Why does a child in a wagon seem to fall backward when you give the wagon a swqz x-c5mj.l sde .nx975wlm 7harp pull fl9 7lmjm5w.q dwn5.xecsxz- 7 orward?

A box rests on the (frictionless) bed of a truck. The truck driver star-yxps3q-c8 ua/m+(t .v3svisdmh 6tl ts 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 lh-+sts - q avpu.mi 8syvxm36ct/l3 (daws, 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 8ovyh +d: hq;izero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object havuh d cx47f4yrl,s(7swe zero acceleration? Can it hxwydl u(rcfss4 477,have zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) wcci,z - b3g6 h)*d8b-hkdb aiIs a force needed to make it bounce back up? (b) If so, what exerts the f)h b8 gk-a6dw3bbicz-*dih,c orce?

If you walk along a log floating on0 o y:0:bo vtx5pcn8br a lake, why does the log move in the opposite direx oy0:8or5 b:ntbv pc0ction?

Why might your foot hurt if you kick aowxavr+/i/ 6 l heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. *v;g:ao1-honck, ge +k9rl j:o t*ae j(a) What is the origin of the force that causes you to stop? (b) Estim:*t:ehn,aa;kj9ce gk jvo1 +ol-o *g rate (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 the7(p) k:lc *wvh fbdk d-((oazc 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 liwadv *pc fb:(oz7kk lhc(-d)(kely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg-zp-6/p jxykt rock. Why then doesn’t the heavier rock fall fastkj6/ty- -pzxper?

Would a spring scale carried to the Moon give accuratep zjd3u2;jn3irr7q( d results if the scale had been calibrated (d uz rrp332q;(7njd jia) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table us0wsm*nyw*scwn 7 o/d 3ing an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box 3*w0wyw* snsn/cmd 7oremaining 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 thnwoy psqz1uajp.zr9 z; 7177sere is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Wh ;17a1yop jzn suz7.zq97pw rsy doesn’t the Earth move?

Compare the effort (or force) needed to lift a g x8vk co0spw( 8my/.m10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Mooxpkymg/s8 (womv.c0 8n and on Earth.

According to Newton’s third law, each td7wv (la1zs9v7 tdhb 3eam in a tug of war (Fig. 4–37) pulls with equal force on wv1lv9zsh3 tb7(da7d the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to h 1j)zxnp -yye6:r/z;d:xbv bv old a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a)e;/yy : -bvp6xzx bvzj) n:r1d its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand stillrpdb7k k 8):qd on the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into theddqpbr 87) :kk air?

Whiplash sometimes results frovpm3 p6p dj0up.y74z rm an automobile accident when the victim’s car is struck violently from thezp.6v7ypm3p4udjrp 0 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 trucjd(e ro/9q7dq,7agryb0 .hf t7 l jsh9k accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to7y d9 jl /rr.hq bq7 dtejf0(aos79h,g accelerate?

A block is given a push so that it slides up a ramp. After the block rg 66k2qt oart o:8h;sceaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent8r26tc6:k;sqh ga oot . Why?

What would your bathroom scale read if you :0ckruvy:oz,g w; 3taweighed yourself on an inclined plane? v gw;y3kzo0t cr, ua::Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child-x,;l . exm bchl;y+gb s7k3bh 1g0fbf on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2. syd3( b:(8aao7a qvje30$ \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 ac h9 al64veizrqjg2v;4 celerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of owtk;ng*b-j/cw,tn 1fk : qau.:mik7a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8. 4yy18f3xtuhc ced:hdfnp4 4 )0 s if the car is traveling at 95km/h? -c1u4cdp3 xnfhy)h4f8y:t4ed   

  What average force is needed to accelerate a 7. y (4tc+7iyv) pbwz1ug00-gram pellet from rest to 125m/s over a distance of 0.800 m alp 7t4b+)ycu 1igvz w(yong the barrel of a rifle?   

