Why does a child in a waq*y,f y) ; zgmya9sls.gon seem to fall backward when you give the wagon a sharp pull forward?syl s* qg,f y)mz9.a;y

A box rests on the (frictionless) bed of a trucskd2b;net:;*ow*m ow k. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standwn;d* ksmoe2b wt;* :oing 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? fyos*:x 4d 6wuExplain.

Only one force acts on an object. Can the object have zero accele,pkgt-6u7ue uration? Can it have zero velocity? u7ueu,6 -tk gpExplain.

When a golf ball is dropped to the pa 8ck l gs2/vy,aa6y;blvement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) I;c6baay/ysk 8 gl lv,2f so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposithn- am2q4m3gke - q3h nag24kmmdirection?

Why might your foot hurt if you kick a heavy 8j+ybs9 ; i(qh05h f,esjwmoqdesk or a wall?

  When you are running and want to stop quickly, yy ,jktxh 2ysfs;ro/ -:ou must 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 de-o th;:yys2/fkrx , sjceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the u1ts/7qk z+edceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36).ud+qe/7k t1zs If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kgw g;n(xs t xb l6bawxe*dv96/6 rock is twice as great as that on a 1-kg rock. Why nsw9wd etb/ x6 (*xa6gvb6lx;then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give acc-/uvhtir1x r) wsi 5z38toj:aurate results if the scale had been calibrated (a) in pounds, or (b-zhx8orti w3i t)5as1r/jv u:) in kilograms?

You pull a box with a b70q: ib,0f zblleps6ud:z0 hh-eng 3constant force across a frictionless 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 tu6h0z7ezdb-e:bbfs 0pqg0hliln3, :he acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely63y w zjcqyfy + *w.nu)nl3yo* under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opqn3w63cylj yo nfz* )u*y+.wyposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed y lt j+b(wfy6b+-5)eqcpgl /vto 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 b-+ypj)lt(g+ l q yw5 ve/fc6bthrow a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (F5ja c sq,ia7e,ig. 4–37) pulls with equal force on the other team. What, then, determines which team will we7j ,5sqca ,aiin?

A person exerts an upward force of 40 N to hold a bag of groceries.mwbig v.7/h d; Describe the “reaction” fm ; i.bdwg7/hvorce (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 thej1 n48m21 opwx 9(w0pxxyr ejk ground exert on you? Why doesn’t this forp8 02xj k1rnxx9mw je1oyp w4(ce make you rise up into the air?

Whiplash sometimes results from ans wt0;0ip 365vvdydyo automobile accident when the victim’s car is struck violently from the rear. Explain why the w50o6;pvvydd 3i sy0thead 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 accelerajoj4z tb 9q3iit5m0 nr4en )(7klzi3g tes, the crate remains where it is on the truck, so it, too, accelez qj9n3k reb50to3zjnt)i 7i4m(lgi 4rates. What force causes the crate to accelerate?

A block is given a pug iy0+:w zpnm yj8mb./sh so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on thbp+g .0ymz:jmiwy 8 n/e descent than on the ascent. Why?

What would your bathroom scale read if you weighed y.;aevvz*b fzc q)qq:4 ourself on an inclined plane? Assume the mechanism functions p z*ve) 4 :b;qzqacf.vqroperly, even at an angle.

  What force is needed to accelerate a ch/z(u 6+ 497cognkw ebojc9;qhgtzq h1ild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike an. v.y; n, aym*pvu,ntcd 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 u,qn+i+wves*e w6xn f*np/: rkoaj 42s sed 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 2u wnggl0o64w $76-\mathrm{kg}$ 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 req *ji77-gnjpq muired to stop an 1100-kg car in 8.0 s if the car is traveling at gm n7jqi7-*jp 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pell3 u.zv8(sgs df tg69pyky.nk ,et from rest to 125m/s over a distance of 0.800 m along the barrel of. s6ytv38pg(,yg u 9zkf.ndk s a rifle?   

