Why does a child in a wagon seem to fall backward when you g5p n+gqvm c5r;ive the wagon a sharp pull v+p c;qmgn55r forward?

A box rests on the (frictionless) bed of a truck. The trur u ttk 4zy*kj), ;azy5bj4,knck 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 Maryzk4a, ,; 4j t)nzbut*y5krk yj 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 for* wnkbc70gvkoh v:d+-ces acting on it? Explain.

Only one force acts on pr b p17- lwug5 ,jvuxu3e5g;f 0tic)jan object. Can the object have zero acceleration? Can it have zero velouj ;7l1g5tgj pbcp,uu3r-xfi vew0 )5city? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a for y,05wwtxwoh( ce needed to ma(xo0ww, ywh 5tke it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the op7sy ;vjsf. e08z1qbhp posite;p0qs 1fzy87jbh.vse direction?

Why might your foot zn jp20(q0/z*4cpd vy;uflxc hurt if you kick a heavy desk or a wall?

  When you are running and wa,t6i(sg*.+cpxur5b fz 2uk xh nt to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the max,2 6sruu(f x5zbg*pixtk +h c.imum 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, andedg rx)4c9utg2k1/jh 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 dangluxhk4 degc)tr 9/gj21ing thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is tc0o 0-4g/2(8q 4mj 0ppwklyfptcx smuwice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fastex0 w(o 0f yp/ 4m-pg 8qusmctp02jcl4kr?

Would a spring scaleh9/ wmh/ wf4zq carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (bf h9/wm qzwh/4) in kilograms?

You pull a box with a constant force across a frictionless table using an attax+8gfzy 9:8p y;5hu1(a- a no xlxnvhpched 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 table), does the acceleration of the box (a) remain tplgynh+(n18a zx vx5p y;-ohxa :f9u8he same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a tb jm l+bus4cpe1 v;.39y j:xfjdkq;9net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force o:by1u;t jv e9.x cmsd4 j+b;lpqk39fjn the Earth. Why doesn’t the Earth move?

Compare the effort (or force) ntrp eg.b.9p+h m60ihceeded to lift a 10-kg object when you are on the Moon with the force needed to hm+.pe9bc. tpr h0 6iglift 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) pul8:3)aoawws )9akjp zsls with equal force on the other team. What, then, determines which tea)ao:wsspzw9 38 akja)m will win?

A person exerts an upwardk/a m;7p/j/o mdpzjdo5 eelf8x9l t,4 force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it i4p87jjkld/ ,mxf//eotez l;a mop 59ds exerted.

When you stand still om t:7b.o;uhlbe 0vhub63pcd ;n the ground, how large a force does the ground exert on you?v73c0bohu.btdh :mepb;u ;6l Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’c,fs3vr*qgp)((n9u/qupn v k s car is str(g3, pq)ukfv (pr/ cqs*vnun9 uck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acce9x3-upt( scmf56 wabelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes3-9 c6as(um xfbe 5twp the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachesra4+ wj 9tmo-u its highest point, it slides back down but the magnij 9-u4 w+motartude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighervv9 mt3j1w,bbm 9o1 ld yourself on an inclined plane? Assume the mechanism functi 3mvb191vjortb lm9, wons properly, even at an angle.

  What force is needed to accelerate a child on a sled +3 rs2+cdiix ytl-ge 7at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2ot z8a5jn i0ia5;unx2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is ussuw 0qn.s/vy- ed 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 qz:bswxp y0 1r(de vxzc.0t,8a $76-\mathrm{kg}$ 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 cx6j56:-khn3di;lhks yn ei m0 ar in 8.0 s if the car is traveling at 95kmi:nm5sejyh3kx -0i 6h k;6 nld/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fr:zr1v 1(,nrqsal 2biyo 6q w1nom rest to 125m/s over a distance of 0.80ao1w2q(qrzs1,iynr1 ln b: 6 v0 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an yv88am0 yq es0acceleration of 2.5y08 0vsya8e mq $\mathrm{~m} / \mathrm{s}^{2}$ 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 qu4d loz*:2pt mnqro4+jarter-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.6wa6le22 iu 5uajc hs be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportiu6 s22 e.auaji5wc 6lhng 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 thew) kpx*tvx;i8q*nyg/ elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the vw tgyq**/p; k8)x xinelevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125k vitx50 6or2 wq9tv 9y4cqy8q-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without brey9r4qvc86q2ktiw90 xo5t q vy aking?    ( two decimal places)

