Why does a child in a wagon seem to fall backward when you give the wagon a sharxn0 50o ra*tmz-8xl5 g2da) hcdzibr0p pull forward0*z2an5xt5mo8gczdal0r)di - 0xbr h ?

A box rests on the (frictionless) bed of a truck. The truck driver starts s4 o0i2qshs1 10 e5cg.ioctowthe truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discucisooshg1q0toc0 w s24.e i5 1ss 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 fo;7/:tkil v3c za;qnbirces acting on it? Explain.

Only one force acts on an object. Can the object have zero a (718ls epjhqw46shs rcceleration? Can it h8sshhr16pwl4( s eq 7jave zero velocity? Explain.

When a golf ball is dropped to the pavemeivz ).-:e0a4evbvf tint, it bounces back up. (a) Is a force needed tvi)e atev:f-.b 0z vi4o make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in tf7fq enh4 dgr;-eq/9a he opposite direc -ahfd/ rq7eg9;ef n4qtion?

Why might your foot hurt if you kick a au15),yudx,thjd/ 5qx e z0kjk7yp8k heavy desk or a wall?

  When you are running and want to stop quickly, you mus)toxhy (b7w*it 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 thi7( *)owyxb 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 kd )pjkk9d:0ul3n 0yv a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: belydn)u0 kpkl: 30k 9dvjow the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that o70g b+/gvpwsbj .vo*:sy3kh 0uyuib ;n a 1-kg rock. Why then doesn’t the heavier 7.:w0kphi *ob0 3sby s/+ uujy;gvbvgrock fall faster?

Would a spring scale carried to the Moon give accurate results if the sc,(bq,:usg w jgale had been calibrated (a) in po,sb: ,guw( qjgunds, or (b) in kilograms?

You pull a box with a constant force across a frictx,k/jtt8 j+f;5j fh wtionless table using an attached rope held horizontally. If you now pul+jtk, txjj f w;tf8/5hl 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 there is a net dx 1*l m)3:perky y3epforce mg exerted on it by the Earth. Yet by Newton’s third law the object exerts a1 ldxpyry3mk ) pe3:e*n equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) rcbfs9+a yl83 needed 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 andl b8fy9 3s+cra on Earth.

According to Newton’s third qzl4 h0bz -pss5-q( mk *l*tjnlaw, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, q sz0 lh -pqj4zblnsk t**5m(-determines which team will win?

A person exerts an upward force of 40 N ttp17k6 cmdccgj625xro hold a bag of groceries. Describe the “reaction” 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 exertedpg r cx616m j2tdck75c.

When you stand still on thwie-m h ,m3fe;e ground, how large a force does the ground exert on you? Why does-3;e ,e imfwmhn’t this force make you rise up into the air?

Whiplash sometimes results from an automoy q4zw cly1 f7;i/d7bcbile accident when the victim’s car is strucyi;w 1fzdl7/cb 7qy4ck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck aclb,q6jt (h ;osn )zut1celerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to a6h oztsbulq(;n,t) j 1ccelerate?

A block is given a push so that it slides uk4z+ dx; gt44:tlntrfp a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acce; +r4ltk4ntdzfx4 gt :leration is less on the descent than on the ascent. Why?

