Why does a child in a wagon seehfw.2+n ) 3 +gintqj n63gpk7nwr/fzem to fall backward when you give the wagon a shar t)nn36w2wz np/ij+fe rfh.gq73kg +n p pull forward?

A box rests on the (frictio u ukl si--sr*.6rnp-at5tjw/nless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motust-/.kj sira n5r6u- lwp*-t ion 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 objectc 0keo 1ry (tkt9r69x aoh)+px is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object havl q46o.53z+ zybshm xwe zero acceleration? Can it have z+wxq m3hzo5sb6.4 zylero velocity? Explain.

When a golf ball is dropped to the pavement, iyzy s53okw;3pj :qhw(t bounces back up. (a) Is a force needed to mqoww 35(h ypy j;3:skzake it bounce back up? (b) If so, what exerts the force?

If you walk along a loh3;.dxbisz1 gg floating on a lake, why does the log move in the opposite dxb 3zdgh; s.i1irection?

Why might your foot hurt if you kick a heavy desk o6ewct 752/ c;tixt qmmr a wall?

  When you are running and want to stop quickly, you must decelerate quic)5nvv7ybl rmfy6.*+ fei2nyl kly. (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 running at top sf y5vyf+bv.)l62ym le *irn7npeed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the)f.b 7;fawm. jhx q6x b1r-bhc ceiling, and a section of the same thread dangles from the bottom ow;am hc.xb x jhf7-.6brf1)bqf the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice a l8fob o)2s4cls great as that on a 1-kg rock. Why then does24cs)l lfo ob8n’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resulttpei*rsri:q/ l --:vhs if the scale had been c/pv: q ihi:s--tr *elralibrated (a) in pounds, or (b) in kilograms?

You pull a box with a conoj),smq75 bu25kf qtkstant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the qb5 5 u7f)mt2sjko,qk horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influe 9*oe:c op7v7sstaj6w;w4. i t9clx fhnce of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exe*c;:o lips ts jh7 .49xfa9 c7voetww6rts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg objee) 4w5bqeyl(tws96 ym p k5vn5ct when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontall 6e)t5wkb5 s5 mln4y p(yw9vqey with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls wl7 snjg+sf3,df92 b beith equal force on the other team.sl b+bn3,sge dfj f972 What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe th;wjgr ah4heuw(y ;(2ychz csz ub 34.6aub,e*e “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is e4 rbyzbwea.h*c 36chs ;u; auh 4w(2 jy(,uzgexerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert y6;xp:wkk*y l6cwp :qon you? Why doesn’t this force make ypq* lwc 6yk :k;:yw6xpou rise up into the air?

Whiplash sometimes results from an automobile accident whem ,1cat.94osvsy( e ja.-emhj n the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be th-a . e.somhcate 4jvs,9 (jmy1rown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accey78(up69zu rt sq f9jilerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acce9 zi8st ur6pq7uf9j(ylerate?

A block is given a push so that itvo;6jw;rw8 vm+4a lgl slides up a ramp. After the block reaches its; a+;jlwov 8lv wrg4m6 highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incl(zuea* lela k169v48pjj2 hud ined plane? Assume the mechanism functions properly, even at anvuual92leehkp *j8z( 4 ja16d angle.

  What force is needed to accelerate a child on a sled at 1.25m/2wh p:1k t5 aah4l-n1fnen2sls$^2$?   

  A net force of 265 N accelerates a bike and0 kp hs//tuso97ee )/u8.- r pksutbdc 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 withstand if it is usedc11i-+v sdziva z7n nnz :yektg77:8 b 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 4-,fg l)bz s9ldr z+c+)z)btpl udbf( $76-\mathrm{kg}$ 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 tw m7;q kf,z5d1100-kg car in 8.0 s if the car is traveling at 95km/h?kdw5 qf,;tmz7 -  

