Why does a child in a wagon seem to fal 8-d.e)uso5o.fgd ) p zram-ivl backward when you give the wagon a sharp pull fo ae5uzsivdmroo8 f-pd-.)g ) .rward?

A box rests on the (frictionless) bed of a truck. The truck driver starts thetfyf z 0+/37 /sobe5.qrlprn o truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on they 3so7z5 ot q.+0l //pfenrrbf truck

If the acceleration of an object is zero, are no forces8 l su k2y-r+z6l9flkp acting on it? Explain.

Only one force acts on an object. Can the object have zerod+zyka.1 0m ym-9sjnu acceleration? Can it have zdn y0+m u-sy 91kjm.azero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a foxe 2v7fb uc0zl*rj3;lrce needed to make it bounce bac ;*e7jrlcl 23f0xuvz bk up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in j xn3+v3aehu8;/*f8e yw kwnj the opposite dire *w8h3 uak+8 xjneefv;/y jwn3ction?

Why might your foot huoaddj2 373hqv rt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelehj zu:4+rke.jqg,i n3rate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the m+zk :j3er g.u,qj4hinaximum 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 section of rgw.mxi 48t7;hi 0fy*k bw6e ethe same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp k67rgf tei4y8. xei0hwbw * m;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 240.ik/cl3b y45iso*xr xxsqn -kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fasteoks. 4qx/lx3ri*0xb4 5 nsi cyr?

Would a spring scale car- 3tjf7ubxtwk;1( f frried to the Moon give accurate results if the scale had btrkx (jfu-31 wftb ;7feen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with p ,+zw4hk6 g oqn0uzt:a constant force across a frictionless table using an attached rope held horizontal qp+6kgz ou,4hnwz0: tly. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freellosl9tt/pbv c ei 7**znp.9d (y under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newtonn7/. lvtbps**9ltie(c zdo9p’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) af6ma, fjwi)bm9m h 08fqb/s+needed to lift a 10-kg object when you are on the Moon with the )/aa,iw0 b89fmmfs +m jq6 fhbforce needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s+:c r+ijexed(92 e75anizski third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines w+(rid5zjs29ie xak c:+i7 ee nhich team will win?

A person exerts an upward force of 40 N to hold a bag ofywq0 + z -nm+)otzeoj4h4 ,c+xevkxb0 groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted,zm4eo j 0zxqtc-b v ky+we+o4n+h,)x0 and (d) by what object it is exerted.

When you stand still on the ground, how large a ,xad* sd7 b0poc57wwcforce does the ground exert on you? Why doesn’t this force ms7dwx pbco d57*c,aw0ake you rise up into the air?

Whiplash sometimes results from an aut )hprh2 q3ft-epy,4goomobile accident when the victim’s car is struck violeno-ehq 2rtf )3p4, pghytly 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. a1s1m9f kwgq 9) xsk+lWhen the truck accelerates, the crate remains where it is on the truck, so it, too 9swflag xsq)mk k11+9, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block rea10b z6(+k eymf - bdg9bqilop*ches its highest point, it slides back down but the magnitude gbqz+kpo0 ledf -1 mib9*by (6of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed you6zzb0()s98 )m k e*myhv tuzhurself on an inclined plane? Assume the mymh (zhu)6*v0em t )u8zz ksb9echanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/seve 506 *ldm8tt+avm alf)+gn$^2$?   

  A net force of 265 N accelerates a bike and rider at aj4j +v7jo up9-lqbq(2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a / c6p9 rwzmby0 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o+zw z3,2xqho bf a $76-\mathrm{kg}$ 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 rehy3/gnmj-hgx :k;*au ;8idpk quired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/hng i dx kkj8ghm*h; /;yp:-au3? -  

  What average force is needed t hq54 wedqt 3lv-hlb1z q1vo49o accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel o hwl1 4hlobvz-d3qv4q5 9eq 1tf a rifle?   