What would your bathroom sqxy2jy i l( oi;-k7/wgcale read if you weighed yourself on an inclined plane2qj x-iy g;w(ik/o7yl? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate jvvvak kjx1m -44n)b;a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike .inh j6u)5uvt) clf0jand 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 txy w+u)i,pjt2 o accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a+7cihf 5lv i9c $76-\mathrm{kg}$ 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 car is tp;h +f4k v5ira)mqk +vl2my4i raveling4h54+ir q; i)lm2kmyfv p akv+ at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet a 43p4m/*tixi (txy1pq mvhj +from rest to 125m/s over a distance of 0.800 m a ia*v yqp4ji/xtmpxtm 1(4h+3 long the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an b/ /llcwj72c0b vf1ea acceleration of 2.5feawl bjvcb71/c2l/0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 qukot5w ,;fw3ip:5 its yarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed2e1 h jmpvm),6rew;qx so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cjheer 6 1xm2m );vpqw,able? 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 s:n7du0ow ,y6tmw,k jbathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of w w76nj,sy,0m dktu:othe person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum stre7elo2* hy41t rntqe(angth of 21,750 N. What maximum upwardq4 oa(1*nee7y 2 rhltt acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg incj51 t9.e m)lr e6 mk1jgwxdezfmd6q08luding parachute) when the upward force of air resistew51m r9fg jd k0d xme m)6jq86ze.t1lance 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 he1ao 2 aq1t9u;r8 adzad strikes the ground below, he bends his knees so that his tors1a ddra 9at8o2;uaq1 zo 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 rope tied to thec ubh0s)ug )4e 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 bosubgh )4 )uce0x 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 plm1cmo1v7,lnyxst a2sov - 7 7yayer
(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,q 1h)yzql8f80 q5eiqv yb 9ck is hit by the bat, and again (b) after it has left they8qzfe1,8)icq 0qb v h lqy95k bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. Amlngg+ r6eqf3dwve .6;t; 0lc second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with +qlltwm v0d36gegc;6.rf e; na vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betwee-4qet*laf3ne7(x. ba;n uoou n two buildings 10.0 m apart. Th4t la ;no-uxoq*( 73b.fueanee sag 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 bd5gt u .l-r3bzy a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14 15bsisat+-ag drl4rvv j94y4.0$-\mathrm{kg}$ 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 a83jqqdu8 7b gz*-wqmtc-e f 1i new location at McMurdo Base, Antarctica, as shown in Fig. cg1ti-3jfqub e* dq8qz-8w m74-46. 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 :9cw3cy4uzt8 dee .cysame mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweez9c.ccd:wu t eey34 y8n the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bun hhs.f,b )/sicket-pulley apparatus shown in Fig. 4-48. (a) How hard must she .)bnh /s,hs fipull 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 b+ofuv *amn* 1f06 hnicegan, 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 bf.syt,x subt 9*v pyb8 v6n+g;lock (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 fro h9e6 l1maq7opex7ot gd 52,oictionless horizontal surface are in contact with each other, as shown in Fig. omd ta52oe 7xoge 1oq l,6hp794-51. 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 ini1jaahhvp6wy g ; x:p6pkzq570 vt7x,dtially 1.80 m above the ground, and the massless fri 7x wjda 0ta5vvpkxphy6zh:6 7,1pg;qctionless 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. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy colyai683 )alj.y oj8t n6vp i2rrd of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using 6jit8n yr38 li2volp6a.yja ) 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 betp rweuh8)n p6;ween 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 requires5p,xa22 ixc.foexmjt ij,gl *x 4* poa3n1m:d 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 ati/:cx1se5 w +ox(m txg 0.20g. What minimum coefficient of static friction must exist between your feet xx mogc15se:+/i(wtx and the floor if you are not to slide?   

  What is the maximum acc)*i w50cld cwaeleration a car can undergo if the coefficient of static friction betwee*cd lw 5w)0iacn the tires and the ground is 0.80?   

  The coefficient of static friction betwee qr7f4jyz b2rv08cqb, n hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parkedjb4,qfrr0 y 8 2bvqcz7?   $^{/circ}$

