Why does a child in a wagon seem to fall b*ae-sc pr-449kbdkmqh+cj 1 x ackward when you give the wagon a sharp pull for9*d+b-xcjchmr k s14-ak4 q epward?

A box rests on the (frictionless) bed of a truckxpk(9fnn86q 3mua m 1f. The truck driver starts the truck and accelerates forward. The box immediately st9 mnp( 63kfmxu af81nqarts 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 inp ji 9..:cqvgs zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the ob9 lupnfj7x 1z7,fr0zj ject have zero acceleration? Can it hav,fzjupl0 nf97rj7z 1 xe zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounb54n 6u* , qfmnebgg4aces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the 4nb,fgb e6amnqgu*5 4 force?

If you walk along a log floating on a lake, v sz,vd 3r5ad +., zcm.lyj3nnwhy does the log move in the opposite j3dvzn sc,r y5ad3+, .vmnlz. direction?

Why might your foot hurt if you kick a heavy desk sqwl l8g,9dc: muc)n0 or a wall?

  When you are running and want to stop q*4. -czvoja g6 v:iqnluickly, 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 top speed to come to rgvizql:o*4 jca nv.6- est.    m/s$^2$

A stone hangs by a fine thread u2 :nfke l1*qt0pcz6wfrom 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 dangling thread, where is the thread likely to break: below the stone ore*k q201lwznpu :tf6c above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on )bo vhzlhy 5,jfa3s c4bq7-i7;nv8:e4 dx cjb a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall 58oqb bcenv7b7- 4y3zcvhj4sl; f ,i)x:jadh faster?

Would a spring scale ryk9 b q,95 ddh,wl.hgoziz9: carried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilo5i wol hkz9gd 9zb,d r:qy9,.hgrams?

You pull a box with a constant force across a frictionless :yhsz d()f9shkd d30j table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining fd3shfdhj9kz s:yd0) (lat 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 9jiyq-.6 b hg),9u wx0izq vrfof gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force )9ybifu qx9wgz.q 6,j rh-0ivon the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object whx3nv9y 65 hax m5ql6glen 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 given 56hq6l3 x9vyl5agm x nspeed on the Moon and on Earth.

According to Newton’s third law, eb2arvsudp.28f idd))n( v2 k0tx7wt cach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determksb)pwd 7( fn)u.28 dacvr 2xtdvi2t0ines which team will win?

A person exerts an upward force of 40 N to hold a bag o,hzo ciq 0hl3*3m2; td qi.znaf 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 o qhamq.3zndlc;* 3 2,hz0it iobject it is exerted.

When you stand still on the ground, how large a force doeszu amjst*)6 oqzz ,6iu54q3ry the ground exert on you? Why doesn’t this f 3urzmq56aqizs) 4y6otj u z,*orce make you rise up into the air?

Whiplash sometimes results from an automobile accident when zl )cs2 rlgnt2tz0u5i h l.gzlc.8,l: the victim’s car is struck violently from the irnlt,0..ggctl: z5z )cu2 lz lsl28 hrear. 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 j4+6)igfxjv *kkfp h7 truck. When the truck accelerates, the crate remains where it is on the tgffk*7h)+p vx4jjk i6 ruck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachg4 qms3e)yxu9ub v8.0zgqn+b es its highest point, it slides back down but the magnitude of its acceleration is less on the deseq+ 9b3nusxvqgg)0 4mu.z b8ycent than on the ascent. Why?

What would your bathroom s3jr*r-d 8t( oac ;ejp12jmno7k;svbxcale read if you weighed yourself on an inclined plane? Assume the mechanism functions prope*;t;jsd b (-oma jnxr3jopc 1k2ev 7r8rly, even at an angle.

  What force is needed to accelerate a childdzpxr2 i)3n23cr o)zmmmk9 3 o on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bik6hnbrdjq4cp,f4j 6u6e and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it 1 *jekcotn(kb;.w zv)4+ b.,2z2i qqizxfnab 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 jyby5*i-b;e j eln -m)8e9aty$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s 5j+g- pj udvy/if the car is traveling atu-j/y+ gpd5jv 95km/h? -  

  What average force is needed to accelerate a 7.00-gram p.7sml+nh xj :pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rif:hp.l7 n +msxjle?   

