Why does a child in a wagon seem to fall backward when you give the *2obp;aphhwz3m y g4. y-b ga2wagon a sharp pu2 oba .wp-*p g2hyg ;4yabh3zmll forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the e.t)q9w*,c /bgi.c lgd tcrf7 truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding onql,fcte/ gcgr*tib9 .c).w7 d the truck

If the acceleration of an object is zero, are no forces acting on ivl9uxw+q:7ba;cfr6 -qro fs5t? Explain.

Only one force acts on an object. Can the object have zero acceleration?b8qn, pl 3ngp) Can it have zero velocit8p3n),pbl q gny? Explain.

When a golf ball is dropped to the pavement, it bounces back umwa 3jbf9dn)r. d9riq5ct- 07 ct,zufp. (a) Is a force neededc jz90) 7 u ar 5,tf9bwmcnir3.-tqdfd to make 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 aqxgfsm-h i,, r 32ht2the opposite direcfhgt,q,arhs 3 2i-2xm tion?

Why might your foot hurt if you kick a heavyh7t0e2 msn-at ,mf0k c desk or a wall?

  When you are running and want to stop qzoluf9f l1w/2uickly, 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 lo/z 2fl9u1fw of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from th df-21cupd5jv- ox2x5 ux 1xbpe 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 pud-x21x- 1xuppcfvb o2dux j5 5ll? Explain your answers.

The force of gravity on a 2-gmj2mq9 / by ;3h0wlzykg rock is twice as great as that on a 1-kg rock. Why then doesn’t the hea 9h02z l;wymb3qm/ jygvier rock fall faster?

Would a spring scale carried to the Moon giv3er ,hq;egf: ie accurate results if the scale had been calibrated (a) in pounds, or (b) in kilograme:hfg ;,e rqi3s?

You pull a box with a constant force across a 1yxmn:z5 kr7x frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with n: 71xrzk5 myxthe box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gra55 e-vf2y3*zlm, vymk m9x cqavity 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 foxm cazmfv35k9y v5* yl,m2e- qrce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift s)3fnl5zx :+n qixmsd /b3np2a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally widn)s3 l/ zpn3x2 ifns5qmx:b+ th a given speed on the Moon and on Earth.

According to Newton’s third law, each team inbpvt8 9p5pk -2+dcoqqrws2 *x a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team r cpdtq2+ w9svx5bp*kp8 oq2-will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe th-p./g2wc azr de “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direcg- /a2p zwr.cdtion, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert onis,;5j wel*sb yoils5*,b;e swju? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile org 9d,bu/ u/oaccident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is ir/b,o/ odug9u t really?

A heavy crate rests on the bed of a flatbed truck. W): lgz9 lkasorink 7dt+4;e 4+a c7jyehen the truck accelerates, the crate remains where it is on the truck, so it, too4+ge79ldn7t kczk: s y;4lje )r+iaao, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachesjjn5;1q kw98zms ,y js its highest point, it slides back down but the magnitude of its acceleration is less on the descen;s mksyjn5jq, zwj918t than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined psicz g-yz 5zr5x 5h11glane? Assume the mechanism funcxrh1ygzg-1z 5i5zs 5ctions properly, even at an angle.

