Why does a child in a wagon4:, qypcie pl/jk7a3d seem to fall backward when you give the wagon a sharp pull forwarp,qa cp:37e 4ldi /yjkd?

A box rests on the (frictionless) bed of a truck. The truck driver stnz. lz./kc/ xdarts 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 beside the truck and (b) by Chris who xl/c/z. zk. ndis riding on the truck

If the acceleration of an object is zero, are no forces h)z+l fbz*o-29had(cg;hj0rz2yi4ajm*d o f acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratiz4 c1yt(he) i 5vgw(dmn178 lxwhm;ywon? Can it h n1dyi58x h(wwe(4h wt7zlv ;yc m)mg1ave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces bac p8gxy04.9ia vjl gpi)k up. (a) Is a force needed to make it bounce back up0g y)ip.98 vip4gxajl? (b) If so, what exerts the force?

If you walk along a log floating onkid* kk 5nx*5tm: 8jvnk3hai3 a lake, why does the log move in the opposite i3hkk5nv8 m5*tk:id *jax3nk direction?

Why might your foot hur m*mmwny c/n f7x0c*)7fr.xki d3dt2vt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must y bzn 6djv5r6e2/xdul)4 yk c-decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maxdy d5cvk)6 x/2n-ru4 lby6zjeimum 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 sekxcqqsy48ca5,gln 5-ction of the same threadxcg,k5aqqs 8 4 ycnl5- 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? Explain your answers.

The force of gravity on a 2-kg rock is twice as gpxbg5f55 :rjt reat as that on a 1-kg rock. Why t5t5x prgf:5jb hen doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon 0hn1)bo*r:xt-i spdn give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogra)-st pdxb0hnr1 i*n:oms?

You pull a box with a constant fg.hoep8 /+n i xisn 9:+dtp9l: g8fwzvorce across a frictionless table using an attached rope held horizontally. If you nip8o+:n9 gvt eg8infdwp/9xz. h +s:low 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 under the influence of grcf17z vrn17c jbx3mn mh2g11mavity there is a net force mgf 2nv 11bmmcgx3r nh7 j11mz7c 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 the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when g xan;3hidlpxu,) -l8you 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 sp;3 lpl- ,x8niugdh x)aeed on the Moon and on Earth.

According to Newton’s third law, eacn8z e kw:ys53 t1cp3v9zje4c zh team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What j1yc9 wz5s3t4pevzcz kn8:3e, then, determines which team will win?

A person exerts an upward force of 40 N to hold*q,zr0fl7tb:l txx* q a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d)x l * ,ftlb7:0qtx*qzr by what object it is exerted.

When you stand still on the ground, how large a force does the gnouqquq0. xcr) 4oo9)round exert on you? Why doesn’t this force n0u 9r o qqo)4cou)qx.make you rise up into the air?

Whiplash sometimes results from an automobile accident when the z,3e8f hly2eh(p9 e-is2 f fbuvictim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this sit yep ( h3ff i9,822bs-eeufhzluation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck x:xsjl *1 :rmpn+ tf0jaccelerates, the crate remains where it is on the truck, so it, too, accelerates. Wham+ jxs01nj:trf l*p:xt force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itsi7rnup3w )p3j -nfp 9sh3aj*u highest point,- hwp3 9jjnuspfu)p3ar n7*i 3 it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined planeyu ikez*8,tv- f d ett*)g8p0e? Assume the mechanism fue*et8 0tf*ipetvyk gz,)u d 8-nctions properly, even at an angle.

