Why does a child in a wag:3pgl haoq(7 i)v- g5t6;5hszqcp vtwon seem to fall backward when you give the wagon a sharp pull forwardtog-phs6 zq5( 3i:tc 57lg)hp;wv vqa?

A box rests on the (frictionless) bed of a truck. Thep83 suow0/4o- p10xsu q+ke x(kise jp truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion op/wex1qi (k-8k0o su+o x u34 sp0sepjf 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 no forcescvwwzxk1 gryvmw 1 +cofv*m) i(x8;/* acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerationr x)4ei 68sl:zpqrh1u ? Can it havhp 6 :4u sr18exqriz)le zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) I,ur 06z-.fquz habx/bs a force needed to make it bounce back up? (b) If so, what exerts the forcah/ uxb6b.z,r-u0 qfze?

If you walk along a log floa jo3(iig/nqg8c2 b fr3ting on a lake, why does the log move in the opposite d2ir (b/fojcn 3i8qg3 girection?

Why might your foot hurt if you kick a heavy desk2s2/zcauw62w6. 9 fc pi22nvc*h almccl npe, or a wall?

  When you are running and want to stop quickk1s3v);b ,bunnvi cr0g6q)y)q 3wlbtk 1 e*v uly, you must decelerate quickly. (a) What is the origin of the force that causetvb kb3k6)yu1 cu3,v;*)bs r ng q wie)n0l1qvs 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 from the ceiling, and a sectio j4wa*d/ wx80(sj8delxsd e 1v cn)4+ffrw b0yn of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the deenv0fw bxyd+( s sw raw0*4jdfj x84c)1d/l8angling 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 tci(icxpww spm 5.,wt 53p6d+twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock f65d+,pps.( cwipwxm3ci 5 wtt all faster?

Would a spring scale carried t /h s8n53,cpgrt x3attwei0/co the Moon give accurate results if the scale had been calibrated ts/ chtw8/ecaxr,35t 0g pi n3(a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attachvfq r +,1yafi;ibs,0ted rope held horizb01,iy+iar, qfvf;ts ontally. 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 underi/jdna *pr3.0fndm o: 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 Earth. Why doesn’t.*anmpnjdi0fdr/ 3o : the Earth move?

Compare the effort (or force) needed to lift a 10-kg object eu wa/ff3 pe7;when you are on the Moon with the force needed to lift it on u;f/ p37wefa eEarth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, 6.3crd04 k imtjbee3yn1 jwr( each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines whic (w jtr4d31cj . nrbmee06yk3ih team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe thsv 9o-uh+t m.ae “reaction” force (Newton’s third law) by stating (a) its maa+to - 9vuh.smgnitude, (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 large a force does the gror-8rez*mo la8 und exert on you? Why doesn’t this force make you rise up into the air ar8*r-lemzo8 ?

Whiplash sometimes results from an automobile accident when the vizz3i.+ c(aib4vv r iy-ctim’s car is struck violently from the rear. Explain why the head of the victim seems tovivi rz43bcz(ia y+.- be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acl5f 5ox.o j/b::(gowtx5hllocelerates, the crate rem.ox 5oljh(5towl5 l: /:xfobg ains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides k;b3 a5uy6f5 z0rikreup a ramp. After the block reaches its highest point, it slides back down but the magnitude of its accelerationr5ki;3 f60e akbz5 uyr is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined37qgb6(qy mjb plane? Assume the mechanism functions properly, evenmjgb 3b6 (qq7y at an angle.

  What force is needed to accelerate a child on a sled yhe.k muy.ja+qk2.6 v at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikevs 3hlj:2;* pccnrre ( and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if * .+r q 7jrzye26;maop y -allwi5xs)tit 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 in;cj:. 7 t47 qjakkfva $76-\mathrm{kg}$ 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 requiredkmr4 (uxaptw6+rt * j5 to stop an 1100-kg car in 8.0 s if the car is traveling at 9 k xta+4 mw(5tr*jup6r5km/h? -  

