Why does a child in a wagon seem to fall backward when you 3b92etpa q*p-fwe)q,r 2 y kazgive the wagon a sharp pull forwfqwtpe r y-,a2) kz3 pa2eq9*bard?

A box rests on the (frictionless) bed of a truck. The t4b x(jg1x 5livruck 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 Mary standing on the ground beside the truck and (b) by Chris who is riding on the trucx i1g4 xlbvj(5k

If the acceleration of an object is zernm2 baj.(m pu (nb/wg/o, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceu7*o.wx xokk )leration? Can it have zero velocity? Exk* xo.7) xokwuplain.

When a golf ball is dropped to the pavement, it b 0jhwywqpy(zx +y;g*-thx y4/ ounces back up. (a) Is a force needed to h;y*+0wwzp/j yqy4x t-gxy(hmake 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 t v.hhu)q2 kxn8 /4bqgbhe opposite divkg)8q4u q bxh.nb/h2rection?

Why might your foot hurt if you kick a heavy desk or a wall*hn zyb zyg0;e4gd7 to (a.v8r?

  When you are running and want to stop quickly, you must decelerate quicklyrb. 3g+q nnzz-. (a) What is the origin ofzn .b 3gnzr-q+ 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 f dep4zdt.pg2(.e;7oe xbjwi 6rom the ceiling, and a section of the same thread dangles from the bottom of the st ee;ixjbgd2dt. opw(p6ze7. 4one (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. Wp.*5cjfidgb68;ywl,r- r sf/yxxq 3 chy then doesn’t t f/x3b6.cc ;lpid q8wfgr y,5r-jxys*he heavier rock fall faster?

Would a spring scale carried to the Mookh+7 * :l,oyo xunfcui pd6z1(n give accurate results if the scale had been calibrated (a) in pounds, or : 6iyh7dl(z, o nf*1poxucku+(b) in kilograms?

You pull a box with a constant force across a fri 4mx7c r4x 1gm96m5nioi mi7zfctionless table using an attached rope held horizontally. If you now pull the rope with the 7iirx6mcm on 944 7m1i5gz mfxsame 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 influence of gravity tmagh zo i3:y+wc6qxx/-/rx .qhere 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 dxxi /gqh.zm -/c :r+o3qxayw6 oesn’t the Earth move?

Compare the effort (or force) needea3j0 tf+,mz0w cb+;rw: asf vud to lift 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 a 2-kg object horizontally,0jrfv0;zs+uwfw b3ca am :+t with a given speed on the Moon and on Earth.

According to Newton’s third law;w( 6npdu4 c5tla*n sf, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which t cn tn4l5sdu *w;6afp(eam will win?

A person exerts an upward force of 40 N to hold a bagkry9bfkt;ry s0u-c 8+ of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what obyucbrsk 9r8k0 t+-fy;ject it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a forchtcsfen;mm)9vt :qf 16xt pjg1 9ht8;e does the ground exert on you? Why doesn’thtgc;8x9vf9t 1 esfhq nmm16pj ) t;:t this force make you rise up into the air?

Whiplash sometimes resultjiig g +rqy.a kgn9*:0bu/:b os from an automobile accident when the victim’s car is struck violently from the rear. Explain why k9n0q.o:b yj br/g ag ii+:ug*the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truci3(yonfb b 3i;k. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate ; f 3yi3o(nibbto accelerate?

A block is given a push so that it slides up a ramp. After the block reachesgh-+s*okqt k , its highest po ,tgkshq+-* okint, 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 x9n/llg)q d -j1go*rxweighed yourself on an inclined plane? Assume9/ -q 1gljdoxr*l)ng x the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1. 4e+r tc/u5rvwr sc.(u25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider,fh ,yjthmk a2yz)(t0 at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a ropt*a* ;rxwv 77)edcvw fe withstand 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 of l 0cl2 sxkw(,c;gbko*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 j(ug,gm5a55dd w5jrr to stop an 1100-kg car in 8.0 s if the car is traveling at 9rrjgg5u 55w(m5djd , a5km/h? -  

  What average force is needed to accelerate a 7.00-gram peybjnz ,ra*-8 wllet from rest to 125m/s over a distance of 0.800 m along the bar rw,az8-b jyn*rel of a rifle?   

