Why does a child in a wagon seem to fall backward wh8h q)q(fwmpc lw ny7bc/p)m k36b.bf9en you give the wagon a sharp pbm()f8cl7m.fk6p/cbb39 y q)hww pqnull forward?

A box rests on the (frtfytm+ 5:m1 hzictionless) 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 motion of the box, in terms of Newton’s laws, as seen (a) by Mary 5zm htyt:f 1m+standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are n7ai8e t:oi m9xo forces acting on it? Explain.

Only one force acts on an object. Can the object havew71gqooz g -t) zero acceleration? Can it have g-qw1) tzo7go zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. 3j4: dh6b ::io/yvodhuk9is l(a) Is a force needed to make it bounce ba3h :y9: hkjl/bsioiv :d o46udck up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log xtvt j5.tyl 9 6zlbr /- p;s*dq+v1hfqmove in the opposite diqhq *tv6y/fbvt;d+x51 ltjrl p9z-. s rection?

Why might your foot hurt i(tm 5kgp1 cw9hf you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quick*:nn6bh m/ci sly. (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 n ch6 :imns/*btop speed to come to rest.    m/s$^2$

A stone hangs by a fine 2wo;oz9 mi k9sthread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If iswo929mzk; o 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 that on a 1- (xwt8c6pl6pekg rock. Why then doesn’t the heavier rock fallp6 6epxl w8(tc faster?

Would a spring scale carried to the Moon give accurate results if thjjqdnpd)f:w -+ pm. p/e scale had been c wj/jd.mqpdn+pf-) :palibrated (a) in pounds, or (b) in kilograms?

You pull a box with a const czjz)g-9c6f w ss7ch ;ac6j;rant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same forc6- jgs ;jzahcc)sc79c fzw6; re 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 freely under the nku:lf2 twotfu2 )+j7influence of gravity there is a net force mg exerted on it b22lnf o)fut:w7tk+u j y 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 foe yvqta14m;6ckx:rvjg 9-owji0h l4 1rce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare tei0 t64 gryxj :lwvokc1;9ma jq- 4h1vhe force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls f.nbkul4 pq1j. .nw)ywith equal foqnn 1 bjlwk. )pf4.u.yrce on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Duyb /k iu9wk,3escribe 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 objeu ibk9,w/ uyk3ct it is exerted.

When you stand still on the ground, how large a force does the grdv.9 2 :4jdgrscru0ihound exert on you? Why doesn’t this force mai0:d94jhr. 2du csv rgke you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’-v :, s21gvmui27 myiz*phvnm*c 7 xucs car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it realpc1mg * icnh :zm vu2,iu2*vm- 7x7vysly?

A heavy crate rests on thyc)zh xgw 8 p1mfx(150fzms8ve bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What wgzv m8sxmx()hc18f1zf yp5 0force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reji4y(3a5 exy paches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Whyajiy5pe3y 4 x(?

What would your bathrozc j)fa 7s;yy)om scale read if you weighed yourself on an inclined plane fy;cz)as 7y)j? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a c 4su9* j9yodwrhild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerate+yyt7*zon/ 1ka dx1ssv;q2 zts a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wi j*.uztgr5 p a3kf5h.ithstand 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 ofh5phwq(qckqd42kg d6b +: f z- 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-kg car * w)nq.ha0 gyuin 8.0 s if the car is traveling at 95km/h? yw*qng h.)au 0-  

