Why does a child in a wagon seem to fal9/oyf w l1;siil backward when you give the wagon a sharp pull forward i9 l1f/y;wsoi?

A box rests on the (frictionl-1mgodkc o,semo ,; m+tu++lz ess) bed of a truck. The truck driver starts the truck and co1+, og+ts ;ezm +,-ldmm kouaccelerates 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 2 k)jnlv zh9s,acting on it? Explain.

Only one force acts on an object. Can the objehvv2heu.c/5 kg+hn1vct have zero acceleration? Can it have zero velocity? Explaiv e u/15hvkn+v 2.hgchn.

When a golf ball is dropped to the pavement, it bounc6(+8gpn8h6 yq)s9cyyxd* bgak s+ jj fes back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts tyx gdy c6n+jb86 8(a g p)sj+9fs*kqyhhe force?

If you walk along a log floating on a lake, why dzpl4 hgfz+k676nin+jif n+0eoes the log move in the opposite directengfzf0nzi7+p+ hnj l +66i k4ion?

Why might your foot hurt if you kick a heavy desk or a wallq ozoqs+g3b7mt h..1l?

  When you are running and want to stop quickly, you must decel rl2g/* kp0ajaerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rat0ja/2gkaprl * e 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 sectiokw5/bwo;w.)krumzr (rs x t9)n 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 the thread likely to break: below the stone or aboverrt5w 9s(.;mw ))bxwu/kkzro 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 xc3nk(* mlzqmjlg*+b )6q* x las great as that on a 1-kg rock. Why then does* 3*m6xkmj g cllq*(xznq+) lbn’t the heavier rock fall faster?

Would a spring scale carried to the Moon(l:hikfz+;rf 0m0 bey give accurate results if the scale had been calibrated (a) in pounds, :+fez;ikly mbr(0h0f or (b) in kilograms?

You pull a box with a constant force across a frictionless table using k h*dz6xih7-a an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the tablxh kizhda76*-e), 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 nee i(p 12)u c1pwp3x)gghkub9mt force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite f)g)c9hib mxupp(1e21kp wgu3orce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on z8bphjosvzh29g )lh y 3 ,xb42the Moon with tgbz)z8p 3oy2s9h l4 bvh,j 2xhhe 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 team in a tug of war (Fig. 4–37(c2n3*zk ov bj) pulls with equal force on the other team. What, then, deteo j2 nbczv*3(krmines which team will win?

A person exerts an upward force of 40 N to hol7 wboel1q bh;)d a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction 7lhb;1)wb eqo, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, h);x (fn2j z+wpd5 c:r6tl 0i-f:uaki-rijro low large a force does the ground exert on you? Why doesn’t thirtf+kwc2opxr u;- :ii:llj0d5n)i6a rzfj-( s force make you rise up into the air?

Whiplash sometimes results frohexk)ifzgk9p u-,ri f-l:z0yr;0h* om an automobile accident when the victim’s car is struck violently from the reark)h:9- lzf,e f u0por*ii;xh-0zyrg k. 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 trurko t*rxp94v4 ck. When the truck accelerates, the crate remains where it is on the truck, so iok4vx4pr9r * tt, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slidesupj:ko*1pe ,m up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on e1mu* opj,k: pthe ascent. Why?

What would your bathroom sizc+3 dr7a.ywue )/eccale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an +ce3a/cw)7u r dzi.ye angle.

  What force is needed to 9 ( *rbem .-c55rern d;qimligaccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceu3lkfb9ku/ gyi ytqm87* vd10 lerates 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 istp0ijb jr:8d(4eheo3 3gb4sv 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 0.(o r jy-lfft$76-\mathrm{kg}$ 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 thvo* c,5:;1hrfbmeq i1s8he cce car is traveling at 95km/ce;m1b,e o:sc1 cf*8h v i5qhrh? -  

  What average force is needed to accelerate a 7.00- us ong* q0phe5jrs1f9ad(v(1gram pellet from rest to 125m/s over a distance of 0.800 m along t *1sa5 1qhpf(rn sud jo09eg(vhe barrel of a rifle?   

