Why does a child in a wagon seem to fall backward (n457 mgoec pv4a 0ipfwhen you give the wagon a sharp pull 07 4ifv(epcomp 4n 5agforward?

A box rests on the (frictionless) bed of a tr:qmm:n oh cp; mga6c21uck. 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 (a) by Mary standing on the ground bes q:c :pn;mocmgha216 mide the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no w8g0d :b9bxdcej-fx )forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratio6im 52pcr1fpe tnfo(+n? Can it have zero vnocm i1+ f2(erptp6f 5elocity? Explain.

When a golf ball is dropped to the pavement, it bn(v q7 rk1b-d3z; ai vs*v5 zuaz2b:kpounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what p;(vi*v-2 ka7 z bzrzsd5 :qkav ub3n1exerts the force?

If you walk along a lms*xo-;c5w j 3fbk4huiffk4: /9ygszog floating on a lake, why does the log move in the oppositck js:hf -;/xis49bw4f5 uy3kmg * zofe direction?

Why might your foot hurt if you kick a heavy desk or a zoop:;;chhpp71l* 6 rkw 5 hqxwall?

  When you are running and want to 5j 1c 1+fhfulaxpr7v+stop quickly, you must decelerate quickly. (a) ulprf5cav7f 1+xhj1 +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 rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the 2j:j7opo .;rv3ur jxrsame thread dang;oj7r o prjrv .:u3x2jles 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? Explain your answers.

The force of gravity on a 2-kg rock is tiyzm y(ti5)k )gk 68pe-sa c2rwice as great as that on a 1-kg rock. Why then doesn’t the heaviekp 5crk6ymse-8))2(a igz yi tr rock fall faster?

Would a spring scale carried to the Moon give accurate results if the svssro37z*i6le,gn4x vw 4,nlcale had been calibrated (a) in pounds, or (b)nz6r44, lvi el3nwx 7ov,*ssg in kilograms?

You pull a box with a constant force across ad4( t hoy-s12kf)k8hvxcuq*f frictionless table using an attached rope held horizontally. If you now pull the rope with the same hvo12x -ff kcud(hy 8)t4s*kq force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravityl3oc 5gp4 mty9 there is a net force mg exerted on it by the Ear3p4o5y l 9mtcgth. 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 objec*lsy h)v:gol7 t when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a l7yl) gv*so:h 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of gr 0ljd v.ofn 284kux 6xm1ye(war (Fig. 4–37) pulls witue 6ljrm4f2 dvy1n0(8xx. gokh equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a b /rav mv ke4f6j mj7b/v(6lj; m0dyw)yag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (bmk47je (am// 0ybdvy rm)j fljw ;66vv) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a 3bfcavymiy1k 4h22l .force does the ground exert on you? Why doefcly v2ki4y1bam.2h 3sn’t this force make you rise up into the air?

Whiplash sometimes results from an auto5:kdivtcm.g 1 lp9q1vmobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown bacd1:.pl gtv5 q1miv9kc kward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, b2dh1jwf s ;6 t1qlb p(r*zxan;7qqj6wqfz . 5the crate remains where(d6b1r fb j1*2z.6l zqq7w swqqj5;;axp fhtn it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides uci622ic vr :6bm:ghh azgm9,z98 + d4svw xrovp a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is lovr a:vmwb ,8v692i:gzrmczcs9 6 d 2h+xhg4iess on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourse( tff, q g(0b+rxhoydaa9 )d4llf on an inclined plane(ytf gobx,lh 94 ()ddaq+af 0r? Assume the mechanism functions properly, even at an angle.

  What force is needed to accek8 am9),llk) 0 eqa6gfg(jsg blerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike a+fihcui77oep ( knckeyi; ;b;k;7l: ind 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 wit8i4i-vdn vi74j vw-avhstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of av0g 0bl* v qrnzev:6l7 $76-\mathrm{kg}$ 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 gwjy1 ;pfpxcu cu959 n nl5+f)stop an 1100-kg car in 8.0 s if the car is traveling at 5cfuxwngjpcyp f; n1 99u)l+5 95km/h? -  

  What average force is needed to acc)clr:p*lsj- u elerate a 7.00-gram pellet from rest to 125m/s over a distance of 0)c-usjpl r*l: .800 m along the barrel of a rifle?   

