Why does a child in a wagon seem to fall qx (tr k gl)26+h,xft,g6)fyhd odzt1zl7.mqbackward when you give the wagon a sharp pullx)tozg6l7r m.f2lt)gq,dyxq 1h, (ftkd6+ hz forward?

A box rests on the (frictionless)k) bbzk -l2 bvawi0ll.t9*7;o bo b3pq bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen p2abk0.*ltoi 7 b3 llobv9-bz;bkwq) (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? Explain0rqgmr2 u.7t*zp..p2de l wpr.

Only one force acts on an object. Can the obj 7 sxlx/spvoir10 lt91ect have zero acceleration? Can it have zero lv79so /s0tx1pi rl x1velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is zv *qe s.rq(tlbn4i;nh0tzzr4 ll7p:;xp:d. a force needed to maks; 4dx4q :b( *nrz0i reh.tl pqlzz;lvpt7:n.e it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does th5im: g rcf3pp0- nspn0e log move in the opposite direction?pc fsign30p rp-n m:50

Why might your foot hurt if you kick a heavy desk or a wall? za1s7622 (zi kuasryc

  When you are running and want to stop quickly, yoq(h )t41 y9nmrt qxr7gosj +e)u must decelerate quickly. (a) Wh9ej4q gt1rmnx)yo(s )hrt7+ qat is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sectonknhdlo )* +/don 5g+ion 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: below the stone or above it? What if the person gives a slow and stedond*o+h n+ k5lg/ n)oady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as thatvkf +xtlm/6 wsw .if,jc(kp*2 on a 1-kg rock. Why then doesn’t s( tkf.lci+/ kf,m6v * jpww2xthe heavier rock fall faster?

Would a spring scale carried to the Mo8-dm0 )mt.h; ys ynxeeon give accurate results if the scale had been calibrated (a) in pounds, or (b) ind;mneyx ysth)m0-e8 . kilograms?

You pull a box with a constant force across a frictb0g/;utnvx-s: ua.bt0,pkn rionless table using an attached rope held horizontally. 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? Expl-. k btp ,rgnxb00:/ tuuvsn;aain.

When an object falls freely under the influence of gravity there i: .;xjk2oaqub7o q 3pcs a net force mg exerted on it by the Earth. Yet by Newton’s third law the object epqj; 7b2uaqo kxo .c:3xerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or forceqp fcfpm -n(.-um74 ge) 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 horizonm (ppqnef.4-g-cf u 7mtally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of wv .r 7ysgwo,uq9pw fy 7qk 0opy(.l41iar (Fig. 4–37) pulls with eo9 4q p . wl,yqi.k7rfp0y(ygov7w1s uqual force on the other team. What, then, determines which team will win?

A person exerts an upwa48ecra/xclz so3 i.n.: xpsaf47p8 xzrd force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what objec c s.r8a:3oapxp . zx84ex4 cin/7lfzst it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on .kagwc53, )7)mnrgb+i -q j;z ffvercyougc)v3f k wj-fqz+mc5.brg)a, 7en;ri ? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when bly71 p)xi7zj the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown y)7zpbjix1l 7backward in this situation. Is it really?

A heavy crate rests on the bed vwpjg7gz kj,6rj5 7qf vs .s37of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accel vw76,g jpf5zjsg.js k3vq r77erates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. A:0;ry ifzg x9bfter the block reaches its highest p :;rz fb0xgyi9oint, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scj 18wf iuwz 0v1o+8dolale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at z011udw+ j8ofvwlo8i an angle.

