Why does a child in a wagon seem to fall backward when you gipy o.a (*/jxqt8zy4ube dc2ir k2v f7fu*6o4uve the wagon a sharp pio2 edkuyc(8xy2 47qt6a j/vu4or*fuf.*zb pull forward?

A box rests on the (frictionless) bed of a truck. The n 4ss0:b70decjvik 0ntruck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on ns0bikc jd:e7n0v0s4 the truck

If the acceleration of an object is zero, h-m 11s4ka1coxp1fn j are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerati2tix:*v4f9h79s + hsiwhnzdu n32dzton? Can it idn t2 f4h*27wz:i+zun9sdhx93tsvh have zero velocity? Explain.

When a golf ball is dropped to the pavemenztifs n3u(do)s*e/kru .+c-zt, it bounces back up. (a) Is a force needed to make it bounce back u3 zd-u+r*z .nsif e(cks)u /otp? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the op4fkhno;f0o ,hu6 uum0 posite o40khm,f on6hufuu 0;direction?

Why might your foot hurt if you kick a htynb5/ qznc9yz88 x,keavy desk or a wall?

  When you are running and want to stop quickly, you must dec fmt:g/l+g /btelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estim/t/ l :mg+gtfbate (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 vk)tzry:8fdz/ r 02gy)o,m1qx9 qpexof 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 yr9)fg:)emz8z0 2xxq/kqo tvd,1pr ystone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg r u: k5++f2dr.i pi0fmt hlc2deock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall faskh iplffm: 5.ic tu+ed 2d+r02ter?

Would a spring scale carried to the Moon give accuraf3a .d obmqv07te results if the scale had been calibrated (a) in pounds, or (b) i70 mfb .vqaod3n kilograms?

You pull a box with a constant force across a frictionless table using an attx y0+f bmf;l7vached 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 7l;vf +0fbxmytable), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the in 4d+c((alo1.bk8t)kxt y6sxiv pil /o fluence of gravity there is a net force mg exerted on it by the Earth s68l.ox(od vt1xick l)i4ba (/p+tky. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) neededr i,g4ac s3kq1 to lift a 10-kg object when you are on the Moon with agq is31ck4,r 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, efl:fa t sw:7:tyglz 04ach team in a tug of war (Fig. 4–37) pulls with equal force on 4llzs: ff w:ga :ty07tthe other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a ba0vmfrizb n88+jbb ;1x g of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) o8bfr;1bm 0vnj8i x+zbn what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how larh3ptqh:ct8 miui w/* vo e.8wf9-wt (cge a force does the ground exert on you? Why doesn’t this force make f*w(c8-h3 c mwpiw viq9ot/e8:utt h.you rise up into the air?

Whiplash sometimes results from an automobi dcz :b 31gravqd4sj:v; o.sx9djkg:5:2mw lzle accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seem4:cddbl .2a3:svm kxs9 gzod :q5j1 vrj z:w;gs to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerates,ma5sb q j/ovog6t-z l ;h1f3f7 the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acceler3 6;h1g/vo5a stofl -zjf7qbmate?

A block is given a push so that it slides up a ramp. After the block reaches itkit5k8 103joafqp -efs highest point, it slides back down but the magnitude of its acceleration is8ptf oei013f -kj5qak less on the descent than on the ascent. Why?

What would your bathroom scale read if you weig* m)rpxjv)s z7hed yourself on an inclined plane? )j p s)r7xmvz*Assume the mechanism functions properly, even at an angle.

  What force is needed to acefm(w.uz d4/ycelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ri9mrhg0 (w wd w74pw.ii8qwg+fder 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 ivl2zih97/a gr9s rt gjl,1f; at 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 tt a5bzx2vhvu9j5)ohdip8 08 fb5t q3adk8/h $76-\mathrm{kg}$ 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-kz1y/gmcyxkp hut -31 co2d71 vg car in 8.0 s if the car is traveling at 95km/h? 1xyk3uhd c -m/z2 g1 v1otp7yc-  

  What average force is needed to accelerate a 7.00-gram pellet from restfs+xs,(vkz9 nx 3 h. n+patxu8a jl)3v to 125m/s over a distance of 0.800 m along the b3 s nanvp uaxfxzs39(8) vt xkl++.,jharrel of a rifle?   

