Why does a child in a wagon seem to fall backward when yo pto.li9 :p9hphbx3)msn;bm6dv/ p5 x u give the wagon a sharp pull for 5xpphx l.) t:b9 opbnpmvsdi69/h;3mward?

A box rests on the (39ss) )pf3ijs q*8o.pwtl01 a w cklrzre+vj /frictionless) bed of a truck. The truck driver starts the truck e/+pskv3 .s*)pl caq 01jrizjofs3wt)r8 9wl 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 truck

If the acceleration of1swi pv6waf /0 pu+oar/mo8y4 an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accele+a/ rk8 mwc8tkration? Can it havekm+c88 kta /rw zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force s8z*) q 7umny2:b.lphokg8 ld needed to make it bounce back up? (b) If so, what exe o8gq 7h. k )lbm*y8punzds2l:rts the force?

If you walk along a lw3j;hlw xh :us4- g9akog floating on a lake, why does the log move in the opposite direcuk4x:w;l 9 jsh-wa3hgtion?

Why might your foot hurt if you kick a heavy desk a7tq b3ye5/e:ebv9 aq vz-b3vor a wall?

  When you are running and want to stop quicm tw7htv+wec(0d n;5o3 awz;vkly, 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 deceler oewmt nth0+a3dvw; 7(cw5v ;zation 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 sectior 0 hz41(8hnyy kv; w bsnhiqe s/8siim4:e(;mn of the same thread dangles from the bottom of thee/w (s;v4inkrhhhes i z48biqms1y0 (n8:ym; 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-ksiz/ 0kekh3e(qo94gf g rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall f kqh/sie 3k49g(ze 0foaster?

Would a spring scale carried to the Moon give accurjkxh6n(23 reu ate results if the scale had beux2( h6rkj3n een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using ; 6uyawk2s8 *ljmi-zfan attached ropm yl;f8kz*j 2usw6ai-e held horizontally. 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 freelun2;a;: bm4osyk k-dl1 ;epxvy under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Eartskxamdu24 ;v :k yln-p1;bo;e h. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg 1nnuoj()+nh-j mcb +q 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 horiq( +jn-n)1ocj uhnbm+zontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tiayfh+x52p aw5 l r59yug of war (Fig. 4–37) pulls with equal force on the other team. Whata9f 5pl5ywh 2r y5+axi, then, determines which team will win?

A person exerts an upwar1a n59*cgqy rd i*4-/zr/vy(x qbbyqz (6a ybxd force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) bcxby(61y* ayqn *( xgb /qrvz di9q/ y-ar45bzy stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how l/s+dpvv(o;a 3j 1ls alarge a force does the ground exert on you? Why doe+v3/alsd(l; 1v spaojsn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accidentyu3jw5spt i i0(z hc13 when the victim’s car is struck violently from the rear. Explainy i j0htc5zu3ip13sw( why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed trcqm .e3q8nks ju-g**ouck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerco8k gqs3 m-jnqe**. uate?

A block is given a push soy:hl+ hhp o;mi:e;2xjtm5cqi az.(w* that it slides up a ramp. After the block reaches its highest mlyzj i.* :+whh5i caepxm:(q;2;o ht point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined plaz57 zla9j:yso2asrmem ) i8)l ne? Assume the mechanism functions properly, se)oz s5:7 zi)ml82a9ymjl raeven at an angle.

  What force is needed to acceek)7ovvlwc +0lerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rgptv v vk00mw: a.g8r2ider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wi*k-r;)e3k,6d teit(h sshth ithstand 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 a oi vv ;29wx(cg:ytpz/$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 110qau)yn6*su c zt*o )ito:h;h1 c+ic 74a pfq5m0-kg car in 8.0 s if the car is traveling at 95km/h? -*7z6a;atchq )cqc)o+i:pi o1 uyuntsm 4*h f5  

  What average force is needed to accelerate a 7.00-gram pellet from rxyklxq ;+)1k kest to 125m/s over a distance of 0.800 m along the barrel of a rif)qylx ; 1kkx+kle?   