  What average force is needed to 7h7 em;ew:lz qn+fm2 3eaubj( dhe 9:raccelerate a 7.00-gram pellet from rest to 125m/s over a dista;23nlhamem7q::z d ehbe r+(jufe 9 w7nce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water wittagpb;jx.b x ct: 04u8h an acceleration of 2. 4;:ub0tjca.xgxtb 8p5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 co7bembv w0 4gv+ver 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 ) is to be d:koe 5/(b9z skenfi j49 y y9cgn6 gob70ad(liesigned so that the maximum acceleration is 0.0680 g . What are the maximum and yg679 ba y4ieofg e5l0(nzkj99/n o( kc: sbidminimum 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. ( (2myyb-h nbnWhen the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration b ny2(nbmh-(yof the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supportingf2 tgve78kf.l(iui : s a 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elfg7fsii(2 te:8. klvuevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky di)e.uf ;0ygrz +sw2v0ukp) z ozvers (mass 132 kg including parachute) when the upward force of k+02evf )r sguzuwyo0z;p.) zair 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 roof6svdf ; zvry-3fwy5nv gd:/:)y( e epj of a house 3.9-m high. When he strikes the ground below, he bends :d g y e (;r v-fj5:sy63nf/vwv)dyezphis knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically u- 7dbd5diijb,ywhv4- pward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that t5vj, 7d-y b4wh i-bdidhe 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 ba yv f2d)9hs1hla;x 1twsketball 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 1cs.sk /jxno*f p21(xo g7sewthe moment it is hit by the bat, k.ng s e2fjpxx*s11 s ow(c7/oand again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 6500bqmazw8 .7dj -N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate youw 87abj .0dmqzr answer with a vector diagram.

  Arlene is to walk across a "high wipwv)d9fz i66)vtfg v -. lskd)re" strung horizontally between two buildings 10.lts-) fip z. )vdkwvf)6v gd690 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket isz(u3m7e bvn .y 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 1;d1v:h: n0 cua.km awo4.0$-\mathrm{kg}$ 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 locat*1 z2uo;k s81eaizndqion at McMurdo Base, Antarctica, as shown in Fig. ok a;zzd2uni e 1s1*8q4-46. 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. 4-47 fz0ly lj 4/9cw; :ctay. Determine the ratio of the tension in the coupling between the locomoti/w yzyl09a ;l tj4ccf:ve 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 upwafte l:m3z1 +veaja,7qrd using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard mu +elfqea z:t v37mja,1st 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 iwv;1deg/0xffr4 mhb5 fg5e /n, 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 o(mmu6bh/72s phoes5l,6m b h block (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 in contact with each otherc4dqd 3j;sq,h5 syb6h, as s3 5bqycd,hqjh6d 4;s shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the ground, a, 8bb qjvuij2j9 j1f+snd 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" speq1s8fj+ib b u9j ,vjj2ed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless 3p .i/gu0km *w*/ ei bgkzn7sytable are connected by 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-bo */73we npgms0gk*yk /.bizuidy 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 *)( fqukjq8uj up g*4s35$-\mathrm{kg}$ 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 aey,gtxfjey 9t na v.0o; dd9/8 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 ahq b y/3mm,1n(nk.it a train accelerating at 0.20g. What minimum coefficient of static friction must exist b1qnm/. ,kt b (yn3hmiaetween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffici c w-zd dg ,qotheb),z5,bk++ient of static friction between the tires and the ground +c)+,d q h kz, w-gitbde5bo,zis 0.80?   

  The coefficient of static friction ophq zxoo3/9/m6zik8/ akk*a between hard rubber and normal street pavement is about 0.8. On how steep a hiq/az3m */z kk6p/ioxao 9koh8ll (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80+o/hp34e1h(dbsl os14tknk e $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough i j eo jxj,:a73vwzt15 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 very ii6d1belr5:vhigh coefficient ofde5i6:l 1rv bi 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 frict.aj4-2c, rfa,jmos l ryz5x6hz2dv(cion 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 (E q/-drfe9b)9w:wb bay xample 4-20) how large a mass would box A have to have to prevent any motion /ywwrqad b9 9:e)-fbb from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it gov8i-dz/m dbe9ego m 27, given that the coefficient of kinetic friction is 0.20 and the push imparts a e v7 m9/bmd-gozei82dn initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and ayyt. pze- ky(/t rest on a horizontal surface (Fig. 4-54). A 62 kt(zp.e/y-y y0$-\mathrm{N}$ 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 zd- --(fpknkdcoefficient 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 decelerate and still avoid having thedzk-kd npf-( - crate slide against the cab of the truck?   

