Why does a child in a wagon see8c3au.or1p4rkx 6 g( v7dus mem to fall backward when you give the wagon a sharp pull forwaeuk dmp 8o3 .(rcsa1rux67vg4rd?

A box rests on the (frictionless) bed of a trucp4s:a fuby(q6i zk o7,)r(eidk. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bedk(i 76f,epszbq:(od)ai 4y ur . 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 Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on i3si9p4w4bznv er9 jz/t? Explain.

Only one force acts on an object. Can the object have zesh)i.; 3h kng ,-zsnkr6e 4urcro acceleration? Can it have zero velor4 rs)g;sh 3h kiz nk.-nu,c6ecity? Explain.

When a golf ball is dropped wlk+h82ax9q8 gr)nq i ,mlf 1uto the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, whu+xkn 2,h1w fqlr9liq ma8g 8)at exerts the force?

If you walk along a log floating on a lake, why does the log move in thedu . oj6dao1(c opposite directdo.(6 dc1ua ojion?

Why might your foot hurt if you kick a heavy desk or a waq tcv52k w/4 a0oomb,bll?

  When you are running and want to stop quickly, you m6milm1 0 q8ysgust decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own exg0y1mi ml86 qsperience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fin*rksytqn7/ i9k+8 yoz e thread from the ceiling, and a section of the same thread dayky89o n i/kq*tzs+ r7ngles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as thatv lg+u nvestf :,3exvo:c 0sp h(di529 on a 1-kg rock. Why then v i+xsgnvp:hltedef,s05( c u9 v:o23doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scalea w .9d*)*e jrfn1gb-s+ *rdbji) sglw had been calibrated (a) in pounds, or (bf. d)sanr*b)gw ew9igsd-j*l1 *j +rb) in kilograms?

You pull a box with a constant force across a frictionless table using an attachd:2gax.g:gvw ed rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flatd:awg g: vg.x2 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 influence of gravity there is a net forch agl y*+j.y *8v /h5lfsl-fhoe mg exerted on it by the Earth. Yet**.ov asj lyg58/-f h+f yllhh 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 z-e)z1 *zlwwnwhen you are on the Moon wzzew n lwz)-1*ith the 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 third law, each tsq(*+mn3kuateam in a tug of war (Fig. 4–37) pulls with +as (*mtqunk3 equal force on the other team. What, then, determines which team will win?

A person exerts an upward force of sqldp9. 0c f1n40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) bfnl9 c1p ds.0qy what object it is exerted.

When you stand still on the ground, how large a force doesag16ir hux2:b the ground exert on you? Why doesn’t thish6ig21ba :xur force make you rise up into the air?

Whiplash sometimes results from an automobile accident4 ta uxdghn h04)es*73rgl 1n )yyk9ui when the victim’s car is struck violently from the rear. Explain why the head of the victim seems trxh4gu nhtnlui)194ay 3gs0ye *d )k7 o be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, h1v-lw6 z//p1euak0 hrppmv4fy y5 l)the crate remains where it is on thuh p 4p)evvllp 5wz1myhfyrk 6/a-10 /e 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. Ao6m *iunfd:u +fter the block reaches its highest mod:6i* +uunf point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an i dm9;g1fm x e3quwfdpy e:07q5nclined plane? Assume the megd: 0fwdq f9;e7umeqy1xm p35chanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled au a.m cx,i*eb at*wthd.3-sf2t 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rid8dq5 ds ,7ui1ci ly5ifxf0h)jer 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 ;x yp(2 fxejvp.m .f)c8rrau4it 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:ypooz1n.4v k $76-\mathrm{kg}$ 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 stopzisz-)5 y x ccwr(rq02 an 1100-kg car in 8.0 s if the car is traveling at 95kzszwxy 5)r2(q -r 0ccim/h? -  

  What average force is neede)ck1p c.egng7d to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel o e cg7)gk.ncp1f a rifle?   

