Why does a child in a wagon seem to fall bacbf- xb*j(dmf (6j 7pgdkward when you give the wagon a sharp djb-jx p*m7f (b(f6gd pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver sto.;ulr; w,ficzcnbmy vwa: 1o0 hofw9, rt74 4arts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of tlco0miw ;fzy:c t1,urnwooa79 .,4vb;f r h4whe 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 n3 9i6 vrqs/kxjo forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleratw rk vaa6 ku( ke)7pcfs 5ytmbz*y:+m12x x(*kion? Can it have zero velocity?( 2kyz p1sf*:tcxym re)v w5k7ak6k+bxa (*mu Explain.

When a golf ball is dropped to the pavement, its;.y4(,l* r/mltniu e.mtg vo bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the force?t( ,l.;4logve tiu.*nym/ rms

If you walk along a log floating on a lake, why does tvgllea j31 :y -w-plf*he log move in the opposite direction-3aflyejl*1l- :gwp v?

Why might your foot hurt if you kick a heavy desk or a wal2 xv.ws g:p,cll?

  When you are running and want to stop q a5b;n)p t- 4d hhhtjs39wxpgw.50utauickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own e whhu sw5x0.)tbtn p945gd;tja-3h paxperience) 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 se ek*cdc3q ( 5a,xttkh(72notu ction of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharutk2(o5* x7 h,t dqa e(3nktccp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kgpa+jl+(n 3-2lqse ed f rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fasterpn+3 lfqe sd2-ej +al(?

Would a spring scale carriea-;ph:hjrf h w*x;5sw d to the Moon give accurate results if the scale had bee:*;hshaw;f-j5pr xhwn calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless tabfdmrl r) l.se38bage1, b*q ot7m+h u3le using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remt. dlo+3me3rbr 8u*qf ,1 se)lm hbga7aining 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 to4gvd: cs6 qy(here is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite for o6s(:y vdcg4qce on the Earth. Why doesn’t the Earth move?

Compare the effort (or forceub vn5;y v79coef8na1) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed;o7ne8a cv 5vb9 1unyf to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s thy+vfq9t wu* 5l. y:elhird law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines wh 9uv :t .ly5y+hewql*fich team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. ;) k8l+f;bhxl+z,kulywu *mn Describe the “reaction” force (Newton’s third law) by stating (a) its magnitud)+bxu,+l huf ;*zn8mkl w;ylke, (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 exerzmi j8 )hhmwu tdb+37+t on you? Why doesn’t thi8z t)whb+jh +7mium3d s force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim(0 5p6o faupc4vyhfb /8 z+tdx’s car is struck violently from the rear. Explain /b6(pzod4x ct 8u5ahv +y ff0pwhy the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the ti:r46 e8v )kph7yt lh .ld2p h.yxmuys4 ml59oruck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What forl.:eldmp 6 9yrk7v)txps.yuo85 2h 4hm hyil4 ce causes the crate to accelerate?

A block is given a push so that it slides up a ramb,s nce y5,i3 b-bh95q4ky(a)yhrfvap. 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 asceib qh9,yyya fr ke,5( 4chbsn5b3-)avnt. Why?

What would your bathroqd //0n6edpdpom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angldp q6 ep//0ndde.

  What force is needed to accelerate a child on a sled at 1lqlyya :oo-m48senuu 53b5 1e.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridera gjg.yni8+ fd.r3b/m at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wit zc0l/nmfmc . kj2* 1urwd85s9zl-m eyhstand 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 rhqf 22kh0qid +d we02ank3 u7a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if th(go *kt1dg gxx5m 26fa5m)qpr e car is travxd5f *51(gqg tg 2o6xkrap)mm eling at 95km/h? -  

