Why does a child in a wagon +up8f klods/5seem to fall backward when you give the wagon a sharp pu5s +uld/pk fo8ll forward?

A box rests on the (frictionless) bed of a truq1o)d klgkk3 iq4q q/(ck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Dikq qq(d kkoqg )li1/34scuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forc0n i8nne0eztoj.u: a 4es acting on it? Explain.

Only one force acts on a l5v)o:wrgb6d pn 6h+mn object. Can the object have zero acceleration? Can it have zero velocity? )brolm dng6+h5p :6vwExplain.

When a golf ball is dropped 9xnm nfgbgo3b85 y** u9fcwbd.0(btqto the pavement, it bounces back up. (a) Is a force needeb(obng8f*f 5d9yb *qc 9.btmx3gwnu 0d to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in * ,gpipueixyk; : .+w0kvxp2ythe oppositeu0xvp2;i*,eyxpy: +k gpiwk . direction?

Why might your foot hurt if you kzq* q,tj u9 r79l7c-+i4mqs 8vrjk3cv cq7hpuick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceh9.2 euni 0qgelerate quickly. (a) What is the ouqg0e2 .n 9iehrigin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a segdn30xc exx cg0.z88oction of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangli c800e8 o 3cxxxg.zndgng 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 that on a 1-kg rock. Whr .hiye(fv3a2 y then doesn’t the heavier rock fa2v.f3h ei (ayrll faster?

Would a spring scale carried to the Moon give accurate results if the scale haq1y 1u1 u.kzo9 ldp)hugv.d 5cd been calipu15ck9do.1u1vz ud yq).lh gbrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a friction4az)ws +5wni ,n5p paehw35n*y(u thbless table using an attached rope hel*5e5) 5 i4w+ptnn(baywp,z hsw aun 3hd 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 under the influence of gravity there is a net force pc)); t7 .exoxc lh2sb.)v( n k7azipjmg 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 movezphk )b i()c2j;..vo7 a7)c lnxestpx?

Compare the effort (or force) needed t8 (bmig.hh n:zo lift a 10-kg object when you are on the Moon with the force needed to lift it on Eart: .zbing mhh8(h. 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 lawu f0mxzhqf(72wtacdb;2:uj 1a94 bv y, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What,4u cxb(tuzh 27jd02f:bfwy;1qv9 aa m then, determines which team will win?

A person exerts an upward force o5xi) f/+ wnzgp*u8g;*qo zcm bf 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s thirx c *w*b+/z io5z;pgq8mu)gfnd law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on yr3+ygkd, xn fr1i5x*8yd qo85r s os1uou? Why doesn’t th* kdos i11r3q y5o+,fdg x8rx58nryusis force make you rise up into the air?

Whiplash sometimes results from an automobile accidenzobze4 cv,55rv j,hp p.qg/9 tog8 mj(t when the victim’s car is struck violently from the rear. Explhtg e(4p c/o.z5qj rv, vog9bmj5, zp8ain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed 30.6;muc w m*bt27o:kjr; y ycvopkxwedx:3nof a flatbed truck. When the truck accelerates, the crate remains where it ism3w;ru.cekm; t ky onycv:23 jb* pw: 7x6oxd0 on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that igm.nkwe q.)(bt slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascen.ngb wm)e .q(kt. Why?

What would your bathroom scale read if you weighed yourself on an dd y3 z:yitebs-a)f22.dnx3l inclined plane? Assume the mechanism functions properly, even at an anst y-2i2x3 l yd.n )de3z:adfbgle.

  What force is needed to accelerate a child on a sled at 1.25hfr7;a0qa0;ka okkn9 y jyr)lrfko w)7 (k1l/m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.hsce/og(* b ncx-,6fo30$ \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 accelerate 3-u ch06 znoy ad4:2fket-rlpa 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a e ai9,)4o;30v bd +yyf8a eikibpotw3 $76-\mathrm{kg}$ 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 110ss:41l oji.jl4tldx c 6gc.9p 0-kg car in 8.0 s if the car is traveling at jo9 scli4:cj1xg4..pt 6l sdl 95km/h? -  

  What average force is needed to accelerate dhx,au7y +3gkp(8xx,3qbajdmf t1 z9 a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a 37m aaxqhgx(u jd+,fktx3z918 p,bdyrifle?   