A fisherman yanks a fish vertically out of the water with an accelerav/tzakcl+ 021d hlp 74)th rirtion of 2.5 1hpkrl 2h rt04zl vt/c)i+ad7 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (402*y)aa9eihql2 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleration vjw1azb u2gn9i o)6b .is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting b )2b1joanu6.zv gi9w 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 elevator. When the e)s u(/a )zf2w5kddnsslevator 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 a( 5)asfsw d)dk2zus n/cceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whay - by2tdvg2*lt gl2b yv*2d-y tmaximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of tqsh)ac ;0aj4l6c.k4k-pdhm nwo falling sky divers (mass 132 kg including parachute) when the upq6m 4.nj a4d -)klapschch0;kward 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 strikes tvwq2 m9q3 y/kqhe ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding leq9qkw3qy m2v/gs) 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 brq bb9r:eqy2 bml+rg(,-+ob uox runs vertically upward over yuqrlgrbb+q9bm,2b r(- o+:e a pulley and a weight 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 bask, mb / pb11v1xrl+ls1ofcatg: etball 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 baseba63ye,6tr ord vll (a) at the moment it is hit by the bat, and ay,r 36vdet 6rogain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N/et 8q4qh*qcn force must be exerted in what direction so that the resultant oh*qq /qcn48etf the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" struncme0 k 1 9m b+-(-j*mgwdi4uo3thzjing horizontally between two buildings 10.0 m apart. The soj0iu et-w1m +im*jcg(d m3zh bn4-k9ag 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 gkk,vxs4ad:pyqlo3-n*g 2 -a 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.c6kg nlp)r6 n*d 9qt)h0$-\mathrm{kg}$ 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 nopk z 5qsvrg.*b/l y4ip w.v*5ew location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sumolsbg 4r*y*pz5kp.qw 5.iv / v of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of thgs;w rf,tk f;:e same mass behind it, Fig. 4-47 . Determine the ratio of the tension in wrg;fft,;sk: the coupling 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 bucket-pull 8*ioopfn-y g(ey apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself soion8p g-*(yf lowly 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 b1vl+gzsdm-: k25a 1por ybb7wt:-qw qec mv:7egan, a 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 j (f j-omu ybyu10//agblock (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 surfsfy2s*6gd; hgg 6fh *zr- wdg-ace are in contact with each other, as shownsh6 -hdff2*-dz ;gwr6g*s ygg in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m )eh,wkxg,cs3c2 kva5 h 1z sh7above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the ligcgzw cek2hsh3kv)5 , s 1,xha7hter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy 2aqw hf 9;ab*si-rn;gcord of mass 1.0 kg . Calculatgi9hqaafw* 2s br;n-;e the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic fri ghoi2rbs6cr4erck6qk.t 5 / w*z-2 yuction 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 starkyjwgcbg5 l )w;(-7 mtt 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. What minimum ha d8k0easd9 -coefficient of static friction must exist between youeadd-sh8 a09kr feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stati6 u 9:.lyjuk2o r3hauqhk b/u:c friction between the tires and the ground is 0.80?l bur:k k32 oh6h.:yuu/9 ujqa   