A fisherman yanks a e )5lu( temlb/fish vertically out of the water with an acceleration of 2.5 )5mueb ll(et/ $\mathrm{~m} / \mathrm{s}^{2}$ 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 (402 ;hp3rs7+xqs6 s;izdy ) gwwg,$\mathrm{~m}$) 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 485m4r:a jxp f5*t0 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exera jp*4rt5 m:xft 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. Wf7 dg mdbo159gio +l t.w6ll1xhen the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceler it bmdl5o og.ldf wx1l761+9gation of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N.5d-1neq1yw ht9/xe sl What maximum upward acceleration can it give the elqeh5/d1 1xty 9se -lwnevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling skf4ey w2gng*7n(n;oo 7 vfs6l yy divers (mass 132 kg including parachutlsg *7n6 oyo;vye4 (wff27gnne) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9nt aw5+r05xw z-m high. When he strikes the ground below, he bends his knees so that his torso dex0+na55 rww ztcelerates 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 vertica7idb4fi ghos1 04b mo+o bom+c9o9m;ally upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tablh mos;o4bbm mi+aoo9bf4c0o19igd7 + e 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 basv o07 g/tx.yxp-:u:dxi iytg:ketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the m95u z xs2+fe2 8.spphdyp gt6aoment it is hit by the bat, and again (b) after .8epsy a hsdu2fg 56t +p92pzxit has left the bat and is flying toward the outfield.

A 650-N force acts in a northwest9;l m,zo)y ylzerly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illuzll y;9oz, )ymstrate your answer with a vector diagram.

  Arlene is to walk across a "high 3h t1/wogavi ;wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope whe/a1t;i wv goh3n 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 hangincbom) 7.wumo /i2by h*g by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.oquqkr22): ye5ecuc p0 *xpx. 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 locq8zjcf -y 3g;-j:1yd g bdzbp5ation at McMurdo Base, Antarctica, as showjg8b-:jpzzd c- fb3dy;1y q5gn in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling t5c uxzx1+y m1ft,*hz rwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fitmxf5cz1u 1+y*,rh zxrst 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-fkd3au2 hc)8ae2la; lpulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to a2al claud28e;k)hf3 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 qg0eb,q;:abdw1rsqd ,.v kb8 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 (mastk lvxya1zty9tbe)bmx5c* m z08q 3(7 s $ 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 i5: dopb28,mqtf umn5+sle 2ean contact with each other, as shown in Fig. 4-51nm,fu+o 2estm 8 a5b:dlp2q5e. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 a-9cor:s8./ dvzl tz6vy0vkp7m ot.lhre each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximu.tm vp60 y79 dtzvo.lv lc/s8r-z:ko hm height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of macl )b,ub(. rjass 1.0 kg . Calculate the acceleration of each b .)bbja ,c(urlox 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 ofu600 .f(ozbzr8poifq 5o zbsd;bb, u2 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 ku,x1xfttpf: 4jc -2y required 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 trag sqo lc0315ylin accelerating at 0.20g. What minimum coefficient of static friction must exist between youc0y ll1 o35qsgr feet and the floor if you are not to slide?   

  What is the maximum acceleratwvt7zmr5 suej4 :j7pu *l x-q+ion a car can undergo if the coefficient of static friction between the t e-4: ljupz*7q+sm5twu xv7rjires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemenwlc, 6ep5/ zduegnj:2t is about 0.8. On how steep a hill (maximum angle) can you /j 5l pe:2u6n zwd,gecleave 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 v b1lw ,8fe dnnqw)40rat -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 t.obhxv-bta2 o2r t71 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 ay31b 9kncz2 *rj .xfzcoefficient of static f.zy 13jr9 bkn c*xf2azriction.

