Why does a child in a wagon seem to fall backward when you give the wagon a s9 jj w*(wva/rzq9 ep-eharp pull forwa (a-jjww*e9 /rp9z qevrd?

A box rests on the (frictionless) bed of a truck. The truck driver starts thflnkyyw30md *.:wx2d e truck and accelerates forwardfdx:3*m ynw.y2k0dl w. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are nou 1juf r wk1.8teuz/of3c a4 l:utu70z forces acting on it? Explain.

Only one force acts on an objecbyx2 oe a8tlu60y 7y66h2 k 0x9us lpempy4ne1t. Can the object have zero acceleration? Can it have zyl0xetu yy 6e6b0hkye pu9np x 726o821 4aslmero velocity? Explain.

When a golf ball is dropped to the pavement, it eq gi,/puft;s, 8f,qb bounces back up. (a) Is a force neqt gb/qffp8,ei,;s, ueded 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 the oppov .a:gd epp(6csite direv.ppca g:e d(6ction?

Why might your foot hurt if you kick a heavy3tuzp6y,:v fo desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a)hoa 1s/0rx 7 6bc.gfgi What is the origin of the force that causes you to stop? (i.1/c sfoh aggr0xb76 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 from the ceiling, and a section ofsokk-pl 619au the same thread dangles from the bop k o1u-a69kslttom 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 your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. W1 bqwhx xu.qjjw/m/-l,d: d g8hy then doesn’t the w1:u/m,dx b xj-dl qq/gw. 8jhheavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scal0 5q ycrka o;wru:a)l3e had been calibrated (a) in pounds, or (b) ina 5oac: rq0;)rly wuk3 kilograms?

You pull a box with a constant force across etb5/8 muxe9 pa frictionless table using an attached rope held horizontally.5 xmeep/bu t98 If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the inf: ccct ie,8bbq46i6b p4h oj0eluence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the6qi4eeip6 04:c cjt ob8h,cb b object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift t;ts1gl z(bp,4 imfj )a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw azgm4,1;p(j s)blt f it 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 07pms87c5 byep*lcf qof war (Fig. 4–37) pulls with equal force on the other tylbsp*c5qfc0em 78 7p eam. What, then, determines which team will win?

A person exerts an upward force of 4k5xe/ tyt4 6mo0 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (dm /6ke t5y4oxt) by what object it is exerted.

When you stand still on the ground, hn4 n5bbt k-3ht)y8xlpow large a force does the ground exert on you? Why doesn’t this force make you rise up ihlbk8)34yn-p n5xtt b nto the air?

Whiplash sometimes results frv*.cc8vr+(aat hk pi 4om an automobile accident 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 i*hav( 8kaitv+rc4p.c t really?

A heavy crate rests on the bed of a flatbed truck. When the truck acjnx , ik/vy b,89 wr0z6-vrr6m(ask ubcelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causenx0va6y,9bu rz6 r iswv bmk-8j/r,(ks the crate to accelerate?

A block is given a push so that it slides up a +w*w) p8mp8zpomew 3m jep.g 0ramp. After the block reaches its highest point, it slides back downgzw j8*mwe pmmp0 pwe+8.o p)3 but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale redb1r n9(.j(ocil uxr ,ad if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even ,xo c 1(9li.(nu jdrrbat an angle.

  What force is needed to accelerate a child ohk- sc3x m:m:nn a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider )e+z-+2 l c)b,hat cl*bied dk(ty-zn 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 8wpzl5nr);p(xeu) 0 nm:enkp 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 af:cf zywlm7-9 $76-\mathrm{kg}$ 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 rg4e*r p-h f6vdequired to stop an 1100-kg car in 8.0 s if the car is traveling at 95kmhp - 6ve4rgfd*/h? -  

  What average force is needed to accelt,a 9k x*wsqs;erate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifsqt 9s*,;wx akle?   