A fisherman yanks a fish vertically out of th 4rlm:i//kkau e water with an acceleration of 2.5 rk:m4au//ilk$\mathrm{~m} / \mathrm{s}^{2}$ 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 tracj6 owdi1jrtj 4)2bt3 gk (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 that the matyn18 k- 7ycqrximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should8ncrk7q t1-yy 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. Wm;y/000 1csc9avloa6-+erhsv5(hr fgn rxhwhen 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 the direction of yrcr /( 1v eh+ wnrva0 mh;as9xfcg0lsh0 5o6-acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of k vs(bpa.y m)5g db -+0dzqk)f21,750 N. What maximum upward acceleration can it give the elevator without breaking? ab+ k) g(d fq5mzv)-.ybdkps0   ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg incd hk;kmz1ipyp m3 9w71luding parachute) when the upward force of air resistance is equal to one-fourth kpd7 khmmi3w; 1p91yz 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 housej/ ktgu.a j7io8z5at 2 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 mzj gi8. t5/k2a 7uaotj. 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 cbncw xyqd d +l45m6+i:2z.rpruns vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine thedcdxzp2rm5:cl . + i6qyb+4wn force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for83y 6znd no-w s)*lqtp 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 a baseball (a) at the moment it is hit 4ue+pn6 tjcb7 by the bat, and ag cbu+pt4ej6 n7ain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly gf,b2l;hwe 3e 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 vector dia3eg;efbhw2l, gram.

  Arlene is to walk across a "high wire" strung horizontalcj sp. ym*f09m3v c+hkly between two buildings 10.0 m apart. The sag in the rope when shefyk p9h cm+* 3vj0s.mc 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 f3wyv7v2lzg6 is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0 g*kfw615c8zt 8c;lmqoifgs9y. .w l l$-\mathrm{kg}$ 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*ms .v4d6pbxn McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces b4mxvn dp6 s.* $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 pull-+*viqq 5fg2c.dd now ing two cars of the same mass behind it, Fig. 4-47 . Determine the ratidqnw5 o2*q -.cfv+d igo of the tension 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 hewu o r+37 a+fx lpwyum95r3)ejrself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hersel3pu7 )fl5r e39a +y+xorwmwjuf 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 begapw0*+ sryfl+x n, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mnqtf7:s0f k 3wass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each lo/*4e(z 7;iapokjz5msur g 5other, as sho(gmials7o5 urpz*jkz/ 5 e;4own in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abo /nfl4vlyopci;r/ 0w1 ve the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of 4/vif0l ;lp/c1w ynro 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 td*p 2cbt w;t)a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams;b t2t)dpw ct* 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 fx0d 2i.xdxdt0 riction 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 np30-w,r ii/ jqo9 lu34zqiwhix s;0 wstart 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 t7vw)ss f:;z purain accelerating at 0.20g. What minimum coev w ;7)sfps:uzfficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficin5o-z)k fxc1y8rgm* 1 f(v 4xcr fouo5ent of static fricti8rg f-x)o yko1c5 (fozfmru *x n1v45con between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber andn;pkw*f 0u1 aw normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?;kpnuwf*1w a0   $^{/circ}$

