Why does a child in a wagon seem to falne9 q h5.xhe36q sbiy:l backward when you give the wagon a sharp pull forward:39bi56 ehhyqnq.exs?

A box rests on the (fricti+oka 4uqgcp;r7o eu.n9 yzr.-onless) bed of a truck. The truck driver starts the truck and acceler;- o4nrup ug o.79yraqc k+e.zates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on i 2e:cbqzm-0asrc / ch-t? Explain.

Only one force acts on an objeco w+) y937phskpmi(rlt. Can the object have zero acceleration? Can it have zero velocity? Explo m9h7wr)3 (ys+li kppain.

When a golf ball is dropped to the pave 8; d8wd5qg0 hdeoj7whment, it bounces back up. (a) Is a force needed to make it b750o8h d g8ddwwe q;jhounce 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 of uc)) cdc1 x5nk(w4acuth;*ypposite direcdh)cu4c1(ct* u5;yc x)kwfa n tion?

Why might your foot hurt i.cc2di(qrf h 2yb p42tf you kick a heavy desk or a wall?

  When you are running and want to sto f- ,*ibha,upfp quickly, you must decelerate quickly. (a) What is the origin of the force that causes you fah* -pbif ,u,to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of t(uv,5xxl3a rlvn8j8)7l yglg he same thread dangles from the bottom of the stone llv83y(g5agrl7)l8n x xjuv,(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 ae+kzm; gq*n*17 f d7ilr cv:dfs that on a 1-kg rock. Why then doesn’t the heavier rock f1:eqm *7;klz +r*fgidcvn 7fdall faster?

Would a spring scale carried to the x1q * w(xfqkg,Moon give accurate results if the scale had been calibrated (a) in pwq*xgxk1 ,(q founds, or (b) in kilograms?

You pull a box with a constant fo g)k1kuufeaj-)h afvf b/a:75 rce across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to)va e-kjkfh:ub/ u ) fafga715 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 influence ofl5 )p-bz :t:s4do1q)/jjl5zd mwlns m gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and owj-dms:/b5 sm q1 nlt :5zpo )dl4)lzjpposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when ysat (.p;1/ xhrm9d s1 -cbjchlou are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a givent(dh1ar-1pjsch/xm9 s.; clb speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war*g:un;ld d 4q* hp1ldi (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will wi h14l ndpd:i qu*gdl;*n?

A person exerts an upward force of 40 N to hold a bag of auvy lwq.70s/groceries. Describe theq s/0.auv7y wl “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 object it is exerted.

When you stand still on the ground,,tlkdb-m1w2cn6nn s5qj *cy2 how large a force does the ground exert on you? Why doesn’t this fokq-bcnmcd1ns*l jnw6, ty2 25 rce make you rise up into the air?

Whiplash sometimes results from an automobile 6h zpcu;f:d7e7r wd9jaccident when the victim’s car is struck violenzjc 7rh6wp7;9e fd:d utly from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelun4 hhf )vq)vfik)g a w+6yl/1erates, the crate remains where it is on the ))1h kluv4wff n/aq6i+v h)gy 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 blocg:at u-:)7d egk8radbk reaches its highest point, it slides back down bagu8bkegd: ta: )-dr7ut the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weiggdz/:y2lr9 rr )7yrftttd: l3 hed yourself on an inclined plane? Assume the mechanism functiz:gd yyt) frtrr29/d :7 3rlltons properly, even at an angle.

  What force is needed to accelegjor2 )(bbdi, rate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike andl, :rm f/jpz 43btzv2i 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 athk wc 2++ h(tj;pw;rxccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a o(mmz: ca* 9tt $76-\mathrm{kg}$ 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 casy9, uo 8uub5zr in 8.0 s if the car is travel8,s b o9yzuuu5ing at 95km/h? -  

