Why does a child in a 9-c*wdqglm d;wagon seem to fall backward when you give the wagon a sharp p; c9d-ql gmwd*ull forward?

A box rests on the (frictionless) bed of a truck. The truck driver s5 z7;nj5qkkqr tarts 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 beside the truck and (b) by Chris who is rikjn575qk q;z rding on the truck

If the acceleration of an dc822pj9rtbyy j r6f+object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object p kf52zf7lv.dhave zero acceleration? Can it have zero velod.5z vl72kffpcity? Explain.

When a golf ball is dropped to the pave /(b;nyx kore/ment, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the ybrxko /n (e;/force?

If you walk along a log floating ovta nfkhdvlkmt k3.g15i f.p( 44b,i0 n a lake, why does the log move in the opposittf a(k0kl4 p5 3vi4fb,mk .hn.ivg t1de direction?

Why might your foot hurt ifi;fo3a;cbj) y you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you 904, u qqod:yhfwp7 7e- o*8s cxqwjybmust 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 decelerati:d7owpb9 0jsqy h, y4 qwc-q*ox78f ueon of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the :rzu.8v xyu5 nceiling, and a section of the same thread dangles from the bottom of the stone (Fn5 v.8 zyu:xurig. 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 on54p*blhqd;y )mcpd(yx+as g .xq )0in a 2-kg rock is twice as great as that on a 1-kg rock. Why then doep)pn (0xd)ayh.gqsq xic 4dy ;*+mb5lsn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scalr t0tc/.k*x ike had been calibrik/ktr 0xt*c. ated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acdi3 q0k ns59gv;wy9vdross a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an an yd39 qs0gik;5v9vndwgle 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 fre)ii r/ecao * +vuxf0a)ely under the influence of gravity there is a net force mg exert))xr i+ au 0c/*fvoieaed on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) neededly15ih kufp3,a-d,gk+6yzh /my;:nm e b1cg v to lift a 10-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 Moon 6fhc yybmgzh 5 /g;ip,1 enva:lk+ 3ykdum1,-and on Earth.

According to Newton’s third law, each team in a tug oj/x,zi l muo*a,cr3c8f war (Fig. 4–37) pulls with equal force on the other tic c8r, xal/uz*m3, joeam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of gzaqtm. /c qyscmm-hm **:9)woroceries. Describe the “reactiowmt*c ).z9amm */cyhqos mq: -n” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does th;aoj)i :m jq4ze ground exert on you? Why doesn’t this force make you rise up intq;i:o majjz) 4o the air?

Whiplash sometimes results from an automobile accident when the victim’s8f+lb(ojapd8-rn; toibg /o 6 car is struck violently from the rear. Explain why the head of the victim seems to be thrown backwa-rb8ijp; bfd ( 6ooa+8gnol/trd in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When ts/ pwdgv ahg8unbuw15;c 5mf,+*b*ud he truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force cauugc hb d;+/u,b ap55 1sw*nu8wfgvmd*ses the crate to accelerate?

A block is given a push so that it slides up tt nb /;,u3awnmwg2ix svv 55*e8kpg:a ramp. After the block reaches its highest point, it slides back down but t,t wtk nse5i na:8pmv325vbw;ug */ xghe magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scablgy v-4n4ht9 le read if you weighed yourself on an inclined plane? Assume thl 44nv9ghb-yt e mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/x+l1tfqx/g ; znxt g(:s$^2$?   

  A net force of 265 N accelerates a bike and rider atx z b2yw(3-hvt 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 acceleravzn l)lg,9q+w4ewt )gte a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a y28-u zqf: awx $76-\mathrm{kg}$ 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 t0:b dwalo pd 600fu-3dy t0koin 8.0 s if the car is traveling at 95km/0to 0:0ta-3 bdlpkdfuw6yo 0dh? -  

  What average force is r svx t5u fj9aj6z)6obam3*/yc 7a 7ipneeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 uvs mi/j c6ay7*zrao xtf9pa3 b)675 jm along the barrel of a rifle?   