  What force is needed to accel96 oz) hh5 pn7nsnh/hlerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and re5 ko sbdeq5ogf:f/+n32uwn*ider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wg* svod/64* git xmn1githstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofl qtub rj3ze;*)c1zuq5zt-f 6 a $76-\mathrm{kg}$ 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 i(s3uj6/ph bde:m.wcj lus-; an 1100-kg car in 8.0 s if the car is traveli/pcbi l3h;s jjs(6u:me-d .wung at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fromo1za i1kiyvqj*n)-8s rest to 125m/s over a distance o)- 1i qyv 8osk1ai*jznf 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verk9e+rdkyhzm2 hl, xg29exd-w t4o6 9 ctically out of the water with an acceleration of 2.5 299 2lydgx+r9d,6ezwmktk ex hco4h-$\mathrm{~m} / \mathrm{s}^{2}$ 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 ca1pmdt)i4 - hbir can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg (istbn2 ;dwr 7) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cab;s inr(dwt2b7 le? 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 thsr0ir nsm8qz*;;0 e xee elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the ele0;08n;qi*e r xesrmz svator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting apb +pcs2i:d g: 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give thecsd2pp b: :+ig elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of y)z x(4zaa9j zeokh m0/uor 8(two falling sky divers (mass 132 kg including parachute) when the u9(aoz km/zo( 8 0)y4rzjhu xaepward 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-m high. When he strikesp89 vgr;2 9fd7d q)5 dlk; ndr;5xg9bozzknqo the ground below, he bends his k;z9v9 8x2d q kq;nrop 97dog; dlnkrd)z5g5fbnees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tiebmsycvl3+ -d-2xgq0: jqux pj5 fq6f(d to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box (fs5xxbl:3jq y ujpq f- 6dc0m-2v+q gif 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 diag1 qip8u43uiya6r k/vkram 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 baseball (a) at the momenpc52mxe8 m46j..vmz- jehjm4a2 ygay)i(z m lt it is hit by the bat, and ama.v5l-me8 g264jymi2 x4c jm(apjy m.ze h)zgain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 65i:piz;w*;0 y q)d-ym rjl )rpdsu t-.ru7nvc,0-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrarscmtiqupyvpulyd:ri*.), d zw -;j7r ; -n)0te your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buibd6c*.m+ vn rildings 10.0 m apart. The sag in the rope when she is at the cd*i6v br.nm+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 bucketajij,8ed0.v8ddps 5spsi + k8 is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.)g:q; (cgatwj2 -ofmf 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 l :i0 mhk7y/2 yxoeqph9tw0co* ocation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The :i o70/hhky9tewy*xc p20qo msum 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 cn i6-p-n;dtrtwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling ;d6-pr nctin-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 bucab 9 *;s *mcgdx3w2fdoket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constan9gc* fxdw odmb32;*sat 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 65ke9 oi 3 rqnz5s7oj53u$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass ez)b-py4a7 oojqp4fhu/ 2/uop* wx2 q$ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with eachdi + yq7t3*pqz other, as zq3 *p7+tydqi 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*:v+r3.j utamx/s tsa .80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't . j raatt:s/sx3u *m+vhit the pulley.]   

Suppose two boxes on a frictionless table are cont lkx fr529gmk f.q6c7nected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the coq 2 59krg 6lmcf.tk7xfrd, 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 kinetickmc6 jkh h (/zv*o .avzztnf*,r0. az- 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 8 e+5j6w wab rumpgdb4+r4zw *e wff28a 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 0o 5)4pxtcb nu7.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slx) pnt5u 7cb4oide?   

