Why does a child in a wagon seem to fall vpu u+6xf6z*wbackward when you give the wagon a sharp pull f *x6+uufvpz6worward?

A box rests on the (frictionless) bed of a truck. The truck drivelmt1cqym m.8-xz+f4 fr starts the truck and accelerates forward. The box immediately starts to slide toward themxq.fmlm-+f t z4y1c 8 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 the truck

If the acceleration of an object is zero, al,ngjnpi5 c,/rrvm; - re no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acf (i l:p,xcozj,y0u(o8g /f tgceleration? Can it hax :f,f8g(p yg, u(o t/ozl0jcive zero velocity? Explain.

When a golf ball is dropg y+/2 jy5byk:wrqy c,246xo vsgve*z ped to the pavement, it bounces back up. (a) Is a force needed to mg2k*g5qzyx6/yy:vb, +2 o4cv jwer syake it bounce back up? (b) If so, what exerts the force?

If you walk along a l(7k noh21tgh*qsx nke40dlsmrb8;: pog floating on a lake, why does the log move in the opposite dipg 08hkhrld;q *ok471se m(nsbx2 nt: rection?

Why might your foot hurt if you b n(z18s8 vbqxkick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelstzl epq*jzsw b6p4.-x d 5806 xai6oyerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to combzs.66 ew0-qd4ix p 5 t8jxapzy*osl 6e to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the;p.s* y(rqeka 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 sto;p(k*qy.e rasne or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice su2h n3d/3whe as great as that on a 1-kg rock. Why hd 3u neh/23swthen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale s9jdcnmct 1t.h5f 5n.had been calibrated (a) in pounds, or cn51td9sc t.5mjhf. n(b) in kilograms?

You pull a box with a constant force across a frictio,pq g o/sv-8a7 hn8oshst7bd( nless 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? Ex/vo7snpa7sb-t8, d qhs(og 8h plain.

When an object falls freely under the influence ofh--tbz o;nlbkmj ;q *, 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 opposite force on the Earth. Why doesn’t hl,nkz; t-m o;*-qbbj the Earth move?

Compare the effort (or force) needed to lift a 10-kg omybu (x o1l( w+f)7.k o.rkcxvbject when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objemklxv(xcwor.(oub f 1k).y +7ct horizontally with a given speed on the Moon and on Earth.

According to Newton’s third sxm+c s8st 8pa/obu76law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, the7ut c/xsopmb s+as688n, determines which team will win?

A person exerts an upw *82*fr+e,t v)adswvepp7jcwq 4a9w mard force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newtcwa ejavq r,)m4ef72t*vp9 *+ s8dpw won’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 groqb*zb qhwo,.yq nd;2zdh4y-0und, how large a force does the ground exert on you? Why doesn’t this force make you rise up zqz .w;n4d*o-qhb, 2 d y0qybhinto the air?

Whiplash sometimes resulx5p1s9v9d fpq hf4 mh,ts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the he91fxp 5h9 h dsf,4vmqpad 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 acceleratwkhc7 p opbt,- gry;0jnv1m -(es, the crate remains where it is on the truck, so it, too, acceb0-ck ;1,7r-wmvpj gh(o ytnplerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a r;dv ob o7uj)szo)2oc t-:;tr namp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descoouc-sr)2 dnzot7jv;; :b )otent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself 7;bo a2ih5pr qxi *db2on an inclined plane? Assume the mechanism functions properly, even 27q;biap hx i5 rb2o*dat an angle.

  What force is needed to accelerate a child on a sled w: g;4fjab zulu*6pn7n 2avv;at 1.25m/s$^2$?   

  A net force of 265 N accelerates a f zc5 1f5klwd7:l6zl6z r4 wmabike 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 rope withstand *w xdudw; bo4;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 ofx gqr:yj, (8dhys: h6u 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 required to stop an 1100-kjq1h6l-jw4kkunp3e,9 k wc4 xg car in 8.0 s if the car is traveling at 95km/h? qp xk6n3 j 4ej,wuwk1-kl9ch4-  