A fisherman yanks a fish vertically out k c*xzft:3 9n 00c/erf6lbbsyof the water with an acceleration of 2.5y/ es 00 ln6zkc9xtf f:rb3bc* $\mathrm{~m} / \mathrm{s}^{2}$ 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-m p-sp vu.mfdb s0l6w7 f58fbm/ile 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 maximum acce +:e/c/5lu/qs tbzy csleration is 0.0680 g . What are the maximum and t/el /zycucbs/s+ q5: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 moti wpei0cl7-z 6p0m:x asonless elevator. When the elevator begins to move, the i7m0x:6w-sec 0pz alp scale briefly reads only 0.75 of the person’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 elevator has a maximum strength of 21,750 N. Whaz7mso1 34 etu t+n/obft maximum upward1b +e u3/onzsotf 47mt acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (rbpa4r 3m kw-p((xgqip+4ji2mass 132 kg including parachw+bp 3j2(m - irp(api4rqgk4xute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-borio9 +y /(ms3 uwd.jm high. When he strikes the ground below, he bends his knees so that his torso.si/bydj (o oum9+3 rw decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a ta7/ffl .sgf (muble. A rope tied to the box runs vertically upward over a pulley and a weight is hung ffs (ufm 7f/.glrom the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskg.(1 arnpknn6etball 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 moment it is hit by i j..ri;j*qeythe bat, and again (..;j qiiye*j rb) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a nortfh.w n :05fbccu0 w1nmhwesterly direction. A second 650-N force must be exerted i.wnm chfb: nfc05u01w n what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bu bamu6). ej:.4ofywmqildings 10.0 m apart. Theqwb.j:4yfu6a om).m e sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless corp6v vhcnq/7*8n ;v ruad 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 14.0; .kg32bo+ux qyvv/ qkgc+v7 o$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctic.6gzi l v0z;f j0/xczva, as sz6 c/0gx.;0l fzizvjv hown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. gs(at66zy 3x 18ohsre4-47 . Determine the ratio of the tension in the c6ahy e1(sorz g8x 3st6oupling 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-yq i i,bq0z r/:rj zt:8rn-w1mpulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?zniw 1y r0:r /q8q,jrizm b:t-   
(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 +-vhvde,7zq6xw q, 2hnztq*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 block (m (ijwjxn2-4gf ass $ 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 horizyqesf zj)lv1+n azuf5g3 7z);ontal surface are in contact with each other, as shown in Fijz l+fvfz qa7)u3s5yz g ;1en)g. 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 0,wk0r8zf d6e/oeeb z s;e;toinitially 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 determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits tz0o/e,zkw;6d8er ;otf0es b ehe ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cqzqfw 13mfd/v ikc-74 ord of mass 1.0 kg . Calculate the acceleration of each box and th71kqd 3/ -4ff qzwivcme 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 (t yfbq31(ste)ys ud*kinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required tvg2scz, d7ye fdgccig85+g -3o start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you areltgx+oeih 6i2,/ b8u q nlr04i standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you ar40b nil +qxrt /i26lie hog8u,e not to slide?   

  What is the maximum acceleratio/yd vzk r1/6lvoec6yjkoqnuf- z(5 8 -n a car can undergo if the coefficient of static friction between the tires and the gro16r-zl v5y / fqzu -jedvoo8/6ky(k ncund is 0.80?   

