Why does a child in a wqr.n(c* fyca) wn +gyox6x,3cagon seem to fall backward when you give the wagon a sharp pull forwar ,f3cx(cy6 o. awngn+*rcx )qyd?

A box rests on the (frictionless) bed of a truck. The truck d.l- 5z*a st*+rj lfgy9jk;nbariver 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 tru*rjjg z *.saynlb9l;t+ f-ak5ck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Explain.sbje:i7 0 wfjb*- bf8h

Only one force acts on an o* g gcq6 a:amu1u;mj4object. Can the object have zero acceleration? Can it have zero velocity? Exp1m umquagc *;: o6agj4lain.

When a golf ball is dropped to the pavemenj)71( 8 jtbus as:ctmyt, it bounces back up. (a) Is a force needed tst: a7)cus1tbj 8 (jymo make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposi0m6 59qvgms5pi*em cf te directionemi9m65q c 0psmvg*f5?

Why might your foot hurt if you kick a heavy desk or a271hmfk6-aiy.t ,fjwm l 8y lr wall?

  When you are running and want to stop quickly, you must deceleratesj omomrj g: *mt.mx4v5s /n)( quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of m*x(nt r/5o4gsjmjm .omv:)s 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 86 fvpm0f:jna5s nzmi,g,usfl3 l5/b of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is 6: zfmin ,pa sm/s5lnf,853bu jlvf g0the 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 0)gojm0; g xui1-kg rock. Why then doesn’t the heavix;0mi 0og uj)ger rock fall faster?

Would a spring scale carried to the Moon give accura:;pr1 7gzm:pru 8x9g wx*uxac f47jxste results if the scale had been cal sxw4:arg7x pmpj9*xz 1f uc;7 xrg8:uibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a fri(f-v6ksq3.i*uard+k k)e m phctionless table using an attached rope held horizontally. If you now pullrude3h-a +kk ps vm.i ()q*f6k 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? Explain.

When an object falls freely po jaamst,jg 44b((i(y6c.u4 x mhyn-under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exertsmpby4 (c,(itoxgsj a 4n6 u4.j ym(-ah 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*:s4(7div ),q p6sesikxu/tedcnpk 7 you are on the Moon with the force needed to lift it,nk(qk tcs7p:sddi*p x e7ui/sv64 ) e 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 third law, each team in a tugeov c/m mj g59 besr m3v07,a5a*1xrku wdp1/r of war (Fig. 4–37) pulls with equal force on the other team. What, then, d,j x*rmpe07sdrg ou15r9cmv3 k 1ae/wvma5b/etermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. De88tqr8a: /hkx3;an,dll czl lscribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on wa :,/lznrl8dl88qkcxh;t a3lhat object it is exerted, and (d) by what object it is exerted.

When you stand still on th): ef*xrziwlvw jb ;)6e ground, how large a force does the ground exert on you? Why doesn’t this force make you r ;6ezxjvbflwi) :*r)wise up into the air?

Whiplash sometimes results from an automobile accide;kbwc g9 .5ssent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown ba.s5;s9ewgcb kckward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whennp7j m27k jx0fr ntj 0e(.si0d 6plla2 the truck accelerates, the crate l6en2l7 2(dafti n 0p 0j7xj0 smjk.rpremains 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 the bojj y iqp cf r*ogu)f9d:8e,avd,,;t9lock reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent thapjg)c, 98dioutjv ,ea9*q:ffd; roy ,n on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined p :vpo:vtsb/z9ua;znt t u b89pr- q3/klane? Assume the mechanism function tpkp voz n:;qvrsuz :u bt8b9-9/3/ats properly, even at an angle.

  What force is needed to hm )np+- i7m,gtu 9c3oli,pc haccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 Ni )*kf) m 5wqhpfvb*ecbpb9cf +ss )(1 accelerates 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 withstand if it is used to accelerate a (tt5qqs(l62klyl d)p 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o3rfcomj()q:kxf( l yb3/ t:nsf 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 in 8.0 s if the93lwuy5 eyb6ey /u xj78 u,iox car is traveling at 95ui7uw ,eex/uylx 89jo3b yy56km/h? -  

  What average force is needed to accelezcs iftho4,/cv9de 9;rate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alongsh9;i4cz tod/v e9 ,cf the barrel of a rifle?   