A fisherman yanks a fish vertica9x7-kuddd 1kpi/rw * plly out of the water with an acceleration of 2.5u-rw*k kd xdp17/dip9 $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile tralnh2 g*9)bapfb rs x*7ck (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 48g 3q l42dpq)tc ktmig6,jfc/) 50 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximg3 mjdpg c,ict)l q4)/qk f62tum 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 sc,c,x jr nz*9)oo.q iiyw m;:urale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find t:r;cx, mjin q,z o9r)oyuw.i*he direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg eleva3 u62me yezz4pnj8 g(ceaw32utor has a maximum strength of 21,750 N. What maximum upward acceleration can it gw8ez6nau3zmeg( e y 2u2pc 4j3ive the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of tiehw : /,qda;lwo falling sky divers (mass 132 kg including parachute) when the ueiqwl/;,a:hd pward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.jm-s)3gnzjc r0a b8w 19-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximz r)0 an g81jbw-cj3smate 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 ru;42w),rw k( wuzyfow fns vertically upward over a,( f;ozyuk 4r2wfwww ) pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagra, o// nghzkne1m for a basketball 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 arz4x f44m rjv8fy(t9i baseball (a) at the moment it is hit by the bat, and again (b) after it has left the b4 j(t 4i8fvy rxrmz9f4at and is flying toward the outfield.

A 650-N force acts in a northwesterly directiott f s2(i9bqbf + y0-dcd)sgx.n. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vdx 9 yc2ibf()td-q0sbgtsf+. ector diagram.

  Arlene is to walk acro2laaqm gbt;- op3xw1,ss a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpwabt;a2glp-om,3 1qxoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from an zigbnl( *i n0ocs.6;c hrhybgs-o /7.other 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 143r6v4elglch 95z hjp 1ajac) 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,f4kucw 0kgy wzhu vh+;+ ;vh, McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fo+u ;fw; ,v4khh y0+,vghzkuc wrces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 t)ju s5s bcki0;wo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the ts ci;uks) bj05ension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herskfg2rq 6/lds1rkry4 + elf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constantl 4rrk/ 1f62skyg+qdr 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, a7q/m/czj nr:fu *cu-c 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 eomt43u( u sexumk; 8 thj6u.2(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 contactfrunfq 2;md ; 4xpcm0( with each other, as shown in Fig. 4q(x pdnf4; ;m mfcu2r0-51. 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 nr:754lkwnx l.yv 8sf n14qkhare each initially 1.80 m above the ground, annx5nr s8v qhyl7lknf.k44w1:d the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connectedj )dwajq -xsfnhik0 9o3qe x3*x/n 1i6 by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each 6qx0ihj*jd1i 9n/ofwx3q -ksn3) xae 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 fricay26u arci04lt6 y+ qn+d*tvction between 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 5h hc;l-a*c/agx( 9do e.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 aq tu21zdq9 8zf4*q. ohc6x: ujmejx8v train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not tx.2mcz*z18t:jj8dqq4hu xoqf9vu 6 e o slide?   

  What is the maximum i4,-(s dvo j+u c/p zv*d.puexz)i.ncacceleration a car can undergo if the coefficient of static friction between the tires and the ground is - / +*xjzv(.zivduds inpoc4 .p uec),0.80?   