  What average force is needed to kguvfd* w-22lb ;q) mfaccelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0m*2bul qfvf)2;dw- g k.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertical89tprvv w/y5w h/h e4zly out of the water with an acceleration of 2.5 5wptzhy9 /v4v wrhe8/$\mathrm{~m} / \mathrm{s}^{2}$ 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 track ap2(1 0cb)yy1xdgmdwhucs -hmu5ke1 .o d3 p+ (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 ) 4/:jimd o.xk;8ll oce6d8c bcis to be designed so that the maximum acceleration is 0.0680 g . What are the maximumdjxdml 4 c/:.ike88bcc loo6 ; 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 batqueoq;b rf8w1 nwxdao9;t :dg j;;/: whroom scale 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 aco8qwx w; 9 ;:/abr;gfjtq1on we:;dd uceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting uv dmr+c2 s5u5gh d):wa 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give :ddc2hr)v5uug+ sm5 wthe elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132-s2uuianf8798i d3jrp .mb xk kg including parachute) when the upward force of air resistance is equal to one-fourth of their weig u92ujxnd-7 p8.b3m 8si akrfiht?   
(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 hous-whgt:c t 6 fkyb5v:f-v-, snge 3.9-m high. When 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) isnf-:,c w f-vyvb s 6k5tg:-tgh 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 td n1nm5m 95bkoohij, )able. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that t9 hmk moni5jo,)ndb15 he 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 bas gl1a) e-u6 nxlxca/esdem n q,*x9)r)ketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diag-dv n o,+x::dqcxcd),rz mfc*:0 nlbr ram of a baseball (a) at the moment it is hit by the bat, and again (b) +f bc,dxq:dd,- :nlvc rx0z)m*orc: nafter it has left the bat and is flying toward the outfield.

A 650-N force acts in a norv2hhe i6 zo8+)ilnn+pthwesterly direction. 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 vectio p)62h +hvze+8nlinor diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildingczj3h6/xs 3kds 10.0 m apart. The sag in the rope when she is at the m6sk/jz dxh33c idpoint 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 acandu n,szp811cw,s3l6 xj ,hnother 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 14.0:tjm-o86tq k5 d )e* ccuz(qzp$-\mathrm{kg}$ 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 ak-1swehn 76hq4g i6xx9hx2yf new location at McMurdo Base, Antarctica, as shown in 4f26g hxhqekxswn 9h- 1yi67xFig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two +f9ua)ts h9mpxe. .od-e7b wucars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension d s7 -+ wpteh.9muoaf9.b)xuein the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-puapogfav ,(;,l p0)sj qlley apparatus shown in Fig. 4-48. (a) How hard must she pull downward t ,f;g(v0qsopa,a)ljpo raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a f)w6seioiapuq1 ;b /m4x1 s f0 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 (m al(mqaot /)m :o9 pvwk0w,/fgjf. l2uass $ 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 surfo*yw 5;w7l v08ufkwh cace are in contact with each other, as shown in Fig. 4-51. A for 8hvkw o*uw;y0 w5flc7ce $\overrightarrow{\mathbf{F}}$ 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 .wjq-kia(/ou 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 u.q oa-kij (w/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 connected by a heauxld 6ln2g37cdk3j*. t,hwu j vy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end.3nxdlulk ucd jjt67*3 , whg2 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 between azlv.b3u0w 1 uk,6hrny 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 e4qq/l m6y xg3nh(vl*required to 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 a(t/sn ip*md9k58o/bfx caesym/ej 69 t 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are e6(fb /kpis 8dyx o/9/m mecjan5*t9snot to slide?   

  What is the maximum acceleration a car can underd2 x cizibj6;,: jcn0igo if the coefficient of static d; n jx:0iz2icc6j,bifriction between the tires and the ground is 0.80?   