A fisherman yanks a fdo) .b.k9oggsv46s(-zi vobrish vertically out of the water with an acceleration of 2.5bz.do g - i)v9kov s4s6(.bgro $\mathrm{~m} / \mathrm{s}^{2}$ 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 a7 t u1bpu+gk1j5wpu.sdu;j:d 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 desigtd +kwqa4e.u9 ned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable?a+w9kt u qed4. 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 elevatoroy)96 h(bjuf a begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction ofoy (ahu )6jb9f acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N.(jv9rt b3brrr+eut pc;e5 38o What maximum upward acceleration can it give the elevator withor9bec+8j3r5rtp(e ;3 oburtvut breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mypv,q a q(-at8e 4kc ma;bho.1ass 132 kg including parachute) when the upward force of air resistance is 1o- y, k cp.h;aqtme8 vaa(4qbequal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. Whsem;.2 bn uqj2e z9bsir4 wdf; l-x,g5en he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs)2xwie2ndue lg5f9- m, ;r. js;sbzq4b 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 lhn y -q,i1mfj23mv-ctwa fqu sq ,29t 0sx)v7the box runs vertically upward over a pulley and a weight am m3xfvqs7c,, v-)j20 n1s9 whyi lt2qfuq-tis hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player zg79t iuf(m/r
(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) a6 wkfd7a(f7 *l5gozi4d1 a isht the moment it is hit by the bat, and again (b) after it has left the bat and is fl7adig4 z ikls f*o(5 d61w7hfaying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 6qd re: o2u-jp7i d3*zb50-N force must be exerted in what direction so that the iuoq7-d *dp2z:3b rej resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two btrc k 2sp6)s7huildings 10.0 m scth7pr )2s6 kapart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a masscmvl *2gd8:gm less 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 1ib;teyrqu 82cw0(h g*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, Antarc6v4pyr yb+u, fm; nn,atica, as shown in Fig. 4-46. The sum of the forces v+pybr ;a ,yn4mu6,fn $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 . b98 -rsow*gpe-hzo u; Determine the ratio of the tension in the coupling between the locomotive and the first car b;e -opw8-hog z rs*u9$\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulln el- ;ovegrmk63wsevn7)w 2 )ey apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constantwev s;kelr62m-vo7wgn)n)3e 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 ojbh di;36+,5 w*yk(gxfmcec, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block tg8i*er9 sd2m1 e)egg7wdfx l*ys 1s 4(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 v)xmcnv*i6sr vp367 * 9dbdbycontact with each other, as shown ivr*7si6* v6dpx nb 3vdycb)9 mn 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. 4-524q50tf qnv2q w 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 i2w0q n5vt fqq4s its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table arecb 8+u3/qmpa6t j.v (k-)szgutjb -sq connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of e( kb pjbc8qts.36m/ujtu-qs va +g) z-ach box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction betw5v vy/*mnk18h3rf9ij. oofjw een 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 t obza+w :,1ys:xd6cnu o start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. W8h ob tak4*2cjs+hz* jjeh8-nhat minimum coefficient of static friction must exist between your feet and the floonj*aj*s2kbj 4h8c z-h htoe +8r if you are not to slide?   

  What is the maximum acceleration a car can u3on7j33nxyz rl 9 s oeonm/3o6ndergo if the coefficient of static 9o63oo yn o/xj73n r3e3mzlsn friction between the tires and the ground is 0.80?   

