Why does a child in a wagon seem to fald2 mssa5y0nbben c4v25 8k),w ubv;dcl backward when you give the wagon a sharp pkby sand5,2vc54m e;suc2db wb n)80 vull forward?

A box rests on the (frictionless) bed of a truck. The truck driver s ;n3(bcx(qv nktarts 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 standing on the ground q3knc(v;b nx(beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forcesu0m3kiv 4jf3y:( o j+6dp gvox acting on it? Explain.

Only one force acts on an object. Can the obje w)n4 k7.rmr gnn2 ,4jchmtmf7ct have zero acceleration? Can it have zero velocity? Exw jn7 4 )mcn4mgrnt.hfmrk7, 2plain.

When a golf ball is dropped to the pavement, it bounces back up. l:7a m;g08es d dwrje2(a) Is a force needed to make it bounce bm;ls2a8d0 wde7jg:e rack up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why doesah bi2a0 tw9w1mvb)zxuvx0/7 the log move in the opposite direction? aw z1b0bvw)v/am2tuh9xxi0 7

Why might your foot hurt if you kick a heavy desk mpg) b +zvude-a9 )k+kor a wall?

  When you are running and want to stop quickly, you mustx,xn;vqhg ) x6 decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration ofh6 xxx;,)q ngv 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 3;nemnrx qk+1section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explai xrq+3mn ke1;nn your answers.

The force of gravity on a 2-k3h ,6qlog38x,q 2nv 51lw ru i4vvidzbg rock is twice as great as that on a 1-kg rock. Why then does2 qblqn35d1xowrg,ui64 zvi v,vhl38n’t the heavier rock fall faster?

Would a spring scale )7uxw 1xc6c7pr5omnt htd 7w8carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilo )76cr 7mp7ct5duwth 8x1noxw grams?

You pull a box with a constant force across a frictionlef49bay ,vp* miss table using an attached rope * pfia bm,4vy9held 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? Explain.

When an object falls freely,a9* ral- hqzi6mww e6-t.pu w under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the objec9 -.r,quwia*wwamp6ze- 6th lt exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (ob9jj. k 86odtp6hei*vw iz62vr force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon h6 *ivodij28wvep6 9k.6tjb zand on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4fg0;jb0k t/gmc* c;x a2k 9a6an9rk au–37) pulls with equal force on the other team. Wh;baax r9 g0 ;tc*g a/nka6kcj9umf 0k2at, then, determines which team will win?

A person exerts an upward force of 40 N *9 6mtq.5vm*vpadykq to hold a bag of groceries. Describe the “reaction” force (Newton’s third law)pv*. v6qd* 9yqakmm5 t 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 the ground exert ono h) lg,vx9r y4ig w*a iotoz11o921im you? Why doesn’t this force make you rise up into the aiozi xi9g 2yrmh)1*14wtg , avo1oilo9r?

Whiplash sometimes results from an automobile accident when the victa:f(ui ndyxu++*m ut8 im’s car is struck violently from the rear. Explain why the head of the victim se 8y*:(uxdauun mfti++ ems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whek6s.jvsh:v 1ons i.1rn the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate tivsk1ornsjhs 61.. :vo accelerate?

A block is given a push so that it slides up a ramp. Aft4 za ,8btgeo3ter the block reaches its highest point, it slides back down but the magnitude of its acceleration is lat ,g8oze3bt 4ess on the descent than on the ascent. Why?

What would your bathroom scale read if you weigh rq15bmui rfy o5 ;xw/-;vk)baed yourself on an inclined plane? Assume the mechanism fua5obx; )ru/ - rybmq;1 fk5iwvnctions properly, even at an angle.