  (a) What is the accelerationiy1plfp *v 5-f of two falling sky divers (mass 132 kg including parachute) when yif -l1p5pf*v 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 roof of a house 3.9-mc, 8qn 8*u+vtgjyht7 r high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate diu8jv+,yrct*q hgt87n stance 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 tc;b2cblk 9)wiq b agc42 inv07able. A rope tied to the box runs vertically upward over a pulley and a weight is hung fro 2w 4banvicbc;7qc0) igl9 k2bm 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 diagramtgu8 g.*k(,)ulmgwb dcn.g /4p:sgk j for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a bas h,mzx s;o g kxl0w,wya)s..kc( ,y1qfeball (a) at the moment it is hit by the basxxh.a sf,,(k1og0yyzk)m w ;w l c.,qt, and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directionhuxigu*wi6. dq (6d8m . A second 650-N force must be exerted in what direction so that the resultant of hmq6d uxiu(d.*wg i68the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bak5iq rdb ,-(ud/mtruz**o* b uildings 10.0 m apart. The sag in the rope when she is at the midpoin/td( -5zbru * am*i,urdobk*qt 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 u2n32xfb1q l , sdo0q9btr dh8massless 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 191pnrlz7 l (v,xb9lm :eal8o l4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Bn .dcbsq:lrv7 kc1qhzm(7p 8*ase, Antarctica, as:7lmprznh (qqk *.vc8cbd7 1s shown in 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 tp- nxmj; ia/8sprq0-bn e 2fnyszd6r ;8q3f8d he same mass behind it, Fig. 4-47 . Determine the ratio of the sy6xs d ;3-p;8r2 p-dai8fznfnrq b /8nj0eq mtension 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 inu jl kurh.ef729k0 )ux Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant spju2u.7 r9)lexhfk0k ueed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a lvb7zn 808ipw du52vi65$-\mathrm{kg}$ 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 blocto k+p6i7n 2efk (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 surw9gilk 8,hit( z9c9jg face are in contact with each other, as shown i 9 hcz ili98wtg(j9kg,n 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 above the grou 3g9lly lf3w3 qyg29hcnd, and the masslesscl9lyh 93qwf3g3 2 ylg frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cords2 qv3d cyhnxvvq ;5s l4 8ags/ql*0a- of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of qs34 gvd-c0nlhx8yq/5q;a v*a2svs l the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between aol,l;*illsze : q;nxsy fb /-0 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 requirem4g0j go+4udud to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing dl), dq ;gs(.)kfswzzgxhv -v 2j,5bd on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and thebd w2hsxzd ),z5g,vsvf() qk-;dj .g l floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient s+ 5gai0vnt(42ntsxwb92n lxof static friction bgwv4 lb0+(2ntxn xs5at sn2 9ietween the tires and the ground is 0.80?   

  The coefficient of static friction bv, q92m n)nitjetween hard rubber and normal street pavement jv2tmn)q 9 ,niis 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 -4( krrdv4 clj81.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 30hr+zcbyie:9 56lj z4i $^{\circ}$ 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 ver. b6sz*u6lfi ly high coefficient of fllz*is6.6bu static 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 kine4wj +f8iw svjay9a59v1 ;kqgco1 5ot atic 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) how large a mass)y eu-yg, q09gfc -eaa would box A have to have to prevent any motion frua,e0a -) efgqy-9cy gom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesht8 r7:5*e0abpwr.um aw8 k ro across the floor. How far will it go, given that the coefficient of kinetic frwo uk0*wt8aheb 87.:mr5p rariction 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 horizonta*zw,- gr zp,:dp ,peraeth* rc54/nexl surfacea /hp*,zz4,n5exrp-c peewrg r: ,*td (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 c1s 2osp05zgqio78 -b heh. fxprate. 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 avoid having the crate slidxhss0z p ie15ghp2. o b78-qofe against the cab of the truck?   