A fisherman yanks a fish vertically out of the wat65oa y)d g2ktfer with an acceleration of 2.5od)6 t akygf25 $\mathrm{~m} / \mathrm{s}^{2}$ 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 quartepxavk 4vi/3:(jdyu ps c u-b46h)x:ww r-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 dew4gzil+1;h vr )rz2jco3 dv/j signed so that the maximum acceleration is 0.0680 g . What are the maxim)z/hvlo4r rvj+d32wcigz j 1;um and minimum 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 bathrowrxpk eb38a6 *om scale in a motionless elevator. When the elevator begins t3wbp x6a r*e8ko move, the scale briefly reads only 0.75 of the 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 elevat1m6lbi(bpc8 h,. tz fuor has a maximum strength of 21,750 N. What maxil(c6 f8tbbm. uhip,1zmum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includinul9gud3z6n g f7uu0/xg parachute) when the upward force of air resistance is equal to one-fourth of their weigh3u0 dfguzgu 79/6lxnu t?   
(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 6cx p kc0b16hs,d,,aqsu zt *kthe roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is d,zhqat k1cxp,0bc *u 6ss6,k42 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 rogv*u yj: i-2rwalon .4pe tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on* .2vy-oniw jrla4:gu 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 giuurcb.bl,tx/) b2a))/d : or y5fwwplayer
(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 momenccire; t s60*y z)o 3uu1fa5zlhe p44bt it is hit by the bat, and again (b) after it has h*l c;f5ztuipa osz43 04rb6ece1y) uleft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N 9ar fwv2 6b 3yhe+gj7x,qkk*tforce must be exerted in what direction so that the resultant of the two forces points westward? Illustrate yor, g +3 thqkefy*k vb69wxa27jur answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between twcc .a5km aut0*o buildings 10.0 m apart. The sag in the rope when she is at the midpoint is0uct 5*a.k mac 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 g fml ew9jy9-+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 14cd+rf6z0omsxln .-. i.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 Base, Antarctica, asu* (yqy/na x6-ez qybd0wk f3 .2cz.fs shown in Fig. 4-46. The sum ous-z cqy26n. 3bke dq.(w/0fy*ayzfxf 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 behind it, Figo3* 8caq z 3yg+0rnu3th)yk gx. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and t0 zo)+ug*3 r gqcyk8y3xn3thahe 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 bucket-pulley apparatus shown-wk10r g2hcxvg d fp(2 in Fig. 4-48. (a) How h2rw-0kf x1pdgg v2(chard 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 rac:mg* .1gk ddpwtlazck8 bh4w/i4(zi sg-+w0se began, 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 (mass l0x2vwp)7;ka (lxxk) 2d 4cwjd-hzos$ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surfacew uebli* y:z.zb.8;)nlyz xx 5 are in contact with each other, as sho8.. ylxxyi;bze uz5nwzlb :) *wn in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-et;xnrl ;vs, b4wr ho 96(9djy52 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 mass and then its velocity at the moment the heavier one hits the ground. This is its "launche;;6 wo,sd( 4xlvr rhjty9n9b" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionlessu2hsq;xf .j)hpb5;7zr)psc qm , -wlv table are connected by a heavy cord of 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 v hxjs ; 2p5)ruw zf cbmph)qlq.7;,-sFig. 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 frictqbh 2/jjak8znlz,tpw8 j07b 5 ion between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to startkdl+: vscytq )t.+frz.o; b:t 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 standin1mscz/6 w/o gcg on a train accelerating at 0.20g. What minimum coefficient of static friction must exigwoc/m z6s/ 1cst between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffic3 z8r6yy6 +s mfl)ehbrient of static friction betwee3m6ry8 bze hf)6slry+ n the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pf,cc:l 5;rkelavement is about 0.8. On how steep a hill (maximum angle) can you leave a car rcl; ec:lf5k, 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 cbpsyyi b 0;fzj 3dga.*cbx)-+b 4 w(g -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 rough 30p0a,avdc4 quhlw w48ndu7 9: l$^{\circ}$ 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 wititzdoqhks)-ac- -a0 5;hw n )hh an asphalt surface have a very high coefficient of stat) q wk 0zscn)oahhtah-i;d-5 -ic 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, x lf)i5qai-exg+.g w 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 l 1isc8c;fbnt;+pzoi7 bv bv7(arge a mass would box A have to have to prevent any motion from occurrinivbcvizc7sp+7(b ;1;o8 n fbtg? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. H md,hi24hg-yl emr dnsjf0g6 a7p(v++ow far will it go, given that the coefficien4pdg+fl- h0smn i+ rveh6j2gd7y (,a mt of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg*anj 1zvi 1 3,p3icnsl and 110 kg , are in contact and at rest on a horizontal surface (Fig1z,3c3snil *injv pa1. 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 crat -v exm)7z8lej7af0ane. 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 agains8leax)n a f07j-7mezvt the cab of the truck?   