A fisherman yanks a fish vertically out of the water with an acc2 k 3e36c8lexcbe3lis khrj 1.eleration of 2.5e3 ec3c ekb khl 2s.lr186ix3j $\mathrm{~m} / \mathrm{s}^{2}$ 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 track2 mtgug5l2 p,*d kka( o4)natl (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 maximum yd8kq1n*-y tl7ju2j eacceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? m-7du2te 1 8*jylnyqjk ax =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the n ;a4 qu0ybw+hr, onc.elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calw+,c ua0nhyqn;r.o 4b culate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator ha3np sukn1fk -(jbacz,j q5 5 i/fv4fh8s a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? quh4ajnz5pf3(/8kvbc5f1sjk n-i, f    ( two decimal places)

  (a) What is the acceleration of 4zf md(r ilh6qhr)+ d-mg 6*w wve-sl9two falling sky divers (mass 132 kg including parachute) when the upward f+*6ldseirdg-w9h rmv4hf zw 6lq -m)( orce 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-m high. When he strikes the ground yop ut dg+-7rxlyvuq(52*;mnq k 2b(fbelow, he bends his knees so that his torso decelerates over an approximatpurdxy m2o (l(7g-n y5t;qqbf+vu *2ke distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box rmxquui )99a 2wuns vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine thx9iw u2mu q9)ae 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 basketball player bniuv1 b w7f46
(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 z, p3pb1;ln1smh u6n2q db:xo9q/ jpaa baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfi/n dp ; m,j3ba :pho9s21xb qup1l6nqzeld.

A 650-N force acts in a northwesterly direct j; e1px(d5xfnion. 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 pxde(f1x j; 5nvector diagram.

  Arlene is to walk across a "high wire" strung horize4 m0rxqy .xxee: 56igontally between two buildings 10.0 m apart. The60.x5m x4 eer:xg qyei sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from anothern s +30fpj1dkpv4prb f1 w8jw- 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 1ojyz5 -jdkh 6q 64h0dm4.0$-\mathrm{kg}$ 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 t zcy+8ojqv+ovs kou:-v7t2t3 o a new location at McMurdo Base, Antarctica, as shv+tjo-kzq2+t7u vso: 8 yc3voown 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 the same mass behind it, Fig. 4-i046jj k tj7:(ra m ti5uespj747 . Determine the ratio of the tension in the coupling between the locomotive an7mi0 6ierka:t 54p7jjuj (sjtd 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 a8,ya fcn v1tplct 6a:/pparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constt cpfl6tc/8a ,vyn:1 aant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a wb0x 9s. w8zchfk+y*f65$-\mathrm{kg}$ 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 blocs (ud. /7gzrvgk (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 suip1*ph)wmw drct3 x,)+ )neo i.fpj;qrface are in contact with each other)1 d;etih+wjnormf .cwp*q) x,p3 ) ip, as shown 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 above the f;8 dmei . qzle11ssv-ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after isz- 1lmqesvf .18;dethe 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 x utf8 zk2ezgjg-5,0h cord of mass 1.0 h u5k0 ej z-z,xggft82kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction bet:og)bwl eh/ s2ween 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 start3 rtu 3s)aco+.pm*a sq a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. Whasrouq7q2m9ss/ nhs36 2 lmev1 t minimum coefficient of static fricts7qr3so2me2 6q 91us/ svm lhnion 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 coeffici9l4 /)k rrgkynent of static fri4nr9 /k lgr)ykction between the tires and the ground is 0.80?   