A fisherman yanks a fish vertically oute) t+fqbo-:safdb3a) of the water with an acceleration of 2.5bt3+:s ef fa-))dbqao $\mathrm{~m} / \mathrm{s}^{2}$ 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 qua zgh - d8tfy5r7c84ijfrter-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 designed so tha wsego/1iq l a7.h -0uzbz8yw8t the maximum acceleration is 0.0680 g . What are the maximum and miniozel.0 8bwq/gwyu8 zs7h1i -amum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When the elevator 05 : ziq(7/akogobpr23b3gfc fy zpk7begins 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 of accelera73:g0 7 rib 5k 3opyca (fbpgkzfozq2/tion.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengz3 7 3rftk;r)jsol21oco7nhu th of 21,750 N. What maximum upward accelk2ut3 77oc3; zrr on)ls1jhoferation can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inc t al yd0,:az/x*zhf.cluding paralzd, :xt ay*.z0/h cfachute) when the upward 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*mzqxq5ox26 z roof of a house 3.9-m high. When he strikes the ground belozox2xq5mqz *6 w, 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) 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:e16sz)* z5yq8ln w7ny mi1i,n oxkqa the box runs vertically upward over a 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 si1x1q :6i *nimyykae5), ln nwo7qzsz8de of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for fr;m0gfn,pk( 5+be(e) jl4z u2 o atvha 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 a baseball (a) at the moment it73nihh,+bca w is hit by the bat, ,a3hcb i7wn+hand again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A secon4wpg 7* 5p0udcgkgat (d 650-N force must be exerted in what direction so that the resultant of the two forces points westwarug(ctpp5a0k 4wd 7g*gd? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildingsx jwf u1x4cdo. to4 k*n82kws9cij-h9 10kocn*ud-i cjo8wws 1f49xxk.t hj942 .0 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord /5e (g6hbby4o:gwxuy 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 14.ha vb;qmkna;opxf5j87 a3 -)b0$-\mathrm{kg}$ 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 a)pv0iy+r fvdjzc0l( u q*bt47t McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forc)7d0 cfy+p*i rlqvu04v(tzbj es $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 p(jh e/i2uag ( cab-c.x;;te vdgn/ld4ulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and te(gccbte .4 ld;2 naj xdau;g/hi(/-v he 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-pu) d s9fgojm ,t7ff9x9k)wwm5ulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raisffjs,w9 9 kgdmu oxtw5m))9f7e 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,yqo a6wkzhv,v*u77 c , 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 (massso 5(-pt jydz) $ 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 conta2 vue 4fhkv5 c;7sz 6jkjc0b,dct with each other, as shown in Fik2vsd u0;4c vfkzjb5c je67h,g. 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. 4-52cgz :jm 8z15qzkto3f+oogh 5 ; 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 z 5t5 okzcg8j1o:qgm;o+zhf3lighter 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 avj4y.rizn t j43v9tf 5re connected by a heavy cord of mass vitv.f 4z94y rtj5jn31.0 kg . Calculate the acceleration of each 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 kawyg(v9 y va7*e h1rgf(tp-r.b;6xg 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 0;(k x;oxjntpzsg3luc. nr(6 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. W:fs ,a)5caxvgurbc3 y,r1 ,fo hat minimum coefficient of static friction must exist between your feet and the floor ia ,, u1fvars,3)orgcyc:fb 5x f you are not to slide?   

  What is the maximum acceleration a c.dlq3 . z05j+9djg:u ktmar7k)p/b mzgak -zl ar can undergo if the coefficient of static frm. t5zd:l) zg7.+ka0/3uk q -rla9jkd pjgbmz iction between the tires and the ground is 0.80?   