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 kineti)1 x3 d6t fy0ic6bi:wnzy aw+dc friction 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 rshx-v.l: wc(vw,(yd bkg;5v 4-20) how large a mass would box A have to have to prevent any motion from occurri w5r lvy(:v(h k dsv-cb;w,x.gng? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wxgc8)w;sowb:t70 f vv ill it go, given that the coefficient of kinetic fri:b w);0 xowt sf87vcvgction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at resjrsh :y-ipf13 t on a horizontal surface (y3 h :pfjis-1rFig. 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. The coefficivx 4k*a6mbq*ozf.4agja4d u4 jl e+p 0ent 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 and4lg vbpmuax*4 .oqf0 eda4 64jak* z+j 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, zj- 06ta//r4cd q 3aasq,owtywhich has an i, ad y0//4zr3tc-tjoaq6awq sncline 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 oy ff v60va*tnp49vnv s;8 h6hwith 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 plnqpy0 4,u bnq*y-klgfx81ia 8ane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initiv.q+vr .9 wyeval 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 theae- -ed w;ln/ir(qdo/ 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 w9,j/ ukxc;eo8ib jvf+all by someone pushing on it with a force directed upward ivb+9kfu;j j,oec/8 x at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they melt. C*xrk185 z4hzo*n kzt wonsider a chunk of sn15t rxz8o*kzhwk 4z*n ow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stoppin7uex;rr mw -b3wn6*k xg distance for an automobile traveling at speed v is equa7wrk; bx3u wmre*n-6xl 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 dashbt.g5u fwhip-p8xf 6 ,vhd.9dd oard of a car slides forward on the dash when the driver decele5igpf-vx9 uhfdp, .dd6 hw8.t rates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given g3 6/p mj khb7*yxkl;pan 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 theyrwf/,s.,/ u.qc arcw w are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final hf.,cwwrwqa// rc.us, alf 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 frw dw;4h yofvq9w.2 s-liction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) *3koc2e5*rkpm upw+w 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 hebn 51moy/0yknt jj.62 zw2xwoart, at each pulse approximately 20 g of blood is accelerated from 0.2 b 5.xtnywwo6oj mzk0yn/2 12j5 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the deceler+10aitr.)l/mjg dr7mhb -aa 1zfv2u iation is no more than 30 " g 's." Calculate the force on jt2/-iu gh71r z+d f. bav am)lira1m0a 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 eak5;fc z (9ji, and if an object is going e9 c(i5kf;z ajto "hold its place" 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 an ag,( clon:b1a:;k ns0kyez lncg5m u57 ccident 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 kyn1mz ulb 0:k5:g(o75se c,gcnl an;the initial speed 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 trave5vsb;3(w7d /,dtomzi h ki6ua led along the road, the elevatihvz6bd;a uiw do3 /,k m(5s7iton change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa qs k6ol4n81zp.ypqtz+ /p9b land falls 55 m before reaching the ground with a speed of What was/6kn9 llpt .q 48 zby+qp1sopz the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a3h4u mq30hmv:xk jv.x muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without mv jkh:uv 403xhq.3mx 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 redesignti t; hj2bw5 jd8y(oob c(lla d5t/ c1,vw97pq 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 , can accelerate on a level road from 7j1dcq;j (598( hy ,cpbld2vlwatt5/o i otw brest 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 piece oxkmv1il7 gm1vxb 99 + (,cwqapmuar86f string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the s 1 m+qlbvvk9x(w6a1ra8c gx9ipmum ,7tring 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 se8xvdfuk wm+zxpce,71n ) , *nfveral ramps connecting differek1f8+dwnm , )pevuxnz,* x c7fnt 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 for2p +crt +mo hs:sxs-3ace F is needed to lift the piano (mass M ) using the pulley apparatu:s 3 cpm- ohr+2+sxatss shown 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 aia9;us3hxp e; t 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 processew ob-zb97qc3uqbcr6bt4 ..o for a child-restraint chair, an engineer considers the following set of conc.q t.6 9e ou4 b3rb7c-bwzobqditions:
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 Itax jh20qp8de/mlian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, B1mu hl2q:rqm ab5b* :rill 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 r h*1q5 ma lm2:rbqb:uover 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 uabk 3pj r43b4(bmwg j(sing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall buildinhb1j6aa8cu)k6e0 t4 q 7hgqgjg 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 ascenddyu9bw zsf1/ w-k 8k3w*cf7w xing an ice field inclined awd /-8wk f*3cwf yub1z skxw79t 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.