  What average force is needed to accelerate a 0oxarq s6 , *jjlftw./7.00-gram pellet from rest to 125m/s over a distance of 0.800. t06rw,/sj*af qxojl m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the wateyq3wriju .+ p/r with an acceleration of 2.w rqypj.+/u3 i5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 z3* dfcn654y nfdplm/ a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratioi11qq- jzjea l *(,opfn is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cab-lpi,1* z ejoaf(q 1qjle? 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 en.lj:avw7q). ,v8u 1 enndxmbathroom scale 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 theelxmw)v,1unn v neq.7a: j. 8d direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N2xd50n s3v+p9 jj5ol r3ocm3- tu oayq. What maximum upward acceleration can it give the ele5-vl5t 32xc+oqno3j juo ar0 m3sdpy9vator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including p u*tse-cd(8 vuarachute) when the upward force of air resistad* cse-(t uuv8nce 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 ground dbcqh /;s/d4vv ,qer1 below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the ,d/c r/ 4bqv vh1;qedsmass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vers ehk3ul2:)eatically upward over a pulley and : seauk) leh32a 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 diag5m*)79t1rf+vw3 evjk1x t)zk xendc x ram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the bac 0c ui7vlza5)cdl2i, t, l c,250zl )a uccdv7iiand again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forcyn py j y4l(0yc;/*rhx;wh0dke must be exerted in ycl4rkyd;;y 0/h0*xy pjw (hn 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 horizontatf lh28vdy(5slly between two buildings 10.0 m apart. The sag in the rope when she is at theldvyf2th5 8(s 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 han *ecxfr s7z-a)ging 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 1x (4mhy9 u-*3jc0mr/w 6dd2yotlc wnd4.0$-\mathrm{kg}$ 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 od;/e7t /uva k4dodd 2to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. Tdvdt/ ;kao e2/du7od 4he 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 f ;jd4obs,,yicars of the same mass behind it, Fig. 4-47 . Determine the ratio of the fjboyd, si 4,;tension in the coupling 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-qvrk0n1* v59 d pt2etepulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at const2dqvktt0 n15 9er*vep ant 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 k. ,*s,v vufyc9zb6q 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 (mass uh 4 ay6t 56y:yytsnw0$ 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 arei5oyt)3l omx8 in contact with each other, as sh 8tly3)oiox 5mown in 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 initiallg5zktr 8uc sfkmu9wzy (o- (;-y 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 acces -t5wc-gr(;f(z ukukzo m8y9 leration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are conne3bh p2pdzd 5 5bca(8kpcted 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 spc 8d(3 p5pa5bb k2dzhhown 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 beti.38a *lxsatk ween a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.0sh q(bn-lee0 hvn4h-) $-\mathrm{kg}$ 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 minz362:b wkfrw jimum coefficient of static friction must exist r: zb2wjkw6 3fbetween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeax 5cq8;8rmb. *ns +wpnm7 pahfficient of static frictionp. 7n mrc8sa+*8pnxa ;5 wqmbh between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber an ltu w-/pt(p3ed normal street pavement is about 0.8. On h3p e twp/tl-u(ow 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 -4.80e;flew ct, +wz;bm8 q6gyi(e/ $\mathrm{~m} / \mathrm{s}^{2}$ 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 roug0y)f g ii(uttg .:8 ocovgj26wh 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 cx 6-e6fwqi(.gh ym/jnontact with an asphalt surface have a very high coefficient ofxn(/.eqywi j-m6 h6 gf static 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 a k xy*beu*z7zi(o vhen5s()zba8*m,v $ 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 ma q.wdy:g vzt4xr) yzb19pf9r 9ss would box A have to have to p:yzzyprqf9 ) v b4r x.dw91g9trevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slid kye.gq+) w2afes across the floor. How far will it go, given that the coefficient of ). qgaf+ k2ewykinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 pk7qvjfn 8*0w kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 78q0 fnvjp wk*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 codaq8w /vlqsdy, :cd 51cm6m3 vefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver ca8d qdsm5mac3dv y, c: lwv/61qn decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car5i*m 1ul9,rr :fj,s wmlt hfpdj(2fd1 in your driveway, which has an incline of jd, jmrmffd t f s:l,2w5ir(p1*91hul 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 slimdh:k+ r6we/ 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 an anbw+0qvf h+hyfck 998*nx9tct gle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed ofq:yr0tvzl/u wl-.k 9bls 2-mk 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 wiux2b,ik -an /7q u4hghth 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 roug4hedlh zjjb:q v. 1,n1h wall by someone pushing on it with a force le4,bh n jv1.:jhz 1dqdirected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous proje, qdqn,(w: gbm8e1nioctiles as they melt. Consider a chunk of snow at tbw,ge( oq,qn:m8n di1 he 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 an autofa,(clh ljgokdp;rj03 .. q-i u6 myc-mobile traveling at speed v imh f dogca..c-rj;i( - 0kl y3qpl,6jus 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 zx89l4qy)w un the dash when the driver decelerateqy4u9)ln z8x ws 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 ls4pt5vk6kre*. rw5o an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt fr-v*kn vkfz)t:h cvge4 v+h-w3om where they are filled 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 cocvw hefk-vht +:nv4z k-3gv)*efficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction between :cnyj ,0( k98ejdbs; 3;jnyo grhlfe-$m_{1}$ 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 thedf+sg;wi :;1 6+v3oxmv guqfb bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammpjk+(;7sd 5l )q drdvcalian heart, at each pulse approximately 20 g of blood 7j pv(d+dk;sr)lc 5q dis accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile co: 0nlx dd8t/c8-t uawrash if the deceleration is no more than 30 " g 's." Calculate tl/wx 8unt c8-a:dot0 dhe 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 earthh)ai1 nruwzm0fy l ,q4w:.o;k quake is a , and if an object is going to "hold its plww1hl ork.0yai) u,z4fm: q;n ace" 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 sce3l, zh7 /kkypfne of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initiall h/ f3y7kkpz, speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for2 fv25/x6ji2icor zh-v ona8u each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom afterhxo-c 2i52r/f6ij82v n uozv a 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 and fvz1las;qhz7p . a :jmi *6ud9dalls 55 m before reaching the ground with a speed of What was the average force of air rh:7.1s da;d9majvzz6 *q iupl esistance?   

  A cyclist is coasting at a steady speed of 12f40rn/,bhgb k m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the sp 0bgrkf n/bh4,eed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city.*ptfqz-15 +k0lg 5mhf0 lihqli0* k an An important 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*i+ g0aq5 100-pi 5lmnltlfkkhz*h fq 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 likesu3,bsco:wt na 4oe 6v7h,e,a z physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of eewa,v: on z,act3 4h,b67uos25$^{\circ}$ 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 sever72q7s q2mjg1 hy5e yxpal ramps connecting different parts of the store.y21eqj m 7y2 q7gphx5s
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 8 hyg7cc/ ei:ult07rq needed to lift the piano (mass M ) using the pullieqh7/ 8rucctl7 gy:0ey apparatus shown in

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

  A jet aircraft is accelerating at yrk9c-vdx24 v1vd b q( 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-restraint6vhrw4 ( 9:aiwbofd.k chair, an engineer considers the follo( a kdbw:vhwr6.9i4 fowing 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 q cmm/jnf-f+: 5)7ig2xwejf sItalian 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 safety ropes of similar x1r u8wr/(ll9 jrnn9v 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, assumi(rj 8nur/lvnx19 rlw9 ng 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 using a " 10* ;qx/jdsn1amh, . gmg-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 b106d4if vd; 3y:l1zjk qlrrxusg k:,d 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 together are as5v,:t9 k u/pwniv-thx cending an ice field inclined at 2/5:w ut,pix9k v t-hvn1.0$^{\circ}$ 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.