridge of a roof with a puleq4yucx-s:k *7 4 reitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at spee)jae :l9m5 (ao z6 80*z dmmrqa7cjjoud v is equal oo5cqa8 6*r zm:zj mm(u) ed79j0alajto $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 8*n9ob ,0x3h kweyupx the driver decelerates from 4h89*yb0 eun x3wxopk,5 $\mathrm{~km} / \mathrm{h}$ 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 given5.pyfb2*bobm hxlr - . 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 arexg1z2cc +)rj38l4 zh/4:eetuq nz hjs filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accel 4t:1zzh 2 egjj+xhzlc/u8s3crq)4enerates 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 kinetic friction between 9s,j.tj6- xj;tu )rl;kdja 2h6s 37dkdzhqgn$m_{1}$ 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 bicy:rww, 5 t5p(syqxim*rcle) 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 approxi ft/b8z-xps cg:rg );th55t-gzs 5vgymately 20 g5 s)zgtzbt5p-vsc;gf r :y- x5g /thg8 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 automobile crash ifnpql *3lbes,2 vb 3l+)j1z ; g1kfcfbc the deceleration isj3 k 1)3f +q2f1c, zpvg;cb*blbllesn no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and a kog2f )z 8vm)ul/ iq+3. cesm4mq1qv6yx0mkif an object is going to "hold its place" on the ground, show that the coefficient of static frice/zkmxcuqq + mv 06 ml)ya og)81 ivq32f.smk4tion 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 accidey+c:j1sb os :int 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 spee s ysob:icj:+1d of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m trapprl54b8()a /eqghbp+ k:vnf hxm0o *veled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom/b+8 nh(opkpmrb4) el0q5af p vh*gx: 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 Tower of Pisa and falls 55 r:opsmn x09ij,q25ys m before reaching the ground with a speed of What was the average forcjq2: n,ry9i5soxmps 0 e of air resistance?   

  A cyclist is coasting at a steady speed off2 /bznn,:t pw8eomr isy: fnch201 0u 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emermf1rfucn:e , b08ni2 2:yo sht0zw/npge 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 workingwd/t r/oxu -b7ici/dd+6vzh ) on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can gvrw/icdi b+6do )xutd// h 7z-et 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 experiments, dangles her watch from a thin pe1odp.-l aqucrcn-8 b/) rt3o iece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58)e-nurr-otl 8c)a 3po/ .cb1qd. She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be se0pvrwpp4c/+q2df a8 n21:kt gz-hpr rveral ramps connecting differe2 kpf1z84ca w-r0dppnvp:g+rrq2 /thnt parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using/ccbc)droxt+9 / c ;yy the pulley apparatus sho y+brt/c;/) cocxy c9dwn 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 accelerat9 l.s,ul nc1vy t svkni8t-t1q0c tlcap* .1(zing 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- q ib+9yo::uizya. v2crestraint chair, an engineer considers the following set of acbyuzv+i 29 yoq:i .: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 ma-t c6 ;3mrvhl:wih2whfv on5 7ss of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes)vwv l;2uv*k vvi1n u- 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, assumin; wunku2i1-vvv*) vlvg 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 qoly ,(uy*dl:+c xof,y;v .ym $\mathrm{~b}$ 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 tal n-i8p03bnydz l building is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an icecx/*v v gb3ghfl-k+bvh4h6 p; field inclined a*hgkbf g3hh4vxbv pv/ ;6 -cl+t 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.