  The coefficient of static friction betweenw:/e6+4t wq, mvs b1: sytaj rql0j;ui hard rubber and normal street pavement isww/rtqvqsibl , :ts+mjy 4e;ua:6j 01 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.jgsrk.r v wu9hb72)j080 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough9 jjtf;aecw0 )s :mbb, 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 ;sv, kdw+8u;ja pyei-with an asphalt surface have a very high coefficient of staaw;;s -p8ie,kuyj+v d tic 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 kin*+vm 5hze5sg fetic 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 would box Ao 37n5dr2 mygu4kh ;ro have to have to prevent any motion from occurring? kdh4mroyo; g723u nr5 Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go,*,u4a,s) ozbzck+6c./ek uu p2q)gifa6 a l vn given that the coefficient of kinetic fu/+ig, 2oze ubv zc fq66,aupa)s*na kkc).4lriction 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 contacp4 ks7z;: ujrct and at rest on a horizontal surface (Fig. 4-uz; p4jrs7c :k54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static frictiscnw r-0lu;)qw. j7qr;tzsj4 3ce:uron between the cratc )qsn4w ;jj t-307surrqc.w erz;:lue 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 slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has an v d(/o: /)nahxfffy2y incline of 1)/f(y f vn/ofxyd:ha 22$^{\circ}$ . 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 b0lpa gmiz b8x l8-)*kslide 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 5cyyc deoclw o.(m3y5 1qt *)oplane 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 initial speed of 3.0 qdq zp zng1r+*3 vakjv :2)k0y$\mathrm{~m} / \mathrm{s}$ 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 theoij4 2*gnute)+aqsi6- cz /wl 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 someone pushing kqmtkd )3i:*edfo 6f-on it with a fort )i-qdf*36f km:odekce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slip;raes (lk 2cd9u9 f+lup)fw8 jpery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge oefw)u8;ll9 2a(cu rskf9d p +jf 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 distasx2y43 *mxdvl8 xn7lf nce for an automobile traveling at speed v is ely*msx2v xlf8ndx743 qual 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 w;se qfe .oe02lhen the driver deco. seleqe0;2 felerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given anvcs19c2z l / rr:r65z-yv.mctb q)jtq 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 nhw*qgp )-p3n are filled to the packing station 11.0 m away. The belt is ppgnqh*n- 3)winitially 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 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 kmrv(kyq o v)k 92/y3fo/-ggwninetic 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 +mro; fiuw2lo3,g m+tthe bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplifc0)i:a7gzfxwe3m u+ i*4cbm vied model of a mammalian heart, at each pulse approximately 20 g of b4g+ ic0 wif)c aevuz7:x3 m*mblood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the v*7p,vp q5 tijdeceleration is no more than 30 " g 's." Calcupv pj* t,q7iv5late 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 accelepfq;;5f th l+cration produced by an earthquake is a , and if an object is going to "holdqf;tc ;hp 5f+l its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene 2 skmwr*2wpp9of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about rkp wpmw 2*s920.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down q)zsvd oisbnn/v r;14*c-v-bow )9x ta 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friv-) r/4bso -ox ;bzvs*9vnnqc1dw )itction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the tov,kj *i3 ,iaxzp of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Wha ,kaiv *zj3i,xt was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mu.99p3jg wofakddy stretch where the effective coefficient of friction is 0.60. Will the cyc39ojk a f.gwp9list 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 workikxb *sm 8,r1to+ 7cixrng 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.+s7c r xom8 ir1,k*txb 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 wxm tg:r-u,kh5atch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the strinkut: ,rmh5g- xg makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps coyu f/v w(fo2s2-r fcm.nnecting differentf rc2mso2 f(.wy-u/vf 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 6 oc e*+ 7ez-rnodnu,mpiano (mass M ) using the pulley apparatus sh*,- 7e6r mdo econz+nuown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3)c; (flfh,z huq1i1dne2( gyp.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 processvn*:ve2i x(k z g,f.ta for a child-restraint chair, an engineer considers the followi *( viz:v tfg.kxn2ea,ng 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 metric tons wb-t,zi8lik1tt nd(,. n ci.n(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 (nrnljz 1pes .l. vyelhf: /(,m 1lj7wKaren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bil(/mfjn.:l1(.s1 y,w7z vleejr nll hpl has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-wq hy3i s7xw+g u,x25m1 $\mathrm{~b}$ 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 o/4cg1b:j ts qlf 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 ascending ant xliej nmms3 u9-*z7- ice field inclined iu9* ltm7 -n-smzje 3xat 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.