Why does a child in a wagon seem to fall backward sk5v; muk mo-lo22x v4: iqlw7when you give the wagon a sharp pu 4xl -lwsqou: ;5kvkm7m2iv2o ll forward?

A box rests on the (frictionless) bed of a truck. The truck 6nr:h*w o ;(- mgkqujl.7lznbz49lk k 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 9knhug6 bnl:w( ;rk l.7zk-l4jqo *zm 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 act.z537vcb joc 0uqt)p te1nk9eing on it? Explain.

Only one force acts on an object. C96 ryf3z4fjy oan the object have zero acceleration? Can it have zero velocity?49yoff3 6rjyz Explain.

When a golf ball is dropped to the pavement, y0w* eik g.) 0k*leb tw0jxxwc:ac8 z.it bounces back up. (a) Is a force nwbzea0ic 0yce:xg j0.*l twxw8 .k *k)eeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a la. yqptymit5wh2mi+bw;08 0r uke, why does the log move in the opposite directiy8i.th0p5m w q+b0it; wur ym2on?

Why might your foot hurt if you kick a heavy desk oopngf-gf15 1b2ymt plqbzq o-9 f+u )(r a wall?

  When you are running and want to stop quickly, you must decelerate quickl(0j x-g/uk oepy. (a) Whatgp-jok(x e0u/ 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 rest.    m/s$^2$

A stone hangs by a fine thread fromvfkgjv7o.x1h8 z8zn+ v1t)cu 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 or above it? What if the person gives a slow and steady pull? Explain jx81t.)+ 87oufn ch1vvzz v gkyour answers.

The force of gravity ogk9aze 5:,2 5him5a7 :hdgc rc pkcs;dn a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the m92 gc r5ha;iaedcs :c7kh:z5,5kgdpheavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scaf tw75 (9n e+1snxwvrile had been calibrated (a) in pounds, +9tn7vx w (5iwresnf1 or (b) in kilograms?

You pull a box with a consxe7ksr a.ih)f+k t-2v tant force across a frictionless table using an attached rope held horizontally. If you now pule2t 7v)k-fikx +arhs .l 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 the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the inf.vp8t wwy/5 fyluence of 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 on the Earth. Why doesn/f.y ywv8pw5 t’t the Earth move?

Compare the effort (or force) needed to mem, sd8s1l ()zuw+j8hezb + qlift a 10-kg object when you are on the Moon with the force needesme,ubl1 8jwzzmsdq (e+ )8+h d to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls 7d3k*a mutcf8 with equal force on the other team. What, then, determines which teamf78t 3dcm k*ua will win?

A person exerts an upward force of 40 N t(y p6pre6r; hto 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 6rt erh6pyp(; object it is exerted.

When you stand still on the ground, how large a ;(sf.w1ecgqi force does the ground exert on you? Why doesn’t twifg.q1(ce;s his force make you rise up into the air?

Whiplash sometimes results from an automobile accidenkm 2omc+fh o pumq n;yh741d67t when the victim’s car is struck violently from the rear. Explain why the head of the v6 hf2mkm 74pq7yhc;mn+o1du oictim 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 acc-dpry z c*cs+ /do.h1qelerates, the crate remains where it is on the truck, so it, too, acceleratqdso. yr*1dp hzc -/+ces. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blr (dqh +d96gij1u*vp0f w/wza ock reaches its highest06wuqv9pah/gz w +fdj *dr1i ( 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 18p/.m bnil *xtk dul8on an inclined plane? Assume the mechanism functions properly, even at an1i n8kdl8um*/ptl . bx angle.

  What force is needed to accelerat3m2ro ) 7kf4ekj)b pjme a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and r*m-9zj x itxx(:j,k,svp i h;9trx+f 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 is used to accenzh9yud p,h- -lerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a0jk : ieqmy8/84zpliu $76-\mathrm{kg}$ 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 i:odoe .el,na wwbo,yq0 / (u,pf the car is traveleob(w.y:aewq,, op/, nldo 0u ing at 95km/h? -  

  What average force is needed to accelerate a 7.0ddl:08y ng wl31v1bg q0-gram pellet from rest to 125m/s over a distance of 0.800 m along thel1v 08q dwbg3gnl1:dy barrel of a rifle?   

