Why does a child in a wagon seem to d8adbk5)4t zk )myk)fj.rcg c q,+a5cfall backward when you give the wagon a sharp pull forwardykcc+jk.)qgcad m ),r bk4f5z8ta5)d?

A box rests on the (frictionless) bed of a truck. The truck driver starts the3g)byqb yak-lio 7h vwr9,v ;2 truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of th )wa v32ky9i 7bvqlr,bogy;- he 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 objectugobe1i95vf mr fe9-3 is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can or ,/1jg z,8 vq,iljreit have zero velocity? Expll/jz,v1 ,gj8ri ,reoqain.

When a golf ball is dropped to the pavement, it bounces back up.o/z xojl 9ifi1 bf hl2( c6vkxz0;r26x (a) Is a force needed to makehxjzx/ll9k ( irv66 ;1oo2cfix 2bf0z it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lak/ nvrhw.- +k(ig(cylz e, why does the log move in the opposite n.r lhy (zi -/kw+cgv(direction?

Why might your foot hurt if yhthktn9,9h (oou kick a heavy desk or a wall?

  When you are running and want to s2p9 p*sje:6pc u 04alwn+seeh top quickly, you must decelerate 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 running at top speed to come to ressl:phu 60ns+ceje*w 2p e 4p9at.    m/s$^2$

A stone hangs by a fine thread from the 1*hg j)/l wrg3im*tvrceiling, and a section of the same thread dangles from the bottom of the stone (Fig.wm 1i3*)t/gr*jghrv l 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 as great as jopr;u,91 jvn that on a 1-kg rock. Why then doesn’t the heavier rock j,9onj;ruv 1pfall faster?

Would a spring scale ca7gic m4 vpftf4q /:ug.rried to the Moon give accurate results if the scale had been calibrated ( :t qicfgu /gfv4m.4p7a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attc f) +n(7 msp.kqzjp4hached 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 acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Eq)4 +m7pzfhcsj .k( pnxplain.

When an object falls free 1wk.nrx +bj+uly under the influence of gravity there is a net force mg exerted on it by thuw+r jn.xb k+1e Earth. 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 a 10-kg object when yp1dfm52m sve6 ou are on the Moon with the force neededf m5pdse 61mv2 to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s thiomy; g eh;q7-.m8jbdgrd law, each team in a tug of war (Fig. 4–37) pulls with equal force on 7 -jmm;q8ge by.g dh;othe other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceriesqczf8j1su t4 gm(c w4+. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what objcq wm(j4us+ cz1 8t4fgect it is exerted.

When you stand still on the ground, how large a force does th 9eu;6u;f qme wjgzrlzo35p3,e ground exert on you? Why doesn’t this force make you rise up into the ,m93zl ;r u6g jze;5ope3uf wqair?

Whiplash sometimes resu)2zwbupg gyo (25nc d,lts from an automobile accident when the victim’s car is struck violently from the r2no,ypzbw2 5ugd cg( )ear. 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. emp:i66wut7m When the truck accelerates, thew:i 7m6mt6 peu crate 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 slides up a ramp. After ld;l5cttd-fq5676b )e j3ilwc+a p qf; d/gspthe block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the 5p;t5gd llw;d7j c spffd6+q- c/6 iblate q3)descent than on the ascent. Why?

What would your bathroom scale read if you weiydfohk1c-g /xl. 2x+f2j47gsa olk 8 ighed yourself on an inclined plane? Assume the mechanism functions properx kl7 oyi822o4/-g1csfxf.j+kld aghly, even at an angle.