  What force is needed to accelerate z c6a;4jedk/ ya child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accezz5n:nq rg vz:9ik,s oyn88h -h23quolerates 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 rgn q,jf mqaj);uz*z*c6 u3 pc8ope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a b/ga .wvotcg iu n3 ii,9f9h*:$76-\mathrm{kg}$ 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 st1k8bse4k 0ku 8(wa mzvwva2 )iop an 1100-kg car in 8.0 s if the car is travewmkzaw08ae2 iv b1() 84ksuk vling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from r th1k9i (tybdgj9 3notq7 bn93he-a2rest to 125m/s over 7a1 i-ntnde2 hk399jt9y(bt3hqgbro a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an uyrl/r7joo- g:pz r4p 7dh5 7bacceleration of 2.5 5z-g o7or:lbr/hj7 pudp y47r$\mathrm{~m} / \mathrm{s}^{2}$ 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 tretdjuyorzi*ea;9h 0oy*t0 29ack (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 t- gn26 yahaykd7q0an7o be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minik7a0y dh7y gnn6aq2-a mum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevat.g / w5ch7x4 he::mkxig agh0ror. When the elevator begins to move, the scale briefly reads only 0.75 of tr m ehx7g 5a0kw:h gxi/h.:4gche 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 strength of 21,750 N. Wx jaj0nv5o z-m*r(,h fhat maximum upward acceleratio -rjmxof nz0*(v,h5aj n can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accet3e ;y0 ba qtrb6qw/d.leration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth o./r6q b0;3tt bdeawyqf 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. Wh5o2jp) q,j 5t(*pac 6g icyvacen he strikes the ground below, he bends his knees so that his torso decelept5*) gq6 2vaoi5c,jayj cp(crates 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 oa+r 4 :p p+gqmskcfd4(n a table. A rope tied to the box runs vertically upward over a pulley and a weight is hdc(+qraps:gk+44m f p ung 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 dia(/rl;ioilpmuz3 : z0pgram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the mom.g m.j/ph6m ,i3 xfij.4vvkj tent it is hit by the bat, and again (b) after it has lef k .vvim6,/jx4..f 3jijhmgpt t the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-k-u+irgs.u:(/ wem wkN force must be exerted:gu i./ w+ k-wmuk(esr in what direction 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"5ls5+ zbukux 7 strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is sk75ul+bzu5x at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord n(b7:to; )pv)7j bhg5gxz rr wfrom 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 14j7/iwsby2jm :lk + 1xa.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 ho6 / laqqlstsd7.t9l;u 4mext/using unit to a new location at McMurdo Base, Antarctica, as 9 6ts/; q7eqsl/tmxtlad4.ul shown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behindf)x4wd f hl6(qv,0x)/bxdy uiwf0p g4 it, Fig. 4-47 . Determinedx v,x(i4 0 y 4)b0gfxu/h qd6fw)plwf the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself pe/ zfj v1/7gmupward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downw1 /z p/vgjf7emard 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, +;z(;uwsaqddtr)hr9 *o st4i 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 (waqgw7xa)75:j lya q: mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizo 05mu;si-,5jrpizwzfntal surface are in contact with each other, as shown in Fig. 4-5m 05zi,-u5f pj; zrswi1. 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((hqioplkx-o e / n,-a in Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter--eh kxlq(o,aoin /p( mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord o+yg 8y nj5bqek,9g3u:bvrwv.f mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53.rqbj5g,gvy+:38. uyn 9ewkvb 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 kink6 -vcww+1na letic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required t;-vm l vz+uct/o 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 at o tvfjr)5)m:sk*ig3ccelerating at 0.20g. What minimum coefficient of static friction must osig5k3r: fvt*jtm)) exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can;5kfzctxm5q-k: 8axqz d5 2y7b+ um su undergo if the coefficient of static friction between the tires and the ground :ut8 zf27b5 zm-kmxyadxcu q sq+; 5k5is 0.80?   

  The coefficient of static friction betwoqsqp9p,kl,y v2m9u)jv0 gf :een hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car puf: 2 g0,y9,qv vkq ojp9lsm)parked?   $^{/circ}$

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

  A car can decelerate at bt7 z-:,irgcq -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-x.0kskpvmfl w.bg 3dw02 b1f 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 v 0pd3pj5y,gl 1u+dgobj2 p:nnn42krvmj.x; aery high coefficient of s. y4a3 jvk1jndjpn+ 5gln dp;2p2m:g ,rx0 ubotatic 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 frictf).6 ph8;pky bj 7aiokion 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. 4-37l0r ;. mafhh4c8bvnn2 (Example 4-20) how large a mass would box A have to have to prevent any motion from och.rh0 ;nn la4vmfbc78curring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that i0akj ci,n(,j l*zz1tst slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the pusi* tzj1 jk,c(n0,szal h imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at nptc2wo fu:lcn,sc1m02d8 g :rest on a horizontal surface (Fig. 4-54)g,2m uc1d l8 :coc2fpwn0n t:s. 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 carrii(g.h hycsl,*f, 0smfw;gq4 ying 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 cab of the truck? f*,sif gci(g;,.hs wh0mqly4   