  The coefficient of stat e2 **iqz+y.lutq 8dneic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a ca qeztn8e+.i 2 q*dyu*lr 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 k a1 +j q*kevk19cqh4u-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 u)obm2-quf) p8y7nev r:fj s jj++t/w30$^{\circ}$ 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 coefficient rapn.wq)8j 2r of st)nw2 qjrpra8.atic 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 fore)brs2kq ,xikr7;n8o 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 (Example 4-20) how large a mass would box mjmr7:4ts ) wpo5v2rnu oo0)uA have to har om2pwnrj4)0uosu:m t57ov)ve to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fl g6kjx g4-a(. qykx4yj:f4tgj oor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 gtxkg fq(k4jyg:.44 j-ax6y j$\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a hollr iw gjlm;z4s;-g +(rizontal surfac;-l sl(j g;g4m+wz ilre (Fig. 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 cxi ibok ; +6mts 64iao3tq8p+harrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. Wh hioips;kb+m6t6 8aiqx+ 3ot4at is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry n e2i6qh6 x.q()vvqxi about parking your car in your driveway, which has an inclv.xh eqvx 66i2nqq(i)ine 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 ;sovm/sw8c8 j with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an an tgk,pey )r *s;kn37usgle $\theta=22.0^{\circ}$ 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 un+w0gw4 e2f+9u +/ j iywaunginitial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill wit*.zirb6z;j2xc ye ono2:)a oih 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 pl7 j/8wh agwz6/+lscc face against a rough wall by someone pushing on it with a forchl w /6 w7szf8gajc+/ce directed 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 5b;4pd w8,wzf-) ctg ;vdzpih become dangerous projectiles as they melt. Consider a chunk of snow at the ridg;8wf5; bg pvidc4,h)pz-tw z de 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 automobilet)r i ho06ogsrbbjyu33 +j d58 traveling at speed v 0r6 o5jrit 8h j3g3 byu)ds+obis 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 dashbj.blch0 2,u:t pqost/n;2+ctgxcxx. oard of a car slides forward on the dash when the driver deceler2;hcc :,xq/ pt..xtt gn xs+20 bucljoates 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 initialigog*;wm*msrsl r ,oo/m:7:6si/iq s 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 conveyocy/var io9zvrbi- fn5. (+df(r belt 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 thivf coyd( i(.rfnab+9 rv/5-ze 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 betu uwrk:tkd7vi.u a;5nxz :x6) ween $m_{1}$ 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 (mno0chz :p (-f2zc6uwsa /6-3mrmiawincluding 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 each pulse ap i rs+b;3a)eg y(bc(xvproximately 20 g of blood is acceleix ;v3 csa(g)ey(br+brated 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 q7 doz27 kx6m7mn:lbc if the deceleration is no more than 30 " g 's." Calcu7zln 7kmmd 6 2qx7:boclate 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 accel.o8y.: jtud rpn3l a/ 3icl1eweration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mlye d 8twcp/la13u3i n.. roj:ust 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-cnj4)v ,p4k-e ,dp pi1hlsn ving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficie-4v )jink- , na ,ppeldphcs41nt 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 1-in-4 hill (1-in-4 meansmgbjc ; *(oq6w.mj ;mq that for each 4 m traveled along the road, th 6.b mg w(mjq;coq*mj;e elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower o :(3,plxcma zjr;zta 5f Pisa and falls 55 m before reaching the ground with a speed of What was the average force of a:mp3 5(z xac,a;tzjlrir resistance?   

  A cyclist is coasting at a steady spu)x h0c8o7 oxz c2b wc+2xz8caeed of 12m/s but enters a muddy stretch where the +x2aw )c8x xb7u0ccch8o2ozz 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 worki7 vyx2egg5ds6fsj 6788u3dxckhp jg0ng0dm*ng on the redesign 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 without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road 583mgg0hx 6dnu6cjsfydj s0pxggv 2 8e7dk*7 from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin piece oftquu b2*gpx3sm5f- :y string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). Susu5m -2qx t:*fy3gpbhe notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting dimi 0 f yi:*svss-rv1a. w:yw,kfferenta0* ymi,rwk vfvs sw:.syi:-1 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 (m-dc9auxqv jp1 7cj:+i ass M ) using the pull9:c 1d-xjqvjpi+auc7 ey 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 at wcf 1m 68 el9,su,cmrb3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer co5heaxt 1fj 179ndd rt05l6hwsnsiders the following set of condlj5sr hfte7t6xa dn05 w91hd1itions:
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 metric tons (660,000 /o k mfm7*ucj9z 8*gx otbos49$\mathrm{~kg}$) . 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, Bilx))opc7 .k(e)z3rjffn, mqvd l and Karen, use 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 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 b,3)f7 epv(rc.)z xomf q njkd)e hurt?

A fisherman in a boat .a,g/ iwvkq 5i08zbvkis using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of z3mbu9ig m;we(: .csc3.5 $\mathrm{~m} / \mathrm{s}$ 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 whpw 48zbt+b0/s3d kr2/mxm xwtwy m: f0o are roped together are ascending an ice field inclined at /4 m kw+y8 2mfpm3dsxw:trwbzbx/0 0t21.0$^{\circ}$ 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.