Why does a child in a wagon seem to fall backward when you givwk n fs; *8r2mq;ihvkkfg. +7ze the wagon a sharp pull forwav s;km7fg zihr*;q+w 8.kn2kf rd?

A box rests on the (frictionless) bed of a truck. The truck driver steat,n5 +7pz vbn /io0ni,sbc (arts the truck az (+pos,ebnn ni5vic0 tb/, a7nd 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 the truck

If the acceleration of an object is zero, are no forces acting on it? Ex;eswom 3,:ejzplain.

Only one force acts on an object. Can the object have zero b;fgca, v*p y2acceleration? Can it h p yf*b;av2,cgave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces jp m1u3 2fdxj4lz9gr 3back up. (a) Is a force needed to make it bounce back up? 4jj23f pu 39lmgrz1 xd(b) If so, what exerts the force?

If you walk along a log floating on a lake, why do y ij-hbj/ozj7-re5 *ees the log move in the opposite direj bh e*r/e7oy-zi 5j-jction?

Why might your foot hurt if y-6 t*er)h1qy+ux d7fof 8ob stou kick a heavy desk or a wall?

  When you are running and want to stop quickle d7j(t5hgm0 l0 l+)wgnvw e/py, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at t(pt57 ng m h+vwe 0dj0)lel/wgop speed to come to rest.    m/s$^2$

A stone hangs by a fine threa)9)bpxf jgnk.o; qv,pd from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the danglikjp.qv 9 p )g,o;xn)fbng 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 isxth-pkr1*a xmyvnf 7i u2y; 20 twice as great as that on a 1-kg rock. Why then doesn’t the heavie uky0y 21x*i2ap hnm;tr-f7 vxr rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale had 3ws: txlq3,-7 a2rjevftu f1hbeen calibrated (a) in pounds, eh3, qtfr2fux vl3w:j-st a71or (b) in kilograms?

You pull a box with a constant force across xzi g- f51zt0e ocx08ea frictionless table using an attached rope held horizontally. If you now pull th 0z5 fe1octx-8ez0 ixge rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net force ip 8hsqpk,z243 grsu/mg exerted on it by the Earth. Yet by Newh,2qg4kspu 3/8srzp iton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-* 1di -fom ma3r ,uybs,cy:eizv:;lu9 kg object when you 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 gz b9v;ydmu, :*iflia 1 :c,eou yrms-3iven speed on the Moon and on Earth.

According to Newton’s third azp fb4 dnjr4eqs ul,/o97 c,0law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team./0dpuljoezcq f , ,ba79rn4 s4 What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe rdue3u715u m p j61c44jdslw cthe “reaction” force 46uj c 5sjd 7 u4rp131mwedcul(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, how large a for0z.34idacjz v ce does the ground exert on you? Why doesn’t this force make you .a c0i3 dj4vzzrise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s cax4bx-4r- +m j un u*zpp9dk. hc.cn4gjr is struck violently from the rear.dbun4p+x9 z- pc .4njrck.m*g4-h uj x 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. Whency 327dyif5s55 ezti n the truck accelerates, the crate remains where it is on the truck, so it, too, acceler5f 3n5s2cedi yiy57zt ates. What force causes the crate to accelerate?

A block is given a push so thax,b2gcbfk+ ; gt it slides up a ramp. After the block reaches its highesgc 2fg,k+xb; bt point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined c49 6j u v/xjgaqm;hw8plane? Assume the mechanism functiqc8j 6wh;gavj/u m 4x9ons properly, even at an angle.

  What force is needed to accelerate a child on azo dgd4ty0(5c sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider a:hn+2a tch 1iut 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope witvk2g.b :djt+ipf :9r6vo6 ymchstand if it 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 asc1jvflunq loa727n9w) n 0pu8kbx/k g2fo3, $76-\mathrm{kg}$ 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 8yhsg xyvf*1g-+/+tb,gql zk2.0 s if the car is travelihkz1 ,+2gfx vyt+ /glb sqg-*yng at 95km/h? -  

