Why does a child in a w-u o,rkjlru2 6agon seem to fall backward when you give the wagon a sharp pull forwauu-r ,2ojr6lk rd?

A box rests on the (frictionless) bed of a truck. The tru wml, wx 9zeh4bsjnx5v-4un;0ck 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 besi0ue44;xsmnlz n-ww j,vb5hx 9de the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Explai:fa0ko9 wkidx1l9ahp p0y .-x n.

Only one force acts on an object. Can the object have ze- lsklt1cr;a6o +h,o jro acceleration? Can it have zero velocit+,s1oocll ;-h6j karty? Explain.

When a golf ball is dropped to the pavement, it bounces back u8+p8yx )ixq9 ketp(l.4dybsg p ib7f:p. (a) Is a force needed to make it bo+9tpikbyp 4(s88g:flp ibyxdq x .e 7)unce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the lgaq98gqk.zykeb3a*q4 +zia 3 og move in the opposite direa qi4. k3qa* 398azqkzb+ggyection?

Why might your foot hurx:2 vq xc jtbw8c*)p qo,i+)wxxw:i0pt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicklyjvt fnuf).7nm5rv.w/ . (a) What is the origin of the tf)rm.7/jv .5w vnnuf 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 frzfz 2*)fd:hb som the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to breakb*: zz fh2dsf): 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 tw-51b 2fn n1 7dn6kwczwx qa3sxice as great as that on a 1-kg rock. Why then doesn’t the heavies a5d62-1nn wwk3f qxcznb1x7r rock fall faster?

Would a spring scale carried to the Moon give accurate results if the e vx/fld.58sv(rlq lj)k3lg+ scale had been calibrated (a) in pounds, or (b) in kilogramejqv5+d .3l kl/xllv(f 8)sg rs?

You pull a box with a constant force across a frictionless table uq7r8b*nmx h40okq /ni1blb3 qsing an attached rope 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 accelq4b0*br3 /qhinxklnm 1 7b8qoeration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freelymsw)-xskmm b)i3hxf */25s rz 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 ai/ m2x)rw 5z3*k sxm)ss bhfm-nd opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a8 jkg ya1p4z8d 10-kg object when you are on the Moon with the force needed to lift itd4 a88jkp1gy z on Earth. 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, each team in a tug of war (Fig. 4–37) pyhypbq x4 c8,3ulls with equal force on the other tea4c3p x8yh ,yqbm. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocepywwih gx qu3t/;8 3ab-esjze w1-c/2ries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object itw1phj;s 2eizut3 --w3e8/bcwxg yqa / is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a forcsit7e0a: ue0 pe does the ground exert on you? Why d:p0usaei t0e7 oesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident wn)f 9,qofd3 swagweg st -.59uhen the victim’s car is struck violently from the re,5swt9aw d 3qfsn- )ou9fgg. ear. Explain 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 truck. When the truck acce*:rq r8) i+z kpp4e5azfru3qllerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the craz pk) *85rpqfqliua3er+4zr :te to accelerate?

A block is given a push so that it slides up a ramp. After tfe4 d r 2ccnq+g;jp:c9he block reaches its highest point, it slides back down but the magrj:p 9e2fngdc;4+cqc nitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself/.ummi uu.6 8z;l qu+zj1iajath 4m(k on an inclined plane? Assume the mechanism functions properly, ev uz6ml huz1j8+kum ;./ qjiai4tum.a(en at an angle.

