Why does a child in a wagon seem to fall backward wh m:(xt (z*af;fx vw-jhen you give the wagon a sharp pu;( f-at(*x m vjzhxf:wll forward?

A box rests on the (frictionless) bed of a truck. zyp (:hsjb 441xkzjy 1The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the b:yzz4bxh( j yjp 4s1k1ox, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forci 7nu3,- 9kxnufhj1azk( x so(es acting on it? Explain.

Only one force acts on an object. Can the object have zero boa enz-.490m gi2wrracceleration? Can it hanr9m iore-4.gbz 2 w0ave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forcp7 4qp pedd 3rl ;a;+lqa4,suke needed to makp q47pra l+eap,4;3s ;uklq dde it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the ot7( /+e h(ecg 3ymx-mhyo*qyfpposite dit q-cog(* /e(fyhxy37ymh me+rection?

Why might your foot hurt if you kicka.dqp-vr0san8 n ie-9cq:y,nl;ma; j a heavy desk or a wall?

  When you are running and want tm q f:eybp.+t+o stop quickly, you must decelerate quickly. (a) Whatb:yqtf+.+epm is 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 th,f, g+s:rnoy-ox sn+ wread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a ,:wgoyxo+ ssn-+,rfn sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1- -r69fh,iz2pw6c4zbep m wa*ygs(u; e kg rock. Why then dow9iu z,zeywa-rg;b6p2ehp4m6fc (s*esn’t the heavier rock fall faster?

Would a spring scale carried to the M + y+o74cfnaeioon give accurate results if the scale had bafy+ + no7ie4ceen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictiog*g/q jmmz:3z nless table 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 remaining flat on the table), does themqmj*ggz3 /z : acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity thswsh+1q;c-v w) 4eqwe ere is a net force mg exerted on it by the E)s+e v;q 4we-s wqwhc1arth. Yet by Newton’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 af87be*n jexw +amr2 f0 10-kg object when you are on the Moon with the force needed to lift wrem70 a*x efn+fj2b8it 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 team in a tug of war (Fig. 4–)o48i7fx,kf fxt (gdj37) pulls with equal force on f odkjgi)x7ft4(x8 f,the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocef.40n4 qlne leries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerte.l ef4 nq04neld, and (d) by what object it is exerted.

When you stand still on the ground, hoi/lpn;o; czu,d3a)a dw large a force does the ground exert on you? Why doesn’t this force make you rise u,i;)lo3 dc aapd/u;znp into the air?

Whiplash sometimes results from an aubb1cibr;)i-6/rmql a tomobile accident when the victim’s car is struck violently from the reabci ) ar;ir6q-bl/1bmr. 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. When the trkr52fo4z tk/yuck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerat5kz4/tfy2 okre?

A block is given a push so that it slwi bww1i*1f1vx/ no3lp-wc o: ides up a ramp. After the block reaches its highest point, it slides back down but the magnitude ofio vw :fpwc no*i3b1/ wl-w1x1 its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale roxg b hc/n702)5qgsahbjg* izy.,l ,h ead if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angl7qh/lc 02,g. aibgz5goh y,j sb)x*hne.

  What force is needed to accelerate auk 4j f(txd:tmju+) *(3f zmmx child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratevt ip/g8 aa*d l08)lzes 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 withstaql * rr)1)d:dq- mai-gvw0dwrnd 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 a4bk7s kf-jf8uhbt ), l $76-\mathrm{kg}$ 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 the car 5aqsf 1 q+ohx6x9*qqgp*5z es is traqqs** 1fqhp6sz 5x95gx q oa+eveling at 95km/h? -  

  What average force is needed to accer uqyp-rbdpl + n4v1 w3hg4/n*lerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rgrl/4dn-brp1+ quny3 4 hw*pvifle?   

