Why does a child in a wagon seem to fall backward when you give the ddxzh:2e r)9*bu4p 3 rkd cdq2wagon a shar2 *ru39xpd dd:2bqczhk4)dr ep pull forward?

A box rests on the (frictionless) bed of a truck. The truck drs,b* 7pmpao 9siver starts the truck and accelerates forward. The , pp*oa9 bs7smbox immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it?b )mqxc u+8 6v)1leypq Explain.

Only one force acts on an ou bo4ve x9kq:0y hx(kwnxw:5*g 4dtm,bject. Can the object have zero acceleration? Can it qh45nyovdguebk049t x,: w xk(x:m *whave zero velocity? Explain.

When a golf ball is d 89*t, ajw:2 l2jqe jhxxvpay9ropped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If s:x j298jla h2exty* wp qja,9vo, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppositxb)4u4q 2wumre directiuwu) m4x4rq2b on?

Why might your foot hurt if you kick a heavy desk or aq4, 8v8mkfvfp wall?

  When you are running and want to stop quickly, you mu2w d/9v wm9v 0omfyhz6st 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 runninvd20 9y/ whfmoz 96vwmg at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sec3 9a c7c a;k+ije.l+j2 gj3nzhmylp-ition of the same thread dangl7yiem3- ic.c al+ng zp2l+k;hj9a 3 jjes 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 twice as great11 0lwb edfjzxj,r: ;i as that on a 1-kg rock. Why then doe,:; ij1rdxlj01w f zbesn’t the heavier rock fall faster?

Would a spring scale carried t5zysug7 di+t;od3u/twwhs5fj-m 8l)o the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) ind-5hoizmtg t+;f syus37d)w5wu/j l8 kilograms?

You pull a box with a9 yzw6+ 3horiw constant force across a frictionless table using an attached rope held horizontally.3wyho6i 9r +zw If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity th -mcetsa4+ ))tj dl)utere is a net force mg exerted on it by the Earth. Yet by Newton’s third law td )t 4u)mlcsj )eat-+the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when youm9gx04a, : xuyzc,l aqr4 7wqw are on the Moon with the force needed to l, : uxg4c90,qwyamx7w q4zralift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war1kkf,t8a c1hfj8wpe/1m9 frz (Fig. 4–37) pulls with equal force on the other team. What, th9hke p8 tmfc8/1jfrzf1 ak1,w en, determines which team will win?

A person exerts an upward force of 40 N to hold a bag o, hq(e, wt9ibff groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what objq,wb9f, t(iheect it is exerted, and (d) by what object it is exerted.

When you stand still on the pyep : 6a uo44xa7o/dbground, how large a force does the ground exert on you? Why doesn’t this force make you rise up intop4dyu4 6: axp7b oae/o the air?

Whiplash sometimes results from an automobile accident when the victimy; l-ou.e: yoi ikjm31’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown bi ;uy31o:eo.li-ykmjackward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed trs hnnr eia44ze3 l0n(h :6lxb7uck. When the truck accelerates, th( :s7 eb 64n0l r3he4axnnilzhe crate remains where 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 slx +j dc:ykzd,+9;u yqnpv1 cm+ides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is:vc 1u md9+xdk yyq; +cj+n,zp less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclin 8o:pw)f a(n25hn zgjzed plane? Assume the mechanism functions pro nhzwa) 258(p:gznjofperly, even at an angle.

  What force is needed to aceo o4lv d(j5f +4thm1jcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accel so3jinz0i75e /vep1 -nn,/a6irez1micbe f )erates 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 ac3bb6os oub )4e/iey. ecelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a l8o2acaxq,n*s 5 vr(j $76-\mathrm{kg}$ 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 8.0 s if the carfgy;gro f(cln4g52o9 z9 hgq9zp49wq is travelingnwz z9l9g 4y( gcf4ghrp2qogf9q9o5; at 95km/h? -  