A fisherman yanks a fish verticaldu w:r6c/ ,vw8+ wf-v zx+rnhbly out of the water with an acceleration of 2.5b+8vcr zd+:xfwv/w h,6n -ruw $\mathrm{~m} / \mathrm{s}^{2}$ 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;jm)5pkij3u4kyu c 1a7 fbygp)5 o)br 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 )mq4 xw3vt+ cv8 is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor3x v4 m8twc+qv 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 ap mp/6pzuzc *1+4 w:yoih9rbw bathroom 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 find the direction of acceprhupzom9 yw *wi:p/b1z 4c+6leration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevc8e(eaw8jpm 0a5hwg:ator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaki(:eww0j8geca 8m ha p5ng?    ( two decimal places)

  (a) What is the acceleration w7y +svdc;(e9ctd8ve of two falling sky divers (mass 132 kg including parachute) when the upward force ofvcddeye7wt+8( 9s; vc 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. Wdy1je5 ;2w7g jxfu5mkhen he strikes the ground below, he bends hi;5 fxumg jky ej25wd17s knees 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 tied to the 1 :y.2x+zp 2zz 2xy+4pz qgl 9yxtbiobbox runs vertically upward over a pulley and a weib9y y2pz 2zq.+4 ogx2b+i:x z lxztyp1ght is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskef68 zm-w;hw mytball 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 basebaloj;wv kc*hguey;yjei9 s-. .3l (a) at the moment it is hit by the bat, and again (b) after it hv9 ; u;cwy eh3*-i eysojg.kj.as left the bat and is flying toward the outfield.

A 650-N force acts in a nor0cl.p2 +iddcy thwesterly direction. A second 650-N force must be exerted in what directio.d ci0y plc+d2n so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung h;db ag0duu4nwt3x m *6orizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midgwd* m0;6xa4budntu 3point 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 u: (8 pm*dvd jutqxur 5vqs+6-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 14.0 d8z*wa+ m-nmk$-\mathrm{kg}$ 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/yvsc82qtii72mnri /t ye5 i/rk95m l ocation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces 2yii5t r9ly/qi/i 8smn2 c5m /v7terk$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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. 4-4k dpz4gu 0j01,gtchw 97 . Determine the ratio of the tension in the coupling u0 k41cjz,0d hgptwg9between 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 pullw u24ur24tel a53rkzos herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at co z3k42ar4e twu l25orunstant 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 3a,7q5tgu 5eha0heuj wf(bi : 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 bxanhwv 1 mqad1:7. aun6o l+8glock (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, 1 k;oy,w zvq nqj8 w(syi0vvf2tl /sbv2d.c) surface are in contact with each other, as0(. ,vdo,jq);sz2lv 2k / wy8yfn tscv1ibvqw 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 init,r 9r9jatci8(q mv o- )rvfe2zially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. Whatz-omfqri 9,) 8r(cjrv ve2t9a 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 tab6(k9l*mqf qvk le are connected by a heavy cord of mass 1.0 kg . Calculate the acceler (k96q ml*fvqkation 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 kineticd-u(:etu ;uri 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.-x ccqmia51w required to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are stan1b:bik jpd lz s(9/-9m nz-ytmding on a train accelerating at 0.20g. What minimum coefficient k (9i- sy- p:bd9zj bmtzlm/n1of static friction 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 coefficient oft;zusl,/rxwu0e h u ta,-le;1 static friction between the tires and the ground iser/;lh0w,slu-zxte u ;,t ua1 0.80?   