A fisherman yanks a fish v2-dtp/jvroax * b 1 az0oh(v(rertically out of the water with an acceleration of 2. jo 0a(( xhav2/1rovbtd z-r*p5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 (9x7 l(3r9c*a qjkjycp3js: hv402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the mmn95m- 9 zy;rc 1pog: htjzyv,aximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting caot95jhzm vy,n p zcg9-mr:;y1ble? 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 motie9w ne1v,3zvv onless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate nevv9vew 1,z3the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximunrh8f,: 5yqc pm strength of 21,750 N. What maximum upward accelerati85crfqny:p h, on can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includingv r)gohb+1kc/+:a9ki 5qv1x i cmsg6z parachute) when the upward force ofqg c/c9a1ho1mrz:v6kk+ x vg s b)i+i5 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 strikes the ground bx;uul b r842pdelow, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legrbx u4d82 u;lps) 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 run**xj+ tmgtv e*p ysd*3s vertically upward over a pep t+jv s*t yx***dm3gulley 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 on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player 3 nc1f(tcks i5
(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 moment it is hit by the imrdqvw,98veyt,+s** n2ijb bat, and again (b) after it has left the bat and is fl*i8*,n2 evyi 9qj ,vmts wbr+dying toward the outfield.

A 650-N force acts in a northw f:twk(r0-2yn+h tjq 5/jhc ejrt-g3 eesterly direction. A second 650-N force must be exerted in what direction yn5w0eq c-(hj:2t fj3hj+ter/tk - gr so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strut.(; jo4nqmaeng horizontally between two buildings 10.0 m apart. The sag in the rope wheno4 (qtmeja.n ; 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 mtt 3k9f ga1ot/assless 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 1.+sbnj *xsyq 24.0$-\mathrm{kg}$ 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 McMurdo Basea5 z7 payh0h)x, Antarctica, as shown in Fig. 4-46. The saa y)phzh7x50 um 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 b0 tq/*jlvs1e mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between thesl*je 0q1t v/b locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using thx z9fec3* rvkp9*g8oue bucket-pulley apparatus shown in Fig. 4-48. (a) How hau f pv9z9og*x*38crek rd 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,rs k0y-c bps4twnx :v*6/enb-. 7nwid a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mas58ufh*1l sj pjs $ 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 fricti8nvuq7.uj *;z g+ivq 5yph5nfonless horizontal surface are in contact with each other, as shown in Fu5 i7j fuh;z+vvyqn n.gpq *85ig. 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 are each initial8oj.m yhgosw* *r/.ez ly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum heig o sy*oj 8*rmgz./e.hwht 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 tabw sdp/ae 9 ap55/y s;azpgz1)tle are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tenpa5//) wgada;es 5pp 1zz yst9sion at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a 35po4ndt3dq .f8z) mt+r $-\mathrm{kg}$ 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 5.+-h7uqrdlw / o 4.kbug0$-\mathrm{kg}$ 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 accelrwt o3z/uok 4eccj779 erating at 0.20g. What minimum coefficient of static friction/zr3794wk ej ctuo 7co must exist between your feet and the floor if you are not to slide?   

  What is the maximum acc3 *+qpsjak.q 3bvl-2h ftg)i ieleration a car can undergo if the coefficient of static fra*li-) fhq 2k3tvsiq+. bg jp3iction between the tires and the ground is 0.80?   

  The coefficient of static friction betwevs lyf/0evh7p *gq. *een hard rubber and normal street pavement is about 0.8. On how steep a hivels 7qe fhp*yg0./*vll (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 egugr:o z-g* 4bs0p,mb .k2haat -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 avmfkd3 g bl,nx4 p5q31 rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an a-u3f n ctr6-r-pwim g;sphalt surface have a very high coefficient of static frictionrm6 r wgc-ft;3-npiu-.