A fisherman yanks a fv ub.math /zm) ;g;pe.ish vertically out of the water with an acceleration of 2.5 bmhu)evza/.t gpm ;; .$\mathrm{~m} / \mathrm{s}^{2}$ 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- 5t wd+62dzyyw*uld1kmile 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 h h2 j(l1l(ntf- :w13mbwe/ p;vcrlucthat the maximum acceleration is 0.0680 g . What are the maximum and minimum fhlj ;-1pclvhe1 (3(mrun c:tw /b2f wlorces 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 motionles zx,) ,1m54 rsnsflg 8f:mbesbs elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regsn,4s5f rez8,mg)bfls 1 b: xmular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 216,n:rbozb 5dqlo 4+ql- j b2rq25-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give thqb2l-5djq+ obor q6 b,r:zl n4e elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including paz*m c115suys xrachute) when the upward force of air resistance is equal to one5mcy 1 su1*xsz-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 qlsn m16/huw,the ground below, he bends hiu h /1m6,wnlqss knees so that his 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 ropc+ -im k*oy2xme tied to the box runs vertically upward over a pulley and a weight is hung from th-2c xi+yk omm*e 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 b, hp8q;1s yobqz y*ag/asketball 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 ba4;r-lb oxaix 3seball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying aox - i4x3;lrbtoward the outfield.

A 650-N force acts in a northwesterly di4n y gp.,;lwt mhrx d5/0kat-drection. A second 650-N force must be exerted in what direction so that the resultant of the tytw r5/m xd4 h-p 0nkg,;lt.adwo forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strup ,pna+j26aa eng horizontally between two buildings 10.0 m apart. The e+ 2 a6pnja,apsag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord fromrx8i a6*b/9jppf x)ar 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 1d f )pf:3*c5o fobszhdjvg3v5a; 42zn 4.0$-\mathrm{kg}$ 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 location at Mc:chb h4vu/*f3 g,vxdenfi6v4Murdo Base, Antarctica, as shown in Fi4, n4 :fvb* uid3ghc/ef6hvvxg. 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 p2;yg 2 lzifrv4ulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the cou4z rilg2v2fy;pling 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 upwardf8 pa)d vi7sfwcy7u3 +s;w2h m using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at vpdays ;3 f)wm+f7wh c8s72iu 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, jae1(8vq9hdxa 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 8v taetr(ia,./su x d:(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 horiz8/su;vrwj)0fk 5c qgnontal surface are in contact with each other, qf;cwg0 5/ n8vurs kj)as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 a *xqgn-/ 2yisire 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. T-iynxigqs*2 / his 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 ijl8 xv f;9-m8fy o4h9fqk9l smass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagl9x9 slk4-m ofiyqh89f8;f vjrams 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 kinetic fri: zveu( pn(m*ov8z 4tnction 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 requahv vs, ilt4t+;f z(5wired 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 mileo3 :/pwwph7jekos),c fp 43nimum coefficient of static friction must exist between your feet l o e),h:pewfk4733 cs p/jpowand the floor if you are not to slide?   

  What is the maximum acceleration1 -bkobgpynyhv+9 e32 a car can undergo if the coefficient of static friction between the tires and t3e2ghobp1nk y-bv y +9he ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemuw;/ub glu6*kent is about 0.8. On how steep a hillb;g 6w l/uuuk* (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -5enwp*je.mwxd) s u) +6 qag-k4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 e3kn*0g+x2lym0 ) nptuoaie(uyn)x1r 4 qs+a 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 surfas1+ mfjr )towy(3 wy3iel c3z5ce have a very high coefficient of static friction.yfr5l3m3w et)isy3 ( 1+oczjw