  What average force i gmt8xx h.gd,*s needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distan,gxt h8gxm*d. ce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the wate9t5yem zy-g7 cr with an acceleration of 2.5-e7yz c myt9g5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 (4n612p -l2u c6icygpui8fk. )mud )r cn02 $\mathrm{~m}$) 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 accelerati/(c(86;htxhkv hd+2w zd.zxi g,s wtion is 0.0680 g . What are the maximum a+k 2(v8ch/stz;,ihxw w( 6ig. dtxhzd nd 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 mwj s9 on;iz+askh8a)s(k)+ yxotionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weigx)+kn +hjssyz 9wk8 a iao);s(ht. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a5pztz zg4 een34m 1;xa 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elexne g4a51tz ezp ;3zm4vator without breaking?    ( two decimal places)

  (a) What is the acceleration of two ,vjx d3d2i yc-va.d.u. *whrcfalling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth o.j . w.xu -a,ychvd3vr*ddci2f 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 hi:d2vh1 pkiwj 3gh. When he strikes the ground below, he bevihjdk :32wp1 nds 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 rsu5mx7, -uj vcnktx(-ests on a table. 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 tvu u--(s,57mjcxn xtkhe 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 bas93w1 u+v1galbfsoj gckq t-w+.j9cq 2ketball 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 moment it isb dlxiuqr-m7 5.ohw./ixdeun:24e *o hit by the bat, and again (b) after it has lnhq ox5meiu*.owd ./x :d7e4-ubrl i2eft the bat and is flying toward the outfield.

A 650-N force acts in a northifs,96pv a/n s*bbn0z2bf 9mswesterly direction. A second 650-N force must be exerted in what direction so thpf609mzbi vsn 2f*/snsa9 b,b at the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bu2zbmfn;oet5;gj.ud u /w g4cz +lf0 n-ildings 10.0 m apart. The sag in the rope when she gonlgwu+z ;tmj/uc 4bnf-25dz;. f 0eis 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 uv (mrf0.33pro2fx ikfrom 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.ngcdjnes5i:5 57s 3mk0$-\mathrm{kg}$ 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 location at McMurdo Base, Antarctica, s fb9ey 4p5ae7o o//rdxb2fe*as shown in Fig. 4-46. The suraoefp5oy9f * 7 /b4 exe2bds/m 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- ;o/fj.)a5itk pdv mn two cars of the same mass behind it, Fig. 4-47 . Determine the rat/dok5.;vimnt jp- a)f io of the tension in 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-pgn j0*mqp)/ /-;qfd sng/jxpz ulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at-d/f ngz)j pxnmp0g/q/*;jsq 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, a 65fd ig*14vb rhbt:pi+ /$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (jlc: pwd7w z3x, l/nt9mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact b p5:n)wvjr g6)2henb with each other : 6bbnvp5)wr)jn ghe2, as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initialc5 di60-kbl oyly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height d bcdolk05y6- ioes 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 frid p9znz sh;j3n)o8jt;6 xtqu8 ctionless 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 the free-body dia8nd6;qj89; )utznspjo 3hz txgrams 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 frict yjq21ha+oo8 pc)+p74bdtc.l 6x oi zoion 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 ref ;)zr+iwi( ax s.i(wgquired 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 q)d;/ k* v9uxejjh7cfat 0.20g. What minimum coefficient v/7qfdc* j9;x )euhkjof 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 of statip hzw9b;h ky5)h(4lbuc friction ;(b )b h9 wz4phhyulk5between the tires and the ground is 0.80?   

  The coefficient of statijw6,2pc dwvnm+.g:nn c friction between hard rubber and normal street pavement is about 0.8. On how st:j .cd+npg w n6nm,2wveep 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.l;l;w l 4 psvi2hknj1 at -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 rest19 l jcpz4fxyvi* p6,yg1lpf- 4iji9 j 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 wit;/zr5 os-w(yzumok ;uh an asphalt surface have a very high coefficient of static friction.z;;5usr (zykum o- /wo

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 kinuws 2q 12rwdt6(vokb 2etic 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 would b; ilwu6e mww i4+8y+lsox A have to have to prevent any motion from occurring? Ae+6 ;is+8u4wwyll wmissume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidwf5g)qhew*q+iz y zwx/3i8lif728a mes across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an i/iiq 2w)*8 gmyq8+ w37 fhw5zxfea izlnitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg andp2 gn6dw/j )neg2a:mm 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54)2: e mpwgn6mn2ja)dg/. 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 cra 6p(nuu9, uw xx-w4wftaw6z4vte. The coefficient of static friction 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 vua(x9ww,tufn4z 6 w46wx- upcrate slide against the cab of the truck?   

