Why does a child in a wagon seem to fall vme nn6i0sgzk b.-(*l9t gcy* backward when you give the wagon a sharp pull for 6*-(slvkcyg* gn90btn mzie .ward?

A box rests on the (frwa u7 f1j(fd upd8i3yyv0( ra0ictionless) bed of a truck. 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 081duy iaf7 (3pdvyu wjaf(0rthe 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 n tmat (uu)0y n8x*pt59th ,8wr/imqvg o forces acting on it? Explain.

Only one force acts on an object. Can the object have,qe n roxu 7:9wsbs ol)v4c lnbquq6 :sj7(p37 zero acceleration? Can it have 3x(e9bu6ulqolcnqn 77 jbps4s q:rs ,:7ow)v zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces bac) auzxr1 3(kpck up. (a) Is a force needed to make it bouncexap 1uck)r 3(z back up? (b) If so, what exerts the force?

If you walk along a log floating on a l6wo22pny-zxs*xvy 7d ake, why does the log move in the opposite directio7xz *p2y-x o ndvy2sw6n?

Why might your foot hurt if you kick a heavy desk o; c:;-tghnwiuu z9atdj 2+ e4or a wall?

  When you are running and want to stop quickly, you zz:m 9be2oz*qmust decelerate quickly. (a) What is o*bz:2mzzqe 9 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 to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sameq-)tn+ln 5 r/tucsf .t thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pullcnsq t.-n+trflt )u /5? Explain your answers.

The force of gravity on a 2-kg roqmhuvi2et 6k/x ry5 -6ck is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall5mex6h 6y u-iq v2/rkt faster?

Would a spring scale carried to the Moon give accurate results k wh3ui f*4by.ev( :zlif the scale had bz:bkv l.ue3yw*h if(4een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an yjtnee.eo y50+4 njs 9attached rope held horizontally. If you now pull the rope with the same force at a0y+jyj.9ne5 te4so en n 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 thehe5r 4 hk)inm1 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 th4e1h nm5)rh ike Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lilaxbihc jz 5 -s(5+fm;ft a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to thro5ajmcx;b+isz5 - (flhw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, eac;) oq,/.2, x o kd6bfny*guskyv9fty) ff7qgfh team in a tug of war (Fig. 4–37) pulls with equal for7fo. )x6 b*qofnfvu)gytyk2y;,d q9/ ff,gskce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to holf4m ; am8kwqt3gi5y. zd a bag of groceries. Describe the “reaction” fa tq53.gki8mz yf4;wm orce (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 the ground, how large a force does the gr8+gu if2gfr: 3-zrb qvt(1kbeaba z 9.ound exert on you?t3 :e8(gqb.kb92f1b vrru ziz a+fga- Why doesn’t this force make you rise up into the air?

Whiplash sometimes results fromh ebk* mht./h3 an automobile accident when the victim’s car is strt*.hhhe k3/bm uck violently from the rear. Explain 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.;1 makge 21hv*j9rl wg8cs.sl When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes tm ea1vlgg.w s9rhsl*k;1c82 jhe crate to accelerate?

A block is given a push so thqjs ql0)3 eozn4uy (1fat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on lnzeyfq qjs0 1o3)4(u the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined 9gh,sj39pem y +kl/ afplane? Assume the mechanism functions properly, ees ,+km g3jah9lyp9/ fven at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/sv )y)l tpo0c(v$^2$?   

  A net force of 265 N accelerates a bike and rider ayplm j c;f8gbt3;s)7+pa 9tbmt 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a r/p3,h 4ok s1 .c(;w pr6vmi2 crqufrflope 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 3w77b i4luutxe)c).s)ecnt b a $76-\mathrm{kg}$ 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 ancbms 41saj ;av(-uulg.k. )tr 1100-kg car in 8.0 s if the car is travel)amrgk 4-1jusc ;.vt. l sba(uing at 95km/h? -  