  The coefficient of static friction between hard rubber 32lw inhd 2*:7dfuy5*tcm ykhand normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car wh 2 7lnydku*d:5m*cyhft3i2 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 akxf 920+inaozt -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 on a rough 2g 6*em cp, oyr-fkh.o 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 coer(c h0t9x.twr7x kn s.fficient of s. 7kwstcnt9x (r0hrx .tatic 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 frictiob99-010e4idvvd5sron;e bwi xvtj7h n 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. 4-3fg; :udm: boe(2 (Example 4-20) how large a mass would box A have to have to prevent any motion from occ:(ud:mfg b ;oeurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. r*1 6 xm9w tueq.nn.j6z5psnt How far will it go, given that the coefficient of kinetic friction is 0.2zj*5tnu tn.9 pe1 wrms. nq66x0 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and9/vrwq s0p5g*guf 1j0rv,h(bv g t0 xw 110 kg , are in contact and at rest on a horizontal surface (Figv/uv0gtwgvpfj q(wg b59 rr,0*x10hs . 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fricti l5bx)b/i s mo)k*qwg6c5pym0 on between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerateiqg)k/sbo m)w* c pbxm50l6 5y and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your cay(hc88ik,,xp fli 7 m:2+ litlil +aabr in your driveway, which has an ina,x 82l+hm +l:iilit8 yi7(aclkf , bpcline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 28j:jak ahr8c.:t u0 3db$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a pla lic*;tncpdx2 k37d1swqfi6+ne 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 ov( g9wkq ,(5hen ja9yhf 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 steepes()j,7uyys c uct 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 rough wall by someone p w d:lkqa4mn 7n -5rp1u/:ffk) j3kpzlushing on it with a force di4:m-jpku z153/wn: lfd) lqfp7k raknrected 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 ailf1 hh*;c )idangerous projectiles as they melt. Con*h1if) a;chli sider a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at 1szbw f8t0 3pygd / j2otz2z72dj) wetspeed v is equaldgd/e8t zszbtyt 0pj1wf23 )w2z2 7jo to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when1 vqsk+;j+ nqqj2tv 7c the driver decelerates from sqc1t q k2;vv+nj7j+q45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial b/g5/wm 0s /jh+edgkos(dg 8v 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 rsocmey8 g 7c6n/o5t:sfpk). from where they are filled to 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, whacfst6gsrp:5 nmeyok /c8) 7 o.t 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*i ok4h(l ):7dkfwifv kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including tyjp 5-j2zg+qt-iwp i/ he 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,:kop2t4s ,lbal:va a; at each pulse approximately 2l oa a:: kbps,4al2t;v0 g 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 decelergg*den8 kk i15ation is no more than 30 " g 's." Calculate the fkn5k81dg ge*i orce 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 earthqu/oqx(+oeq3: 7q4oxd h. scss gake is a , and if an object is going to "hold its place" on the ground, show that the coe ohssqgs/ :(.o3qxoe4qc+ dx7fficient 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.u6,j nyd 2gmy 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 th,dm 2. yjgn6uyat car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each-6 0i(ldtk+1h8m wpgp4 j4zxmiwzq0a 4 m traveled along the road, the elevation change is 1 m). How fas04jdq0+-z igizm(akmx14 wh8 6pwlp t t 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 vgf 2yvu4d0n 6b:xgg) Tower of Pisa and falls 55 m before reaching the ground with a speed of Wh62ybx0gnfg :u 4gv dv)at was the average force of air resistance?   

  A cyclist is coasting at p3o62 f.8t4jamkfl tfxnbdc 4me5 0-pa steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the fox fbmmp4cn0k8td.l5 e -4j6 2t afp3speed upon emerging?   

  A city planner is working on the reu t:n6:i3f ceedesign of a hilly portion of a city. An important consideration is how en6:uie:3ctfsteep 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 exp6h 2wtbom 5/etd)z.n2 ftd yax)2 9ofberiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from )nydthm)2 f9o 2ab/x56f. bzdoe tt2 wJFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there l fw,8.r5ylp r,zyum/are to be several ramps connecting different parts ofrwz,5 mryl,uyl/ .p8 f 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 ap 3fnxtuz-09.6no rxneeded to lift the piano (mass M ) using the pulley apparatustn p3 9o0n6.x -uxrazf 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 accelerati; *ypha+lku5 hng 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 chilsp9 1on:s sn+um j23jod-restraint chair, an engineer considers the following set of conm1p9jo+nj u 2 :nsso3sditions:
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 masserf zv, (xraup 9md(,, 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 ro *b3z5q;(u5c kle9gk epauicah:.,e spes 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 frg,5ueqz (eb35 l9* iau;esk. cchkpa :eely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat ispkru7 p s4ex4/h-uc. s using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall buildi ai6 ,l:5mbkk;q8fd ytng is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are rop5 lwem)vd5xfo82o -yn ed together are ascending an ice field inclined85)xnd 2 v-owyoef5 lm 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.