  What force is needed to accelerate a ol0fx+ a o)7hkchild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ride.9pjhxpw dbx4z0fi5tr ; /j m 7kh+2qxr at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a ropn,x63w +duhmze 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 d14snzn0(z) igpy8ea/4jc w daeh4z4a $76-\mathrm{kg}$ 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 requirzr7rgrbz0.n b-vug1 j .y94uh ed to stop an 1100-kg car in 8.0 s if the car is traveling at 95. ubr1ur4yv0 zrn.-gh9bjg 7zkm/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125ihh; nbkn hzz7754fl6 m/s over a distance of 0.800 m along the barrel oflnh5i 7 hbnkz6f;4hz7 a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerfeno-r6 g fkof:y.qy5gbq3, 1ation of 2.55rq ,.y3:g1gfoefb o fy qk-6n $\mathrm{~m} / \mathrm{s}^{2}$ 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-mil3 r7za kp wceu(-h7z.1inti(g e track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg zzx2czltd4,8d wj4 , p) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor shouldtpjl,z d 48 dx2wzc,4z 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 elevator. When the eletio57h0*alj,aavpb w5 p4 5 hqvator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration pabhj hqp,50t5*a47 i wo vl5aof the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevata+nqnzq)63 wfcsn/7/r.qc pp:y pfg1 or has a maximum strength of 21,750 N. What maximum q +qsfznac p/3c1:p6f.qr/)wg7n ynp upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accebgk32 ydg5yzw4.* qrj leration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weighrky.4d 2bqyg*wjz 3g5 t?   
(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 the gs8q(y9gtw3* ebrc9rl1or g)cround below, he bends his knees so that hir8rw9 qcbg9eo )r l*st(gy13cs torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied tfgy2-9pj;7:tl bkzalp pnh k0*,0f cn o the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that pnp0h72tjl-lz *0a k,9fgnpbk ;:f cythe 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 basketball player soe5*d q rz 6pkye3z8:
(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 baseba :m3dspb,8,aigkj f86(0yu5coy anji ll (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfie: ,msk6au38afc5jb dyi80 n,gjypoi(ld.

A 650-N force acts in c u4c a.,leua2a northwesterly direction. A second 650-N force must be exerted in what direction so thatca,2e c.la4uu the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hore8el0n ig5)lzizontally between two buildings 10.0 m apart. The sag in the rope when she e5)g8lez0ln iis 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 from another gjrk4t5 c.ip)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 14c 1k9ic-iyek nxby5. *-a0tfl.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a nej:ob ::-nh bukw location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of thku :b:-: ohnjbe 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 the same mass behind it, Fig. a4e 0f(( 3bjfp wbe.*r-tjqq9qgzn;s 4-47 . Determine the ratio of the tension in the coupling between the locomotive and p b*g.es;0 nfbar4q-(ze wf(tj3qjq9 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 jpcs1 iy6 v31 bauvw7*the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must7w ib 1c vs6upa31v*jy she pull downward 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 rach 6 ,k)kledsi17v: lipe began, 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 b 6z: n6uhzrhjqf ,a5hgr4w 7z7lock (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 surface aa0 d73otw mxe g eu4wj5t:9fl7lc/(wdre in contact with each other, as shownf adwxlmjtu:w( w 075e9 deg /c4t7ol3 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 1.21 q j8l6juwfb80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass2fu b8j w6jq1l 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 yh h7wc24yr2 3qh 5q0z.goato frictionless 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 ty3 2gwat0 .42hr h yqqoc7hz5ohe 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 friction b:-:ldh dyd;,eu( 3d/ jypaxsuetween 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 uqylit 9;gt,-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 duh6l;g; cbq q tzv/ez98s:z5standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet anuqs/cz d9t5: q6zgbze8;l h;vd the floor if you are not to slide?   

  What is the maximum acceleration a car can undee 0xif e t5;kpxp;97x.pimn,rrgo if the coefficient of static friction between t tifi 5k;7;9,rn.xe xexppm0 phe tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavs-vs td61j*ou ement is about 0.8. On how steep a hill u1os6-tv sd*j (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 -4n3 v*, ly3mfvr.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 rough 30:z*t xds7 yy05utj y15 nmg8sd$^{\circ}$ 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 wiuzv4dp o; i1134 ntxq4-uqmaf th an asphalt surface have a very high coefficient of static friction. m 4 1fv-3;d4oaq ptzuxn1uq4i

