Why does a child in a wagon seem to fall backward when you give the wt6w;- el yqr9iagon a sharpy6rie-q l9 w;t pull forward?

A box rests on the ( n ndmu5m5l7;az8jj/ 6x0ieeffrictionless) bed of a truck. The truck driver starts the truck uajl5865jme nn7f0mx;i d /ezand 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 (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no fp-.zmgk rjp zr s5y99(orces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it u-x ep9mb8 h74srz wz3hav9z4u -p erw3bzm8hsx7e zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force ,9gv6t-o7f thqwo k.nneeded to make it q,. v7nhot-g6 wkft 9obounce back up? (b) If so, what exerts the force?

If you walk along a log floating on t6y q- xagxu*eeo. *.oii6o*e a lake, why does the log move in the opposite dirii-eaxe*6 6 qgo ot u*e.yxo.*ection?

Why might your foot hurt h)3l7 uy mjos85mrd3k if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelera9ayscryx.,vv :s-0ev hc ds((te quickly. (a) What 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 runnisd(vy9rvsc0ve,. :ac (x h y-sng at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceilingd 8znd/6:huzh , 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 dangling thread, where is the thread likely to break: below the stone or above it? What if the peun6 zhhd: 8z/drson gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is t1czc- gsht*5fys :l6xxyy( x5wice as great as that on a 1-kg rock. Why thyyl xst yc5(x6*hg-csx 1fz:5en doesn’t the heavier rock fall faster?

Would a spring scale carried to thbx*f2 a2*gqg8 q/txx ae Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogr2x* gbqa*8xgtfx/q 2 aams?

You pull a box with a constant force across a g-f iq,t4a+ze frictionless 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 the acceeiq,-tagzf + 4leration 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 forcgl5)(hef 4nprlwm ka)ud / 3y(e mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal anduad nw (43hg)fkypl/ )5l me(r opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kgo6k2 (p.hhyu,0t3ggby hs; ny object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a gykt hhnh y(036 oyps., u2bg;2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s(.vd nc:3 gh0 tvhls8ghh8b, g third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the vln, c8.h0h8 (ggsdtbg:vhh3 other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Des + 6od/bd6j/xm)xww nfcribe the “reaction” force (Newtfw)wn /djxdmxo/ 6b +6on’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.au.gq+g taf1 on the ground, how large a force does the ground exert on you? Why doesn’tggatu.a.f1q + this force make you rise up into the air?

Whiplash sometimes results from an auyphcnz /5t ektws: )t 8pj7v:9tomobile accident when the victim’s car is struck violentz:pwttht ep/:y 5n)97ks 8vcj ly from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed ofsx sqf3 h)k:k1 a flatbed truck. When the truck accelerates, the cra1kq3sfhxs) k:te remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it s1nh uqq koy fg45u.v+9lides 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 asfvyu5kq9h 1u. q+4 nogcent. Why?

What would your bathroomc:*yzxs*nnbp:18h.di xjg /v scale read if you weighed yourself on an inclined plane? Assume the mechanism func cbyz8 i/1:hd.j*:px *sv ngxntions properly, even at an angle.

  What force is needed to accelerate a child w..o +da sy+xcon a sled at 1.25m/s$^2$?   

  A net force of 265 N -:8b ty r9gqzxaccelerates 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 mus jtj00 m*-pv-tgayrpm(56xt bt a rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a gjedk,8m7u3rjz. a b7t s/iy8$76-\mathrm{kg}$ 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 3ri b( ke9z.bz: z2c q*gj,bdethe car is traveling at 95km/h?2,.zq*ked:zbj 3 bzi 9(be cgr -  

  What average force is needed tmyh i1l )f1or*o accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the il*1)1hryo fmbarrel of a rifle?   