A fisherman yanks a fish bdnireaz4e.s/ f9 ( gl.f48ty vertically out of the water with an acceleration of 2.59ge.r .self af4d/(4tybzi8 n $\mathrm{~m} / \mathrm{s}^{2}$ 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 track (40kf7 ubb)5-,szc j ax (z5xgo6r2 $\mathrm{~m}$) 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 theku jza/4is tay4v7xmi e.u4k ,9cmz2; maximum acceleration is 0.0680 g . What are the maximum and minimum fsvck. ak7a2t /uz,9e4 izu i4m4x;jymorces 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-e4t- mtpqa jb;81ld x scale 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 acceleration of the elevator, and findp;tj1atx--lm8 e4 qbd the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator hz177bibv3a r.ja 1xg t-:lfiras a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking1 -.3b a ra1:jigxztr7b7livf?    ( two decimal places)

  (a) What is the acceleration of two falling sky diverx snbz ,3tsnq4-lq e7)s (mass 132 kg including parachute) when the upward force of airbt,nzn q4se-qs xl )73 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 stri3fmq6b;y2j4u05ej qf xpb3fv(b2 d orkes the ground below, he bends his knees so that his torso djffoefj42bq 65 r (2v033bqpd; bu xymecelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the p3*,2tu +jk * nsltv7eflfwc9box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the jvslpu+ *2nt7k w9,*ctf efl 3force 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 d.lqu(y-sstczqn 6 8)6k;xrhu iagram 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 m8 9+yk.yb fozr*pip 9diagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flyi.zmr8 *f+ b 9y9ippoykng toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fo8kt;w/ /kqyherce must be exerted in what direction so that the resultant of the two forces points westward? Illus y/ek8;/qhtw ktrate your answer with a vector diagram.

  Arlene is to walk across a "high wire8l9nn8 gsz .jv" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0g.n8 vs8 l9zjn$^{\circ}$ 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 hangini 0;,gcwoz0m onlb1 ;jg 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 14n i0/fmcqe0m9x cv5ngfh5 /:a.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 nem2:/w(ss nhtj 8a37k/olhsgn w location at McMurdo Base, Antarctica, as shown in Fnns7 s8(lmj3o:/twk/s2h ag hig. 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. :krj+8ihw6w 58 wfyyv4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first c 58h+w wy:wikr8jy6fv ar $\left(F_{\mathrm{T} 1}\right)$ , 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 8)effzijy91tnyiffi, 3:0 d w in Fig. i i,ew38zyf ifynj tf)0d9f:14-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, ash38i-msv6 w zr9f ebijp: 2q8 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 kv7wj h21jtj .vfwxw v;i/p/*block (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 chr;85:0s3sa agxt+9kdk8 xf.zt j siqontact with each other,x8rt35h98x a+sk;aq if: gkst0 ds.zj 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 ea;i0l l++p jmznch initially 1.80 m above the ground, and t jzil++ln 0p;mhe 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 it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connee(64x7*vsu3tsul hk4 oe 5 -x fxczb+bcted by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assum4etc+vxuubz sxx3k75 -lo6e(4 bh *fs e $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 kinet1(/r pcjcldrs((w q/dic 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 ie-z8wdpo u0jth;+5gp t.* eq 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. What minimryb dycd7btw.8ljz6/f; 0/ v qum coefficient of static friction must exist between your feet and the floor if you are not to slide? y0ztqv7 cy8//;6brfwj d bdl.  

  What is the maximum acceleration a car can undergo if the coefficient of2.x+kq* k lj ,,fltvvh static friction between the tires and the gx,j +v*f,k kqlthv. l2round is 0.80?   

  The coefficient of static friction between hard rubber and normal stree,5fj*ocxt ;e in-xmxh3ix l 80t pavement is about 0.8. On how steep a hill (maximum angle) can you leave f-i;0ohmt83,xxe* xx5lc i jna 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 -4qv5vo 0bq.a y.t38jyh.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 v3+j w-8h klaqfxg ,5w30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficientx zv;-ui;(fhmu5u g)c of 5zuh; gcfivu-( )umx; 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 kinetic frict2hd64r;sy-ly6 e jva +*du jsqlh)cs* ion 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 4-2a5xjqxfqdk t8bd7gtdx ,fu v 45*.1s;0) how large a mass would box A have to have to prevent any,5xx8td1dubaqq s. 5 7k f*fdg4t ;vjx motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push 1a.63rs*n lq*u rdccrso that it slides across the floor. How far will it go, given that the coefficient of kinetic frictcdu* 6calrqr1sn3.r* ion 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 horizon;9z(ne x5vx4o shi hv:nmn .0utal surfimv(n h4:un 5ev;xx0zn9sh.o ace (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficie ppgon)q,; y*fub+qr)nt of static friction betweeno;+ufy,b q) pnqgr *)p 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 slide against the cab of the truck?   