  What average force is ne4m dg t*3wr(/vgwlh;t 5 qb7weeded to accelerate a 7.00-gram pellet from rest to 125m/s o e m h(5q wwtwr7/v3d*tglbg4;ver a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertic5s rahxc *s;)a wg-u/ugf8ia*ally out of the water with an acceleration of 2.5 hcagga5 ;/8 uf-)w iax*sus*r$\mathrm{~m} / \mathrm{s}^{2}$ 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 mtzd- th 51k3guv 48wccover a quarter-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 designed so *k avdl( jey032qah qa62cm5f that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cabl25vmjf*( a hqkay20 eac 6ldq3e? 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 batw + ).hnxzmyz,j 6y2zbhroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculatzyz2 y mx+ 6nw,)zb.hje the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 21..9 d f3 t a3o5ghpkcp*z)ioaj25-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give thet3 )caagi z5.fo .pjdh*o9kp3 elevator without breaking?    ( two decimal places)

  (a) What is the acceley2k:b,c0gi -2 )3 t aftwkkyovration of two falling sky divers (mass 132 kg including parachute) when the upway2: o,a2ck3-yb ivg0wkf kt) trd force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he skc*;sb e3q igrc+jx nbt5, 3h7trikes the ground below, he bends his knees so that his torso decelerates over an apprc3*rq3k ie ;bbghn +xj57,tscoximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs ve1pv; hda+fcz)k2p v6drtically upward over a pulley and a weight is hung from thvhd pv1 2fc)6+kadzp;e other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball play 7ag9lxr5u -wier
(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 ba mgvfxv .e7+r:t, and agrf: .v gx7mve+ain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 6vvvonn3h.55b6 wuhitbtv 9 c3)mdc en(s8 u /150-N force must be exerted in what direction so that the resultouimnd cv8.hb/vn5 65tb3 c9 w)e31u vh( vstnant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two mgz ,:a(v-xg) gxmf z5buildings 10.0 m ap,)z:zga-fv(g5 xm xmgart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a masslez51y us6i, ier3um hg8ss cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.s3yv /iwn /c5b0$-\mathrm{kg}$ 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 McMup 2:5ohi2gf c3ihhgzbdx 58yd0mu pr o/*.kd/rdo Base, Antarctica, as shown iu: p32hpmdd.gb o h// 52iz85gfdy i k*rhco0xn 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 :8+ 5jk+t8xbu dcsmkgpulling two cars of the same mass behind it, Fig. 4-47 . Deted5ucbs:jg ktk +m+x8 8rmine 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 upward using the u:wrb4i n a2t0bucket-pulley apparatus shown in Fig. 4-48. (a) How hard r:0u2n4 t awibmust she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6cv+3z*z2n -mr -ueb1ube i-xx5$-\mathrm{kg}$ 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 q.m3ui ,,dd. 8lukpl u$ 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 sur7hjea 5jj49ku o4lcrk/,)r kntr7m 9pface are in contact with each otherk k projk)h4e9/,a 4 tj7j9 mn5r7uclr, as shown 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. 4-52 are each initially 1.80 m ab 0l i gb,r42mkmp45/ry/)yg bqb upd(iove the ground, and the massless fricti/ypbr4m4yk)2 lr dgm/q,g0 uib5(bpi onless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are c-:a v dddok-m.onnected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at eachd :od -vk-.adm end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a 3ce huya2mfgf /)5;-u78 it0iw f2yemb5$-\mathrm{kg}$ 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 toscg w7a2lt* quwe (x*;iy:sn:qpl ; j. start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating aty/ q. 7 ;1v*rfl :lu3 8lscyzr(wcxhku 0.20g. What minimum coefficient of static friction must e l7fz.qurkyxlsc;h8*/3 wcv: ry(u1l xist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car ckqk g,l0wc+6f an undergo if the coefficient of static friction between the tires and the ground is 0.8g6 wlq0kckf, +0?   