A fisherman yanks a fish vertically out of t+pmiskp1; u (, exf:ghhe water with an acceleration of 2.sxhfi p,ume:1 +p;k g(5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-m, 8*.sp p tikym xekn)ar//n2avev/ rx,hld 80ile 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 tm9u. t8pkcku9 o be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forcesk9tku8c upm .9 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 elen pci-oi6v/ p tm;.l6mvator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s r mm6coti ;v/np 6i.pl-egular 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 t.wfx1h ) nnyzhj(7 wr6m 8ts821,750 N. What maximum upward x htnh 61sf(w8z rm.)j7t8 ywnacceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleratig2iyd(c (v dpu,r7qs1 on of two falling sky divers (mass 132 kg including parachute) when the upward force of air r irpdud71 c( 2,(vsygqesistance 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 hou6c xna:n77cnx 9k*oicyey+ r hc 06;nuse 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 n9cc7ou0 a66ne;*y xix7y :c nrnkc+h42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically u. c6wrrur,7r y5cvh5p w3v.arpward 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 the other side oh3rwu 5vp5,va c7.r6r .rwcy rf the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diapmki(zhoq.jh8 (9 x 3ygram 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 moment it is hit by the iit3d kn)lg55,bye1xbat, and again (b) after it),5bi1yle x 5tnk3di g has left the bat and is flying toward the outfield.

A 650-N force acts in an9p3eeu ,y3fn:h 1 vam northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant ofe3nv hm3 fup 1n9:ay,e the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a " z*m42gqy7 ibw tpm ,4s2w3vn c*-qtdkhigh wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mi* ywq-wktisq tb34 ,dmgzcpn7 4*22 mvdpoint 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 from e h:086wxq+wk w5)d*xrs uvpyanother 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1 t;oe/js2;mfd l9 .xlvpkg/ 3i4.0$-\mathrm{kg}$ 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 tzp7tgs/ n,fzi z)(4 oko a new location at McMurdo Base, Antarctica, azp)4(s k,zngft 7/ozis 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 behind sz 9.g isevc.5mlkp 93it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and 9k.9 mgci.s s3zplev5the 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 hersel3vv* 8)v lmace1ug9nmf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward t v9 ev38)g1ua n*vlmmco 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 racerydyw:eon-lzggv + 17 ep,g01 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 (mavpv v 4pp:gox*q4tw+.ss $ 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 hoq m0nr-+bvqg276wkeb rizontal surface are in contact with each other, as 0 ebwmnqgk+q b -rv267shown 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 ffsm-/*hyvbd y4 g,t/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 obje vf/yy4*g -hf/b, msdtct 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 fmtik- le-axix 6 t 0j(ot/hwq 7;7l(nwrictionless 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 Fi-wx 0t/ tl(77wnqmxeh6 l oji(akt-;ig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between s x g6zpkbb5zio2l5u9s5lh+- 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 /j +jtb5 ie))v arm3kzstart 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 acceleratlflj8zb3 3o,u ing at 0.20g. What minimum coefficient of static friction must exist between your feet and the ff ,uj38z o3bllloor if you are not to slide?   

  What is the maximum acceleratif,an2r-s/ 9 p9pmhf n lt87kbfon a car can undergo if the coefficient of static friction between the tires and the ground is 0.80 -9n2la b fppt7sfmr8h/n9 ,fk?   

  The coefficient of static friction between gj 8zkwnoqf*.1os16q hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car park.o8o6wn s1qqj f*kg1zed?   $^{/circ}$

  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 (0 43 b9uillkafisg uth* x-3hat -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 on6h x-7p o -fjmhb,vk.y a 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 coeffi:b ihyghul128h7din /1w )m rxcient of statib8:1m h/dhx 1gri wuilyh7n)2 c 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 frsmi1g 2n(yoawm)8pk7s-:/o gjyef.i iction 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 Abdgwdf ne 8td4*qnk 44* //lcv have to have to prevent any motion from occurringnd d 4/tev4q*b*wd4 /l8gcfnk? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, go)g0+pnzu9j given that the coefficient)gjzn0 uo 9gp+ 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 0ql8lws7 u, fkand 110 kg , are in contact and at rest on a horizontal 78f 0u,slqk lwsurface (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 frichc4v 3x)vd1u g:,vnq stion 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 thesd 4v,h x vqn:)v31ucg crate slide against the cab of the truck?   