A fisherman yanks a fish verticw4v.sx mppm554y4s ;lc u;i m(o-qwzjally out of the water with an acceleration of 2.5 oiq-.4wu lz5xpc5p4;sw4 vm m;my (s j$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile t4 z5thmu*()ak9 -aihbln3y )g sm3p girack (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 accelerationq .0phsc3el 2kf5 z5b6bwn- cohx5q x6 is 0.0680 g . What are the maximum and minimum forces the motor should exert - bc h3z620s q5xf.xk6nb pq5lch5eo won 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 bathre :m w* g/y7 *odwvp+,zyoty.hoom scale in a motionless elevator. When the elevator begins to move, the , g+7d/o* mypoyv.h*zwety:wscale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting aojb m/gce+yax1*/8hi, xtsd * 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward at/cje+ sybd*/8ahxmxo1,* g i cceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration rismx9yktn0 r o(*k7i+tvb+ : of two falling sky divers (mass 132 kg including parachute) when y:x(t*+ nk i7r+rti msbv9ok 0the 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 t a 5a96caa7kgvhe roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approag9 av7a 56ckaximate 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 the box runs vertib+-;wwlwfjs 7 cally upward over a pulley and a weight is hung frs-w+fw7 bw ;jlom the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basv9qc a z3rlh0+ketball 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 5jwp uobk 7:be /qp(cubri).)a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying wpi5e( b :b)r .u/7) upkqcbjotoward the outfield.

A 650-N force acts in a northwesterly direction. A second 69ix)r(pefzm( 3: vdilbag(eq2h:xu5 *hm ( kb 50-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustraep2 ii9ev(5gz(drklhu(q(: :b x*fba )hmmx3te your answer with a vector diagram.

  Arlene is to walk across a "high w(mn4.wjq; ra(4 qck2upy x b4jire" strung horizontally between two buildings2 kajqrjy4q4w(;u4mbn pc(x. 10.0 m apart. 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 massless cord from another 3.brwa fp ogb83:+dmm,b)8 r )mo2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.. ,d7nlwun 5kn0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location a.,5x/dxy jwxh t McMurdo Base, Antarctica, as shown in Fig. 4-46. Th x/xj,w5y. xdhe 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 tdgot5b 9d*p 08db1 nruwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first cab o ud 8dpt9*n0dgbr51r $\left(F_{\mathrm{T} 1}\right)$ , 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 apparatus sh i e3 m7,f(3bmc+*k jtevfiv8ev1 fu6hown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant sv* j63 ebtff7,1vm(+uvef8cikih3em peed?   
(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 + u c,wzz9dvnd/bw:bsv /i.4wv8+rg t, 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 blocki(* h( c yp9,dmgs j5secix1i4 (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 hxm1 chc+u4 +q*ot7wvj orizontal surface are in contact with each other, as showth qvm +u 41jwo+*ccx7n 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 in,e,aw s gfpq /m ks+.36lv7fsx/ab) vcitially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the li fs wv /) kcvam,3,xpbq/s6eg7asl+f .ghter 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 connectedr*4he5ph n8c (mbxtb8wpjp1) by a heavy cord of mass 1.0 kg . Calculate the accelerat8)hn8w r4 bpmc* bxe 5hj1t(ppion 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 fric0p uqdlyo1 bdt/tt+bw;l s*3j;08mx dtion 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 requirw eo8uhx 6pxm.ri n,er3im/pf kg(hk)t/-e* :ed 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 standing on a train ac2 m *ze2 w+b: pn,oy h94rzndv3f4xtnocelerating at 0.20g. What minimum coefficient of static friction mz *yn wbr znpo,f4emn: 3xvhd+4o922tust 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 o3 /tgabty- +ydf static friction be bg+/t3ydyt- atween the tires and the ground is 0.80?   

  The coefficient of static friction between hard +0i3q euy0 v9uambxi p1ed25q rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car pq0v a9ib p +ed35u 1uy2em0qxiarked?   $^{/circ}$

  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:ktc3v4ml y4k at -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 oi4y pqz+v9 xr4vls;h jh1s4/ an a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have acger, .py.x 6rok4tin4sd+8r very high coefficient of static fricyxsp4r gd.it 64er.8ork,nc + tion.