  What force is needed to accjv+g9d, f8 q*h /nbkclh xds-:elerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accg2x3v 8w qhcf4llj6t.r/ qp .jelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is usedgwfjp3od .1:d 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 au(fssj n9jm(q(r . q1x $76-\mathrm{kg}$ 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 110094aryrdp 1m3; 7c mxeea7; meh-kg car in 8.0 s if the car is travelxh;ym7e9 r4arm;1 c p aeemd73ing at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from r6x.f -im+ia-3akzedrz7 ahw4 est to 125m/s over a distance of 0.800 m along th6 fmza+iawie 3 4.a-hz-r x7dke barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratiovjtm y5 /9gt;tn of 2.5vtg t9tj ;m/5y $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile trbs cr2i+ (b+( ylp)r0)q+6zls rkj fnxack (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 tdy;p-92 ca11 gjfymggo be designed so that the maximum acceleration is 0.068pj; cggd11 yfm 9gay-20 g . What are the maximum 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 bathroom scalekcjh/a1l,z)p z4 p8 gg in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction o 8g, )jplhp a4zzck1g/f acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximu3gj5kexh9 9 +ifu v0nrm strength of 21,750 N. What maximum upward acceleratio+vkx9hf j 3 0eiun9g5rn can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fa +ow.*pdo4 a f/vxup)wlling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weigh.a+dx*po4vpf)/oww u 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 the roof of a house 3.9-m high. When he st9qdl2+ qgxsc8 rikes the ground below, he bends his knees so that his torso deceleratesxq9+qg l28cd s over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests onoo66kskk 1qhh, p8* uw a table. A rope 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 the other side of the pull,8poq 1u6okhh6 w *kskey weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pla.;:koh a5dos nyer
(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 c7aplr;j w gbv2e,, p8,bmg*ois hit by the bat, and aoe p,g*crj;bp7 vl,b ,wa8 g2mgain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. avbss,e h(0 qy8( k,*zh t-sewA second 650-N force must be exerted in what direvh w(s, (-aez*0qb,s yk8thesction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontal m;5 tija8,ihmly between two buildings 10.0 m apart. The sag i5h ,;mjaimi8 tn 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 masslessenr qjh;5u. kei/a ek56 +2kmk 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 14m)h h2bi hlf5k i;5.yx.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 zfmjm0l3du;xjm: 5 e 5Base, Antarctica, as shownfl ;m5edzjmm 0jux53: 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 ip zwov e726ijq88z n.fs pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the lo8q7z8fzjiw o 6e2vp n.comotive 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 bucket-pulley apparatus show q jwt0l1bj:o(z,.nq a,5ecpwn in Fig. 4-48. (a) How hard must she pull dolw(bqn w5 ac:j, ptqejo z.1,0wnward 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 65y) ;rz 0oal;jws, xx5m$-\mathrm{kg}$ 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 (mas l)ht5/gy)di z5tstkplo7q/bo 9( 4l xs $ 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 +y 1 q 9pzowrrsh5.j5wsurface are in contact with each other, as shown in Fig. 4-51.jqpw+ 95 whr5sz1 yo.r 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 e7 wfed g)ynd; hi oif)y+h* ai7:z60bdach initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum heighiedy h0 f7d+b6)7fh;gid z:n w o)yi*at does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heav17k+n,hn* gl+,mu pdd(pcn n,r3i h eay cord of mass 1.0 kg . Calculate the acceleration of eachrd phm*pk+d3+ a7n(enu h,,,lni1gcn box and the tension at each 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 fro:w3kutx bov3370en59f clv3dji 6ne. pb4kinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start: o rswyhtx1:v+n/h +1sp6ala:zgm-e 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 at 0.20g. What mimr;y2aau; vy;jqy;9 zk)w7he nimum coefficient of static friction m; juyamr;yhwy;9 )2;evz7k qaust exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if tt c(s.pg1e/ nrhe coefficient of static friction between tresg/1.( ntcp he tires and the ground is 0.80?   