  The coefficient of static friction between hard rubber and normal street pav( -9 iaupui597kkni nfement is about 0.8. On how steep a hill (maximuin9ku(fpiia -n 95k 7um angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate-sih:1;gcb smvrx/) t at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a r;i2qgld6i3 +s/j mjdyough 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 con+z qr na9gxy8zcx;f*. tact with an asphalt surface have a very high coefficient of+q8 nzz* xycrx9 a;fg. static 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 f.eqf/ ia1iz:(h ptb k/riction 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 ; lt ujcog+ r/(wuwy2)A have to have tot);wg wjyc/2lou( +ru prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor 1dxe9mnqcn:2)n e x()o zts6c. How far will it go, given that the coefficient of kinetic fricoe:c(smn6n t1 e x9qn))cxz 2dtion is 0.20 and the push 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 rest on a horizonta z:do/ido 1)zal surface (Fig. 4azdoi/o:dz)1 -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 coefflf,1p/-v odiv myhl r35pk3(8pzee,uicient of static friction between the crate and the z3- ,3(1il8m/d eep u lpfy,5rpovkhvbed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whichf 1e9q-zzut;:+u/r qkhj6m4fyf;1c1ngv tuv has an incline ;mqk u qufg 61e; 14vyf-v:jfnt rhc zu+/z1t9of 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 a1o c ug /zap;5tbey/r- 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 plan)jlcywij y . (/h( 1sqfc-b2zse 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 sp4 i5dhwhx. m x,ujow*p1na/yt 9e/2aaeed 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 reach .dyb.lk4il1m v:fu1mz * pil0es the top 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 .r 7z/(g owfe5odxlq )against a rough wall by someone pushing on it with a force directed upward orw.x)7dlge qf zo/(5 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 danger)cxprb5yp *px ;nu(;u ous projectiles as they melt. Consider a chunk of snow at the ridge of a roof wit) nxx*rcb;;pu 5 u(pyph 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 traveling a2/hxhe -(y b9z5 r2z tfok7lyet speed v izx5t-yzoeylh h2f /7 (e9r b2ks 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 on4 eh htsd-w(b(4:bq pq the dash when the driver decelerab4 4wpt (ehb(q hs-dq:tes 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 isu+d2 ciqgfd ndk /:(6q 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 frh)mx ( -+4jhgydl5mrndsd yihz7 5 2 /;hirq/illed to the packing 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 acceleratq irgdhh2i/r-n 5+ds/5 hd)yj ylmr7;mxz( 4hes 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 between69ufw4n7feta;doi;t4trcr3 qt 6 5rm $m_{1}$ 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 (includ6sr /o/0 bo9dzz.zy fxing the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each puls ln6p/ /h c sysuh19n/r:1yac80fh htce approximately 20hhtl cfu19ny/pr c h8/0csh san:6 y1/ 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 automobile crash if mmab+hr) xy 31-+cc6yagx i0mthe deceleration is no more than 30 " g 'amhi+m+yy x3ba1c -0mr)6 gcx 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 an ob0du7 8bkp+pdwe;m 3zzject is going to "hold its place" on the ground, show that the coefficieu0zd+kzpp7wd 3 e bm;8nt of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident inq-l tgl kj6hxrtw bb,* )k91.jvolving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the parl , g 6qxjk-)tt1l9w jbhb.k*vement 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 thatcwv2f6p1q *q;3c n;ypiho/ +g tu:acy for each 4 m traveledpwaqvc6: *g ny h2+t;c/iyc1 p ;fu3qo 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 friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Toweargaf,-a1 v4 bz0b7wd, 9phrtr of Pisa and falls 55 m before reaching the ground with a speed of r9 -pv 4 g1a,awz,hdbb7art0 fWhat was the average force of air resistance?   

  A cyclist is coasting at a ss z n7ogi*d b1i2bzt+-xs5 n0iteady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will tn 5 bz7-2sziot0 d1gisx nib+*he 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 o:w 0jzlb pwnmn do,8z. ,ah8t0f a city. An important consideration is how steep the roads can be so that ew bm ,dz:l8pha0 n8,n0jtoz.wven 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 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 f.9ss6t 1s6gh 4 xceczm4c-jajrom a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an s6-4 hszca61.sgmcc9jj et4x 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, t6ta6 o 6em:v2rv*dxp;dd 6/blkdkv r/ here are to be several ramps connecting differentlt;d6x2pv r d *6: /mkdedrv6 /6avobk parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass er.24;t7g l t emjafx, M ) using the pulle7fe etx4m.g,tjr;al 2y 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 accelerating at c (bonbflc ct-,::yy8 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 considers3xfej2 -) abqyz -t0my the following set of conditions 3b-mf-x2e0a )ztyj yq:
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-h:vtxo8lm+ je ;l (3jtcar Italian train 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, Birfol9.j 9j5rb wekzp4 49lz/( n*duboll and Karen, 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 weightb ( nw4599j eu/j p.f*kooz49rbdrlz l will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat )h/m 41inwzdyl;*n9t8rqthfv; 9p oeis 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 speed of 3k 6l;5k sobo/s,r-84tlteff(q eqv 1h.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 aavd039zq1 bj pre ascending an ice field inclind9 pbz1v 0aq3jed at 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.