  What average force is needed to ac*yny 58somb+x psm*3kcelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alongm py5b*n+myo3* k 8sxs the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water witstg,1 tp v5rd1t( n,pwh an acceleration of 2.5, 1t,t1pwstv5r(p gnd $\mathrm{~m} / \mathrm{s}^{2}$ 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 fy96kg 9x1zywnva7+/ce xpn0 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 to7tyxekanp a 5o1tz3 r597 wo4x be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor s4o59at51 tpky ewnoa77r3xxzhould exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless 3 dxh ;qe52jiselevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of tx 5hi23sej d;qhe elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,75 p o fdltd9.o4jla+h3(0 N. What maximum upward accelerati.dj3l fh(o 9+ d4ptoalon can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accelerat/*y0dvlrn: x;+ .8u hbdhv kuvion of two falling sky divers (mass 132 kg including parachute) when the upward force o vud8yxuv /v;*l0nbr dkh.h:+f 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 3.9-m high. When he szxjxsf4flfvse )a4/ f7q 8,z7trikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the masszz/l 8f xf4x7aqe4j7fvsf , )s 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.2xsi5xs rol; ;tdf)d 1 A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging ox; t i1d;rfxsd 2)ls5on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playk1vssto+t zy 2pv02j 3yiba/; er
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body di vj6.29fmo v1sm2mnu nagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward tvs j 61.u9mmno 2n2fvmhe outfield.

A 650-N force acts in a nori,h47m6j y*l4fm sw ljthwesterly direction. A second 650-N force must be exerted in what direction s imy4, 674sjhl f*mwjlo that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acrfhk r u(s)b3,goss a "high wire" strung horizontally between two buildings 10.0 m apart. The sa kg( 3bu),hrfsg 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 massless0*0 4zbya7irtlir xz9 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.; +w4peimi n:o0$-\mathrm{kg}$ 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 hoapf-o:1 : shcjusing unit to a new location at McMurdo Base, Antarctica, as shown isj :ch-afo 1:pn 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 two cars of the same mass bemq6lsjm :zg:i p+7vm/ hind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and th/p 6gmisl+zvq7: :mjme 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 t.a0d/i tlirfr 8ir7 3fhe bucket-pulley apparatus shown in Fig. 4-48. (a) How rlidf. r7 /riit380afhard 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 65 260wucs j+ownjf8 f*23 kmp42zlke zw$-\mathrm{kg}$ 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 (ma(e6g2 y.w;lzq7)-f6 lnsdiq tkoro9jss $ 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 iq, )h(h ip8rskn contact with each other, as shown in Fig. 4-51. (rs,qkh8)p ihA 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 are each initially 1.80 m above the ground, anvnbm1s 18c9u yd the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is relean81c ym uvb91ssed? [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 co6y5(f u6wbgrr ind bg0i u9l15rd of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body di1dlb0 u6gyiif brgw659 run(5agrams 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 fril3dy f/2ovz*igov* m) ction 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 a /4nueek. lcf jm2+ eu2.yplbs8a)bz(5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimum c.,w zdcksaz )5pj8b eb d(xf0-oefficient of stati8dzzb- ,0kx 5)fe .bjawdsc(pc friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undeqklkghitojf1hx7 x6c9+7u278q zua :rgo if the coefficient of static friction between the tires and the ground is 0.8uj1 +6:u ktzifx7 lq8g7ka9h c qxh27o0?   

  The coefficient of static frict rl x7y;.(atriion between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you l7i ly;x(t.ar reave 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 j-sqisbvrer4 26m px ...bk6q at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rougycmv3 73a3)bcag ;zh bh 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 coeffici6otvs.xn ywj2 jk ()e fs+o3j(ent of stexs(jno. v(t3+kyfjw2) j6 soatic friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic fricta ms+ igm6bi91ion 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 ,w/q m i 0pb0fq.7xqp(jy5jaf(Example 4-20) how large a mass would box A have to have to prevent any motion from occurring7xfjmjqpi0 f/ .ybq( w,05q pa? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slide -an.l9h+ o+ddqfppi8s across the floor. How far will it go, given that the co9dof n ip. q-h+ad+8plefficient 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 , are in contactxy+ s kpq7i65r and at rest on a horizontal syi6xrps5kq 7 +urface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is c8q */ sffwl vdvhq6x6.arrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the caq6l*s.qf8 vvhdx/f6wb of the truck?   