  The coefficient of static friction between hard rubber and normal snu :0h)-pjk z8b0edu street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a carek0zbjh)8u-0n :dus p 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 o5 5sx97b)j,ywj ep;vzk o3xd -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 x*kg9;m 0e3naaapwh,jxl; p6 on 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 havdn .ci9*g 29h jiocdh/e a very high coefficient of sic9*gi ho dn/jh d2.c9tatic 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 for a yi2ozxj4s+a *)7qko( ibq+zt $ 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 ,xqm)bk1t:4lomf .6im df 0ob(Example 4-20) how large a mass would box A have to have to prevent fob km6:.i)x4mf tbq o10m ld,any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so tx423ez9vyv ithat it slides across the floor. How far will it go, given that the coefficient of kineticixz 2vty3ev49 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 antcuz/8b320wrhuip 2 zqtl6 6ua oz .y7d at rest on a horizontal surface (Fig. 4-54). 6/3uhptw czo .ztbu07ar2 y6i q8zul2A 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 heavyppdk 145)0nex3c y8c0bsh naf crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is 5 h1k)0exdc0sy4p fc npnb3a8the 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 zt3qn;t f9ms -3m( ;- gizexqhparking your car in your driveway, which has an incline of;q xe;m m-sz nh3(9f-3ittz gq 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 sli8lx,31a pwjyr- v mnh )ga(ma8;4x4zx(drsvbde with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 4.fuujz08j gswgw vk8f2:r9 alies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speeozl)c9 (kpkms8s b;k, d 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 spb9gm*hhgjm(j *- g j;,0asoiueed 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 wallud( v u)c1f-gc by someone pushing on it with a force directed upw -)1fdvg(ucc uard 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 becom.ux:u teiv*g:65 ydx le dangerous projectiles as they melt. Consider a chunk of snow at the:5yu *.ltvxg x6 ude:i 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 travelrw)*9;mkxrhxim zw2s(rk a b /.s-tr, ing at speed r;)k*bs r.m -r atw2k(/ mis xw9rxz,h v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward 4io2yuw9j1jfon the dash when the driver decelerat1i 42wy9 foujjes 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 5x bgtx ;/-(7fpj;;ippbiv akgiven an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to the packing str. jwuy.o39su()q z gyation 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 .ws 9zyy.uorq)u3jg( 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 fricvl*pen7/1ho::: pmq lmn7ac j tion 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 coas(mwpakiq 0qjrv+6 34kt down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxik 2(q+krgm4h;gp)dgvqvt s:* xn1 ug) mately 20 g of bloodm+vgp1dur : gkqh x4g ) qts*(n;2vkg) is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile db 3nw3w.en b7oc, m3fcrash if the deceleration is no 3b on3de,bw3nwcm.f7 more than 30 " g '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 acceleration prodo bm7/1;tdz-b f sc6vluced by an earthquake is a , and if an object is going tb1c 7lom/bf6dt;s vz -o "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two c ,1is /k i9yr5 :kp:2chmviw/ r;rjrhaars, measure 72-m-long skid marksrhi521 9imyrap/,ijkvcr; w:sr /h k : 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 means ty3 fxb 6y,nf +r:z2*wzmnb2 lyhat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after travelinb+ yy*lzwf2: b62yfnznx,3 mrg 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from thl-gem3f1o, ,i+0y +subl.ao truqh r6e top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistance? 0gqoshim. r3-1l+6l ru ,fuebt oy+,a   

  A cyclist is coasting at a steady speed of 12m/s but enter ,cjaab np0e6s6n/ e60mcpysfq 4/m ;xs a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed uponsyep m6fc/ 04p 66ebn;xajmcqan0s , / emerging?   

  A city planner is working on the redesisgqq0f+e.a( bgn 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, withqsaf( e.0+bq g 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 likes13a 6ld l8xm c0j6gdmcxlcx9v 7cu ,0o physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angl9uvjc6gx,x70d lx3 8m16m alocl0dcce 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 supermar c6.i1ky lwln9c(qow- ket, there are to be several ramps connecting different parts of the storeo (9 .lyiqw-lc 16knwc.
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 npdkrt3(rb j867dn+v oeeded to lift the piano (mass M ) using the pulleyv8oknp+r(67tb 3rd dj apparatus shown in

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

  A jet aircraft is accelerating at aw w9: ad b k5v.//e8u)gvjnpk 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 fo.d2h)tn7 +tc gc qj-apllowing set of conditions: dhn 2+-t7c)tq.jacg p
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 Italiana0 dbp+ nfs-5g 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 safety r( cj; nwez.kw8opes 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 rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming jcwe .8wnz;k(that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-,, eok:n dcz,y/ cuos m4te*y:nmt*d81 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed ay c9afq4, qa,p;z/wkof 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 ascva9.b+a w(qbyending an ice field inclin+b (.qb9wayaved 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.