Why does a child in a +l 3lz. pi :ggp,ky4lf//b dofwagon seem to fall backward when you give the wagon a sharp pull for/,/:df 4ll.yfpgobz 3+g k iplward?

A box rests on the (frictionless) bed of a trui32rv u4rb m;8a-qsb ucrto.o + edn4(ck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the m etud4-uv. m2+;iqsbnc 43o(ora8rr botion 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, are no dyi16cpo56z c)vl6zhforces acting on it? Explain.

Only one force acts on an obqa4 iu/-nwum 6ject. Can the object have zero acceleration? Can it ham/w6aiq 4n -uuve zero velocity? Explain.

When a golf ball is dropped to the pavement, it bouxapjw:v +9nk2m+4zwe nces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the for4 nwjk+v9a2 zx+e:pwmce?

If you walk along a log floating on a lake, why does the log move in the4 6 j j(3 -+qd wryk5b/kzagmu0tzw)wp opposite directiona6pb 3dkkg+zmw(wt y qwu)0jr /z 4j5-?

Why might your foot hurt if you kick a heavy desk orc0o0+y tgv .fmeq;a ,g a wall?

  When you are running 0 4:+gvzr (zd,zk cclardbp+(and want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed t v dz+4bz:lzcdrp(g,kra+ (0co come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same thrj-:xb3i /f b2wkd8vap ead dangles from the bv 3kbfjw/-bp:xa 2i d8ottom 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 great as t6biv7tfv (:oxoco 2o6 hat on a 1-kg rock. Why then doesn’t the heavier rock fall fasocovto 766x2 (ov b:fiter?

Would a spring scale carried to the Moon givc;o m1a/n f zdz:3 2cr6ghmtr)e accurate results if the scale had been calibrated (a2a;zrtc )r:n3 cd6mzo h1/m gf) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table83f-dw i (ca i :zsjw.sli ne:)uq0,am using an attached rope hes:m)-w nwf i3u 8dq(esiz.jciaa l: ,0ld 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 nbrwfsi(+yxh 8j(e eg09a7z 9 7ce) uiunder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on teeh+f s7xi aunc 99(0wei7()yrgz j b8he Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you x:ggd n;nopz l:93:hlare on the Moon with the force needed to lift it on Ean:d;g:x l hzl39g: pnorth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4dmj.75 ojq-d o–37) pulls with equal for5.q 7oj o-mjddce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N toc. giwta3o r7;j lp4:e hold a bag of groceries. Describe the “reaction” force;ap: or.lwi t4 j3cge7 (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on yoet9 prj4-c, mx* mj1the ground, how large a force does the ground exert on you? Why does ceyo*pxm, 91jmjtr4-n’t this force make you rise up into the air?

Whiplash sometimes results from an automobile acckd1g2s k 4a9qo7nn)p,f8sedqzj gb1-ident when the victim’s car is struck violently from the rear. 11sf7s9gddpkbk g aq2 ,8 zn4eoq-)njExplain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,; sd(6lgdmz+n the crate remains where it d6n;z+lsm ( gdis on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Aftw8kirqa0ox 2( er the block reaches its highest point, it slides back down but the magnitude of its acceleration is less ak q8wi0r (2xoon the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclinsl, /b lr* 2yvy+joq-icfaj0)ed plane? Assume the mechanism functions properly, even vs,f bi yj2 0-rj)oc/aq *l+lyat an angle.

  What force is needed to accelerate a child on a sled atl(dde7bw 4cj9 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rid bnmf8(.fm px6er at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope owswyspok863map9:6 uo a,j j f6op ,)withstand 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 of a lyylbz::i r; z i0:dnz5-lnj)$76-\mathrm{kg}$ 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 11jg2gsglz;:ug*9 o xp900-kg car in 8.0 s if the car is traveling at 95km92 g;s:g zolupggjx* 9/h? -  