  The coefficient of static f4u7*a7q ehihrriction between hard rubber and normal street pavement u7h*i 74aqheris about 0.8. On how 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 -8z hymt:*e90q 6z1 fthu)e fvm4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 3lc(, 0e)g wkng0$^{\circ}$ 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 coeffici( b -yv7pso0cdy: pxx4ent of static p:oxpd-4b7cxs(y vy0 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 kinetic71av6tyu/gpoto7 7 c i friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20)iah,. wb. dj.l- 3ep2 u.s)kz xbee,ek how large a mass would box A have to have to prevent any motion from oc,bzedjk. ae,hxwi.pe )e l. b-23 kus.curring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides ac9 wff3s)vb o9jross the floor. How far will it go, given that the coefficient of kinetic js v3bf f)w99ofriction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a hor- pf2akk d3g gsul73z*izontal surfal3 72f-gkdp* sgaz3u kce (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 carrying a heavy crate. The coefficient of static snk*n)if5x;kn tg ,2eoj *mz+friction between the crate and the bed of the truck is 0.75. What is the z; on5)tmx 2k f+*nigj*,e ksnmaximum 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 about parking your car in your driveway, 1zy+yddf7(0 lq iy0n3ce p6x hwhich has an incq yxdl03pdnf zy7h1 +e c0iy(6line 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 nt*tca1 0uoo5))h nz owith 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-uj bwk z 3g,:9.m4sjfr55 lies 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 initiat9ad3ig p .js7l 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 with a speed ofl3t/ 3i yq6npk 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 aga2a6qd7kfy vr (inst a rough wall by someone pushing on it with a force directed ukd yfq7vra2(6pward 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 / brygv*n.fprhf-+qh) xn./y roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with fnyrpg v/ h-/)bqx .hn.*yfr+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 dist m .wt3t 5jo6mq )djvqk(s2ad+ance for an automobile traveling at speed v is jq3vqd)6.d5jtk(tw2 +oms m aequal 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 forwa z*l- 4xwf*9i-zqdken) w:yn zrd on the dash when the driver decen zw-ken zf4*-)9i* yzxd wq:llerates 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 massmsawvqs )0.p v91n4x*;b k cjd m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to them3r ct -og9bt4 :lt9:4 wninog 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 halfmn49i :t -3r t twcn4l9ogb:og 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 kr 18jz ;9mcivpinetic 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 the au-fn gy5.qi 9bicycle) 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 ea7fl )ch 54- ;pmikapgmch pulse approximately f5) l;h c4pmm-k7iagp20 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 a.3882gq m jqs6r v+sbij zgv2butomobile crash if the decelerationrgqb62v3 g+b.m i qj82szsjv8 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 eagg v c c1jubk-p2i+/n0sib6k/ kf9.parthquake is a , and if an object is going to "hold its place.k/njivc1 a2 0bb9uf-ksg +pc6i pg/k" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining th d,g fqtqsa;u.k 2 f7dvlk2q8)alb:6obv us 38e scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed d,qkf 27;s:sbl .28bvu og tqu86aqfkad l3v)of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4mip s.m-g3lx9 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 55 m? (a) plm9gx i-ms.3Ignore 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 Towe s6kbv came/,(r of Pisa and falls 55 m before reaching the ground with a speed of What was th(e6,/akscvmb e average force of air resistance?   

  A cyclist is coasting at a steady oc2dgr o5.fa: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 sdgc:f25 a oo.rpeed upon emerging?   

  A city planner is working on the redesign om+atz ;hq8:.viug:xd1y v-wlf a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cahy: qit-1 8l.;v z+gvwduxm:ars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch fro :jwj0,7 ekfkzia n++jywyggcq34 .w6m a thin piece of string while the jetliner she iy:ny.g w7eafqkkjjz g+j w0ic64+w 3 ,s in takes off from 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, there are to be several ramps connectin1qzl xjuh0 6+stw .y z2i8agz0g differe.gzza 0621 0hzlx jstuwy +i8qnt parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) u,f1gz+(ml5aorhu u q/sing the pulley apparatus shownq/g h(a ul u5fz,r+om1 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 acceleratrlg4vhf.0b r) p+jg r y+ix,g/ing 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 proces3b;2wd 67amqi 7stctls for a child-restraint chair, an engineer considers the followi6 t73bastl c ;qid2w7mng set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian traink25uy28ghfg2:,o75 cru fzqh 7mdum g has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. w;2q(kc xscdp 02.qf8cwp0kb 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 stopspk8 0cbw0(2qsq p2kfxcdw .;c 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 is using a " 10-g5(+k)to+d t )mxkceh1 $\mathrm{~b}$ 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 396 9 r.fr ycs)zcwenn6d5 (lns.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 roped tol;hs 6v4 rrjash,fp, 4xy ;v9cd .)mgkgether are ascending an ice field inclined at 2y 4asl)c6fm 4 k.9x;v ,r,gvhj;s hdpr1.0$^{\circ}$ 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.