Why does a child in a wagon ser 9.qqt2j 6:xdnf o+ca/sg8spem to fall backward when you give the wagon a sharc /p2f9+o.:qjrss 6dqtanxg8p pull forward?

A box rests on the (frictionless) bed of a truck. The truck driverz8jd5qq 57 klyy 5cw,p starts the truck and 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 Chr5kjq yzd, 5 c5ql7p8ywis who is riding on the truck

If the acceleration wk)kfw8 aro/ujop+ aym o51,)of an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acce* 2ae4cpc/e3lly gr b(leration? Can it have zero velocity? Exc4 ebla p /*grc2le(3yplain.

When a golf ball is dropped to the pavement, it bouncac3 k3 *0zabqc (ozij3es back up. (a) Is a force needed to make it baa33oc c biz( zk3j*0qounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log movefn6yed(n s): r-gizs/tw)zh 4 in the opposite direction?d(zs )6-iw:eg 4sr)/ty nhznf

Why might your foot hurt if you kick a/h+t +uovrj j0bp-*6jk3ttjb jd63 al heavy desk or a wall?

  When you are running and want to stop quicd5 x efglf);j+kly, you must decelerate quickly. (a) What is the origin of the force that causes you to st dg+l)f;5fjxeop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same th;yt x4e2ly59-vzutvcread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thr x4yyvleuv95z-t c;t2 ead 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-kgq7 q ,dkml4 f6n-q;ely5eax -b rock is twice as great as that on a 1-kg rock. Why then 67k4 xea- 5lqmnqq;,-feylbd doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results ifsqtprdr9 ov( . +ik72v the scale had been cr7p. ts2qd+k(v9 oirv alibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an hkr7w3 cbza6 s crbu4f+l2*/mattached rope held horizontally. If you now pull the rope with the same/a+ 4ublk6zw r scf23h 7*rmbc 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? Explain.

When an object falls afi(. i.t, (nbh09 tx,nf fjvnfreely under the influence of gravity there is a net force mg exerted 9nf,x(j .fni.tb tn vf0a,ih(on it by the 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 you are on tvdv878 rs7 vwtr 3 br00f*axnrhe Moon with t3b877 x0nvwr8* 0rrdv vfarsthe force needed 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 thzg yul fiw-2 )m 8w(2ej:aojxww--hg4ird law, each team in a tug of war (Fig. 4–37) pulls with equal force on yz-i :fo a4h8jjw- gwlux-(g2)w2m ewthe other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe the or*djxnwz7 mzqt;2v-zfx6 10 “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its -jw q7mfxzzrz; tx*60o1dvn2 direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on tm 7qbe2fr1y1wpp ,e1j:ox i9hhe ground, how large a force does the ground exert on you? Why doesn’txp1o e1w2f7h epijb,y9r 1qm: this force make you rise up into the air?

Whiplash sometimes results from an autow*em1 wgswg9e(z t,g+mobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to 9 (we1 s,gemw*t zggw+be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a oi 1cn 1 amg5k p, 5-ererc1h38xu4tndflatbed truck. When the truck accelerates, the crate remains where it is on the truck, so r15 4ed 5 mo,x nphciau8c1rk-1ne3 gtit, too, accelerates. What force causes the crate to accelerate?

A block is given a push so tha(s*4r6 1bymywbaczm ;t it slides 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 ty *b(1 bswmry; zac4m6he ascent. Why?

What would your bathroom scale re7t q ni3 :tk.,u bqbwn.5fvt5oad if you weighed yourself on an inclined plane? Assume the mechanism functions properly, ti oq,.wktf3n5q bvb:.tun57 even at an angle.

  What force is needed to accelerate a cb (n:nx;obpb :jj,gk/hild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates ,2 szy.e7c wjnd-ty+ba bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wi.+(vsrua xcb t:,tw2tno z d eae4+,6m v0eeb2thstand 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 jj 4ntuzh*q9mj4, u2x $76-\mathrm{kg}$ 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 i5ht*f3fk /.x, yfy8k/ z apfi5nqea p)f the car is traveling at 95km/h? -a5)/k p5xf.n*pzf/y,fkyt qa3i e8h f  

  What average force is needed to accelerate a 7.00-gram pellet from:wvgds q6na;v vo:djs257e p 7 rest to 125m/s over a distance of 0.800 m along the barrel of a rifle?s77 w6dv5oj2deavvn:s; :pg q   

