Why does a child in a wagon seem to fall backward when you give the wagyw-;r*2mx tgcjy q 0*xon a sharp pull forwaryy-gjr 2 *0c;qxxwt*md?

A box rests on the (frictionless) bed of a truco, 3nveazrcxv ;9qa mgk /6j79k. The truck driver starts 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 ongeaa6,9ocm7 vkxr j; n3qz9/ v the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are n oducx3- j6d r vs(ik*aa8x8cx, (gzc/o forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratios2s. weku5 .vun? Can it have zero velocity? Explaiu svw25e. ksu.n.

When a golf ball is dropped to the pavemendnl5 /0 jqay o+;rfjy00l) mvvt, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exert;00v 0dqf)ja/5rl+nymo l jvys the force?

If you walk along a log floating on a lake, roh2fck h:f4 /k 4de0uwhy does the log move in the opposite direction?fcoerd40 uh:24 fk/hk

Why might your foot hurt if you ki5,6:u a uy6p h1 vfo6vov0bieuck a heavy desk or a wall?

  When you are running and want to stop quickly, you must decvsw/ gx;a5ij1 elerate quickly. (a) What is the origin of the force that causes yoa gvs/1;iwxj5u to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of thgr28 -qc3tmo vhr)t v5e same thread dangles from the-35 82r ghovcqt )rtmv 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 twicecc )n qo4qyzxb*1se4+djb 18at)7qco as great as that on a 1-kg rock. Why then doesn’t the heavier rock fasa17cx bojdntb 4 +yco 4)cqqq8z*)e1ll faster?

Would a spring scale carried to the Moon give accurate results if the scq/.(pq j)z85ai; cmz*w0c yozmncg , sale had bo (wg,p0)ncc8j*zy zqqa z/im;s.mc5 een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a col 2zsoacewxt0o zyp2y.b :w idhy d .7,.;v+-xnstant force across a frictionless table using an attached rope held horizontallyixvce + -yx.d.sdz22.t; h ayz oy,wwbp:l07 o. 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 under 7a8e lyi9g/;f rn6ood the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the n9r a/ofi68;oy e7l gdobject 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 oje8 rx/a bjee-,sqwj/qy04 (cbject 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 ,a/xb-q8j rj0y4/ewq (c e jeson the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37heo(22qt:++wkaw6k vq 5pj fa) pulls with equal force on the oh5vww(2 +ktpa 2+f :aq6qjoekther team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceriep5rr5kqu.nc ;81 hwlbs. 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) p8bk;q.un1 rwl 5 r5chby what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on yafwfq37-*5 i3co xwr6vz;r kpou? Why doesn’t this fx *-76w r5 zk cw3aro;pvi3fqforce make you rise up into the air?

Whiplash sometimes results from an automobile accident when jxeojem 1.o67vg*1 c ( yct:lzthe victim’s car is struck violently from the rear. Explain why the head of t7yl z*1cjv oe(. jo1t:mxe6cghe 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 trutkw/p4 lguzhp1s.mj o: - z4v9ck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to azzm4-14 ku.ghl9t/pwv op s: jccelerate?

A block is given a push so that it slides up a ramp. After the block reachen4qpgw60 he8 edr0n77 h/mypa s its highest point, it slides back down but the magnitude of its acceleration is less8h7n4nr wepdapy70 ghm 0e/q6 on the descent than on the ascent. Why?

What would your bathroom sc5milo;8g b w)kale read if you weighed yourself on an inclined plane? Assum il5mkgo);8bw e the mechanism functions properly, even at an angle.

  What force is needed to acceleratesrxp+d r5gp )2 a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike t6;w0*v h kwdfno3e 3pand 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 used to acceleratea3 ey-76lawq )tzaw 7ab5l*fu a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a 5g0k mauzolp57 mnd;1 $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.qhd .qj. pqzk2n(d0z)0 s if the car is traveq) ( h2j0z .k.pdnqqzdling at 95km/h? -  