  The coefficient of static frictdg/28ra xhb2uc;3 4rz0qw, iug.og zgion between hard rubber and normal street pavement i3uqz,dg8grg.ga2cuw4z;b h /o2x r0 is 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 -4pfi/w,ts9d 5r.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 omx+ y i/;7rnx*-x7eetgg ume /n a rough 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 hiwet, 4cz,z.h ogh coefficient of statiz ,,tezwho4c.c 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 frictioy9) eht z ztbvg887+non 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 bhx/2 xe-1 -c:k5.k h 7e/is xbul oimmvajma.+ox A have to khxvk jexa.h+m m- a:l2oii/c-.m x1s /bu7 5ehave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides ymffk3sx;z x4jh; z;6across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impart;m;yj xf6f4 zhz;k3xs s an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg1bu3zxr rj :k6ht+l, r and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). 61,hxtzl u : rjkbrr+3A 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 vejz:lq r/( h+n4i2jke 3k t/oa heavy crate. The coefficient of static friction between the crate and tt3/ + j:hkj4rnoziv/l2 q(eek he 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 dttkfizc6cm xr22e- e 5we1h2/riveway, which has an incline otwe2/f c5 mkxc16er 2 2hei-ztf 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 wi)d i4 0xkt-y/ /f-hew;fqrbo e8ydu 3pth 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 plane tiltn hb/pdsh, (w2ed 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 iw9: ub5l+ed.p-nwwwl c; vw.e nitial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reac6 qszf4d.;him9 yr jkxq1mo:t8 4d6ukhes the 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 somm0f2yv rnl( j0im56myv1,w -uvfzur5 eone pushing on it with a foywuf um5 rzm1,n2 rv-mivj5f(y060lv 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 projectusrj0 ,etaac9wxb;7nh :9f. xiles as they melt. Consh 9 besrn0cw.9j7u;x t a,:xfaider 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 stopping distance for an automobile traveling sz5t;pgv5yr 4f-. dtd at speed v is equal -d s.tzf 5 rytg4p;5dvto $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 c0pg+ v+ rnnc1m0 9 . u5vrbpm0esd bmd;/;snimar slides forward on the dash when the driver deceleratd5 dme/n;gb 0mpri ;9sm.+nvv 0r+p b0ncs1umes 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 initial speed jc6z: o:te*5hpk7 yyu$ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the packp+1(jvrgue6 r4yvb + ging station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplise r14r+6(ggv upjby+vhed 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 kinetrs.hi 21 o010evj7o05qjk f2x-dz xubh oc+bwic 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 dowb fbdx+:2s, f+2dvcrwl4f,/qupx bb4 n 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 simplr sn8;jn41lro ified model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 8onr1n;4 rjls $\mathrm{~m} / \mathrm{s}$ 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 automobqzgo u: )gpm,.ile crash if the deceleration is no more than 30 " g 's." Calculate the force on a :)q gp u,gomz.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 ah621x g eqxbd+n object is going to "hold its place" on the ground, show that the coefficient of static friction with the gro6d2beg +qhx 1xund must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two car.e94g-gvq fxh2 dkls5s, 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 xe-2 sgd.g l9v5qk hf4is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travfctgat9+lf ; sn),q4veled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (aql 4tg,ff9an) ts;+cv) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falif.48fvrz f z:e ddc(m *2*cxtls 55 m before reachi2td(ecf4z 8zmifx * vd* .r:cfng the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters :hk hjw6gb*zn8*t-hk a muddy stretch where the effective coe *hkh8ztwbj:6 *-h gnkfficient 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 the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion ofwr17+d, zvw 7 (hpwygk a city. An important consideration is how steep the ro+pwyg7vz1hk,(d 7w wr ads 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 expe/mew y 4g/ri6wriments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airporwrw//4 y6iem gt (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 supermarket, there are to be sev09fkfki5w 2io . 6vbhveral ramps connecting differen w iko9 if2.0h56bkvfvt 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 piano (mass M j1 e2qjzib*ibb7t.2jnhs 1n2 ) using the pulley appara2 s2.biqi1njje *thjb7bn12 z tus 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 accelerh n* r76 fwqsmpo9n9w,ating 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 fb1 ywpor,u bbr:8j( s9ecw*w+nslq 8;or a child-restraint chair, an engineer considers the following set of cond8bo9; :bwc,w(lnerw jqsyu+ *81b psritions:
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 gx9-b*dmdyos9i sm4( train has 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 a*z3p-dw:5iaq4:np w2(nx/6) nu hwfuhqeio safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the w-odinnwuzpqwqa(fhen/ )4 652x:aih *:pu3 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 usinp: ch,h 8hsf7hg 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 bueyr6h hk-od :4m93ae nilding is allowed 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 a*a-q3t f popxwr n)ib8; t asu)::fa9field inclined at 2pif9aa q *sr)u- x:wa;op3btt8a fn):1.0$^{\circ}$ 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.