On an icy day, you worry about parking your car ins .:+e megy(3iqe 3nowr:pr3 e0rdtf0 your driveway, which has an incline of 12. gwr0r 033e(:eeoityq r p:n3f +esdm$^{\circ}$ . 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 vy) a6kj8o;cs slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 e1lf ) e;tml(st/b (ynlies 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 initial tzkv 8ibqivn54c 6ofn :t-/8sspeed 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 steea zjp m67/9fay8dka( vpest 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 aga 0;tkqx7xrsl )inst a rough wall by someone pushing on it with a force di0x)lr q7xstk ;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 slipp 4p:em)(u4 jwcdeuhg2ba 3x r*ery roofs can become dangerous projectiles as they melt. Consider ab*eu3 g42e jw)(xch mrap4d:u 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 stopping distf;1bg.uoeh:wf. umt;/tekpm* (h,ypance for an automobile traveling at speed v is equalu.epbu,fm;.ktetp 1w: myh(gof ;h /* 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 sli7c )k2c va8 n5svrzah.des forward on the dash when the driver decelerates from 58)v a.k r zcahnv2sc7 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 initnsj. tx *y;: ud1qnhb*uk 2yo.ial 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 the packis+a bk) q6uu44c8lzkw ng station 1 zq)6 c4k +ka8wsluub41.0 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 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 between )uae;vteap/48 ghj6 p$m_{1}$ 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 thb a9rphsysk15vxt(t /;;+f g ue bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified ;(:p;kjfzyu/8b wzuirsq-) umodel of a mammalian heart, at each pulse approximately 20 g u ukuz;fs(zr) ip q:;/b8y-wj 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 automobile crash if the d8u,4 j pb2qmvveceleration is no ,8 4jq2pvb uvmmore than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced m:0g hdhh1fq ,by an earthquake is a , and if an object is g1 0hf,dhmg:h qoing 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 the scene of an accident invola.0z ry-vmx1an4n1lo ja 7nh4ving 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 z-4 nalj0nm7h xr1 1oany4va. is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 ) 4bi5n yyqj1l)6l jha9v zw(ohill (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 afylj w5y ov)zi94b )6 jhnq1(later 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 toh-g m.x)rv9,b- zs p,bn,fuxsp of the Leaning Tower of Pisa and falls 55 m before reaching the b,-,).f su bz ng,p-mvshx9rxground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/z5lo9, osmr:f s but enters a muddy stretch where 9l,zrms5:ofo 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, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a cityv*5khlfzigx9bm ,5o 7. An important consideration is how9gihokxfl57,5 *mzv b 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 thixees kb c+f773n piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle ofebfc 3+ks 77xe 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 ramv l ox6.o,l8az7*f luyps connecting differen l7.8vozl yaof*x 6l,ut 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 to lift the piano (mass M ) usii) yh yso*x;cre(e5:i p:0h f2ip/nipng the pulleyfirh2pie:n:px s(i5pc0e y / )o ;h*yi apparatus 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 acceler/m3q 2u4b: v.q,ezgqzteb: ax g;zln 7ating 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*7rlrtt6q*5(-vg tr,c(nrm 7 z slg bv-restraint chair, an engineer considers the following set oflsz*gl7r6* (rm rqnr tgbc5(,vtt-7v 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 mq swkj1+l;tc 4eg(k 8a 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 lengk;d1i +gtmfc) th. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weigf+dt;)igk mc 1ht will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a kpsh6j*p 9 2n un,vsb/" 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum spp wel:li qu/ea438/6( cicivc0nqt 9jeed 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 climbersiub y8dv+5 hew.al4br ;o:)dk who are roped together are ascending an ice field inclined aiwyvk.ehdr :4do)al+u b8; b5 t 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.