  What is the maximum acceleration a car can undergo if tc3ps3fe ndk:9zy1s t-he coefficient of static friction betw:-z1spsc edknf yt39 3een the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street paveme s6zadwqv 1i6;+kl2 y3tt7anbvps4 )vnt is about 0.8. On how steep a hill (p6s;63zvv b 7tk4 t+dsn )yqawiav2l 1maximum 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 ats6 cz0j 7qiusja7 /7pd -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rst fa50i, snk2ough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high c,d 5l;+fht up8for( sqoefficient of stat(ltfr +os;,85hfqdup ic 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 friction**oy)w gvjkf0sm)oc :11x pnq 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:wb o fetk0j9. would box A have to have to prevent any motion from occ0oj9ew. k:tfb urring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across lvg(3bvy5-a bca9a b5 the floor. How far will it go, given that ab-lv(cav9a 3 bgb5y5 the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on d61 bts,cj3 wb9xawa sg.7je0x2sn r)a horizontal surfas7x,)d6b ar e1ws b2na c3sx0j .gj9twce (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 coefficient of static frictionorft 49os5* 45sk:pv szj e tj3osl47k between the crate and the bed of the truck is 0.75. What is the maximum rato44l3tfpe skj*57o rj: k54tvss9zso e 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 hf xnsyij:ibp :/- ai-d67 ds8zas an incline of 7d/:s- ibj6xin 8y-p:ifasz d 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 1p pdlp.+ohw *28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane lmc qdv 0a(;kg ka :jtn3+z(w0tilted 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 spee9l noc//ygt4 gbf-l p.pl61ixd 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 steepest hill with a speed of p;cohbq ,;2tq) akq l*t)h:*b,pbprl 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 o0q xyupeeak.c8l0px4k.je-fmd0 r 9 5n it with a force direct 0 .4x p pda5j8mux9-kf c0.eeq0yelkred 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 slipo+ x))r*avb*/qbmvzo 4m) icupery roofs can become dangerous projectiles as they melt. Con */uv ca4) r*+ooq)m z)mbixvbsider a chunk 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 stoppwnjza2 z, k;-qk/; qd :x)jjheing distance for an automobile traveling at speed v is equq;hj n/k: d-ejkw )a j;zzxq,2al 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 when the d(q+ qif/e vas7o )8w8cefwl; hriver deceleis7 (eqwco88f qvlwh;a / +)ferates 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 an initiaelq/x:4k)w b x+t (u v(ktgy1al 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 th; xn6b)9 ;ygjftaw-vrey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the d wb-;y a6txn;gfv )9rjistance, 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 coefficivz((( 2xkbufr:o kxs4ent of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast downz0lpfcd*ch 2ujmlirzi* , 7*do (k h-( 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, yy2s s*lg2tp2z/oqjeoo 3 u:;at each pulse approximately 20 g of blood is accelerated from/sso2 j3uz;leyg2y*2 op o t:q 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 de- xf5qcly92viceleration is no more than 30 " g 's." Calculate the force on a q-c xlivy5 f2970$-\mathrm{kg}$ 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 1c me ez,c.ph1z+we r.produced by an earthquake is a , and if an object is going to "hoe.wc ze1, h mrpze.c+1ld 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, examinia ;ho,y-v3 4+b)uqh3l0.rhncbn/ghwf2 etwdng the scene of an accident involving two cars, measure 7q+uatcb; wy3)hd w .e 0-/hb3vhg l2fron,4nh2-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 b9w-x34upc9ohe vhr 5a 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 t uvb9-c he49hwx3r5pohe 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 thnr/ 4f pkq;- zcnpta7752yv qre top of the Leaning Tower of Pisa and falls 55 p7kvny/qqc7 n -z5; f2ratrp4m before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stuu:tm :*rxfr5eady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will tufrx:mru *: t5he cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a ci47tqyz 1 ,va(,xe mwqety. 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 pamqe1 ,at4(veywx, 7zq rticular 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, dangl5fc(*0cw 5 fo2zfa 8pvfuuzd(es her watch from a thin piece of string whilea0cuf 52c up(zv8 z(ff5 fdo*w 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 sup6/ agl3v ly+ibermarket, there are to be several ramps connecting differeng lyi/+l 36bvat 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 - yq7j;w- kpalthe piano (mass M ) using the pulley apparatus shown iy-kl wj7;a-qpn

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 accelerao 2988coqrxib ting 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 9xi2lx+lqypa auhr p5-6 h;u.-restraint chair, an engineer considers the following set of conditiol5a ;rpl 9xx6y-uhah+ u qpi.2ns:
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 mai-h1qez7gw;d 9c21sd o2a.gqofqe k 6ss 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, us/ aa cp4r4g (.bkrgm/.kyitu 3e safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a stai//ram4.(c.3 4gtkup rykbg atic 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 usidwz.) 25fov w;ddb1zkng 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 alloh3i,j ecbh w.. /tk1)mamqc4m wed 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 ice field incrku a5-ch/povh,o- .clinedopac,v5/o hhkruc-- . at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.