  What average force is neededozqyk+ m1vh,+ to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m am kqo,v+z+yh 1long the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an 5zushbz 8.h /5tr3o znacceleration of 2.5 z.h5no /trsz3uhz5 8b $\mathrm{~m} / \mathrm{s}^{2}$ 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-mil;*ciu6p :dqzsv9n-p iu d*m +je 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 that the vt(pv gq ,jwvj cz0+fa6/k7d8maximum acceleration is 0.0680 g . Whav86, jcqgvta7(0zvfk d /pj+w t 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 s/-lnq cou1llx;2ae24.rrdc scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weighq;d xeuc n. /s4r2ll2oacl1-r t. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wzvmj4b z * w-c5nnkt30hat maximum upward acceleration can it give the3wzv-c 50z tmn4*jnbk elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling skyqydmka8jf-ugi*+y-nxjy :u+ **) don divers (mass 132 kg including parachute) when the upk8- uy-jmud)x*yyfq+a*nn* g + :jdoiward 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 houert:fg-sdy 6yzur6 u5 zu:,m .se 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the matf-yru6:5r6dy:e gz .sumuz,ss 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 ropqe f6 hjf7wl.-e 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 olhwj qf7f-6 .ef the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbalql7/ gf7jphnqry ez( k//67qk9rs f 0ll 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 ( k (dy d:z)5o+z rnbnc:oxg85ba) at the moment it is hit by the bat, and again (b) after it has left the bat and ib)y rx8:z:nob zc+kdo5(nd g5s flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be ex0 lgzxw jy*6rw+uu79h erted in what direction so that x9gr607uuh+yz*j w lwthe resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between . o wxde bes88 (nf./zjj(faq9two buildings 10.0 m apart. The d9/bx(8n ew oq f.a(e.fjzsj8sag 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 ha o s2alihkc). 5jgx5s+1 vo)jfnging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1 29lwsbl4ezyglwl0 9j0m 7lf +2,bmwa4.0$-\mathrm{kg}$ 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 locaty lgth/1d ,ba7-s+yvy ion at McMurdo Base, Antarctica, as shown in Fig.ygshblv - 7a,d/t yy1+ 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. ::tt f8qiwrs u;69-qcvcom1+ j5l puy4-47 . Determine the ratio of the tension in the coupling between the locomotcqoqvt u ; :j:fcps 8l1+yw6-mri95tuive 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-pul7y am6 hbn(::f/msd q)x4dnerdqx* n:ley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to rdbm)nn6xr* x:: 7(msqye:n/adhf4q daise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a rac yl-ynasw.9:o6:.ww moi 8 +btxit,l je began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a g, k(ui m w,gt4*/coumblock (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 surface are in contac. wl6i8dlf,u at with each other, as shown in Fig. 4-51. A force 6.,iluw8fdal $\overrightarrow{\mathbf{F}}$ 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 above the+/s ov ei,.3.lm9d bkxhe8r fd ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one h/3xo.vdrf8i smkl.hd , e 9b+eits 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 heap7a 99l9k.wd n:ay.m: vvjuqz vy cord of mass 1.0 kg . Calculate the acceleration of emajp 97: uw:qdk..yv al9nvz 9ach 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 kinetic friction betwy/xg(c- gar* g +ebguz9;(eb leen 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 a 5gr +ny-,)e qjk.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 standinn(c4 71up l;rv ezc ,g*-kiiheg on a train accelerating at 0.20g. What minimum coefficient *lik1 r4vgep -7eczh(u;c in,of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sta 1 cxq5h44/bj(8ex2h7z 3ltawtyn gf,qeqi (stic friction between the tires and the gr/( wa4t8sb hix3gt ljc 4q(z,52e1qe qhy7 nfxound is 0.80?   

  The coefficient of static friction between hard rubber and normot26ew( rc(xdal street pavement is about 0.8. On how steep a hill (maximum angxc(d6(2wte orle) 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 atux vx jpi/40 ik6c/y-y -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 spyz,zv5g// .6jgapz .cg4:spkoq0uough 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 ( rsr+yzeop ;*asphalt surface have a very high coefficient of static friction. r*r( sezoy;p+