A fisherman yanks a fish vertically out of the water withmo -k bdfq-p98 an acceleration of 2.58q p-od 9-kbfm $\mathrm{~m} / \mathrm{s}^{2}$ 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-m7r7bh n):hvsn ile 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 48v8hwq*z zm ,y;50 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum andhmqy*;vw zz 8, minimum forces 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 scale in a motionless elhwt8 n(2 wit1s(l1r1xgqbs o*evator. 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 accelerationosq( txgw*i1b 2st1r1(l n8h w.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 75o/2q30 v4empoc w7wthlfbkN. What maximumf/37wmpe5v7 0bk4c wt oqo l2h upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of *,qfsy pt1z 3x4mfu r7two falling sky divers (mass 132 kg including parachute) when the upward f1rs ff,zy*t7uxq4mp 3 orce of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. Whend:-.i vsg) e c* fllr76w3n9fjm3dvgl he strikes the ground below, he bends)gde d-l f:7fn.6g3mv*9llc3v rsjwi his 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. vdiqce03aa g1wjyfm0-8z :2o A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force thac y020:m a3 eif8-wagd1ojzvqt 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 basktjyzrb xi +e 8,w8zxkwb6 (+lo +s-uj6etball 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 mome+76apgm8) 3kwgfz, j t vli+iunt it is hit by the bat, and again (b) after it has left the bat and isjwa)mk+tf g37 g 6zi plu8+vi, flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mustcpb /i2-a (k1vh7ml dv be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a v1-h/(i v72cpbkvdm a lector diagram.

  Arlene is to walk across a "high wire" strung horizontally betwef 8f5mblr xbv06yz *4men two buildings 10.0 m f*0zyv lb56rx mmfb 48apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord fromnysjads2 pi (1op9pz- y30(wo 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 144 i- hyqbbwy.4.0$-\mathrm{kg}$ 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 unll4lnj 4e7.g lit to a new location at McMurdo Base, Antarctica, as shj lgln4l4 7e.lown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars0rs c6(aez ,ya of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couyc6z e, ar0(sapling 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 hers ,6d l8wrdg5+ fzwzxe3elf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull dod xr ldwfz,ew3 z6+85gwnward 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, a4:l0su4bl)kz, nz bm 8b1xctn 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 cp+9hymu- ;ybblock (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 frictiony -kk 6 (bwh( .ql:5yu5frjfd6t5lghj less horizontal surface are in contact with each other, j u-5 6f gr(y ty.kd(65blj:h kqlhfw5as 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.7reugb qq 0(*s ko(kbfz,(lq / 4-52 are each initially 1.80 m above the ground, and the mu,b gs0k( klqqo f7(q(r eb/z*assless 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 frictionlessoghzfg(ndqf-pm 1 )99 table are connected 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 tfpg (zgoh991)-mnqd f he 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 ofi;lewzm jc ;l1xqa/246;8y iv dskc)p kinetic 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 .40vc jw(*t lt,7xjajn)blg shc3:wl 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 standing on a train accelerating at 0.20g. 9a;o3gwy,*n ux1zci 1ykx6wu What minimum coefficient of static friction mocy ,k; awiu1wu69gyn 31x*zx ust exist between your feet and the floor if you are not to slide?   

  What is the maximum zc11e. ;v5y:am /fxm r1nrcct acceleration a car can undergo if the coefficient of static c1 ev15cr;r.cy/zmf m1a :ntxfriction between the tires and the ground is 0.80?   

  The coefficient of static friction:ab8p a8kq yad+ua) g4 between hard rubber and normal street pavement is about 0.8. On how sa8b8q)ua4py gaak +: dteep 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 ly7ohs3 :ttk4 mqzn6 . -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 roughyivag :ua;enwo6811j 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 surxlls9 88hxv -oface have a very high coefficient o9hx ov8l -8lxsf 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 kineticidbg z fs4 (k *,/dduc *pix/frvm)+8r friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass wou ll31+7h pazxbld box A have to have to prevent any motion fro+ 7 lpl1xa3bhzm occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will e rd85,,huj6.wtr ps . nil9itit go, given that the coefficient of kinetic friction is 0.20 and the push imparts an 8ip6jirh5urlt 9. , tnd,w.esinitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are 7x*1jkmcjnq z;sc8ri./ 0yf n in contact and at rest on a horizontal surface (Fig.c/fjn 0s;qcjn1km z.*r x 7y8i 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 frictionam2 do6h+ *by :b) -okzcmm.sn between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab +kbnm sam:*co6 m o)z-h2y. dbof the truck?   