  What average force is neededgq**o9 r/a9 ifcbhm5f to accelerate a 7.00-gram pellet from rest to 125m/s over a distan*5a omih9rg /f9bfcq *ce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fisrl vd,8 (k q,wep-jg(th vertically out of the water with an acceleration of 2.5 d rqt-v ,k(wl8 (egpj,$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile trhw(zg i9w 3h,uack (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 acceli tfs5x .95kjseration is 0.0680 g . What are the maximum and minimum fkxts sj i5.5f9orces 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 eleva- )nuwz r24oj10:beq8 wiptjj tor begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceiw8rupnj j-4z )10e:t 2bqojwleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strxm3k vke475szq,b4sef ))d etength of 21,750 N. What maximum upward ac4) )mbe7qvxks3ts ez54edfk ,celeration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accel8k n0pn vr07xqeration of two falling sky divers (mass 132 kg including parachute) when the upward force of air7 k8xnqrv n00p 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-m high. When he strikes the groundzw:ni bu9m 2ya0-gj :) q(ciuu below, he bends his kn2: g0n (i-muczuw 9aiy)uqb :jees so that his torso 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 res4bl36l7ziuvc+ nc x* xvt 0lp.ts on a table. A rope tied to the box runs vertically upwardi 6zc lc 7xvl +lv3.x0bp4*unt over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbv6x l fvvv(9:dall 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 2)g q aq u)p;si/6h/xwp6 7b +f qost(a+gonidmoment it is hit by the bat, and again (b) after it has left the bat and is flying toward the a;q/sg(o6pqsowdhaugi q ) x2t+) p 6ib/n f7+outfield.

A 650-N force acts in a northwesterly d188 30dzek,w/n -8 zdoraxuhbe8g ei direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points zedxg/kor d08w1z ine ,8h8-u 8ea 3bdwestward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horisml1oh6 mt,. ezontally between two buildings 10.0 m apart. The sag in the rope when she is at the omhe1s,6m.l t 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 cord fr7p:ah10 dwsf mphpn(: m ant0)om 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.e5 a sjw61n( ar2,nxyn0$-\mathrm{kg}$ 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, Antarct) vdu7/o h:n :ld8 pkmtw4vbr k:vv.8)xlm b6xica, as shown in Fig. 4-46. The su 6.)l4dw)v phtm8dvmv:x 78: obvkrl /ubkn:xm 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 carsp ny;(tkpzqi7e a8nx+3g ovxl *q0 5,v of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firste i; *qg8(7 ,xnaoq +tzp3nxp5 kvv0ly 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 uspo+5p q)l (tmxl,d1c4)dm pl king the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pp5lmqp (+k,mc)) xl 1o ddptl4ull 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 ;,klh,bukbahl(fe d 4 )9f rr: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 block /mw;kyal/wg* 32nz zn(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 lgpi y v.z7v y*;05.9m cddygzare in contact with each other, as shown in Fig. 4-51. A f.g*zp.90vylyydm cigvz ;7d5orce $\overrightarrow{\mathbf{F}}$ 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 ea2 kywi *zf9wadsitu0f-2s *k, ch initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. Thikzyta *- wks9w22i0d fs*if, us is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictiz 5is4, m.3dwbn:sijkonless table are connected by a heavy cord of mass 1.0 kg .j: 3,5i.swd4 iz bnmsk Calculate the acceleration of each 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 between uj. e03b6kekk:hw v/w 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 aos(py m 35et2wl whjz38c- se) 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0th t yr .+g(gpt/;zgu,5s5 wtvxr(p7p.20g. What minimum coefficient of static friction must exist between your g5, r(xyrv ttus5+7g t/;h (.ptgpzwp feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo iue a 4j ri(7frg-jtnm8pfz3fm4 -vg: /f the coefficient of static fe3mn/fr(-ga p r 7uivz: tg4jf8mjf4-riction between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal jc ipx8p2w+ntg.-sj bo;63wog o 5e g2street pavement is about 0.8. On how steep a hill (maximum angle) c; -spw2gxo3oijojpt6c 5b 8.n2gegw+ an you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at .rt qma7hyyi;oqkxiv8c(0xf1y )) o9 -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 gq2 kolrznmw*48k*-n cyveg. z./sw7 on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeffic y5r)gh)c/y;qrcry* qient of stati)/rgc ;c)h5 rqy*yq yrc 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 kig seb ncc4z1( /h5(zb-d6rv/lx-e dq: m3bentnetic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A have h1yaulv0-y(0 t- cb blto hav l0lhv yyct(u-a -b10be to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wiwoa(8 pfw,e1xovw:b i(-q9ndll it go, given that the coefficient of kinetic friction is 0 b-xe9w(wqno , 1a: 8w(fopivd.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 o9jqv6tz7 e0q e kdz(v+n a horizontal surface (F9 tjevz6dk+(q7v 0eqzig. 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 friction behmgn9+(w (j / jjona/itween 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 the cab of the t(man+ hji/ogjn(/w9 j ruck?   