On an icy day, you worry aboutx;x7-4 z y odjfcw*xk6 parking your car in your driveway, which has an incline ofkx;z*y 6joxwf7-c d4x 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 ap u rzep/3).ia slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a planej7 w+/ ya f(*zfr(trkl tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of oirx )6j5tjb;j ,t*o v 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 tocro8w x3*;35c dbqbizp of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough bgs6b t cq0m+x(qv7xk x9-z83tzy 1 bhwall by someone pushing on it with a force x+(3x0bb hk8t gz bqc -x9q1z7vm6y stdirected 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 projec)xv11 mvk8bgvtiles as they melt. Consider a chunk of snow at the ridge of a roof81 g vvm)b1vkx 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 trzb,6- /sc ldqzaveling at speed v is equal to/cbz,l- sd6zq $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 wgv0/g8 uc4kschen the driver decelerates frosc /g0cku8 g4vm 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 mas wz+ yrh3s(;3lrz/cgp s m 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 fillf*1fuo t+ef( xvdc-b3 ed to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomp duoexf t(+13ffbv*-c lished 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 coeffici.2sdt7igd3,k0j3clwo(gftf9 dc x. p ent of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can- fwc.y(csjch8aur7 + 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 hqi)srpq 5s(,l g*4rugw 1 dtfgpc-i,6eart, at each pulse approximately 20fg lst)wu ,dgrc4iqis 1r g-pqp,65* ( g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an auc;j3j 16a tgb j9qdkm3d6lb y3tomobile crash if the deceleration is no more than 30 " g ' a b1363 cjq39 mdltjjk6dybg;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 produ4c /dp hb9bpx7ced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fd/497pbxpb h criction 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 cars4az n-pa ,bwrt3k vil,cdog6v hiy0:,i.0n r; , measure 72-m-lor4iv 3coh;ia.,zvg,pr ntw 0 ,n-iba6:yk l0dng 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 initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m trave8otttiw );j y.led along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55t t) .jo;8ywti m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the )g d2z9;wupq hd jvbs5,og.;i Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Whatd jsq.uzgvi95dg;w h) p;o,b 2 was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 172r-hq8 ffjss2m/s but enters a muddy stretch where the effective coes7 8 qshfjr2-ffficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working84rwla o1i3 .mgekp-u on 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 small car, with a mass of 1100 kr e4pl 8mog.k1w iau-3g , 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 expet/6nv5-jxqsj v8n9 kf riments, dangles her watch from a thin piece ofq5f jtnnk 6 9vs-8/jxv string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecfnz0fak sjyfra 3 k/*r11x89g ting different parts ofs09/8kzrfnaaj1kxg f r*y3f1 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 neede-und- eh 4xt.fd to lift the piano (mass M ) using the pulley apparatus shown in fx u4en.h -d-t

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 acceles,u 8 +wmq1znlrating 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 cod 1mv - m6u2-.xkatpuunsiders the following set of c.d--6p v 2xk tmuma1uuonditions:
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 (660t+m)s-g: o8n0 i s bmgk-tsqb1,000 $\mathrm{~kg}$) . 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's rlorn*pu*t6 ku9*hdm- ope 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 th6 hu o *lprm*dnk-*t9ue force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a2ccak:3j lx is87nt u4 " 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 z efv1fm9d2 /cg7t2m cmaximum 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 ascendy(s * rjp8 q b 9(o)zxjbrsl9j,.dmwk9ing an ice field inclined at 2p x qs*9r8 9b(jzyb (sj.lwkd9,r)mjo1.0$^{\circ}$ 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.