A fisherman yanks a fbd5q jo-16m*zb8 k) r 5gqmqkhish vertically out of the water with an acceleration of 2.qk5rh) bj1k68 b5g*moqq-z md 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 qufo knfu-s: h ecn hxp(-/zu/t2.7by7parter-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+.qr l a2ndk3k that the maximum acceleration is 0.0680 g . What are the maximum and minimuqnr dk al23.k+m forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a moti ,r2m39qrrt(b3mxhg s onless 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 direction of acceleration. t2s mr3 3xbm,rg rqh(9    ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wh3xr1sy-o8vu nat maximum upward acceleration can it give the elevat1uoyn sv8 r3x-or without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky9:foyxf )z j;s divers (mass 132 kg including parachjz fso: )y;xf9ute) 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. When he strikes the grounc.x0f ) (vvxy o-fjm-ko-y:yhrg fc( )d below, he bends his knees sofc:--xmcf0 vjh( f kor)ovyyy (-g)x. 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 rests on a table. A rope tied to theob/6o2t2ma vyf -owf(lzec: 0 box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). D6volo emyaw22(fzc/t b : 0-foetermine 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 fory/ vc+j p,n/ea l60.vd ghut:r 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 d)*.bau)szm149 ny s maqj(xmfiagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying tofsmbqnj a. amx*)u()ysm4 19zward the outfield.

A 650-N force acts in a northwed8brv g8d3j/nsterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector3gjv8d/ rd8 nb diagram.

  Arlene is to walk across a "high wire.0lai( df(w) a;x hdc8 lb2xkt" strung horizontally between two buildings 10.0 m apa(;ad8 xx0ktl(fbhw )acld. 2irt. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a mas9rz8uk3kc yg/ sless 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 13w k hq8*u;www-cgu y;4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a /+tms 8o f49xrw2l eounew location at McMurdo Base, Antarctica, as shown in Fig. 4-46. 2mt8/wx ul9r f os4o+eThe 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 5 x +ssx/r (-3(cef4bgirecgfqto 9k05a. dwecars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couplkr+ g35ic/(w(scrfaoe5bq gtfx9 4e0 e.xd-s ing 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-pulley appa0g+ u ee( lvksvicp4q0u537usratus shown in Fig. 4-48. (a)40uuveve570is k +lguc 3s(qp 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 racedlmmj:/738i7 igdns i 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 blockde-7 f8px.l3kppx vl 9 (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 horig-6efk +gtln6 nmj5 3vzontal surface are in contact with each other, asvn glm+ 6ge- 5ftkjn63 shown 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 initially*1xjyc;vl 5 y, p7igls 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 determipg1ljsy 5l;,*yxvc 7ine 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 it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cx6(l h c9g*o(ke runb7ruk w5/ord of mass 1.0 kg . Calculate the accelhkcn5b7/rg( urlu ( wxo6ek*9eration 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 fri0qwidbb1ue -de7sm qc./ *rw.xlk 63lction 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 require b8o:kpwm;i+t: ,zpu ud to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standipb2;ddbg41ro ygco7n lw6( dov/cb 56ng on a train accelerating at 0.20g. What minimum coefficient of static friction must exist bewv/bb6pl5dr yc4oo2d;7g db 16co gn(tween your feet and the floor if you are not to slide?   

  What is the maximum ac 55mp0qofw2-m wtnj;oceleration a car can undergo if the coefficient of static friction be5o5 t -f0qw;mm njo2pwtween the tires and the ground is 0.80?   

  The coefficient of static friction b0 m*y/ psz k*rf7omf+wetween hard rubber and normal street pavement is abouz **w0k+y ro7mf smpf/t 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 au;1 uzfx 4 a9ilyfc ,uwhbf v2+y+l42ot -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough1v- 789) vazpqrpgch d 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 hags ;zkxd/ ik3(43rqeb ve a very high coefficient ofkk;z(qeg /bs343rd xi 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 y, 4gx tieu.asawk,li 2+(zg5 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 hy e;dp: 6bt 7xlnw++uh6ku yc(3g z5ha mass would box A have to have to prevent any moth ln;ykwpxh+5 ct uuez3+hyb 766(d:gion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How 5 bwtc6b tgvn; :h2n58*xpi24m dwxusfar will it go, given that the coefficient of kinetic fr2m8ttdpiwc;n ng25:x w s u v4hxb*6b5iction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110z/w,)w. jr enugc*1ud kg , are in contact and at rest on a horizontal surwd1jg *ue.r,nu/ czw)face (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 heavswp:4 zjn8bkax*kyz,f j 53)bgb0-mvy crate. The coefficient of static friction between tx3jf4mzk)yk 5- :g pjvb* 08n bbaszw,he 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 truck?   

