Why does a child in a wy ;x /cqs eew-fi2l.j8agon seem to fall backward when you give the wagon a sharp pulls il8; y qfx/.cj2-eew forward?

A box rests on the (frictionless) bed of a truck. The truck driver stpt +c. n sedf71ay97zyarts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (bf9 yztcdpy ne17.+s7a) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? of b ak+)h,rto8x b0gcs/nq16Explain.

Only one force acts on an object. .ypaegdb/jce4lvsoy ;d gk3/0,o*f *Can the object have zero acceleration? Can it have zero velocity /,l/*gypd4 ek* s j;e bf3ygavo.c0do? Explain.

When a golf ball is dropped to the pavement, i-2c wk d9*ubnrnyv sb-mx*z0k 1vm9 b)t bounces back up. (a) Is a force needed to make it bounce back up? (b) I29 yr-v*- ) 0 9cdkubsmxvm*b wznbk1nf so, what exerts the force?

If you walk along a log floating on a lake, why does the logmzi/7f8 oevwa7r76fln mf+v2dc oe ;/ move in the opposite dirf7fc 2iwe lomzardmv 67n/;f /7voe +8ection?

Why might your foot hurt if you kick a heavkr c. b,m v+hu3vft.c(y desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) fe02d w1k1ywaWhat is the origin of the force that causes you to stop? (b) Estimate (using your own expeak1wd1e 2y fw0rience) 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 c7 63boxf u4/faq nm1r8v7x snieiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the 4xx6/ r778 miu b3qfvannsfo1dangling 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 qcnutg0k r86) v61dl5y 0llrirock. Why then doesn’t the g )yk0qr 60l6 1n vudrc5ill8theavier rock fall faster?

Would a spring scale ca0o,9 e i,ehjyxrried to the Moon give accurate results if the scale had been calibrated (a) in oy,,eje9ix 0hpounds, or (b) in kilograms?

You pull a box with a co ..aqq9j3fdz a2yiq8 qnstant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontaljqq. iqd 29ay q8z.3fa (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 foa .,p+ex omo,orce mg exerted on it by the Earth. Yet by Newton’poxo,mea, o.+ s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a z1,/(d6vigy .tu 7kc floqt b710-kg object when you are on the Moon with the force 7y7 o1l b/ uitgq. fc(d,zvk6tneeded to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each teffnh0r0 cep.,am in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will wie0, fcr.n hfp0n?

A person exerts an upward f u d9-cntv84tuorce of 40 N to hold a bag of groceries. Describe the “reactnv ucd8tu- 9t4ion” force (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 grou1 ccq u9coj1f6p h76-uuwjq3 cnd exert on yq jcjucw3c1fu- co96 u1q6p h7ou? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accid lokln(zte nlr: tj/4(,flc2 :ent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this s(r:t l/ftkzj: llcno 4e(2n,lituation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck ac .3j/uh1 o*-a7fxwce6 alvyijcelerates, the cax vw jy.f7c*aj-u61l3 o/eh irate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push (u o ;x foi(*ji(ycr3fe 9;altso that 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 the descent than on the ascent. Why?yclf t( iejofxi3;(9 *r ao;(u

What would your bathroom scale read if you weighed ylw8ms2k ji7 b0ykq s,-ourself on an inclined plane? Assume the m0 b, 2swskykm 8i7-jlqechanism functions properly, even at an angle.

  What force is needed toi2shd14c, tht accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accq/ n:w8( 6f urs/r 7bi-*mdym6wttdukelerates a bike and 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 withstaneo;o5x d 92v4flfd; b3p) dj ow9.oksid if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a f5.vb .esjycpk+8 )wl$76-\mathrm{kg}$ 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 requhqp,hg (;5t 5)9b1llasbrb dc( rz qf2ired to stop an 1100-kg car in 8.0 s if the car is trafd59b(q;qc rgztbb )ll2hps h(, a5r1veling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gra,wrx7ke- iik5m pellet from rest to 125m/s over a distance of 0.800 m al,i-7 xi5wk ekrong the barrel of a rifle?   