  What force is needed to accelerate a child o.o6/skm e2 jfwn a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ride(0r0bzqr n 7yyew5kd(o-)e glr 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 useehqu0sgm9-xv *.o; ak 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 aacac go.uzpa 5q 83a84 $76-\mathrm{kg}$ 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 require4fbh/ ;z 6vwudd to stop an 1100-kg car in 8.0 s if the car is traveling ;h dw /46ubfvzat 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellh 7m91yoop2wk et from rest to 125m/s oveyk7 1 pmwoh2o9r a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of ice+5,kf.cd1fm n 1ji the water with an acceleration of 2.5 5.m+1in, defc1 kfcji $\mathrm{~m} / \mathrm{s}^{2}$ 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 can3 ra8xeiwi t3. cover 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 des4*2 p4lg;ndvr l 4tkbxesbu0 8igned so that the maximum acceleration is 0.0680 g . What are the m4lg; u* 4b0pbv482xled rtknsaximum 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 scale in a motionless elevator. When the elu38txo7yp2hg.i0ddo evator begins to move, the scale briefly reads only 0.75 of the persono h8i dtu7g0x2.3od yp’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg 5fy:mevv ,b kw4jd8v1elevator has a maximum strength of 21,750 N. What maximum upward accele:v y 1 85w4fkdvv,jbmeration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includiq)r2)u ov vw(fng parachute) when the upward force of air resistanvvf))u2 rwqo(ce 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 j2 k;t34.dgl4zmzbu s roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70bt2zld.3ug4;k z 4msj 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 res;)ar v9uwvg1y ts on 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 tablev;u)w1avr gy 9 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 diagra7 14mze/xkaglm 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) ab6v/, r1p:bozyvzk( rz wpr-r9t8;uzg ,, mbut the moment it is hit by the bat, and again (b) after it has left the bat and is flrvybmp- v; bg1rz,t b,/8 zz9w,z:p 6u k(urroying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be n w5u3yx-rj t6zh h2vyprx2:z35 3lbyexerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a ve35uyxl 2-6y5hz3zjh:3rpvbt 2wy n xrctor diagram.

  Arlene is to walk across a "high wire" strung horizwsi.9 / lfugae:6eh6contally between two buildings 10.0 m apart. The sag in thew :i6aueh9 g.lsc e/6f 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 massless6ve)b6lfjj gql e8: 9u 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. hp 446zrp*8oc,wwrf vkew( 9x0$-\mathrm{kg}$ 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/ (ut2 idev6pu to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcevd(upu2 6 te/is $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 yg96in58dc k-:zfd cgof the same mass behind it, Fig. 4-47 . Determine f9c 6z8ncdgg-:5yi kd 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 bucket-pulley apparatus8a 1, n0jixc;(nt fgsn )in+om shown in Fig. 4-48. (a) How hard must (j +,t 0nigs 1o) x;fcnmnina8she 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 began6b) tcx*/3b m dj(uwj3h:mv kf, 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 bz((:(,vilndqm pj 4rllock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal suz*(e.ndq pv9jio n0 wzxt 5 -tgmy:m*:rface are in contact with each other, as shown in Fig. 4-51. A forc n 9dp:qmtw0 j gomxv* 5*t-yni.(:ezze $\overrightarrow{\mathbf{F}}$ 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 o3vrl*tzjr)1. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determinrvjrt )z1*l3o e 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 connectefcjx q (7nz-c,);hxc6qbd5ks d by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and tdq; )f csqk -6(c7xnhjb5zxc,he 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 kinetic friction between ay v;o3o*8k.oowt l yy3 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 star1 zzv ctoft+p2 )asz4.t a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train(pof*bmkhxq dk 9;5mwtis; y 9x 0y82s accelerating at 0.20g. What minimum coefficient of static frictions5 i8q xt0koyk xw*y9;m2sd9pfmhb;( must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can underg0s/a lwh-xc1f , k)lcno if the coefficient of static friction between the tires andc)-cfh x1w ka/l0nl, s the ground is 0.80?   

  The coefficient of static friction betweb5w e;y+k;zm ei ni 8(;up0qagen hard rubber and normal street pavement is5y0 e +b(gp;zq8eii ukam;wn; about 0.8. On how steep a hill (maximum 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 m1, 7frirw1qpsq5sdgu)c 8h2-4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 resv x,pe*wn.b) rr..x 1oyaawn;t on 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 coefficient 76da7 f29 k nlsvchn2kktn x7;lk/vp we4q1u)of static friction vhs7;lnu/ t7 xk4 1pw)ekfn69v7kk2qc l a2nd.