  What average force is nzd* r9cewki hrzeee c 1) 641q-2b4gfxeeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m f2ezw*iqce4cgr1-19zd rh exb )e64k along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with anqw1mkal ,(u: kqi 3ze- acceleration of 2.5 ek w lm3zk (qiq-:a1,u$\mathrm{~m} / \mathrm{s}^{2}$ 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 canc1a a.or, a1l rja/,ea cover 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 p 7g1,xzc2aju ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on ,7gu jpz21cx athe supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the hz- a2cg4ru/gelevator 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 dire2gg/-a u4zrh cction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-k whp/qf00fz)eg elevator has a maximum strength of 21,750 N. What maximum upward acceewz 0hq 0ff/)pleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky div k/1p.6txmifxc2 u9t wi myd64ers (mass 132 kg including parachute) when the upward force of af.29 k6 4dtmyu xt i1cpw/i6mxir 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 t18fu n1u kzc/ground below, he bends his knees so that his torso uucf8/ kn11z tdecelerates 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 m fsq99tl;o--)qphre)s.a hm rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley wei-o a99 -lstpmfh q ms).eq;h)rghs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a bask w8ikd32hv 1wletball 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 pgc0sw(i;-qcltd; 5f the bat, and again (b) after it has left td( tl; wi-0pc5q ;cgsfhe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mus4 kd).pv0*nmlq6m cwvt be exerted in whmmk64 l * dvcqw0vn.)pat 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 horizont/2 +wx0odh7:q xvapnglt m-c*ally between two buildings 10.0 m apart. The sag in the rope when sheq*-ot:mxv /ha7nxg lp2 wc+0d 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 buck1ftc( hmhaj-3 et is hanging 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 1ci:px8h4un:jmm-e , x 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 new location at McMurdo Base, An-k rx 8g** :xamrf9pictarctica, as shown in -xr mr9*apic gx8f :*kFig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-2/l:7gev dul i47 . Determine the ratio of the tension in the coupling between the locomotive and the first car7/ dveug i2l:l $\left(F_{\mathrm{T} 1}\right)$ , 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 pulls6e7iobv v gb64 herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard e v b6i76vo4gbmust she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race bega) t51ysx6d .f:cqel+d hzv 4hun, 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 hvu rai*0v-9p (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are-rzend- rr -e. in contact with each other, as shown -e-zd. -nerrr 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 1.80 m above t/49u 7 9c tqfh9vmgt 6lvy0wefhe ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits thev 97ht0 y4c m/fu99lfvt6ge qw ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictimh8 x.c.r2;8o lm xg *dr*nfabonless table are connected by a heavy cord of mass 1.0 kg 8r.c8 mm.ra* 2dhoxl;*n fxgb . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a 3zi: (;udp8s/l79hnlnzo tyv: 5$-\mathrm{kg}$ 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 sfp83g vui0y0start 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 acylu/ 2zq2 *6w nex4w cconj:a;celerating at 0.20g. What minimum coefficient of s6naqnlwz4* wu/e cy2c;jo: x 2tatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can unxotmknck 2gf.e 2 455rh js:,ndergo if the coefficient of static friction between the tih .o:,fe2xrkk 5 nm 25scnt4gjres and the ground is 0.80?   

  The coefficient of static frintdzvhj; 2-t6ction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car park 2-njt 6dtvhz;ed?   $^{/circ}$

  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 )y/m v(qzypb8d g z.x(-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 onot4, f07b yvim+*. d6gcqz fxu a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a yq4f/9m d b.fwvery high coefficient of static frictionf49 y dmqwb/f..