  What average force is needed to accelerate a 7.00-m-wl 0m/d+y1ie uebt3g zx; v;gram pellet from rest to 125m/s over a distancel ;me+te 0d zg3ywi/x1;umbv- of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertical.vlmind/ 5r2gxm -+ (hh+jnnt ly out of the water with an acceleration of 2.5 r5x ti2/dnn+n-jml ( hgv mh.+$\mathrm{~m} / \mathrm{s}^{2}$ 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 co +fjw yicx7b8jm,ex27ver a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kw5 s 9;bl-4kj:4kd alg3gnynrg ) is to be designed so that the maximum acceleration is 0.0680 ;a4:-5nr nkj 4lslkw3yggdb9 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom su3m8xnw os 7w8cale 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 accelsow73n8muw x8eration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-9b be5p niy58akg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator9ybb5p8ni e5 a without breaking?    ( two decimal places)

  (a) What is the accelegd:r29 3b 50yxxh udbrration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their w 3rx20gxrd:buh d59 ybeight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m hig i(l6kidwafk 9r2wg)6( v6,9kb rffeth. When he strikes the ground below, he bends his knees so that his i9f2irk66v ,k9gfbeww f ta l)dr6(( ktorso 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 tie ;(itb b0jvpj(d to the box runs vertically upward over a pulley and a wpbi (jb (;0jvteight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketballl6n nqir 2um*) 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 az0pu/ou (z :d(hi5r nfu5piu4 baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bio:huf/uz5z4pud iup05n (r(at and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A sz)b -dsa ,v ): *cv*kzhma9edxecond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answx d:sa*-habe9 ),*c)vdvzk zm er with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally b(1opa* q1rcuwue t5i +etween two buildings 10.0 m apart.e 511i (ta+*qcow uurp 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 ha n8midbq60r 0dt qj i8r727e-wu0awarnging 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 14.0e 9mhqs zc8/e4$-\mathrm{kg}$ 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 McMurkslxix4* j.3qg1twy-do Base, Antarctica, as shown ing*3.4t wk xxiqjl 1ys- Fig. 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 cars of the same mass behind it, Fig. :v ssoa9gi;-;r1hyt d4-47 . Determine the as 9hy; :vr1;idt-sogratio 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 herself upward using the bucket-pulley apparatus shown in:rbxghy56ao s9sg9v egn, h2* Fig. 4-48. (a) How hard must she pull downward to 6 her:9g,*v9hsb 5oaggx 2y nsraise 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 racahoo 4mqnc1i2tf7e) 6e began, 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 +uq48nl1 nknzbew4hd6p03 i kblock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact s g;vq5/ e vyoyv,6i.qwith each other, as shown in Fig. 4-51. A fo ove.v;/yq5sy6 ,i gqvrce $\overrightarrow{\mathbf{F}}$ 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 +)vsq 5j d+t/w uf)g;i,(veeir4eno p Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume ij ionpvu/ee t +);( q5d,ifvswgr)4 +et doesn't hit the pulley.]   

Suppose two boxes on a frictionless tabvru5; )5k )vwnrzq1ukb ,l+ek nxge3.le are connected by a heavy cord of mass 1.u)5 3n 5vgr.wqknueb)rlz,ek1v x;k + 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 k5yb .udug xp: 2ov9/rhinetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a /dh7 e 72mrjvhm r-q+;uk 3axz5.0$-\mathrm{kg}$ 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 accele:u 4(mprin zl8dw* cj5rating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slinj:iu 54r lm8dw*(zpc de?   

  What is the maximum acceleration a car capt *vh/e*,jk6a(rox;l c; ftan undergo if the coefficient of static friction betweenv( x,*c;k* r6htta;pjlf/oae the tires and the ground is 0.80?   