  The coefficient of static frictir t u99 /8e/:oydyxg/nex /uhion between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you x t:d rg89/xyo/e/nu/hi9ueyleave 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 fh yzelkmaz 8d ws()5eh 0 k:dyw6 w;010c*jng -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 r9q2myf:g7l y5d*k,i m f zc2inough 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 coef uglk79 bn+rqbw+g2)dficient of static+ )+b2rgukng d9bwlq7 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 for -vdi4i a/bg9 m0gsea-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 box1q7i(s1wusjr A have to qjw1sr1isu (7 have to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor.xd03 jc2s/pgix*r b+p How far will it go, given thx/3 bp dcs2px+g*rij0at the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rekaw4j 09. ngx qly0;iwst on a horizontal surface (Figwayjql. 0049 nkw;gi x. 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 frubzn( b ux1 m0ai2d-ia 3b4ui*iction between the crate and the bed of the truck is 0.75. What is iu-aa1(u3*bu40bzd2m in b xithe maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your c*y(p-nr bt/up-c zm+b(9lvqpar in your driveway, which has an incline of p/y-+*umb tq n(lc-p (rzb9 vp 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 slb4.ua,bhwv*r ide 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 at auisytvs-6,*8d q z xbc/- q*xxn 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 init892qp ,sil pcfial 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 steepfz6nn;o 5og3jjqy r- /n.+ cnhest 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 c8 :5y l/w .iwwd5iewut9qvjjvb1 6p7by someone pushing on it with a force dire9e6w q1yw.lpj u :cjv dvti/57i5 wwb8cted 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 be l 1/ub(qdg(wg qw j.cy1yx2.e9z -gzicome dangerous projectiles as they melt. Consider a chunk of snow at the ridge of qzc/. gqix1uw2-.gw ybly(jd(z e19g 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 minimum stopping distance for an automobile traveling at spe; ( af(0zhzrjked v hr(kf jz(z a0;is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash wheni3 1x rrut;v6 mbioq93 the driver decelerates from 45i1;9 bmqti urx6r3v3o $\mathrm{~km} / \mathrm{h}$ 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 inkz0g.ou*-:htdg*xyx y)q.qf s/ggb/ d e p-b2itial 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 pa* b3l+ 7sxb*7n gykv fca30w:rvnc)xvcking 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. : yl)w*07bn7kgc+ avvcx*fx3rbvn 3 sIf 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 kine3 ch 7fm 0varmj1q g)6kfk8po8tic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including vyn qw5; ccspv41jqhe68 fi 93the 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 modeq7p-.9 oi bsubvwq *i.+tz4ce*mih,u l of a mammalian heart, at each pulse approximately 20 g oc 9t-bq+i.wvism*b.zhup, eio7 u*4qf 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 1whph9 p+ydd1jw he6 3of surviving an automobile crash if the deceleration is no more than 30 "jydd6 11wwh e3 hphp9+ g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced bdn o96on;4gtg za,. wey an earthquake is a , and if an object is goz,adggto n;ow6.9 n4 eing to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident invo1+v coixvh-x7lving two cars, measure 72-m-long skid marks of one of the cars, which nearly came t-+1xvx7vhc io o a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means tyxsejxq.n 27:l83:eb kp w5mthat for each 4 m traveled along the road, the elevation change is 1 m). How fas8jn .et2bx3xyewsk:m 75lq:p t is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the 2 p ygllacb83g4ro;::b;k bwrtop of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a cpak;rbg43 2gro8:b:; w lyblspeed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/sa74tja(*- e.t8zrby dds yz*g but enters a muddy stretch where the effec*rbz (d8 4ys-gtta dje*.z7yative 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, what will be the speed upon emerging?   

  A city planner is working on the redesi6/s)vkepxl, c3a6yuo /v )0mr ;r krqngn of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powereq),ropa) ;s /mk6u6y lcx /3nk0rrvevd 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 experim +a p4obg )kl0bb9;qapents, dangles her watch from a thin piece of string whi b+9bq abp;kpa)4 0oglle the jetliner she is in takes off 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 toavr: g tmqpju5a- lf 2gg3i447 be several ramps connecting different parts of the storj5faa3p :-vgt 4 rqgl4ui72mge.
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 ) if)zarz 953 ssusing the pulley 9 frz5)sa3 zsiapparatus 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 accelerati 9ms x wbja*dn.j8-jj)ng 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 chil+wsh-kpy3 d ,zd-restraint chair, an engineer considers the following set of c d-h3 k,+spywzonditions:
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 v9m/veqidpi( p9u4/v-w,y dw Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, no5:xfwqx)7 y 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 siqw)n5fo7xx: ymilar 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 abo 2sfiysv7 +y 8 2k:ap-t.hvt " 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 allo x-8;95unemxh;e tk vlwed 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 are roped togetheb2g,ryh5kgws ;e6 d*or are ascending an ice field inclined akhr ,w*2go5se6;bgd yt 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.