  What average force is needed to ac9-r7p w,cdxb6 g4 szm1ve gj0kcelerate a 7.00-gram pellet from rest to 125m/s over akdgbr- 6 ,v7 1wj4gmxsc9p0ez distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2t.n/..bsw681d+nz mjylly q g.5 .1g+l.6nnly8z ywqjtm/.bds $\mathrm{~m} / \mathrm{s}^{2}$ 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 o*/(8d mhcr/ da hgnn) tz0dkz9so*.ba quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the mautwga2r62manb1 7 vc:x6ws 11 arp l(vximum acceleration isc16(w 7 vlaa2vaup1wnm r: rbt612gxs 0.0680 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 scale in a motionless elevator. When the elevato bdj4 p:y(cu/00ej niwr begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and jw(:0 ped0b/cin4uyjfind the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator h k4 jz za2 wa(m26tozlrn):3ueas a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevato oma ( tjlawk)r un64z3zz:22er without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includingwj.s,d8s4 ywm mmy71w parachute) when the upward force o symw.,mwdw8sym j147f 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 thedd wmtfacn+k4-404 ubl,b j /8 hvbyi, 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 owa, by0/ ku44f+c bdd 84,vlti mh-njbf 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to te( +4jen) g)fj jkbsuvm5 i0t0he box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the knmijt j45e)j+(fgu0v sb)e 0 force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body dimmqmj5ns123c +8ji b-huhp s0hicx6 4agram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the mog-/*mz; shqcl ment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfield ls-czmq; /g*h.

A 650-N force acts in a northwesterly direction. A second 650u quc-077 cfgf2o02mzg:y qqv-N force must be exerted in what direction so that the2cmqf:yu f q72 7u00-gzc oqvg resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strukgr/zciq-x 9x1)y7 ghng horizontally between two buildings 10.0 m apart. The sag in -kcyq /ri7xxgh1 gz)9the 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 hanr 6cxrw mi8b 3bj9h* n.u0x2dzging 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 1oe 7 ya8gonk0u-(m6fh 4.0$-\mathrm{kg}$ 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 locatio-bq9ckbyzc vl9 0-s-ovl d de75c(b7ln at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcec9sod9bdvlkvl z -y(0- eq l7cb- 7c5bs $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 thp6l2mqn2d mzf)g iq4* czq89 he same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car icn4 lqm86 m2hd*qp9gz2z fq )$\left(F_{\mathrm{T} 1}\right)$ , 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-x*/f-8 a:hf(jh)clxic qo cc*pulley apparatus shown in Fig. 4-48x )qf(cj-ca8 cihhx*oc f/: l*. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 65ad + at-z i-ayelam48;$-\mathrm{kg}$ 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 (mp 2.u 8bdvg(e /mxyj3aass $ 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 contact with each otheg:kian5ner2+ z -jb(or, as shown in Figo(5 :gnbek2rzi+aj -n. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abon mzzu-- )0cqmve 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 determine the acceleration of the lighter mass and then its velociczm0)qzu n-m- ty 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 bdf h7ikyro-;l.outm (8fr+) ta:rd( dy a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the i:;(mf -8)o ftddr( arryl7hd .otk+u 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+n5sd nl us40ft1a-t 1wtc;8q am.we 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 start9 mhqt)3g7cm5ce-yt36dy w u dqlc)0l 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 0a +ij82q2d+ q mcg 5x3ynhijbat 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if jbxqq8da h25 yg02i+n+ ijcm3 you are not to slide?   

  What is the maximum acceleration a car can undergo if the coaid5csvv q ;hj 0 *krz:-)w-bkkfqe8;efficient of static friction between the tires and the gror ;aekwkdq:skbzc*q;--f8 )0hi j vv5 und is 0.80?   

  The coefficient of static friction between hard rubber and normal 1 +vd + *xogwn;mtsp:rstreet pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked1 dvp mor*nt s:;+xwg+?   $^{/circ}$

  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 ynwd+ 0yfmd0t9 1ii9gat -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 re8 .6 t9zyvoqmi5cwtpybhxt,6 y6 -jc- st 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 surtwhb8xfn23f4x4id 9 r face have a very high coefficient of static94fhxn4fr 8tid 23 bxw 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 friction fos3.58uyvvoa 3 ugy0chr 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. 4-32wnxo0eg+g3y)pf1n9 3 e6k nkb (Example 4-20) how large a mass would box A have to have to prevent any 6kbn 9 n)y3ew +kpeox 13n0ggfmotion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wiluu g 1ktu sby3b*((g.l (gh9yxl it go, given that the coefficient of kinetic frictionybgkbut(hsg 1 (uy.lu *gx39( 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 , arfhc3jphvb : :u (xg;6he in contact and at rest on a horizontal surface (Figf(x gj:63 :h ;cuphbhv. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fricti ) 9i/2niyjcv+if.yxoon between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against t9i +.oyc/ v xjy2ini)fhe cab of the truck?   