A fisherman yanks a fish vertically out of the water with an a) w -ucn3ci6uwcceleration of 2.5 nucw 6u-cwi3)$\mathrm{~m} / \mathrm{s}^{2}$ 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-mxh x u8.q/fjx9ile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be /+ :l5i0ijix r hi-fj*y1qiwzdesigned so that the maximum acceleration is 0.iq j/i+yxizirilf :h015j- w*0680 g . What are 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 motionless elevator. When the elevaj05 gk 6vw *-qsn/uegbdqp0g3ru (d *btor begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and b-b60 k q /g*jgq*ne r0uwd(dpvsg5u3find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. gl e/ccb8m ,z;vb xh:enl.;,qWhat maximum upward acceleration can it give the elevator e ;v.: bcxz/el,h8blgn ,qc;mwithout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (m)8js o8bm od5r :tvnf7ass 132 kg including parachute) when the upward force of air resistance is equal to one-four7n s r5)fv jt8o:db8omth 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 hou,b 8-sdsjjdtbg(x*8lo k09z use 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerabl- 0d88dxj kbj(uz*t9goss ,tes over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied toqy*xz.z34 e cn the box runs vertically upward over a pulley and a weight is hung from the other .q3ye*xc zz n4end (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 baskal nuwr20*cp* etball 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 /*. kttnvz4+fl 1u:0iljbxi ris hit by the bat, and again (b) after it has left the bat and is flying tit+ b t 1nrz:i/ fk0*lxl4ju.voward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forc) snic,p37 u * *ql ijb1ul4 b,aur6ee5iu4cgje must be exerted in what direction so that the resultant of the tw*euri3ls1i6ic7, up,gj4cb u u*n qlebja5 ) 4o forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizomog hre 07c7tql--zzavj + fv 5(+u2xxntally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0lcg2xz0rm+qetu+-hz7 joav7( 5x vf -$^{\circ}$ 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 masslessy,g 6d e()c1qmw g,wt)k e6cwm 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 1 9ajhdhy;-mz u/mkl)+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 vv6;:anltxm(x;a9 irBase, Antarctica, as shown x9a r i;;6nm: vxa(vltin Fig. 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 i( sti l+huy4 d e.0pwc0veo-x,t, Fig. 4-47 . Determine the ratio of the tension +u4i,vx.opdlwh (0 ce-0teysin the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward usi)xnc -rs.g+cf( g40uyw ey *qkng the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she k -ys *f) ugy.0c4g+crxq nw(epull 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, h*wn ve7 g,+sea 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 by/atizhh(r / 44n-u p )dlc,hzna35 tclock (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 ar6qvlb q9 l 8d-giy/fh0e in contact with each other, as shown hq9y 8lfb vqd/i-6g0l 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 1d2bugb*q-/ v2sslc7: yk b r0c.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 systbyb0 k 2s- b*udg:c/2cvrql7sem 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 pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy j: c2+s p0fifbzu hl7z(8/eqwse8-gl cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the fre-78sb+ qee 0fwpuh2g/ sf l8iz l(jc:ze-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 bp 1we0ohgr1 c b4off9os9t,4l)svf0metween a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 535apda76: v) qmxu wli.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 accelerating at 0.20g. What minimu; nnbhtd 84vu6m coefficient of static friction must exist between your feet and the floor if you are not to slu;tv8ndn46 hbide?   

  What is the maximum acceleration a-53trxgwj6y 7 1j- skqghi/ (b(jlzaw car can undergo if the coefficient of static 5bg/jxy-(ag(l j3z1wq i6jrt k-h sw7friction between the tires and the ground is 0.80?   

  The coefficient of static friction s w5z+j6 kne.oqu-2uxbetween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parksw6.ux2o -5+qeun jz ked?   $^{/circ}$