On an icy day, you worry aboutph4fx(:mltao-lw * )v parking your car in your driveway, which has an incline of x av wom)-:lt4*fpl h( 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 auru9c .upqab:00v g6l 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 Fe( vov fzamr+r; esao)0qgo9r3rpi8 ,4rl-r4ig. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 un1vmmy/u/.fc9 t9bo$\mathrm{~m} / \mathrm{s}$ 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 5fr.4a(8wps ;vx fgz wtop 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 r a0dj*uz:v9dw/w-j ekg:y n+ wall by someone pushing on it with a fod+w9zkdvrj- a/nug*0wjy: e :rce 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 slippery roofs can become dangerous projectiles anj a5x4r 4by;,r4xqaglu:qgw o0+p(a s they melt. Consider a chunk of snow at the ridge of a roof with a pitch ofg xg4jxboy0,;l+4wrra(a4 u5 q naqp: $ 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 trq548-v;d i5i,he t(c,sj zcomwyfz)uaveling at speed v imhj 5qtf;yzs,5,ci i(o z evcuw4d -8)s 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 dzuz:emrpq 5;tb;- ) xhashboard of a car slides forward on the dash when the driver decelerates from 45 m hxrp-;z uzb;et):5q$\mathrm{~km} / \mathrm{h}$ 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 initial s+ .f. 5 (-kwhdgodmqygpeed $ 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 bel8ox (infd)u,opt.l ra.h.x7 i t from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zeron 7xd,o.i (.irlu xpha)ft .8o 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 kinetic fric2u/ r t)tom,luoqd+i;ujrx37tion 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) c0y yz 3ubfc2tdix)y; 4an coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pul6 sx(j d-wadk1se approximately 20 g of blood is accelerated from 0.25d(dsk-w1x j a6 $\mathrm{~m} / \mathrm{s}$ 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 dkfpqz(p8- ty;g j8i 4feceleration is no more than 30 " g 's." Ca i;fgpq8z8fjp4t-k y(lculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an objd80cd4i vaa5bz7 by g7ect is going to "hold its place" on the ground, show that the 4v07zdg75abb ca dyi8coefficient 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 scen7 f6r45m.0boxvwz kr ne of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial spekozfr 4xn 6v5mb.wr07 ed of that car assuming a level road.   

  A car starts rolling down a 1-iy8 t-htip9 m4in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fi 4tim hp9-8ytast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top o;),suw b tobb gh.gv3+nksy7* f the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistan*3; bsk.vysug), ho+ g 7wbtbnce?   

  A cyclist is coasting at a steady speedsl7q9r d7lh4 a of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be s9ll7 7 hrqad4the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. Ai- nu* 9mfo5ikn important consideration is *9m ofun5-ikihow 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 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch f *ego8 ygyc0;grom a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makeocggy0g8 ;*y es 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 connectm- p bjsq4r/d:ing different parts of the storr-pm4sjb /:dqe.
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 Fyr8f *7+kb kbj70 rgtm is needed to lift the piano (mass M ) using the pullrg *tbykjkrf0 +8m 7b7ey apparatus 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 accele*0rx;9z qc bqcrating 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 chw g;rqykc z(*;air, an engineer considers the following sezgc w*;; rqk(yt 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 ha9);-;gbu:re 5hnb 7i(i ;fic q hfmftvs a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of*d9q22q cepxm 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. Kax92qd2 e* pcqmren 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 " 47 sv6k3v,o plcso rxe/v5g0g10-1 $\mathrm{~b}$ 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 alli70e7)f9u f mgg6ozhnowed to reach 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 ascending an df 0sh4 ge: wdw7p,s2qice field inclined at ddf0hs s4, 72qgp:eww21.0$^{\circ}$ 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.