On an icy day, you worry about parkingt g: ; u12-dn rheb;cyw9w pj,xef7vs6(4 bwhk your car in your driveway, which has an inclvye9;b-kf7wg bh pscw,tw:j6( 412;hnxe du rine 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 sl3dsk: zgtil+ xj7;vq 0ide 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 avq lrf1jzgs/9 i(mw7y-h hl;:,ix2lxx n:n 2pn 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 speemso1at p l35.vd 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 hill /e b5ly qfp6;lm547,avskn fovbj6:etgk;5 e 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 ckvync4d8 * fyte: 91ba rough wall by someone pushing on it with a force dirc*bd:fy t8nc1v4ke 9yected 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 ry ;ab,apns wpirpnn 2j6957ea+br/*noofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pit5 ns2w 9pbbr py,ana6 *+nr ej7;nipa/ch 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 traveling at speed9my t32fpul+ p v is eq+fp lyu t2m93pual 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 fo.-2irv fn6fx2uv ;smjw. b1z brward on the dash when the driver xfbr.6 ;2. zj sumbvwi1 -2fvndecelerates 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 initial6( gsfz 3xm4f-6xzcenj.hci+ 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 filled to the paco -zvyj-yc1jce x(4g2king station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction betwj-ey c-jyg2o4 1(cv zxeen 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 frictiou3l d ;9m(f5bh*xlhdvn 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)u qps((t g7-wo can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified mobv/:qba 1- urodel of a mammalian heart, at each pulse approximately 20 g of blood is acceleratedq- uao vb/r:1b 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 decele7 3i8k.r0vbtupgv x8 oration is no more than 30 " g 'ru 0gp.k 8tvx87 oivb3s." 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 ,vvm*i8 -kn 8d39 zxjru2bzn ,oic-2wp and if an object is going t mnkov*2n-z-3ci vwur8 pxzi9dbj,82o "hold its place" 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, examining the scene op;rj s t q2.qc65 r;/txwjw9cxf an accident involving two cars, measure 72-m-long skid marx/6.wsqc;jt;t wpj9 52qrx c rks 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 hi/u yckub 0.9cleudz/f)sj;d ;ll (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom y/) udb/zjs;eudkl 0cfc .u 9;after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top6jv1 or8uq+ ew of the Leaning Tower of Pisa and falls 55 m before reaching the ground ejv8o1rqu6+ wwith a speed of What was the average force of air resistance?   

  A cyclist is coasting 6cttvhxhaz9.h z zwdme*royw :,1/1(at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will mhdo:zatyx9z(w hzr1wve h,*t6 /c1 . be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a rlrd0x*8ft gz0 /sv *rcity. 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,xrf lvds*tg0/8rz0 r* with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin 1uz+j f;sve,f piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-zf;1jf u,s +ve58). 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 suzgo8c. e.5bru 24h(jjc sma+ rpermarket, there are to be several ramps connecting different par84z(ae mj2crruo . j.b5hsc+gts 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 tbq lvo2:m3 ;t2w +lorno lift the piano (mass M ) using the pull2;ntmvo+bq:o 3ll 2 wrey apparatus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accm5c*ex;m 4mbe gryox- .r l6ysr0dq7 )elerating 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 cqcbl9u * ccn (yrq8jz4g) )dz14;oqlehild-restraint chair, an engineer considers the following s qbenulgz;4)*(rqlq 8zc9d )cycj 1o4et 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 tmalng4. eeh(lmn-( ka 3)gjq3rain 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 coqdn b);,l sf),;x /exp7 ngi zclv74pc+kr1safety 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 ropcl)o4e / cd,1;nf;zxq, lic )77rsnkp+xbgv pe pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is)0zx//oi : kng4ewilb using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum s1smn6f 1 k2afspeed 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 fix ,,0qg(g q a)xu4h c3gb8lkgseld inclined at 21c uxsg0, , (ga4 xqlgkgq8h)b3.0$^{\circ}$ 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.