A fisherman yanks a fish vertically 6n9vxryfxu.:xug( razl,*w) out of the water with an acceleration of 2.):rxx(z.u nul wf6*,x rvy 9ag5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 qua vfpa*v1bgtr ftd.5 :w.c a2q786dunjrter-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 kg8q 5wgesg -w.7)n*ysewxu e t) ) is to be designed so that the maximum acceleration is 0. e5 g) s87n.wwqyuw-*e )xtesg0680 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 sc1tr-eug1x) h xale in a motionless elevator. When the elevator 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 dir1r- )uxht1xe gection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevato8no/29c pz ygad(kaqv dk 57)rr has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator wd5a7o8y( gz n2krv/a d)pk9qcithout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 du p2b4fn+yxx.mdc t-02a0 mr kg including parachuter2fda 4b2-xt.up0n+dy x 0mcm) 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-m high. Wha/kfa+l.r4e0uj wu(sen he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg.ua0 lsw4(af j +rke/u, 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.qp9az*tjzpu (s d:or5xv7xy 9j2y: u8 A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the f78 9:z2to5s*ya uqpx d r9uy(xvzpj:jorce 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 dia* u ,d0ftihaz*gram 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 bi,u ,d+o1n b6xmhf1sk 7v5qwmaseball (a) at the moment it is hit by the bat, and again (b) after it has left th5q11,hds7v ox 6wkib,unf+ mme bat and is flying toward the outfield.

A 650-N force acts in a northwes63apg4 (sntcqy+oqs8terly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwar4p3ytg+cq n86sq (osa d? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontsywg34y5 y my/a,ki2 sr7k+nfally between two buildings 10.0 m apart. The sag in the rope when she is at t,y+/ynksf27wsgr im5a4y3y k he 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 hangingi5mpf:d 7 h yqe1pya:9 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 1go1ksmu c *l(2dvf5i9ax6ch : jfwp;/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 -cpk89 aq/hel5 7 kn+ gbzar0fb 5cg5sa new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. T5gz 7q0gbkl9 hcr+b8/pksnfca 5ae-5 he 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 ;a.7crrzk v5uy8s*( bm1 l frsof the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firstar ;rfr15y7sukm z b.c v(ls8* 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 pulls1tsszbr*3s a9 herself upward using the bucket-pulley apparatus shown in Fs 3ab* tsr9zs1ig. 4-48. (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 6q(jr6:edt+dh 5$-\mathrm{kg}$ 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 bloc 5kir:;h7 dqwq)7i s dwxzi2u0k (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in cod- ,kjk825c yndz 3gocntact with each other, as shown id- czyg2n8dko 5k 3jc,n Fig. 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 above tn4xwi e+ (ui:vhe 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. This is its "launch" speed. Assume +u: 4ievxinw( it doesn't hit the pulley.]   

Suppose two boxes on a frictionless tabp*tg f3e39v aule are connected by 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 free-body diagrams s3 f9*evtup 3aghown 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 ko4* gx-nv :./j itstuhinetic 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 to start ag e8h9q: sv;qldqfj 25 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 0.20g. What minimum ufgyshr9l/xm ) 28b/i2p u,wm coefficient of static 8l b ,p/yummgh2 fx u/92)iswrfriction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of sz) 0 6zoipr ntwty8)emk )t2;atatic frictionewm))y2t) za0rotz6n ki p 8t; between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal str muq:vndfg1s 3:-ltj .eet pavemennj- 1 tfdsgum::l. v3qt is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4(;zy.5lj 85xoa kgi.)kvwefd .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 +r2u ; own-i,4fn kekmg8hks1 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 surl x;q++h:azzgmqv m8gs le4x;zlk7*1face have a very high coefficient of statiamx* 7xm1; :+ gkllv8z+qsehlqgz;4z c 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 s/ nwe4dr27d;qvei j /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. 4g+i c- k,d1/l nr tk-8h,vtplh-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurrvh d,lt1khr+k /,tnic-l g -p8ing? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floo1c (t6cbcj0kehq x(7 ar. How far will it go, given that the coefficient of k 6xc qcakj7cb1e 0(th(inetic 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 , (:q p .sa5+nx :pabcgbare in contact and at rest on a horizontal surf(q5+sgn b xaa:bppc: .ace (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coeffif1gr7 ym9l0/zc- rhp4ztd k1bcient of static friction between the crate and the bed of tk70 / d9zcmp-lh4rrbty fz g11he 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 truck?   