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 fric4o;zug qy03jw crcqpbw5.3y fnb v +oxp5;y3-tion 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 bapf 0o9h 4xao3ox A have to have to prevent any motion3o9ah ox4ap 0f from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far 9rj; gs51vu(mhb+ c ifwill it go, given that thfs cr buvmhj1;+5(9g ie 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 kg , are in contact and at rest on a hori ;kxh( xl/omxt9x.eu3h3)ibczontal surface (Fig. 4-54). A 62 /3hi;3ml e)bcxxxt9.h(ox uk 0$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fl jb/,nx0i(e rriction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and stilllj(b/ ixn,0 er avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking w/q49 lt/*)egnlcfv jyour car in your driveway, which has an incline of 4/)f * cjn/9wvqlt lge12$^{\circ}$ . 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 s o- et(p:rxf .wkqx7nv0,g( wa 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 lin-fcdsb6( t1n es on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed aka x.c+b;e (cof 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 th06ubc06va(ikc 3gdhgs6g xa2e 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 against a rough wall by someone pm b- vi75gh-l sipqd; qve3/z*ushing on it with a forc vezq 7-3;/-idli*hsvpmb g 5qe 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 cank c1*hdur4yf + become dangerous projectiles as they melt. Consider a chunk of u+h4* fykcr1 dsnow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minim5y-zn-pky.+ul kdmb o6bz 98fum stopping distance for an automobile traveling at speed 9fko .n5- pbzy +-bzdy86mul k 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 da t/xn yn2pu wsd/,.t4xshboard of a car slides forward on the dash when the driver decelerates from y,dpnx/ s/xtu 4n 2t.w45 $\mathrm{~km} / \mathrm{h}$ 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 givejchhqz1k8x6j; 4 v4r in 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 to the pjp wuxmi9 oy8bi x 0c53*jj++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, th mpp05jojxj8+*w i 3uxcib+y9 en 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 h0eg8 7odbciyez-+:-xbc3 mlbetween $m_{1}$ 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 uy59b5 9uyd undjq-c r-6 ,lgq65 kg (including 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, acd+1e47/vvelebm b2j t each pulse approximatelble4ec27vjed +m b1 v/y 20 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 the deceler/o6 *yz*5t6rcu /zxnidp*0fsjd(d vration is no more than 30 " g 's." Calcu v *r/dpdtnzfrc6u*xz/(si5yo j*d6 0late 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 i 3)s)lzuvr*.zjro k yey0lz8* s a , and if an object is going to "hold its place" on the ground, show *u )3zv oez)*0.r slkzryjyl8that 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 involving two carsw* /q iz:q1af;.vju.wn h 8oct va.0tg, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coeffi0. w : tncja1vzq8; *t/g..haoufqw ivcient 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 forzm72opg( k r4s+-lpjkm0sn0j each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignlj nps00 rkzj72(ok4+ms m-gpore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the4wq/ z.r ilfqfiz0.)msz;vx 5 Leaning Tower of Pisa and falls 55 m before reaching the ground with a ;lqws z v/zf4m f5q.x0ir.zi)speed of What was the average force of air resistance?   

  A cyclist is coasting atwowyo33ms8w3y2 uq b4 a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, whatoyw y4b3w 3m2uw8os3q will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An imwlq 2t c4)0t22jj hx-dc vml8xportant consideration is how steep the roads can be so that even low-powered cars canwhtq)l2tlx- 4c 0282vmcj djx 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, danglesw) nl r8gyuw7h2, 1ufy; xqrv, her watch from a thin piece of string while the jetliner she is in takes off from JFKyr )1nvhrlf qu x8w;gwy2,,7u Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be severdhtoo65 mqi z) m4x+nson5) l*zh; yg.al ramps connecting different parts of the stor ;ny) dz5hi5z xsoom6ltom.qgn* h )+4e.
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 -.hadoiu x *8ppiano (mass M ) using the pulley a8o-d*p hiuax. pparatus 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 tq n m9; w8(c(n2et7(ypbxhjxb(v h:jat 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 chilq fm ut;6l zjjh()v*5ed-restraint chair, an engineer considers the followinv;z 65l jhu qjt)*e(fmg 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 mete dkpzgu;4:(a fpr+*zric 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 Ka.u chp b*abz5;cb*3lrr k s;ucq0m1n0ren, 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 onbcr ua1ur*;.bn50pc3 szbm qk ;0lh*cly. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat) ;r)xnk n)pny is 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 maxim; u,fm:qtio:i/iip: q um speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers whxs6x9jk0w 8 p xqz +-biw3qxs(o are roped together are ascending an ice field inclinsw 38xx+ k6 q0p(xw9x jizs-bqed 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.