On an icy day, you worry about parking your car in yolyyxyi9. b2oi(5bn4v ur driveway, which has an in (n5i9.y o24xyvy ibblcline 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 l/ s+h5ujh6 zaa,f-2+ fs;g eg+r htvaa slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted/t/ 5tpcpkdeje.d3. l 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 in w/jqok, /pl7-0z pc 8ma3egcvitial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of mixql+28l,k(b n , s+wy k)8e6 oensxq6.0$ \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 pushing on it with s78s gq9l.r dea force directed 8q.re 7lss9gd 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 dangerous projectin+-cqgz a1znyp)s 5u -les as they melt. Consider a chunk of snow at the ridge of a roof with a pitch oya scnu-z)q+ -p 1zng5f $ 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 distardbb./9dzn9ei l,cv / nce for an automobile traveling at speed v ddvn lb//,e9b. rcz9iis equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on bt8ah,m5-r ra pr 7pm1the dash when the driver decelerates from 45mh pt5 r8,p7r-r1bama $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initiai1lhfz 2oy/z (l 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 thd::af6msx 3 wwd32dnhe 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 deceldwnd6wx:3 m3f2 sd ha:erates 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 o ei+uhq0z2ev.f6cvj ; f 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 (includingm 8)y4 ggel56o6kuuco 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, ay1:ry v9 it8ept each pulse approximately 20 g ofr1ve:9 y8tipy 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 reasonabl4u4dbw7 nt- tn2hwcy7(toy ;be chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force u ob4y4w2ct hwn;(dnb- 7t7tyon 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 br jm2nbtk42fiq+ab72 uytti- :f(gk ,y an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at l- bi,k4kti:b qu7mtyf2janrt+2gf( 2 east $\mu_{\mathrm{s}}=a / g$ . (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 investigatorsdp2p8*q 1wl2ch aeck4 , examining the scene 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 pe4qa k2lpc8hcd1*2 w 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 u ib46uijgmss 5-g+z4each 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) Ignore friction.4mjs izbg6-g+ 5iu4 us   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top qck-0i 35l4dems+bo yof the Leaning Tower of Pisa and falls 55 m before reaching the 5-+lk0iqbm oedy3sc4 ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady spee,uhz w9b-ltn+ja.s y *d 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, wzjh -y + bls,.wt9na*uhat will be the speed upon emerging?   

  A city planner is working on the redesign of a hiln 28byzfk0o; -ifojf7)kqs /l ly portion of a city. An important consideration is how steq8 zb;j20fyl-/ oif kofns7 )kep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics eqhlua5: zltk) r/12tsxperiments, dangles her watch from a thin piece of string while the jetliner she is in takes of5 12tshlu t) qrk:za/lf from JFK 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 sew83gvz17-vtbo8 atqd t 3b0ckveral ramps connecting different paa1wtgc b7v0-33dqo t8vt z8kb rts 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 M ) using hu sa9.*h 2 nwhckm+5lthe pull.nmw2 9h+k5*lhu hcsa ey apparatus shown in

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

  A jet aircraft is acceleratinr3iqf(af td0 2g 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 fzysa1/r6 5zku2 yq6jsor a child-restraint chair, an engineer considers the following se srq5zsay66 /u2zjk 1yt 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 ww/ly 8w; bf,1sv vf/mmetric 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 a e h:lbz:m(dpjn9;g2Karen, 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. (Exp(hnlm: 9j z ;eabpd:g2ress 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 pi c 0g0p7en ovbmpf+(tb;ky89jj0 d4" 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 allowea iyzj/-+sn .wd to reach a maximum 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 who arkciqr4:fzo9. : m pj0bw9hq6ue roped together are ascending an ice field inclined at 21q9f6pr mo0i:b.z9uwk h4:j c q.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.