  What force is needed to accelerate a ztais:.kr)1 kchild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bxvv lw 7rd,z8fio*9e/ike 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 withstand if it is used to accelera) grd(54zswi qte a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of jn ,mmxh)zv9fowcl8 -c+f n+;a $76-\mathrm{kg}$ 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-nf:dy ajd .u3-kg car in 8.0 s if the car is traveling at 9 dyduna .-3fj:5km/h? -  

  What average force is needed to acceleg8*u0.p54x 3 ms lwf* +zf8 vtftfzrgorate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel og0g.lz uf *358 8z*fvmos4p frfxt+ twf a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration ofs:g bsz18l w9a 2.59s8g:w1lbza s $\mathrm{~m} / \mathrm{s}^{2}$ 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 quacmx, 8x0 h14x:e lzj1dj1i wrurter-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 5*b1 jhokn0ww ) is to be designed so that the maximum acceleration is 0.0680 g . What are*5o1wbj whk0 n the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a most02w7vkd ig5ybszc516jjb4tionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the persokw j btz45bs cs56vjyd1 02gi7n’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengtq v+hcsudxt)227 p x hd- 4jz6ua:g7njh of 21,750 N. What maximum upward acc)htv -ajcdu+27:sn hp2476jquzg xdx eleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceler kcf9+q(t yl1y 6zcq(9yii )l jp8s.cxation of two falling sky divers (mass 132 kg including parachute) whckl6ps+1xj f tqq iy.(i99 (z)ccyly8 en 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 xa0+cnjqqn.zgi+1h2 roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates overxqq+ nig1+an 0cjz.h2 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 the box run(q h3 gn8je+vns 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 the8(+3qgn jhnve 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 basketball player mp 3k.6 fhzo*kzuq;d,e0 p(s)ayuf 3y
(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) ar,-yd uz2fzr 1 3:*uh, rg4xfbdhb8yzt the moment it is hit by the bat, and again (b) after it has lezurzy*f:h f 8,h4rb3 -xduy bd2rzg1,ft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direcx l ve:nt/(c 7v3l:hcyfk) d(rtion. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Ilf/(7dy v xn l: eh:clr)(tc3kvlustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally+ b3)p**ncz6phk8jee 7by xxz between two buildings 10.0 m apart. Then3yj6h b x *c*8z xppk+b)7eze 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 co m -+vjk2huufnmy 4w6g: g/4uord 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 1ol5/,jkd2fcbm i r srcny; ,/,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, Antarctifvr;w7 . 0gfdxca, as shown in Fig. 4-46. The sum of the forw7.f x d;g0fvrces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 c , n cs,5hyrthu6g,7vjars of the same mass behind it, Fig. 4-47 . Determine,5y gj,7vn u6,s hrcth the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls1 hy r4hsm;gax5hzi9p4r)lq, herself upward using the bucket-pulley apparatus shown in Fig. 4lpq19r4)r,hi yhzsm5x ;ahg4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 4k2/tamt4+z6gke+85gxxp ;p wtw loi 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass t8-wgzy*5njc $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in lr 1qle6cld*d;*mjs- contact with each other, as sho1lqs el-*l mr6*dd;jcwn 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-y,t6m av/rs.b 52 are each initially 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 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 pula/. v6,yr stmbley.]   

Suppose two boxes on a frictionless table are connected b97vn sr9rp )xrgc8h k,y a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig.g7vr)nr px hk8sc 9r,9 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 35dc1 rbw o kgjczl(1) 7wv7yq- 6:su9nr$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a -dts)s 5qf 0yw 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 acci2 4*jqtzt-klelerating at 0.20g. What minimum coefficient of static friction must e2 ji*qzl4tk-t xist between your feet and the floor if you are not to slide?   

  What is the maximum -gba4;hhtswz(v1 +xe acceleration a car can undergo if the coefficient of static friction ;ez-1( hxsw4 +tghvb abetween the tires and the ground is 0.80?   

  The coefficient of static friction between har q 7h8ro xrk3; oq1zz :kw5c-e)1iabjid rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car pawz a 8q51 e rok):zib;-hk3x1oci7qjrrked?   $^{/circ}$

  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 -4q2i61 21e ae0nsll5g qs tnwm8.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ro ;y9; ,l5 hmrb*zkuxwkugh 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 af4zp- a llu,kf(qw: )zn asphalt surface have a very high coefficient of static friction. q- l k(,fa:z4fzl puw)