On an icy day, you worry fmu+x rwou- x8 ni +m7mcy9m,jmmb)() about parking your car in your driveway, which has an incline),jmoxu+mummfy r-w()xmc+ 9nib8m 7 of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 28rm 5r6lez*j 0hx:i m/djsz,1g $^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an anr: n ;z9xskj3ggle $\theta=22.0^{\circ}$ 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 ini-dqehs7ge 7*w*rzl /o tial 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 sbt7gn 2xor43 yf0t2h upeed 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 placf8bv*+jo ahg r(81cwx e against a rough wall by someone pushing on it with a force directedv(wjh +8 1c*grb f8aox 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 daqs/y y35fvbm0 ngerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof wsfvyqm 0y3b 5/ith 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 stoppic -16wx- yx6;cr mzkrang distance for an automobile traveling at speed6c--ycr1ra k m x;xw6z 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 dashboardv ti*ypv(mdnk* cx. lrn)usyc+/)5c / of a car slides forward on the dash when the driver decelera/s kl)*(cc t ./pc+5vrn *)uy nyixmvdtes from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial speed8c gvj n4zv 5e8-l/bdnwz9 b4,f1txv w $ 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 wo *a,q 1b0ou9hkkv ,hto the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the mia 0o,h,*q1 uwbo9 kvkhnimum 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 vt 5np4ulwb3n 2s ia3)of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coasph b 3v*ukx/6tt 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, at each pulszh:6. gzvm+np/9gnx, 7 ltwd ze approximately 20 g of blood is accelerated from 0.25 dnx :g+,p.7 vzt69lmgzz/hnw$\mathrm{~m} / \mathrm{s}$ 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 automoa ygp)ka:y- 6+ x1*gi bkerji ,xj;,g6ncl7obbile crash if the deceleration is no more than 30 " g 's."i ,jb)- o;*nxxj ypeyrbakg g6gc+a k:1il67, Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake45ns ,uch lnp7r8lqc1 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 aqlr8 nc,7s c45npl1uht 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 a7imm64r 8ws t f.o,ud1droy.tn accident involving two cars, measure 72-m-long skid marks of one of th74d umtt6,r ys8r dw.foo.1ime cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m ax()9flw+6yx fa f3mztraveled along the road, the elevationa3f+x 9 lmw)z6xfa y(f change is 1 m). How fast 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 top of the Leaning Tower of Pisa andtv;e r; i,wf+ ia n0hxml,pz5( falls 55 m before reaching the ground with a speed of(; iwtp, ,z5rvel+x;n famih0 What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s buhx3uy) )j.u re6 pkg, hgb+;dmt enters a muddy stretch where the effective coefficient of fricthkuupg ,ex)+.6 ;j)dgmhb3 r yion 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-,6xl 9z30i 7vwyyn5d jtj p5auulmd1 on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even l jypa9 106 iul-jdylnx5z3umd5 ,t7wvow-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 experiments, dangles her w ao; yvlu:vwin,-l*iy :ng.s- atch from a thin piece of string whi*- yua ,ynigo.i nl :lw;:sv-vle 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, therx; mvs96d,nt je are to be several ramps connecting different parts of the store. xnv,ts6jd9;m
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 t /v1grf, yz7nizv mn99o lift the piano (mass M ) using the pulley apparazrin,vv / m 99gfyn71ztus 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 acceg u y(mukbk+;:lerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restrait *7eg+blxg z),3tgtqnt chair, an engineer considers the following* beg)x 7gg,l+tt3zt q set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric to/: pql96tw90qpn x/ijt 0t0 ysayo+dsns (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, Bill0gb/i3j vwac - and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a simjwi3-vbga c/0ilar 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 g wk bxdg6 t3zszt/6:o1idg*x64m4+p d hi3xra " 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 maximum speed of ry8r91n dx0uvxr*fc - 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 together are ascending an ir9t3/4c+ 2vsw3 f wu. 6wyxwaom;blcmce field inclinet 9 3sxvywc6 /couml;fw3 w2b4.rawm+d 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.