On an icy day, you worry a.4eaijp.16:i pfku h nbout parking your car in your driveway, which has an incli1i ep.a kfh ui.np64:jne 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.,b:w1 qc 5p )vuvwuvwv ol(y1pp( u2t 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-j4u g)vph 8gu 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 spesvfd,fwh3 a/tj5rr 67ed 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 st 7/qrt k+4whfx-qoj ;z 6elq q://ckbveepest 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 plx(q e2mz) wcsd771lbsace against a rough wall by someone pushing on it with a force dwm (7xqs2s17bd el c)zirected 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 projectiles as tx1xod7tggc +9zc):u kd36ixg1 qjyw*hey melt. Consider a chunk of snow at 7ck*x6ugo 9xgzq3d:+ j1g )tiy1 dwxc 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 automobile 33rx 8andmii7traveling at speed v israxi 33 7mn8id 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 the dash when 4 xtpd:y7dqxe ,gj3w*the driver dex 3 xpewyd*g 4j,qd7t:celerates 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 mtq2 ymoo-0 5mr 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 f;1at n ;w,e -4+shxn4rsfekelilled to the packing station 11.0 m away. The belt is initiallnxf4 1 snkea ; r-etelh+ws,4;y stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for 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 friction bekx*fql.6q(ms v (f t ao00vws8tween $m_{1}$ 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 6.00mzv 3*o(z xofu(xshivksol0 2+xd/ 5$^{\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 approxx ru,/,eplzer ny-8pw* ,,lvs imately 20 g of blood lrw vs x *r,e/8,en- ,pzulyp,is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the dei/v;u qjdq, ;scelera q jvu;;qs,d/ition is no more than 30 " g '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 earthquake is a , and if adcf4 qb n(a1dm5nmm;bt *n;2m n object is going to "hold its place2bt4amfm b;*n;d5mc qd1 nmn (" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, exa ilb jqw gqefcd8k /gk6/.)q).g1 lgo:)cut9qmining the scene of an accident 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 b6c).dgllq1gk/w:to)u kc g q)g. / qqfebj98ietween 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-4tgs6d y-t 1a;py he*q( means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore fr t*q p6etsa- hd1;(gyyiction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaningpxw.we/ns: vfi) zh7/ Tower of Pisa and falls 55 m before reachif/s) xizhn v/pw:7ew.ng the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of v 5doqmu52(gn12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Wg 5qud25nvom( ill 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 rvj9e *a8h(+ qx0y dh. hq 7ob;mi7jbtcity. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road i hb7q.v9h*y j+atbr8m0xj eq h7;d(o 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 physicsw+s n,an1nxqh-v2t1/id,ys0 7hp kps experiments, dangles her watch from a thin piece of string while the jetliahn7s+,0 q2yp pnwhsxs i-1n/ktd1v ,ner 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 several ramps connectinfox zy5o4(v81vp4 grd)rn-l is(z6g sg different ri-g 1no8f4 r(x( vpdyl o)5szz4sv6gparts 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-e j rhz(ej*g. to lift the piano (mass M ) using the pulley (gjhjer *.z-eapparatus 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 jl pkk-+gnc83at 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 folcsb3r1 f y6g)o((xca nloworas(6 y3fcg(cn1b )x ing set 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 tk58 a e34 mrj1g ow5eeks1+aggrain 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,/4z ,ksy;rjavbj i/w 6al9oo mo,t19b use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on hiaj, rai l6o49w kvj;/byzmto91s /,obm? Which climber is more likely to be hurt?

A fisherman in a boat is using adgzv h )4 f8iwv9a )ip8-swi-r " 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 bb nsoa74r0c 8iuilding 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 ascending an ice field incli0a:k9 z mk; m;dxed cz+9r2zmhned at +z:zxm 2ham;d0 czk9k m;r de9 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.