On an icy day, you worry about parking your carh 03s-duztyj z/ *jfs0 in your driveway, which has an incline oz d sj*0 y3/suhfzt0-jf 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-q4o m;qw+di 6(oq nlixpjqs k1 71*ji 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 wpv7tl1 lltj++v+ r6clies 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 initiafc-k ez/7(r8+gxy hunl 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 reaches the top of the steepest hill with a srpg/ fgk4(:8, t,ruppe+c-i 2wru pjp peed 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 someone pushing on it wit6dg cjhx9*t- fl58ka eh a force direc le68*h-95faj cxdtgkted 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 projecti- fayge fm l6id6n6)ls; 9hp+kles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of ys 9)6fndlke l;6h+6-gf amip $ 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 mie5y2 o5 ea1-j)s oltmjnimum stopping distance for an automobile traveling at speed v is equal to oeljtms o)a 2eyj1-55 $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 ctcu ke srrxwg:u11.(wn9 :z+ zar slides forward on the dash when the driver decelerates from 4z1 :wew9gr+x 1u:su ck( .tnzr5 $\mathrm{~km} / \mathrm{h}$ 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 is4zkrcf + /dor,gt i2zder5/ pqr08 x4w given 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 conveyo ,ksh0eu3niss)r4 4feeke09 r4fu kw /r belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished ife snfsku344uk/ 0e9 e r 4shiwfr)k,e0 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 kine6 hnfi9ksgm cxgz23/st.p-7 l tic 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 coasx h,q,av+r v7:l,d lynt 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 simpli: g 2nxuw24xuvfied model of a mammalian heart, at each pulse approximately nxux22w vu: g420 g of blood 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 *.loo .unw usnnd o/9:surviving an automobile crash if the deceleratun.9n ndou :ows*ol ./ion is no 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 acceleg:) s1 xu) ,ebesw0hshration 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 fr:ss)0e esw) gu,hhx1 biction 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 tlv 2 o+rarh/.whe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. aowl+/ h2vrr .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 eac m/z2 pkap;+hsh 4 m traveled along the road, the elevation change is 1 m). How +zsa;/mp khp2fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropz 2: bpsts(,rbped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What wp bb,z(sr2:tsas the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s03j0limzjeh yd 2 m(iyyx,oas,v; x,9 but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud 09 axili3ejyhyzvy(j,x2d o s,,m0m;lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a gfy 7b;+qp5as 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, with a mass of 1100 kg , can accelerate on a level road from bg+f 5ya7p qs;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 experdph5l *d by62kiments, 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 st2lydb6p5h dk* ring 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 several ramps connecting differ 11 ji ids5hao rbj8;9ih3aj9oent parts of ther5o1i 3ihdoja 1 ib8j;s99j ha 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 for 4j8t(4 dynxjxgh )i*o1zvocw84w;ct ce F is needed to lift the piano (mass M ) using the pult8w; zcojx4)(1 4i8vy n d4cho xt*wjgley 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 3.5 81cj *)i;jhuum gd;webi/d p7$\mathrm{~m} / \mathrm{s}^{2}$ 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-rest8jg3rq 43d tyhraint chair, an engineer considers the following set of3 4tjhq 3dgr8y 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 Italia-cn c pce/oiarer(jj61-( d0h n 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 Karkeztsrx/u6k+wnp+d3qq 7 ;;zen, use 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 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 stretc;kt nkz rq3dpxzu/w +s 67;qe+hes 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 usic mv geaidyn9;i)7*yd:ij ndl;1/d 0 fng 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 to reach a maximud8 2od9rbaa h/m 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 f -e+ w rxag q*:j7vf0xu;-qatrield inclinet*-u vq:r j xx+aegwaq -7fr;0d 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.