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 kineti- b cop4kid3n8c friction 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 (Exkk+)i 7q l+sq,f)qllmample 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assume +llfqm7q ) ,qls k+ik) $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fl8:rxrreyyp4zez 6-* lgn3,wjoor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts anz3xrj *w4y g 8eznr,-6eyr: lp initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact andmd*-xiqm 1fluq/999h 0lhmgs at rest on a horizontal surface (Fig. m hs1l9*hm/mix90qq 9lgd-uf 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 coefficient of static friction ynu(h:12s4( lofd riqbetween the crate and the bed of the truck is 0.75. What is the maximum rate at w:(2s qly hu14(d ifonrhich the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in you lxqhzv u.1*mya:8j4r r driveway, which has an inclinl:h*x uqa.v zjm48ry1 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 s l zs4+hftswgah82 8o4lide 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 zedx2jf05 p e2a 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 initial speed of 3. duicihq . q/rz nw3/.p,zg(+w0 $\mathrm{~m} / \mathrm{s}$ 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 t// kbu) ygtmn+he top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a85fu j y.isjy+ rough wall by someone pushing on it with a force disyj.8f5u+yij rected 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;/ bx2ir7dg ru dangerous projectiles as they melt. Consider a chunk of7g; rbd2xuri/ snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at r zo*-wjr6l5 tspeed v is equal to*rojr t6z5 wl- $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 t tm.fh2fep;mj q 8y,q,he driver decelerates from 45f2 . ; ,8qjhq,emfptmy $\mathrm{~km} / \mathrm{h}$ 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 givi g+dus:o+od5soh 20gen an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to njs+rox0l); ythe packing station 11.0 m away. The belt is initially st nlr0o;xyj) +sationary 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 kine+)cxi7z nn5vttic 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 6. ia2mp; .ybpi+r*6refnoo.w /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 eachhj2g/ + 5/zc*g0zpfo dr 4bfsf pulse approximately 20 +oc jrsp2gzg h4f0f5d*/bz /fg of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an auta)dh.cvn.f+ i omobile crash if the deceleration is no more than 3+acv. nd .if)h0 " 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 produq:wiapkbvb55 l p1*s4q)dc k 9ced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of stdk w5b)*qs q1:ibvlc9p5a kp 4atic friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two cars, memfwmz.)lz - +ckwz2v n) 4ld7iasure 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. Es7-wz2+w. ndmvi4zl m))lckfztimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 ;.m)dkz,u lj. t2ka oghill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction. mk kjglu,2 .dt.z)ao;  
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and ( 2+nrubn8xk z6psunib;,mc1 falls 55 m before reaching the ground 2+b8nmu 6kb, 1nnp;c xzsi(urwith a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s4 rhaprc-fh3p(4w hxs7 uiw tfv 5k8++ but enters a muddy stretch where the effective coefficient of frihrs8+w wprcxpv47k3 fu 4-+fh(tia 5hction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of vesl yihh 3 xg5c* 0p6g.5a6 ;j nd)jd5qesd.wa city. An important consideration is how steep the roads can be so that even low-hda0ge je6) *scvh5qs gn.dw;yp xd3 .j6i5l5powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles he)8l2y0 qr y-zng6x hz9fvix1pr watch from a thin piece of string while the jetlin1niq-xh0zgy6 ypx2 ) f l8rvz9er 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 arfepby,(lh0ru)/l7 -k .zezs r+jetf 5e to be several ramps connecting differebllzhu fp,) (07 yk5 rj-zf.resee +t/nt 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 needed tojkj2pyau)o893 hv- yrw( )daz lift the piano (mass M ) using the pulley apparatus sod y)2 8k) aj9h-y j3v(rapwuzhown 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 rpajbgve+1 (7 co +n1gat 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-restrv:;(yyn , rwxhaint chair, an engineer considers the followixrv,;y( nwyh :ng 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 traiox15n nel* w95m az0osn has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes t*jmr .rz,z 70b *ajbkof 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 freeajzt7jb* mz,0b .k* rrly 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:q7hc r9nyqih;o6vd9r, )hf j 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 allow 2an15r+n 5aw jed+km)wuqd u3ed 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 asdm la9kir1oe :y1gxi07x2 ) lscending an ice field inclined mi) dl92 :1ysgxlr1o a7ki0xe at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.