Why does a child in a wagon seem to fall backward when you givewev5oyh, 2j4u the wagon a sharp pullu2oh wy45vje , forward?

A box rests on the (frictionless) bed of--7 i3crb2t b xz+abph a truck. The truck 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 32rbbp -x-7zh ai bt+cterms 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 forces acting on it? Expl 7nv0fv2 mex:dn)biv/ain.

Only one force acts on an object. Ca 4sl 8/y1hbfosn the object have zero acceleration? Can it have zero velocity?f8hs 1y4o/bsl Explain.

When a golf ball is dropped to t0 :xd b5n(mv cwiqest:*xnk:2he pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, eq0wnx 2i x::c*kv nt d(bs:m5what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppubw*k c/yf k51id 2o7hosite dir 2 7kuky/o* dcwbhf5i1ection?

Why might your foot hurt if you kick a heavy dq) mh pxgt5. +ci;x*tmesk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) - b ohbui;opyn9xx():j41.q2 aaugm7hvm*j i What is the origin of the force that causes you to stop? (b) Estimate (usinn(*m:o v.7bhypj ;m 9i2ixaxo -j14q) ugahu bg 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:iiyv vzcsb;50y 7c/mc:8lsj6 jrbf2 from the ceiling, and a section of the same threadivmy6cr2bj:z8vi0j7b/l5c :fys;s c 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 break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice aclshrw: rt 6i -p2di1wtn;,v(s great as that on a 1-kg rock. Why then doesn’t the heavi1ws;nwct(v2 ,l:phd- rit6r ier rock fall faster?

Would a spring scale,qib)i izs-w7 qe -2ss carried to the Moon give accurate results if the scale had been calibr-wibssz q)i,- is2e7q ated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless tably7hf hz ms*4-le using an attached rope held hszhflyh 4*7m -orizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net wn7 j(-voxsr y j:dkzo1d2c0:nm7g-eforce mg exerted on it by the Earth. Yet by Newton’s zdvnj nw:k1-2r eo 0s7(xyd gc:7jom- third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force azjkrbw* u+93) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare t9*k3u zja+wrb he 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 ofqx52ot qj1)/qfd*u*jwmp w1m war (Fig. 4–37) pulls with equal force on the other team. What, thenpqjmdm *1*fww qq 5/u1jt2ox) , determines which team will win?

A person exerts an upward force o0a+rf mqdb 59qf 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it isd +f 50b9qqmra exerted.

When you stand still on the ground, how large a foik *6yf-ary p7 dbdru4qb9*7frce does the ground exert on you? Why doesn’t this force make you rib 47d*a d-967ffyp*b yikrqurse up into the air?

Whiplash sometimes results from an automobile accident when the vixf +1 gv+ duwddot 5xs;:/pvqd (e(e-wctim’s car is strvsv- (qde +/f;1 wuodw(et+: g5xpddxuck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the beljh 8pki .ad*6d of a flatbed truck. When the truck accelerates, the crate remains where it is on thaih d*6.p 8lkje truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides - u ve4a e3v-fbsp7js.up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its accelj-ev suve4 abp .3f-7seration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on ag xzk9j9cm o+y -fc4xm*bd . /84a:.evplnpqq n inclined plane? Assume the mechanism functions properly, even at an angyfqg9j.xpn+k/4a 8bo.9 q -c*c4 x mlepdzv:mle.

  What force is needed to accelerate a child on a sled n,absq+vdz08s :a8u y at 1.25m/s$^2$?   

  A net force of 265 N 9cmo bkz,v2u-o hmqhq(,v5sbaf) o ;; accelerates a bike 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 rop5 35y:- ubf oknipues(e 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 a -7vl sbv9x. ss $76-\mathrm{kg}$ 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 i;57vzl2blde umc 2cl7v2w*eus required to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/bud lculm2e wle;*v 7cz 27v52h? -  