  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 +v/j(r5od (ki myi,gmm0u +dl-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 9c7vffj 7g9udowjr(6 on 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 u,pe/ .ei8bvr surface have a very high coefficient of i/eeuv8rb.p, static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic frictionu ss4ev.uw zt-v.ru )9 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 (Examb1rjc j(x)n::o bpxrn ;+,qwuple 4-20) how large a mass would box A have to have to pre)xu:1xbjr( npjq :cbow+; ,rnvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across w,/m f pz;ehzst7gy0-the floor. How far will it go, given that the coefficient of kinetic friction is 0.27ew m zs,hgtf;0p yz/-0 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest okuogi7;l*yv0vo 2x+mn a horizontal surface (Fig. 4-54). oig7m 2k+0; ox l*vvuyA 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 5*a8vg dkypfg/q g7 9pcoefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelv85a fy*g pqd gpk/7g9erate 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 drivewaus:-.g+sv4o5nn p0j mft om5//yp0 sol7kuwj y, which has an incline of mf ou+070 5jgy-n5skonml:4ju /tws.pv/pos 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 wc*axv l ro3hyi7mg8 (l* 7cc0e(idd/l*ur cs; ith 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 ll0v/2zc8p5l w7fuc;if k yazene,r5/ ies 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 initia: 2-vbg0heunc g4r e5zl 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 sdr0g(dsk26u q wkl :t2teepest 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 l kl u4.5/wms dxi5o3) 4kgsuoa rough wall by someone pushing on it with a force directed u/iws )4ok os 5.xgl534uml dkupward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous pecxp v vlip 1aks *b7x7+x25e,u37ob nrojectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch x 72xpebk,bcinspv7u5* o3va1 ex7+ lof $ 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 mint64s q(q xwp+i2 tpnd5imum stopping distance for an automobile traveling at speed v is equal dt+24qqs n6w (pt5xpito $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 d1hd;qadzvh cz 5ce,uh 787les 97,gmeashboard of a car slides forward on the dash when the driver decelerateg7, umz e8l,;vh7dq1 9d h7csa5zhc ees 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 gimp/n x2ilk)opg7/tqbb62 5dow * lxe:ven 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 3r d0x64p xrn.m jt(hjto the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum trx 04(d.xp3r6mjnhj transit time for each box?   

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

  Suppose the coefficient of kinetic friction betwemfe 7end19xacv)ux9 *en $m_{1}$ 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 f0w)rm-3/ ti fx+ihir0a lxo o.6;dne.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 7v 0 fpzyt)tf6 rm;g(veach pulse approximately 20 g y;)t7 0pg r(fv tmvzf6of 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 automobuzo-jfc3kpuq8)h. /dq ar3p)nf+pl*ile crash if the deceleration is no more than 30 " g 's." Calcu lfc )k. *fq+/8-p)ra3 pnqpuhdjzu3olate 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 accelerirovef fgtyfs),.,ql (1h3x1 ation produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictiy 1vofq tl3sg.rih,(ef)x,f 1 on 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 th5.qp f-y xe*jlm1lbi2e 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 level 1b p il*yf- mlxe2q5.jroad.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means blzn63z i0u40f p7z:ai2bds in .g:z)pvya5fthat for each 4 m traveled along the road, the elevation p.v)yapi 42 i in azs uf:z60:n5bgdbz70fzl3 change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falldhc2 3g7 z-n/ -rnmfnbs 55 m before reaching the ground with a speed of What was the average fogrn- 3zm bh- c2nd/7fnrce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch w/nct ojn wpma6, )gbcg0e+ 4r3m)nik(here the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so,)(jnc6g3 rcwe amg04+imtn bno )pk /, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hillw5 mq((s 5pgnuy portion of a city. An important consideration is ho pnu5q(m(swg5 w 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, dangles her watch from a thin piece of 6lz1 hqc;+vjp string while the jetliner she is in takes off from JFK Airport (Fig. 4q pzh6jv1lc;+-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 r /xe6nno6 bs m1yir9v2amps connecting different parts of the strmsiy1 69 eno 6nvx2b/ore.
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 (mhij s oi1,i7br 5 5vj9gm7-jyy 6unms9ass M ) using the pulley ap- j,yb9is hmgi9io6y7 jsj rvn5m17u5paratus 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 accele7)4jzisota +wcf / g3lrating 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 c* idh)12f7hhufn 3rj ronsiders the foll7 2r1jrhiu d3)fhh f*nowing 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-c-i,r0 cgw x .ljx46 wmbwmyct 0/6fwp;ar Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Ko4w; ckiw 1ktdjzege24zl5g e6a*4j8aren'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 te4k12g;d 54cazkw*zj loe4 wg86je iconstant, 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 u0sf s1n j0uhgxu0,vn;sing 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 a32gwqzt4s hdkm1ti 71llowed 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 who66(ji9l,re 9jo 5rv.ri *rg-hrijqqw are roped together are ascending an ice field inclined j6j9w* hir(qq,ivrrli6r-og9j5 r e.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.