  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(mqp sw+ n/xt* 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 ai1ytzspaxnj.5q bx.p,0c 2m h3nwuf),x-l k7 rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficiento p ceco4k0)dct63rm( of sk ecr) 4 d6cc(mootp30tatic 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 kineti le,uv p0c s1qhz(64k hp*p6jzc friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A have )9bb jab;3ux ato have to prevent any motion )3b bbuja9; xafrom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that 791unf2jdtkh77 pv+h 6s :,caa ygajbit slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the pushy2 su7g+7 hpj6jfc1n7, hdab9a: kvat imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg andvr)1yef1mx +u 110 kg , are in contact and at rest on a horizontal surfa)vuerx m1y+ f1ce (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 static frictiomcea2l81s4m tftmq 3 6n between the crate and thtqma8 mc6ems2 fl 341te bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your cv.dyzst4h0oy61f q 8u ar in your driveway, which has an inclinvod zqy ts610uyh48. fe 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 , ew(yy4rl;5ajxntjo 6b+k j(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 n na*z z- s;0 a,bhr*dsaa6vw0$\theta=22.0^{\circ}$ 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 k ,t/hiv3qklmu , 38rry76+nq vjty i6speed 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 co pmb-6: ry4phill 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 ah6,v+*u,zs x 3av4otaexho,a gainst a rough wall by someone pushing on it with a force direct *aauo,+h v, eo,xh4xta3vz6s ed 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 projectilessa6 tm5)/j omkyqik*:c/5n ab as they melt. Consider a chunk of snow at the ridge of a roof wc/5 kyi6 na /s*:tbjam)5kmqoith 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 stoppgr(1fv(5mkssr4me 4 l ing distance for an automobile traveling at speed v is equal t fv5sergr km4 sm(41l(o $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 ud,j1 (u+/qb r uq5dfcof a car slides forward on the dash when the driver decelebuq jqd+,/15ur (f udcrates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial speed q;q-ml50mjd s$ 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 b:ty83/r cmg(8o/ mt osyeix5h elt 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 accompyxmt /(yi:5sgco o8e/8r3 t hmlished 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 kinetic fri)pv wwh+qp7a, h4*c mbction 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 k5cc p7t5,cv-o*ij gmcg (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 simpliyv ,c/ /:ippqified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated fro/iqcpp:/i y v,m 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 chance9lt6y 7do *uej of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the fod7o t9jeu6*yl rce 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 acceleratd, i7yrp-8 m3oezce4jion produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of c-74 8pmoe ziy3ed jr,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 accid.oe.+e( mocwchep1b .n0d. uwent involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate thec.1n0p +wue.(c.mb owheoed. initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 mckybzr, ; 6;.yia7 jkieans that for each 4 m traveled along th.6 kzy;rbk,;iac7 i jye road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from a;s 6ahp2(y 2jal +kjethe top of the Leaning Tower of Pisa and falls 55 m be2 pja(;j6lah+yke 2sa fore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed ofhlpp7 0;: m tq te3vq(ct)7lkq 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the mudec)h lttvpq7 3lq;(q0: k tpm7dy 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 red o-zpcrxn3:o (esign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass ofn:rzo o-(cp 3x 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin pie7 ,f((xiy w +l.:ekojdseq3goce of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She noticeol+,x:ei ewo. dkyjfs3(7qg(s 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 several ramps connectmcol3gn; j(-king differentno( lm;gkc-j3 parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force askxv cg 6kh25tj:* 2gF is needed to lift the piano (mass M ) using the pulley apkv2c:*kta x jg5s2h6 gparatus 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,n/e ikdl(ej)xbkcgi 92y/: l 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-restrd +kuboa-66m q6v ;nvvaint chair, an engineer considers the following set of cond-6qvm ;u6 +kv dbnv6aoitions:
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 tratjl:o*ll g:5j 7vfcpg*f 9p9ain has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safe /wmrro)mgl 607l(-iol +fpvq1c0nrw ty 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 if (pnlm0lr1rc+o)o -w7 vwrli/06mq g n multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " rbdzqx cxd1 9j*p7:j5g *:nyv cr+rc2 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 buil 0:tihz .:kcfmding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are y) 2:tn3p pprf0cw qo7ascending an ice field inclined at 21pf:w 03to7qpc)p y rn2.0$^{\circ}$ 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.