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 fricti.ldh1n:hnj o z(d9 dy8on 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 box2(bpux:m xe q0 ix37wu A have to u:pi02u7bxwxe (m3qxhave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will ix/iafjk f2p7ngj1r;: t go, given that the coefficient of :/nk x;f fjpr2j7ag1ikinetic 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 kjca +osm .,3yfg , are in contact and at rest on a horizontal surfacecmas f,yj.+3o (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The ctcbx/l :0gfn-;0wjzrn, k8ds oefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver; gsc/n,0d: rnk8zwf -xjbt0l can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drivewaa n ln5mq3:/jey, which has an inclinenmla :/ nj5q3e of 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 w:ot1lp 6+xxm;ex4 y5l 2cuwcaith 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 ony:wr82.f/b ,acgywnl. kn 9 c4p zjr7i 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 ini lt*i, quy*v /z2f;e9hgr;ylktial 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 spt4bnx8c7 y dyis 1u/j1eed 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 w9pww3z2 7agutsp)c v0ith a force directedp3v 7ww)0c pzu2ga ts9 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 projectiles ass i4k reni4j/ )u2ju56mag.ns they melt. Consider a chunk of snow at the ridge of a ) 5.iear sn4 i4kn6jm/2ujusg 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 travelixw w c3kd7f)y 0w*yu5/:yw7 l (kxuoyung at speed v iswuku w)y5y0yu owwd:ck7 x(lx7*y /3f 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 fl timc0ett6v5 p(h*m6goh,v.orward on the dash when the driver decelerath0 v(l6vci.ehp*,5g t6tmto mes 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 z6uyop6 ps eb19z+9akm4d)mec1 vz2x 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 conveyor belt from where they are filled to thq,ohk.+w 0okcd 00s hqe packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the 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 fo, q wdhhskco00oq k0.+r 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 kinesn)ncq6d9 b: hc:ely9 n2x-cbtic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast downg1 dpal5l ,le,k55 p*z0t bhsq 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 axc2oc dg+c5h, 4ag)x opproximately 20 g of blo24+ccg ,o)hd xc5 oxgaod 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 changb z,cgm br(1tum0f*4ce of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a (1b0frm* mgbzgu c,4 t 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , axi iql(m f++8qnd if an object is going to "hold its place" ( m8+xfliiq+ qon 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 accijeelvc1o a+edfu99 /:dent 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. Estimate the initial speed of that car assumie9oa:dlv/e c u 9f1je+ng a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for ea76k9m j3q ihhach 4 m traveled along the road, the elevation chang9h ihk3mja67qe is 1 m). How fast 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 dropped from the top of the Leaning Tower of Pisa and falls 55f 6jjye,/z kc5 m before reaching the ground with a speed of What was the avera,jcfzj6 y5/k ege force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretchgu w a.; ()lziuf4tdeabs(th+ e18y ssspl170 where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy st eaueul y+gttl)p f h4s.z8s1(isd7bas 0(1w;retch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An iexowkil );sp:0w /r*2 rg6 ksvmportant consideration is how steep the roads can be so that even low-powered cars c kpio0;6s2s/gl*wr ):er xwvkan get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles he,-bnd,w cncm-fc 7,xdtp)v 9 kr watch from a thin piece of string while the jetliner she is in takes off from JFK Airporx,-t -kc 7ndp )dc,9,nbfmcwvt (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 several ratxjp( 6+k l6 uuh*q.ltmps connecting different papl l .qk (+6*6thjtuxurts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the pul8cs7a ;vt(ly dley apparatus shown in;s7 8dcvy(tal

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 accelerat;zzmz/8pvr( 5 p2laheo0) mlring 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 e1hfs9+7azr m(ga1qr. f4qhnrngineer considers the followmqfra 4af+hghz1q n1(s.7r9ring 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 Italra2: hdh4 rgel -5macj5q:q0hian 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 rop1p4rcslsz2t 2i 8shaa9ck.ih8s3 j.k es of similar length. Karen's rope is more elastic, called a dynamic rope by clpsr.a 883ha24i .stz h1j ssck92iclkimbers. 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 using a " 10-1 7ht hw/uu7+ pt$\mathrm{~b}$ 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 al(;te;u5zg ; : ha9b g wz;rijy4ufc2cmlowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ice field ine as9w5:y z3msz7yb8nclined at essyzbwa:57 nmy8 z39 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.