On an icy day, you worry about parking your car in yo9 (twclgh h, diab0r1-esh/w;ur driveway, which has an incw bhgs(9rh-;/0c 1tl we ai,hdline 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 dg8-r ;4me5c rujfx)4utf q1j 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 )pd),54n1ef q yv iiupplane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spexw /2d2jn *j8iy8uzd9) j qzieed 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 reacx mdg391seqw.fg7q s 5hes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place aga 76qf 0z5jw 3hva1tmsdinst a rough wall by someone pushing on it with a force directqh67z0f 3mawd vj5s1ted 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 roo; /bn qh-wz62ab +zh rd3vff/ofs can become dangerous projectiles as they melt. Consider a chunkr2 zabf vnq-z/fbw d;oh/63 +h of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for lr2m bm3(z: e6end(gpan automobile traveling at speed v is e2 r edm mzp:6e3gb(n(lqual 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 whe((idoy,xfl +.y1y.t uqvd v3mn the driver((3liyuq +tf,yvd.o .yvm d 1x decelerates 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:ha9blbkt*g,o4u ox5 ,.webs pt;o,i 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 filldi/sd: (h/uv ned to 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 /:(i shu/ndvd 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 k2 9dabe 4ezx+sinetic 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 coast down a y2 fuw4.ks rfxiqm vm3,y.-,f 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 mamefej5r bv;w;1malian heart, at each pulse approximately 20 g of blood is accelerated wv1ef;r5e jb ;from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if thi 6ig-;b kuxm+e deceleration is no more than 30 " g 's." Calculate the force on a u ixg;-b6+k mi 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an obje/hyv: hd3 sa/fct is going to "hold its place" on the ground, show that the coefficient ofh 3/yf:h savd/ 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, examingwgh9 f;t+xm nh*f. (ping 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 co;(p.+ n*fhwgfg hm9 xtefficient 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 t2.li4 uxrvuf,ab3a : means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after tr2t.frvua li,uabx4:3 aveling 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 toln,pp *uddi( 6p of the Leaning Tower of Pisa and falls 55 m b d,pp*6iu(ldnefore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mud.)+bd e,cduqg gqukf b:oh/ *)dy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedag q.du def *hb,cg )u)kbo:q/+l if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is work6nlpt4.e rgzne2j qp03 kq 6y5;m.t8ffg2cf ring on the redesign of a hilly portion of a city. An importanntmfyr n6.0qp6 cj4z;kp8r q.f23e 2gl5 f gett consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, 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 watch fro+gdf-1w vam,aw3hp 6x m a thin piece of string mw 1 f-6dah,vw+x3gpa while 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 to be 5e x.:z lzy /9*znlossseveral ramps connecting different parts of ts/ox9l:* .zzyenz s 5lhe 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 thesdo 5.;h.1.aj tk,67e dzetv aql8tde piano (mass M ) using the pulley apparatt5adqdod,e.;v. eaks1 jt8e7.lth6zus shown in

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

  A jet aircraft is accelerating a pi1ty24 sts w *mc8kcund*77wt 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-restraint chair, an engineer considers t2b *2vp*-srls kdvt7ney7u h)rj,e /ihe following set of conditi, vrut -)/nk27h y7s ie*r*pj vblse2dons:
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-ca:r 5htz*y cp*1n g9lxnr 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, use safety08; xaee f rxbb7e14mr ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bilbeee; frx1a87x0b4mr l has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm 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 q((ln. ;sxc 1 swlir s/f6pqh0using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall bw5/l ybxq (fb1iw zqvdf6 c15,uilding is allowed 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 to6) dod0n46qltffysl1 3sef zhe/q11n gether are ascending an ice field inclined at 161 01le4f/f d6qfzy3es)dst lo hnqn 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.