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

  A car can decelerate at -4.80 i-jr2m y..mys $\mathrm{~m} / \mathrm{s}^{2}$ 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 r;q63zhkud u) p:ys;gcough 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 coeffic- ;j a;enmd:cgjg(0 -9mqutls ient of static -j(ac0-el;qtgs:u;gn jm d9m 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 frictio*6 waxhzp rl84n 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 Figytsa,c e j88,xr,kk *i. 4-32 (Example 4-20) how large a mass would box A have to have to prevent ans,e8 ytjk*k, c,xar8 iy motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floa r06n;; py 6cxo2gcoyt 3 )fl+dis.mqor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the p; .t+ oc 6x2ycq 6)fo0lg;apd3imn rysush 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 horizonta-fpcs6 (y1aac hy2.)anq ud4al surface (Fig.a aydp ).c2cy61sq4h-(afuan 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 heavy0t b* 9jni,zup crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoi9 pn,tzbu*j0i d having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your u x8 ,,qbm9m8n5 lvdxjb(f4m fdriveway, which has an incline of jf,v 8 q lm4,(5unb f8mdxb9xm 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 y u::)5pywhx1 :bv kkc 7zfuq:slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilte kuni45 *utc 93h i)yxr8vom7hd 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 initia1npo3a/ z;shbgq(a7dhjvn;+ ewb18eb g f 4)al 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 reacwz pa500)uaf a(4y eauhes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by somes2rh;c rcem:vi(c5k: one pushing on it with a force directed upw ke2v(s;:chc :r 5mricard 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 dange j+ m-mmdo;qxt2wf+ b3rous projectiles as they melt. Consider a chunk of snow at the ridge of a roof w q+w-j;mbxomdt2 f3 +mith 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 sx00sgtafpbt k mq2.u3p og)r mj;w0 ;1topping distance for an automobile traveling at speed v is equal torgu20gpkjf .;apsqbmtt0 0 1)ow3x ; m $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 sl64dt tnf5jj o0ides forward on the dash when the driver decelerates65nf40jjtdo t 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 b hwq4e*ui4c2h4 xn.zgiven 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 tmun4o 5ot/-7 (td1ha. njn zrvo 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 thnut(1non-ojvzr4a7.5 td m/h e 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 coefficigqf57rz/h;5 v d )bmqhent of 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 the bicycle) can coa1mts9ckz21yp st 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 mod+kkxo copegt8oj-,8 7 el of a mammalian heart, at each pulse approximatelxoo 8p-c okgj8t+e7k,y 20 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 reasonaswbd i4n,(qxz3 k 5ew2ble chance of surviving an automobile crash if the deceleration is no more i 4k2wswbd5,(nx3z qethan 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 produc1gfil d5cp-3p ed by an earthquake is a , and if an object is going to "hold its place" on the ground15 dfgcl3i p-p, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the sceng-xy-2s b 6b( rw1zxaqsq97 yke of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a s9zwq-yr 6(1qa2byk s sxg-7bxtop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 mqtvtasns-b x q i8a2-c86yd9m8 .0zxz traveled along the as8nzqt-m8xq- ysz.6dca vx t0b29 8iroad, the 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 of Pibgtp,q b,o 2p.9s/3tqh1yrg k sa and falls 55 m before reaching the ground with a speed of What was the gshpb ,ytb.1 o93qqt p ,k/r2gaverage force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but 8d5:8dobkg; nxr9g7uv1wgrmenters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the mwg9g8kb1:d7rg ;nmxo5dr v8uuddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city.taw-cwp -r.x*s 6)c +mcu:y fa An important consideration is how steep the roads can be so that even low-powered cars can get up the hills wy-m cca* r tw)-f+uapx:6.scw ithout 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*-vpkrm c)w c. watch from a thin piece of string whckmp.r vc*w)-ile the jetliner she is 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 supermav) y 7u11epzloh-uihrgm 69 c*rket, there are to be several ramps connecting differen1ev*uozhu9 1ilmcp -yh76r g)t 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 ) using the1 rrm5x+qr s(a pulley apparatus shownra (x1+rm5qr s 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 accu6;t dzht9jq4v3y3 piu6k.c is6i8 i jelerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an en:lung) *-rp 4 vavsue)gineer considers the following se evv-s: a4l r)pgun)u*t 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 Italijek30nc3o s5 qan train 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 o9vuldc u:-7*brkl x r1f 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 m:vuuk19rl -rc7b* dx lany 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 " 10-1 wbp+h34te b/m $\mathrm{~b}$ 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 realdxcvk6f1jry 5g2* krx 6sm( 9ch 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 roped together are adl wqqt*d9z8q,r7 bj(ppe 3r7/j5pc ascending an ice field inclinejdaqlr*58p9r7/37epwq t cdqp bj(z,d 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.