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 frg ,zxc/i0+ l7lrg zckz;el( h9iction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large au8r+ 6)p:n,f a d2svzvcs+bts mass would box A have to have to preventcbr+)+d 2s,vs6vftau8p sn:z any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the flvf 1ykb1jm6 t 2fdg9g,oor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impa tg2dy1 ,ff9j1vkbg6 mrts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg ,g2a)i:eyt cl6dwr:90 hjio r- are in contact and at rest on a horizontal surfacel eh 9 o6::c tyi-dj0rgw)ri2a (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of stat z) l)3tsbmmw2ic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the drivbl z)wt smm3)2er can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry hdk-v cmp/(d*(9ehkn about parking your car in your driveway, which has an incliv hhnc pkddm9((k e/*-ne 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 with a 2qd/go,x )/vz c8$^{\circ}$ 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. 4g-t v5.3phlj6fpv 8mb-55 lies on a plane 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 speexjduy -a;v;qj)n u4k0d 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 steey xozhzj (4t7o d2i,3g3z)do bpest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by soq i e()7u-oxwfmeone pushing on it with a force directed upward at q(-o ewu7if)x 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 sli f30f1unq.gxof.9g l (vr8:ggac+yzh ppery roofs can become dangerous projectiles as they melt. Consider a chunk of snow atf hv(r+.l.u8na9fg3: cxq 0goyzfgg1 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 8e ikfu/a (gv9stopping distance for an automobile traveling at speed v is equala e(vg u/ikf98 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 gz*nxh+mj:ha8 64.v 1pggda7j ,usvjon the dash when the driver deceler .vhzdgj8614vahjg*apmxg j,:n u7s+ ates 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 m3w qi( k:li;ye is 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 belt from where they are fill( ho:3)s(rzoxl 842tohz ulz;b)l ads ed to the packing station 11.0 m away. The belt is initially stationar 2ao)o h3r8u(( lh;sz)z ods:tlzxbl 4y 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 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 kb6+ y+o iye/chinetic 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 kg (including the bicycle) p2 avftyz:q,( qgj-7.nqrbs1 can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, -p2 q+,dy v:airj: lfaat each pulse approximately 20 g of a-+fr:jp v q2a:lydi, 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 au+ oicflndt)wl,hvx5 .4y cvol9 2t/8ytomobile crash if the deceleration is no more than 30 " g 's." Calculatyvwtc5olcv.ylx , i8 )/+l no9fhd4 t2e 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 acceleratil7omodky /1 q2on produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show th/kdy 7o21loqmat 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 accident involving two carb0(ilwi*r8( n1jxpp o s, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the in1px*wi (ln rp o(b80ijitial speed of that car assuming a level road.   

  A car starts rolling down a -oi2x567tb vz.s sq)hhv3npm1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches tm 56oz7vth- 2xnb psi) .qv3hshe 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+1mzen:wrw wnj8tr; h4w59i f the Leaning Tower of Pisa and falls 55 m before reaching the ground with a spzf:n4w8rw w+iten r9 w;m1j5heed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters 0p)fke v(3b3c/ fczsi+iqn6 s 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 speed (fik3/znp+6f 0bs)cv3 esqc iupon emerging?   

  A city planner is working ox;jpo gw;rodr(+t3 d1n the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular sma1 dp j(w3 o;r+go;xdrtll 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 p/0jj wa.o,pmihysics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the s wo0.i mjj,ap/tring 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, therew 6hlqb ;djy7rixw/2( are to be several ramps connecting different parts of the j/h7wq;x d6i (blry2w store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) usinew nw6 ;2y,gy ln(2vvkg the pulley apparnyv;l6gn2ve( k,wy2 watus 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 accelerating2faat glgr 1z8.9aqkan4*wo 4 at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the fou6d (za vwt+5rllowing set ov(+56tazw du rf conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons +cmkx67vg 2 v.sw qoudqfk /83(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 length. Karen'slh)p;m/) jszbfb 3h. 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 chbmb3spj ;) hf/)zs .lm 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 iay2kzxo :)q/i. vzfc ,8r jx;js 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 allowed to reach a maximum s cr .2f tbm;sr.:m5ljpsv tx 980fcc,ppeed 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 a3xcg;v52 zpguzy8q;0w)q bg i scending an ice field inclined at 2cz;i8gx2v0z)u wb3 qqpgg ;5y 1.0$^{\circ}$ 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.