On an icy day, you worry about parking your car in your driveur crqzb6; 85xway, which has an incline rz;uqr5b8xc 6 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 ckny; n5ky.cdcvda5 ;pjil8a0z c-/(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 pl rkz om;2yh;w69m9mnoane 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 id:k:d q;a3il d3ysm (anitial 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 steep/f sel7.2 zlmgest 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 agai2f.mhu2/q e4u bwvtj d:(-f cjnst a rough wall by someone pushing on it with a force d :(. vequw hfj2cj4dtmb/f-2uirected 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 dangerous proy b);wzlgp z 7x(wd;wzq+4v/ pjectiles as they melt. Consider a chu+w w 4vwqz/)zgpy ;7dbxz;p(lnk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile trgj)q cj5; h6mqaveling at speedjghm 56jcq); q v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash g8b82b:l yq,6bxe ,wsc nr/o rwhen the driver decelerates fro2b cw 8s o8y:rn,qe xlg/6bb,rm 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an knc6klxi 8ez-0t foo c: x/(f7initial 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 fil;f(j0al*mbj a8; seod led to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rfa;lesjjb a ;m8(d 0o*apid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction2xxt s/vau( m) 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 coast down a 6.3f0fv op vybs n3 y:atrp2*sj v6,k:9vwr1cd00$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approximatel9 :pwdgmxj,pmjnkr 8(p)v /p3y 20 g of bloodprp,xj8(:k m d9w/ p jv)ngp3m 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 / w)5 et19gtbxczuiv8an automobile crash if the deceleration is no more than 30 " g 's." Calculate the forccw ux9)tb/zvt18ei g 5e 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 procbi-6xb 3r+jhduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the3+b xcjb ih6r- 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, examininz8n5dr s h5b0ys7 xutru7+ h/edeoc1 ,g the scene of an accident involving two cars, measure 7ehssy5,7t x uor/dh1u7nzr8 c+ebd052-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 road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 meamu vu3i4,.g pjns that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going whj.4p gmvu,iu 3en 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 Tow .rw96mqq*qf ner of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistw6 *r.f q9mnqqance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy al /iry2*bic5f29 byj7uc.xen8 (aihstretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedafil5x nb ii2 yc*.u a(/7r28jcebh9ayl if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is wo7llr;u(.:i)qrz- x reldf.eerking on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 110ulf(r-.:)zl 7x; e dileqr.re 0 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 5hcv)6ks rjy3experiments, dangles her watch from a thin piece of string whksc3 )j 6hry5vile 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 sb 70taotp: d: hoz1i+tupermarket, there are to be several ramps connecting different partht:db :p+7zia o1 t0ots 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 ) usi4o()q* usz(b a tke.ulng the pulley apparatus shown in b.uezqtk(uaosl(* ) 4

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 acceleratri( f4.1nhk vjing 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 enginee0 ztbrzy3rjja.k 4*rym 1z:i 0r considers the following set of conzji:1 ambyk0 .z4 rr0y3*zjrt ditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (pv8pi* -cl1o 6ow.yeo660,000 $\mathrm{~kg}$) . 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 opt7fihoc34g bpr5 1;;0 :w0cixe yzyrf 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.)1e x;ifc;0oyrwcrg4b z5h3: iptpy 07 (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 isn(+ uaj 6cedkymu(4 whb3m5q2 using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reacp:0uu 3 1cysich 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 ch*h-2i 9oppkascending an ice field inclined at i 92 hphk-poc*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.