On an icy day, you worr89q qsvc6x e*wy about parking your car in your driveway, which has an incline of9q6c*v w8 sxqe 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 d(pn*ux rnj 0y a9zd/+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 plann/u *z)ykt7p i6jde* te 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 speed of agp8mc:79y m;tle gp 7v)4 yrs3.0 $\mathrm{~m} / \mathrm{s}$ 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 wi:c.v qny;unj1th a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on i5fu kye8k9cw) ft/ru-t with a force dir8kt/)rffc wuk ye 9-5uected 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 dj8pcv)2.,8c5 *fksm:rht lzcx o4 ymbz8af t +angerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with sf8t2,vzh48 oymkcz)jl cpct8x mb5+.* arf: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 dista 2qq (zv2 6:x:,m i*xv tslpvk+2muwtnnce for an automobile traveling at speed v 6xtt q vvnm (2v:l:mw ip2suxk *q2,z+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 dashbv75/1i5c fw iupesn9 soard of a car slides forward on the dash when the driver decelerates from 5 sn iw7sc1i9fp 5/veu45 $\mathrm{~km} / \mathrm{h}$ 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 anhdbhsb- vw+ / /jsd7qb+ck0c3 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 con s+5uwfgpix( )veyor belt from 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 coefficient of static friction between a box and the belt is 0.60) wp+fx( isu5g, 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 kin:p h 8yikyh.5( 3uq4s*hj iqqvetic 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) c bzsuupl swn991dlh- .a1r.p.an coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxim27 im5ne:k()tiry zy+t ka(ygately 20 g of blood iny2 kr5 ge(7()+ya: tiizkmyt s 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 a3bqm9r7pr ng6s0 q -g3-njul of surviving an automobile crash if the deceleration is no more than 30 " g n-3u3-rp7r b9gq0 m6aqsgl jn 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , any zj:n1oko1( .r0 4esg e/jzrnd if an object is going to "hold o:j0/ okz4r1.ye e 1n nzsr(jgits place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining t 82wzq:syun 3cj0f*sahe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction b8 swncz0y3*u fsa: jq2etween 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 s;kq0 bakb hk 9/fadvno i:6,4each 4 m traveled along the road, the elevation changed/ki0oh,6aa kb nf q4:v;9sbk 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 the843 zrv kozow- top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average 8okr -wovz43z force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy st d8;cxa h7fm5c8:t rvaretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts7h:m;x a5cf tvra 88cd for 11 m? If so, what will be the speed upon emerging?   

  A city planner is worixmsxp.ea-/y )5:j gorl ) (gkking on the redesign of a hilly portion of a city. 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 1100 kg , can al5m ai k:yjg/p)r-ogxx. es( )ccelerate 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 phy 43aknem1k,v/y s8zxk sics experiments, dangles her watch from a thin piece of stri1sa 4,k8/ky3nxkz ev mng 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 several ramps connecting diffoz tdx/)l6(fcerent d)f(c/ lzxt6oparts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M sw-k4tvri:e;rk3a *- mf1gr*s ;kwgsf h.yd- ) using the pulley apparatus shown igd*sgk eh r ;rr4 skt*s3wk.w1:m fvayf i-;--n

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 36lstd* rwxa; 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-:jb z+-qd uqj:restraint chair, an engineer considers the following set obq:uq: zdjj-+f 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 tonsqu he 7lm7at1jo++gw6 (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: xr x/m5fxltgf s4.c: 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 similar fall, Bill's rope stretches by 30 cm only. How many tmrx xtgc5 ::lf/s .xf4imes his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat i:gx*)xwa+ bdhs using 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 building is allowed to reach a maximum speed oz q wnz;8 /f9rieyrb43p q/nb;f 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 areqpx2:in*b(w61lne )cy r-z l w ascending an ice field inclined at 21.0nzy*wp(ql -ec6 2)n:i lxrbw1 $^{\circ}$ 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.