  The coefficient of static friction betwee+dxp rvn1ve.e9e 9kq( n hard rubber and normal street pavement is about 0.8. On how steep a hill (maxpvq9eed kx9 n+(r.1 evimum 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 at 1nzqogk6xz 6 . -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 aw2ivb.rv;m mrr:eg .n:pah.- 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 coefbeiwp2fb,, +aficient of static+ip2,, ebbfaw 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 g t7zg3 p;83kis0qdtk 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 (Exampfay-3dge6o *u ,uuuo)le 4-20) how large a mass would box A have to haudo -y6uo*3u )feu,gave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far ;l gwwq ex/nz(b9 w1d9will it go, givend19; q w z(lwegw/9bxn that the coefficient 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 and 110 i .tvtdjw:v1dml;1 w5 kg , are in contact and at rest on a horizontal sur;v1t .w:dtdl iw1mvj5 face (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 mzbg uv43xe):static friction between the crate and the bed of the truck is 0.75. Whatx4vueb 3:g)mz 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 drivew+p0ynm la ,y;cxsirug2m 0(,ray, which has an inc+, 0rau;ym,i xly rn0(2 mgpscline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with* ai-urmx-v bt lb-wt3s o37n3 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 dcp/r g7czyd s1-jzos65. pf2 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 mhl;0mps)ja1 3ms7( l v jx:z( awgp.w 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 with a speed of .i9*bwyfp;b r 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 againstx *w6n:mc5gmj i kk1n. a rough wall by someone pushing on it with a force directed u 5xknc*jkmin6mg. :1w pward 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 (zuk*6j 0qx h2*abthccan become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with jhzt26 *ba kqu0xc(h*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 adom 9 3ze8y lr v54sgbk9gg-q.utomobile traveling at speed yg-bgro5vqmd lkg489.9zse3 v is 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 aklmsptq 7ks :w6, ;bq. car slides forward on the dash when the driver decelerates from skbl q7p. :w,; stm6kq45 $\mathrm{~km} / \mathrm{h}$ 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 lf dd0btumq ,;3m+7re 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 belv .-iwezbz;ys ;j/,u89 fp q/(vws kmmt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.;w(z sse- iz 8fym/./qpw, v9;mukvjb60, 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/cgcdv f rl,c 3,fq7*zent 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 thvk+z 9k uj.l;ee 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 simplif0 m(oix6+rafwied model of a mammalian heart, at each pulse approximately 20 g of blood is accelamor60( +fxwi erated 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 autom1:pwh m +q*jyrobile crash if the deceleration is no more than 3mj+h*w: y1q pr0 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an b-*ya r)f+ kfyvg(.eoearthquake is a , and if an object is going toar.f)fe(g *y-y+bk ov "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 of an accident jg8 bm84pjz +qinvolving two cars, measure 72-m-long skid marks of one g +pj qj8b48mzof 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 ;rh(hj:e mwi3r,5m t) xj.lsv moe p-6traveled along the road, the elevation change is 1 m). How fast is it going when j;r5mlx- h(m:t6.vhi,mep) soj3wre 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 +di w*e1;sycm 0 uk:b pp9ipehq0mv)9of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air reey suhev+09iqpwdk:ip1 bcmm) 09;* psistance?   

  A cyclist is coasting at a steady slk / h 9(lwiaw ph-5csozv8l*5q0s:jmpeed 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 :v5q8khwlis5( wal0/s oh *9pz mcjl- lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a4ex*p4h5h+9id ac zt r 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 mastc5*ah 94zi+ pedr4xhs 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 .if1n**) ebo ;,gyn4dm9 n ghqziu0oufrom 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 angle of iu4znfd1g*, ;yi0 b) n uogh.q9*onem 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 connecting diffetdp4td1v pejpl(e q.z 70 *o)trent parts 4 edl(jt70v t*o.pt1pp)e qdz 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 pi7avp 4odj m29gano (mass M ) using the pulley apparatg7 v294po jdmaus 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 accelecj8-kag:a q s7rating 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 considers the f1vg *lqfg,,p(ru n7o zollowi1qv g o(lfg,n,7zu*pr ng set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car I zsan7y( p)w ;1s5hlq/r8bigy talian 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, Bill and Karen, use safety ropes of similar length. Karen's bw f6cgg ofyi24( n25krope 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. (Exfw2g( k6c2gf5oyi4nb press 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 a " 10, hp:3 5p +,)qnaabakhsa , dgxgn:br;-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 3.5,: ti8k vc3ukqq 0g3w,kmcz 1c $\mathrm{~m} / \mathrm{s}$ 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( poa+gh6zhea*1;.plls :gix i rtn:: field inclined a:r pi( 1n 6;*hs:g:hte. aa +giozpllxt 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.