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 frepf ,eivx)9zz.2 qr/iiction 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 (Examph) )svjzihl4zi-l 93f p w98mdd 6j6bmle 4-20) how large a mass would box A have to have to prevenmv6sl iij z-m8ld96zd9j) ) f3hhbpw4t any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. i+ijq ct( p(-pHow far will it go, given that the coefficient of ki(p+i(p ct iq-jnetic 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 kgbjzihc9 cc*8 ek cz*(- , are in contact and at rest on a horizontal surfacick** c- 8cbh j9z(zece (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 coeff rlb+b;) cm5zibkix+0 icient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver cacr 0imkb blzx5+)b ;+in 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 your driveway, which has4+t: slis abh; an inclinb;ls4 at:is h+e 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 (ztmzmgncp69al3,o l* pvf76 slide 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 m+,(o v(fzee kan 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 wv; tbr rw ,bjxbgj+.c 6w3 l)w632b62 nvshfz 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 swc1z z 5cy+lqn lw0i7+teepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing tk,mv 9u*(qy by 0ms(mon it with a force diret0m(ubq kmv*ys,y( m9cted 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 dang2:d ess/;l j6r vu k(8.hsrnegerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof:r6k hud ns;s28/.svg rj e(el with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile trave t,s.q0rhwznol78oi2:k +flaling at speed v isf7k+lo: rho,na.liwzs 0t q8 2 equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dala( /lkfki +-vsh when the driver decele +ik lkvl(-/farates 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 speed bph;gp0dsyd, g :v(7r si(;gv $ 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 fill eos tmvn,9)k c4b.t ae95w:qied to the packing station 11.0 m away. The belt is incmo:kei9,bvt)qns.we5 9 a4 titially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the 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 frictiobblz(w- ifq (/ :zlzg/r)j 0 ftwfur s2m1,ub+n 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 pn3y1b ( qj2rk(including the 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 mammalian heart, ssb3 tgw+*lvkk/j;a, at each pulse approximately 20 g of blood is accelerated from 0.25 gsvlk +k/wsa 3b j;*,t$\mathrm{~m} / \mathrm{s}$ 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 the decm(h4ccahn t tlh+e;. 6eleration is no more than 30 6t4ehhlmh(a;. ct n c+" g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced dr4uothau /;.by an earthquake is a , and if an object is going to "hold its place" on the ground, show tuthdr a;.4uo/hat 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, examias 4ecp/ wz+bs7dtt 4.ning 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 coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of 7+s4a4b pd/ectswz. tthat car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 meadm ljwyfzjb3 vl(96 0*ns that for each 4 m traveled along the road, the elevation change is 1 m). f0wd ljly3*9 6zj b(vmHow 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 dro.dmx njy ;;smtfs)n +rc(7h 5wpped from the top of the Leaning Tower of Pisa and falls 55 m be+s xw cdy7;.rs (;thm) m5njfnfore reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting ax . 1 jz5/7*5pd)spzqwefks zst a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.7/s*.z epk5 zzs5 1)qdswp jfx60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a r9qyt:t* jpd /w 4eho;*ab zv7hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered ch*7;4z jqoe:v tpya/ wdrt9*bars 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 experlv. 0rx)ca6g lf7xt 6/*q) -zqpkxuatiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. gaq6l6a)rzvk.x tlx7/*qxpc0 tu-)f 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 rwt*y e5gk+-wpnz* a o1amps connecting different parts of the pe k1 y-gwaz+5ow **ntstore.
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 ) using thedv0:uzzj8mz 7f m yv(f2 ckj)3 pulley apparmv8c 0(vfk zfd:j 3ujzz)72ymatus 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 ac.)f8mlrc(ddp8 u. cen celerating 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-restraint chair, an engineer considers txtusq z, gy3xoz j-fj;n;0.q0he following- uxz;js zx;,ynt gqj0o0fq.3 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 Itdyezn.b 0(w04+mp r*+qa nwf halian 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 andpe9nj . ( uvap5uk5)xq Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a 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 a5 xuu.j)pe p9(nk5vq likely to be hurt?

A fisherman in a boat is using a " hz1ioyp5cf 5 h 3kwg884fuy 7s10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 3iyp4- j1) yopn.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 a6zm tdn oyq471scending an ice field inclined at 2d 41 y6zq7ontm1.0$^{\circ}$ 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.