  The coefficient of static hu/ 7u t2rie ceo(q(5 ldia 4qh75gmd0friction between hard rubber and normal street pavement is about 0.8. On howtl5cuih(mq0qeireadh 2 775g /o(4du steep a hill (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 sxe3r7m09kds.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 ahuy 6 u-bgc5/i;fn)hnw ;x.,v wkp8vv rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficienqf x)royxae9pf8d;4 jygc obq ;)899ft of stat x8oq9cfg8y4;9);xffrqjp e o b9 )dayic 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 friction for a 2ivfjrivihz+4 ) (d+/qya9-iqtxdn8 $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box v fpj (3-qjro3A have to have to prevent any motion from occurring? Assume o3qp3rj-vfj( $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Hof9 gqiwi *t .a.hrh52bw far will it go, given that the coefficient of kinetic friction iatw *bqi9. hf h5.gri2s 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 ) (7bmpd*8x(bzj tcdkkg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 62z km)*7d((bcdxpbtj80$-\mathrm{N}$ 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 carqv y./kfo*c5peyoo: 16yfi /rrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver ca kq/po yie5fcf:o *61y.yr/vo n decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drivd l2* hl)jdp9poun) +slhsa()sye( 7seway, which has an incline of h*o) n)sd2jppll+ ( se(sa)7l dhu9sy 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 with uvl t( +r2 )4hm v /nm;))cudehmewo1wa 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 7s ) +pag 5x8wa(xcvyllies 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 speed of 3oq a (:b1fmp9m.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 reache4,odd1iyu i( xj6k6txs the 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 a rough3jvcx9zkq l+2 wall by someone pushing on it with a force directe 9j3vc+lq2x zkd 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 dangerous projectiles as theypyi*i,5 ywh 5m melt. Consider a chunk of snow at the ridge of a roof with a pitch op 5ihi* ,y5ywmf $ 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 s0 rsufdgtt* 7 ,z4szz;-baz8htopping distance for an automobile traveling at speed v4zzbt dt hgz7-u 0r;8s*zsaf, is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a ca5i awvcy2eey7 r6:yax2yr 2f4r slides forward on the dash when the driver decwar 5ric ef6vye:a27y4 yx2y2elerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an inpbfk4r /ztr; 0q)a( iiitial 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 th q j,7x6mmqnk/ey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed.7 xk qqnj6,mm/ 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 betweenhxi c(,9 p7d,e:rx:;r0rs;alatlja n $m_{1}$ 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 624a 4zvwhm3a3l .ul1r gi3p 7w euhvm)5 kg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at.n r av.99h-5zygph e9blm7s s each pulse approximately 20 g of blood is accelerated fr h7m. n b5g9v.-z9eh9 pyssrlaom 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 automoo+ mgc +9*dbkibile crash if the deceler+o9dc* g+kmib ation is no more 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 by an earthquake is a , and if an soiaarf vdc,z( j;yc430t- u:object is going to "hold its place" on the ground, show that the coefficor0-j4ysau cv dtca:f;, i(z3ient 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 involving ip)5 fl1huoz0two cars, measure 72-m-long skid marks of one ofui p51 fh)lz0o 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 road.   

  A car starts rolling down a 1nasr to7 3+evz vu.p2 a0v.cl2-in-4 hill (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 7l+vps0ro2.v ac32 z nevt u.a55 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 falo np 0t,::6pgkhw -lzuls 55 m before reaching the ground with a speed of What was60:lh-pozkp: w, gtnu the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stret;f :ep8 6b f2iv.cwzsbch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch wib;e8f6:fp cvzbi s.2 wthout 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 redesig+4awzvhmuy(;ad- p; 6x(bm nlb1o i (un of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills withizmph(x; va u+ylwbd;ob6( (4-mnau1out 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,9bof3f bkow .p(e*yr8 dangles her watch from a thin piece of string while the jetliner she is in takes off from3 fbfw (r*oe boykp98. 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, thebox ,ak s-wcr*4n8ryjvl*2l 6re are to be several ramps connecting differe jlky 6rncsrxab,4ol* w2*8v-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 to liftryd,la1*bv43 0cp xqp v (8tyc the piano (mass M ) using the pullep3b1v, xqpc(cr* yt v80y4dla y 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 accelerating fv3/+ufjml m/ 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 engineerde 0i5s :.t nmp-o3yzu considers the following set of cond5zsuyi:dt0. -oemn 3 pitions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 me /ye00pe+qx)sxp0dfx tric 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, usd7nt s cq,-qn55lm2ci e safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how ldmi5 qsct5,lnn 27c-q arge a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " wmu y e1p(h,+o (uhvp,t:/cmc10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 3.4 (pn8z;y r sund) abxb4tv6r95 $\mathrm{~m} / \mathrm{s}$ 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 ascend(p*d; w0++rorenk qo fing an ice field inclined at wo0(+rd pn eof;kr*q+ 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.