  The coefficient of static friction between hjaw );pdoa7 (rfmw1/ eard rubber and normal street pavement is about 0.8. On how steep a hill (maximum mwep)wrfa(7o;ad 1/ jangle) 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 x ; /.h7/:jfs 7muij mfhwff2m -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 zoge )2z,t6uukrff1-v b0r 6i 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 surfacefdsra1h;*7 bz have a very high coefficient of static da bzf*r71sh ;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 g m4:- nq91k6sn utvxb :bvx3zfriction 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) how large a mass would box A have to -ks u,a: b;r/g)qfv02mx f amfhave x ku-af2qsfm r f m/;)b,:v0gato prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so tha 3fn/ow;d1we at it slides across the floor. How far will it go, given thwan/ ewd3f1;o at the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 k,e;c)jsgcyoj(4 c7i e g and 110 kg , are in contact and at rest on a horizontal surface (Fi(jo cjc g)7yee,;si 4cg. 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 crat( faxkx-* 4g mfv5c4ase. 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 dfv4xfam-s*x a( c k54gecelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in yr1rg-a udr / 6boqg,t7our driveway, which has an i,u6 t/o-1 r7aqdbrrg gncline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a pvmh4/imomg qyop2g+vd + 6p;al76-i 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 planu73hyrfv) i q9e 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 v cupawh5:0y3rdb xsatn9* +4 initial 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 steepeyeu9x/ueu37 i4j avbt7(rig( st hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone puship maen ;7o/ j u0qv9*v3nn/uieng on it with a force dire309/u /jnv7n;e v uop maie*nqcted upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerh-f q3u0vrz u(chq(-gous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a uucg3(fr- q-(hq0 hvz 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 distancessyx2,wq1m e* for an automobile traveling at speed v is equalemyqw 2s1,xs* 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 dashu 4h/f3f6 o;fjdmcs*7 xo8focboard of a car slides forward on the dash when the drivehcmus 47f;8dx*3 ocf/oo f6jfr decelerates 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 mas uyut;s (9o*t37eega -nlcg( us 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 the*. zm2fmh xgez1/ o c*2kvvyd8y 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 f*vxdvm ocm82z /kh. 21zg*fyeor half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetbdc:c4idxk 1x (1gbkkj(4qrl;ajr- 3ic 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 c1+nb* jmy1r ttoast 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 simplifc uk4rn-vsyz0*r qm3 *ied model of a mammalian heart, at each pulse approximately 20 g of b m4z -r3*rcuksv0*yn qlood 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 h7t kz enm k(f:u,d7v,an automobile crash if the deceleration is no more than 30 " g 's." Calculate th ,efkmv7nz7 (ut, dk:he 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 hvt+4v cr 2kf,produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficienfr kc2+,vt4 hvt of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accidenth vx edo* lc4s*nq8vxj2-+u:r involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level roa8* e -x2d lj+r:s* xnhc4vuvoqd.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m.wtg ab:x51qo traveled along the road, the eb o5 :tx.awgq1levation 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 dropp) rbv.cz)x:,gf* nzhky4;jcped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Wha:g)c*) zcn 4; f. jkyxpzhrb,vt was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy sv, p5thqz4e(bq ,johhu*n / j7tretch where the effective coefficient of friction is 0.60. Will the cyclivn uhb5/ptj, h(q,z* h7ej4qost 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 working on the redesign of a hilly portionby7e ice:5o6*4a cdoj(y 0vnt of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills y:ytnj*7c0ov de 5ec 4bi(6aowithout 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 w c7tw:.(w6h vdd(mxo iatch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes .oh wvi( tm6:w( xdc7dan 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 a.lq:la3 y.r1* xfjzybre to be several ramps connecting different parts of the stor.3j x:ayll* zfyq b1.re.
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 ) usin*twxz-p:0b hzykfqb )-51 dxxg the pulley apwh xzb* 510 )fb q-xypxzdtk-:paratus 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 acceleo;7le t bcet4e t66,:puddz+vrating 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 chayvn; edx/4i 8uir, an engineer considers the folxy;div4 e /8unlowing 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 train has a mass of 660 l76 )mb echenc;u(v4m 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 ropeyt 9ra0i/g4l qt7dxbaksn/ w-.1nj6hs 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 01 kt w-t/jyq ir /blas4ndh69.7agnx 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 " 0unpdfz6 tfdm-2oiohi2 5ym5 .b 9 /am10-1 $\mathrm{~b}$ 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 l6./n dqk( tjqdyw77b3.5 $\mathrm{~m} / \mathrm{s}$ 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 togethez6y ihtmb6f/ i*;t1zur are ascending an ice field inclined at 21. thfm tbi6u*/6 iyz;1z0$^{\circ}$ 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.