On an icy day, you worry about par/ 6bwl s9s xm 9efjfn-8m;l7brking your car in your driveway, which has an incline of 1mms 69j l;flsb-w9fn 8x7be/r 2$^{\circ}$ . 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 withb3m8 -solz rtkws+u ln-4 .c*8ts,mll 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 planekjdwqc62r8oe fd;7. , mm u)rc 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 )sa+ 5nn qchly 0o*i 3vvsx/e/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 0 by1cg5vjh4:xt1j t24 cduzm 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 agaii )yf9rj vv:io 39(ixsnst a rough wall by someone pushing on it with a force directed upward at 9o9j)v isr(v:fi 3xyi 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 as they melgwy-1rbs: v 2mt. Consider a chunk of snow at the ridge owmg bvysr2-: 1f 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 stoppi/r keqrdc:. prs -;a(ia2 s0xicny(0dng distance for an automobile traveling at speed v is equal to0r2d/ri (dp ;a k0yncias (c s:-.xeqr $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 forwar ci:e.d :beq8pst 3rt1d on the dash when the driver deebdit:t :q ep1 8cr.3scelerates 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 antkc095oezxa7vpo 7*3eoge 4j initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt fromi r5ot y;s,t c97hu)h2nbkf8a where they are filled to the packing statia ktfi,52ysbn 7cr;9uto h8h )on 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 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 fric+,n,m +eyh (9zc gjumetion 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 (i c*u,)y1t yn1hwa;(hzb)lru w ncluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at d5eki0vb+n y3each pulse approximately 20 g of blood d3k ny0vbie5+is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobil+np+ r.)j *goakog9i je crash if the deceleration is no more than 30 " g pa9o* .+k gojr)ngj+i 's." Calculate 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 accel.nwyt3ms ux li vm45jz(2,dp1eration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static ln mm3p,41 wzti5s.2xdvj (u yfriction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two car v16zwu4e3)xhyclen3tc7w ,j s, measure 72-m-long skid,nte)yx wv6uczw 3c3hl47 ej1 marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 q5 +r9kxmvcs1means that for each 4 m traveled along the road, the elevation change is 1 m). How fast 9kxqm scr1+5vis 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 of the Leaning Tower of Pisa anek77v +9.wrz;+c / cgaggjkpz d falls 55 m before reaching the ground with a speed ofjk;/v gg7+ zckrwz+ pg7ec9.a What was the average force of air resistance?   

  A cyclist is coasting at a steady spe u 777z -92uokxqgn5 xwack8mded of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge frx 97 k7ocndugzx7a5-q8m 2ukwom 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 re+0)n.y gphz/dyu.8 o0jpla ukdesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car,.hag.l) pz0u p8d 0u +/oyknjy 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 from a oeqhn5- 8( fmuf ;gi7mrv0aq 6thin piece of stringo -m;u0gr7m 8 ( vf5hqqne6fia while 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 supermarket, there are to be severafujz3y( *5 e74 g kd-nluzq;oal ramps connecting different parts of the sej g*uak3(74fqu-z; dl5 noyztore.
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 x 3 8hx8f(h1s5u4 qzk3ffahw o ) using the pulley apparatus shown 3q8 3(8 1uhxk5shff4hwxzfao 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 acceleratia -oj ,dfd6,vrng at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the fm(:xrp1*.a uwtd lc0k oll 1d0 t:wapclrxu(.m k*owing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (6pr*koa:d:; e n9nto.nz1 k5pa60,000 $\mathrm{~kg}$) . 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 Kare4)s ,jd cx0q ezp4vsm6 cta9-lwfok1 ;n, use safety ropes of similar length. Karen's rope is vtwxs azkm4; 4q,d f)c jso169-p ecl0more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (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 usingkcohln 7 o,6q(fgaja.1f kcq 5:j b:i2 a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed tolnf(kmrn ) -m -5ba8t ppl,n/r 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 ascq/vw1 ;aitz.cx lom9-av1ath wl0yw-5. b yp ;ending an ice field incline .;0 h1wvy 9tz l-wxmq y;-oa/pbila1atw. v5cd 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.