On an icy day, you worry about parking your car in +cf +5toa u9vsyour driveway, which has an incline of 5ta+uovs+f c9 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 w 4zif(ro:+vm sm30xua 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 plan(1(51 qn* byrlq k1tg sl6,nbeegc2bwe 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 initial speed of 3.0w +5 wal/po+l35n/njh ypr :3v)ubwhy $\mathrm{~m} / \mathrm{s}$ 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 thewttl.ai7re h1okr;; / 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 againsteb, g7gr9-r idikuy+xf9n/ /s*qs e8c a rough wall by someone pushing on it with a force di9q/ski9xugrnid, -7e br f8/gs*ec+ yrected 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 :b gyq ake sqx0w0o.f4z2p;w2projectiles as they melt. Consider a chunk of sno4.fo ebw;g0 qqzk2yp0a2: swxw 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 stopping distance for an aut:bnir noqs a/nj,( zz .6cw vj24f6o-vomobile traveling at speed vf- 2j6ac,v6o:4bw/jz zq.nn(so rvni is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on a7:g od,z4tpxthe dash when the driver decelerates from 45 p:oadt4gx , 7z$\mathrm{~km} / \mathrm{h}$ 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 i nz 3fqynt)q/5s given 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 beltmk7mc 1l+lpbm5; ri3 o from where they 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 half of the trip. If the coefficient of static friction betwrc bm13mo;lik7+ mlp 5een 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 frib f g) 1on8,36rvdjb(udbm3 kiction 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) can coast down a 6cfg 0smug6s *rvhn5 .zp3wv6 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 ap*mg4w3gw; bho -t1z n7+rzouaproximately 2 mut*wr3aow 7;zobng1g +z-4h0 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 v. yt 0mikq8yy9e chou7 r*8qh z5*uv*automobile crash if the deceleration is no more than 30 " g i8 my yhvhoqzqr5yu*u *e 0c. vk8*t97 '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 earthquas:hh66g gns9m4j oeb6;kcgo 1:vooo1 ke is a , and if an object is going to "hold its place" on the ground, shooo 6 ohjn6c1:o4 1;gvs9bg6s :ge omkhw 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 .s .d 98ja gon7qvmqb,s l, p.ek9ue z72d9bgcaccident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop bpg9b k,. da.7e jd9unb.lsoq7ecz,2 mv9s8gq efore colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means thjdrtkqxl7.mb 4(c; c9at for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reache.;jrd7l4 (qmtc9 k cbxs 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 droppe+-ynz .e 8y5 dyvbw)pfh5en7 gwtpo)+d from the top of the Leaning Tower of Pisa and falls 55 m before reaching thw7gyh . pvwtfo5d-y) np)eynz 58+eb+e ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a jo2jh s5c17kha4v d 3umuddy stretch where the effective coeff1s uhchad43k 25 jvo7jicient 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 speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. y7mrejrg k7 5,51ttugrf0 q5n An importar j5g7n,etu1705g 5krmyqrf tnt 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 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 experimenk;c9*w 0gxe.wi q/q tgts, dangles her watch from a thin piece of string while 0gqe.ic/k qwxw9 t;*g the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be seve*t )bf-z c)thlral ramps connecting different ftz *lt-)b)hcparts 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 thgvliq705if ob; -wdt7m crx0. e piano (mass M ) using the pulw-xv irg5b7;fi 70m .l0 dotqcley apparatus 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 at 3.5 g5z5* mjary efurus 12z s.t/i2e(y +i$\mathrm{~m} / \mathrm{s}^{2}$ 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 pk*4vw k,.u na (hwz0ya child-restraint chair, an engineer considers the following s.w0khva(np u , k4zwy*et of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a64 5m0vdu vjvp 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, Bill and Karen, use safety ropes of similar lengtu)(-1bhx(op s80qif.id. t:v q sipma h. 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 rod:i0.-quqs1ot(sx8mp vi (paf). i b hpe 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 weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boafdapbjn 5j w79qxrjmi 1 3fx4))vf 4;nt is using 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 is al0,rnc ,nz1wm -cr gf70yxum)alowed 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 ro5qej u/d,f,yvped together are ascending an ice field inclin yqu5vej,fd,/ed at 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.