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 fricti aaovwan z8 4i6vicdt. wk/63 4ag0w+don 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 largzy j 9.,tj5mshj7s /epe a mass would box A have to hhpj ms ej/zjs75. 9,tyave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slideug1gl x8v(xj:0 :9fxb-j1oq+ l ssiibs across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impa:xbgq :-ljfis1io( 9+ sgl0 jvu18xbxrts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contac:tafd-j0j y4kt and at rest on a horizontal surface (Fig. 4-54). A 6f0jdja-y4tk: 20$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fg(ml0 z7)dffx / :*jfhu+q iwhriction between the crate and the be qf )hu7xjh g/i(zwmf d*f+l0:d 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 worry about parking your car in5sxd*z-w gf e51 ri-pn your driveway, which has an incline of -5- 5 x1wer* pdizsgfn 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 g+wyaxg 1)8oi ;c, rxowith 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. 4-55x,uk .p9lvm8g6b 2 om0kq by(f lies on a plane 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 initiax4. ep1qyyr; z-:; zdqk dmhh;l speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the v,j k/q0f4gdfsteepest 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 against3hqnlgll0ba eb:l*- cz,1ku 5 a rough wall by someone pushing on it with a fob 3lhll lqe1 kb:za*c0-u 5,gnrce directed 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 bi*ckl , wm :lw1g5tr*v5ro*yt:rdj3 dangerous projectiles as they melt. Conslwl5 cr:*rt m ro3byt5v*j:w ,*g1ikdider a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum s 7e::xdq mr lbki(4 fk+kt,j2gtopping distance for an automobile traveling at speed v is equ:bqdrjm2 ,xlti(kk47 + :egfkal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when hle aakh 94k+6the driver decelerate +a9khk 6leha4s 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 sp9e 3mbsa,*f 1u 5yxsbok94edoeed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to the pactz*twx5 + yy3yt8ft:m :-ffs kut3y;tking station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the t ty t+m8t-yfxufzf;tkyws3*:3: 5 tybelt 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 oxm)h .a61 u2 +ppztmmzzk *k)of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a y7f5f3tt4oo krd2-t 7jma f m3 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 heauk800os6o qhwf 1+efirt, at each pulse approximately 20 g of blood is acc8fki 60sfe q1 o+w0ohuelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash ivljl- l8/;lhmncq9l( f the deceleration is no more than 30 " g 's." Calculat9nq llh-l;vcmll/8(je 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 pr t1 hl(./tsffp 8apn0/0ey cbjoduced by an earthquake is a , and if an objectn/styj f/pa .b0e 108hlft(pc is going to "hold its 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 thcqn)io-x1 kjsl,/gk;3v x d,ze 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 that car assuming a levzc -k )/so,3,1xg qklj;nxidvel road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 meanhfob a;c nbwd6ds ;+(+s that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55bdwbf;( +ads c;o +h6n 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 t/8pc/wna r1 puhe Leaning Tower of Pisa and falls 55 m before reaching the gr/wac18npu/ pround with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady spe/sj i6, vzfz/ued of 12m/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 u/ifzv,z/s 6 jif 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 hisdunzdf2gf69 35 eo/ nio6if-lly portion of a city. An imporifnu/f 95-d3is6zd n2e gf o6otant consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, danggpsq4 nsg* ; wldw-s28les 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 msn s-s;p4 w8* g2glwqdakes 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 conn:slh 6q9k+pf(rion q :ecting differe :r6qq+h9i(ls :o pnfknt parts 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 ne(yv49bjf(h*t+txrfpbz 70 8m og7c o reded to lift the piano (mass M ) using the pulley app7frv7j(4ochzmgtf b+ by0 9t8rx(o*p aratus 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 3.5;y2tx ,2k79sjq6 e*ekzu zrasx a y50n $\mathrm{~m} / \mathrm{s}^{2}$ 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, (kpqwt* / : (ir9wjvhsan engineer considers the follow(sq( w tw9 */vp:hkijring set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a qgz+6jw bl/8y 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 safeq0r(( bp e(vfe 1x)dxiuhu3* zty 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 dx((h qie)1r *(30 pe uzfuvbxin pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a q 33o0rl yb(go2qj4xr" 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 bu0-w2ke;ma(p)j qlmt*nwf+i r ilding 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 asdv5n t0fuxmy*;rw9m:fi 3b3qj3 gd/ qcending an ice field inclined at 21.53jb*g3 xvntqmqdy f:iur/wm ; f903 d0$^{\circ}$ 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.