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 forzl jnsdhj ;.ljy/cj8(;;nto * 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)ld phoq q: e4 5m3mbfebvy,kd+2 cpbd37:-3vd how large a mass would box A have to have to prevent any motion from occurringd:pp2-eke7 d vmod db,3+b 3qfbc43yl:m 5vqh ? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it sl:h ;/q 0yevmwpides across the floor. How far will it go, given that t0mv w/y;hq:ephe coefficient of kinetic friction 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 , l.bih:lgyvip.o4j3tq7, * qd wu7*oj are in contact and at rest on a horizontal surface (Fig. 4-54). A 6 *.yogj:d 7,jo4lqtv wuhbqpi il*37.20$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static frictidpt y40xzjcp 9p,b ;wg96 gr,kon between the crate and the bed of the truck is 0.75. What is the maximum rate agyk4cbp, j9 tgdxw0 ,6ppz 9;rt which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry s wdz11ouwep6vd:5v4 about parking your car in your driveway, which has an incline of 1p :vs115wz6 ouev w4dd2$^{\circ}$ . 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 39 nj wr*s;tixaoe( t1slide 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 an angle ntt;xgtls 5 5fl.5 3fl $\theta=22.0^{\circ}$ 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+i v:i -fe)gyv x1ca.o initial 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 the top of the steepest hil )-w7ebhn8 yfo .rzu :sej8kf4l 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 :jit/*mj.gyj1yuh jh0+ vlj. a rough wall by someone pushing on it with a force directed up.j:y gmvlyi jhj1. j/u0 htj*+ward 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 casuiv ,:uz;c,.q ;phqln become dangerous projectiles as they melt. Consider a chunk of snow sq.:z, ciq l;uhu v;p,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 mid n60ik f2k7oonimum stopping distance for an automobile traveling at speed v is equdoik02nof7 6 kal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forwardnbyj uvi2ly36 / +o6-**y bk y :fyin8z/pvdla on the dash when the driver decel:dbl* / vup 3v8by26jf*+yl iyk-oyy/i6nznaerates 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 oe b33s:e 7ztngiven 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 to the packing sthc 6)pyieu) x(ation 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for eich)) (x6pu yeach 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 ofj7zh a/h y//xm kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 464ev so,is p1rck;xwkg (including the bicycle) 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 heacdnp l1 2 kj;3gq0sf4jrt, at each pulse approximately q1c2nd4flpkjsj0 g;320 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 automobile crash if the depb. ,2f0al 3kjx-lyt7fi a5ti celeration is no more than 30 " g 's." Calculate,3ft jk.2 i-70 y5aipb lalftx 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: iuil y+z0xb) a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fr :ibzil+)u x0yiction 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 involving two cl nzfhv,):5n+nmh 7 h*oq:h isars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coe)zsh m, :hqnv5:n lo7 *ihf+hnfficient 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-in-4 means hq-c cjb3b 9i /lhpt9fn6 w0j.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 aft-6c/j0 h3cql .fptw 9bj nih9ber 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 .(eo;. yxpl2e901jfz xydlrt Tower of Pisa and falls 55 m before reaching the ground with a speody(pl.lxxt ;rf20y ez91e.j ed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12mwrr8 d4r z/ 2/+rxfkgo/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the szr ordf/kw/+2r8xrg4 peed upon emerging?   

  A city planner is working on the redesign of a hilly portiolvs4+lqa)gc*qb sq9 e bp .r0tr:0r(bn 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 a b:gp9qr * e l4vrsqb. )tblcr(00a+sqccelerate 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 watc /jpu/*dpehd6h from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She*/hpe6ddu/ p j 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 supermarke g.(/chzd jzqv0 lp) p+tap8o:gjv, l/t, there are to be several ramps connecting different parts of ttgo apd+(8q/ .,jv /:jz0hzgvclppl )he 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 Ml,m 8f: avp gc6 6p- oh9*v0sgjasa:hm ) using the pulley apparatus shown0*h6f:6gavm8gopsha a9 vsc ,m- :ljp in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at ,xeaal; 8q7teb* abs7 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 foh s)hb22g wh (trz3:nrr a child-restraint chair, an engineer considers the following set of conditionsngt: ( s23 rhhzbw)hr2:
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 tqn7oik)n,qm ue:ye, )ons (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, u -kde57:vammmwy* 2ljs s6-g use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (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 weie5:26 y7-lmwg* svdk jamsu -mght will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is us5gt lcv 6g/i,lt:0 ggbing 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 building egzwt*8oo ,w6is 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 climbe/ x,-px+xtbj 5)+ifyq1lc axf3b 2 ozbrs who are roped together are ascending an ice field inclined at 21 5)q/ +-fx +2b ,3tblozxajip xyfbcx1.0$^{\circ}$ 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.