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 friction for auzr24fu -ow .y4fb la:li*6k g $ 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 g9k1zw,oqq i,z6o) wk mass would box A have to have to prevent any wk zgoow)q1 6,k i9,qzmotion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. 5. /fbbn7u eqsiw.)*o/jo zliHow far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an bw.ini qzfo/b/57 u os. *)eljinitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest onv /fot1rrnx7lz k:753c80tk7modl b01l frx o a horizontal5:1 3lcrlo m71toxtk v0rz7/ xf8orn0lkb7df surface (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 ak-yykj82fvp8gb8su b 8k,0 5;hgqqltm o /t-k heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate 5 yyu8lmkhk 8-qj,o8g2f-8b tbvs0ktk ;q /g pat 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 yrlkcugaxe ( )k:r;n0 -our car in your driveway, which has an incline of nxur-eg ;:l)ck 0(akr 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 withu 4znc-an/-ha *nq+hd 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 an a4 rsyzji y,59c-s)tzx ngle $\theta=22.0^{\circ}$ 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 sp xz4t mw w/nqd0wa1iowqu -:/ve5 z,e+eed 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 reachcf7kdic0 6vuec ,-ag 10.tfrres 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 i ( zgew0kb9,n(h ptyq/ww75mtulgx8be* 8t )in place against a rough wall by someone pushing on it with a n gmu/y07gti (x95l kwpwz)wtb,8qe* hte8b(force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dang an)(f dn14hcnfqp) cihb18l ,erous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of cp qfd1)nan,1)hflb 84c(hin $ 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 auzqlpcxpl: u)xg ;w10 1tomobile traveling at speed v is equa1:pz cgw0up x ;1lx)qll to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drv 9t.zy*f.nv8ds c c;mfb:gl9noa 9 ,iiver decelerates from :mt 9*nvboivz8d9 c,9ys .a lf;ngfc.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 g bak 3k/j2j3xuiven 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 filled t 5ibl1ve hw+i(gk(n2 xo 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+( ilwgx(hv25 ie kn1b 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 bc- .xgg4xpz( zetween $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 0pf*a)j+brkp 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 7o0b6 fwt fvs*each pulse approximately tfb0so wv76* f20 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 chance3n,ql ny4d0 zwu qpr/9vogu 8, of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calcula9 08vzrp 4q3 wuulnn,/oqdgy,te 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 earthquakhcx,ri4.pc w76u*lgy e is a , and if an object is going to "hold its place" on the ground, show that the coefficient of stat.hlx 67c u pirw*yc,4gic 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 sceneqar,k9 h9 q4fdj p9io(-e.nulrh e95g of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80.qid.r(5krjhq9eue9,- oa9 gl4n pf h9 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 th ncvr2tn+ln/9 54uqgg at for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom afgn/ nc9 +r2quglnvt54ter 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 Tower of .:t tibdc 9r.svf:s ..piz,ejht ,s0qPisa and falls 55 m before reaching the ground with a b i q,hstf9 dze0.:.rtvi .t:jp s.cs,speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s butt2 cq,gkrzn.z(s*pj 7;r*h t l 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 1,r 7gnpz .*htzr2s(kc q;l *tj1 m? If so, what will be the speed upon emerging?   

  A city planner is working on tlx* q6t+rkhu9bi7n :m he redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, wit+b:mu6i khqt* l9n7rxh 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 t u.pz ia1y0ak.i(6zwphysics experiments, dangles her watch from 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 tipwizy . z.6uk0(a1a 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, tbcmbx8 /.:mb ia6k4ow 4d zc4dhere are to be several ramps connecting different doc/ma4b84 zb xkd:b 6m4.iwc 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 +wnoq ,wwq,qu5 9o;b g M ) using the pulley apparatuswoqqbg+ nuw, ;95owq, 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 accelerz+cc;pi wv n.3ating 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-restr n c10v sbb,cb2 kvv*nph59gyi4t )0awg4vy,raint chair, an engineer considers the followi0hg1,s5vw )t vnv cv4 ipr*ba kyg24b9nc ,y0bng set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric ton 3 b/ufyzq24kks (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, Biu, mb- vg gud4+)3mffmlxp 3h zt(77wnll 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 consuv(l-47 m h+fmgx3mf)p7 bdwz3tu n,gtant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-16.r js8 (6h2jkx9trpgkoqc o2 $\mathrm{~b}$ 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 vxhwc*m8 c6vo/tcfd +50 8lq o3.5 $\mathrm{~m} / \mathrm{s}$ 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 i+yc +hj hnmx3x*u6o q/,g ,sbice field inclined nqhu3+s /6xm,o,iyj h+g *cxbat 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.