  What average force is needed to accelerate a 7.00-gram pellet from res8fxbwr 0y85)c w 2o: lxfgs.iet to 125m/s over a distance of 0.800 ob 5 rw0e2w yicfx.sfg:l88)xm along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water wit8sd.zzy8v2yz h an acceleration of 2.z2zv.8yzd s y85 $\mathrm{~m} / \mathrm{s}^{2}$ 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 tfot-;r p.(m kbrack (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 k:1eldwhaj-1 os-m ,vt g ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting oj a--,v:eh11wdst lmcable? 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 elevatjbcj-s04 7 jdar;6yhcor begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, andyjs 0;-j 6d4ca7jbch r find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg:nhmd26jx8els s :j36 gwgk- z elevator has a maximum strength of 21,750 N. What maximum upward acceleration can i-lx:k: 6 j3n2s6mdw8sezhj ggt give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclv 7 gn;ak1a(y,d+ dilouding parachute) whkg;7 d(,nai oyd 1al+ven the upward 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 )rsn q8q 1hi2mw-1hred8b p6oroof of a house 3.9-m high. When he strikes the 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 legs) i)1p2b 8dr1 s-ieqwro m8n h6qhs 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 *h s:l8cj2i.9 bkiec8lyr pwu2 4ee0htied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exec h.ey20e8 ilwprsc*e:jk2h buil 94 8rts 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 flh q(xwq(p0 )qbspy)i3 ,vxo2or a basketball 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 tygmgz38 2cxrye.p16df zp )-b1rj6sa he moment it is hit by the bat, a1gde- b1 2 y8gp3r)s6fazczxj rm p6.ynd again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwestervphh99t5:qe o ly direction. A second 650-N force must be exerted in what direction v5h:h9 9ptqoeso that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high9jtx 2w 42sres7 8ubgwt,flt kwc0;2h wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when w0b h2wk;rx9gset c2t s jt278wl,4ufshe is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a masslezay s b5c:u8/vt;7tkuj)d on 0ss 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 14.00pb/g. e,+ ftcl+ sxvz$-\mathrm{kg}$ 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 McMurd iux1.:ejun w,o Base, Antarctica, as shown in Fig. 4-46. The sum of the j1,x:uwne . uiforces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 ber4/v(f( fmv,d wzd-a khind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first cadk-fz4a ,vwfd rv/((m r $\left(F_{\mathrm{T} 1}\right)$ , 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 , m n;(cpxc..d;kx(ggm v g 84joyvo1xupward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pv kcxp.xooj1(m m;gcx(8 vn ;,g .gyd4ull 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 race began, a gtpq+-u ufcx5;t+p y2j u/1gh 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 block hyr jn8-:+)nf 4ko efb(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 horizonwlor9w(gnkb0 v8m(d6..kk snp9o/ j )dg 4 vautal surface are in contact with each other, as shown in Fig. 4-kwjobsrv)(k6g.pno80 4ldw9v(/d u .9gk nam51. 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 ard;cquvlf41cjod2 b p58(; cubove 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? [Hldcr;(42fu;odq pcuc 5 8bv1j int: 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 frictionlesry (t bvu1(:abs table are connected by a heavy cord of mass 1.0 kg . Calculate the aab r:(t bu(v1ycceleration 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 k.g-+c ivk:fx ainetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is requyzd)j+.o1gg nired 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 accelerdrpu1bi3v 374e nhtv0 ating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if yop4 7 i3bh vt0nr1evu3du are not to slide?   

  What is the maximum acceleration a car can undergo z q.i((n)eio;*s rjzf if the coefficient of static friction betwefiqs; e*z n)(ozj.ir (en the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavdd,jc ialv,i 0cdqr;0ny2e /4szos -;ement is about 0.8. On how steep a ;ns dqz0dcidej0irvl4oys/;a 2c, -,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 att ii2i6h b ys8(kj31uv -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough( 0z3;xctzt3;o lybmm 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 h09s wng hqqdf48t w ci43nuf8,ave a very high coefficient of static f ,h98tusg43dqf04 iwnq8 ncf wriction.

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 kinetbty 0h4 w8m* f+y,jjilic 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 az7vp33ab1br i 4y bw1p mass would box A have to have to prevent any motion frvby3arw4b p131bp i 7zom occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, gs qtj0 rwp+pblrbq i1k1-, ) 4i0rop3jiven that the co0q,tsr4p01+q- )pbbw1ilrikp j o3rjefficient of kinetic 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 and at rest on a horizonk0k-u2zsc-xm vkce)n o/ 7 yh0tal surface (Fig. 4-54). )kucz07/xnmkvec2-h s 0y ko -A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient ofh ,dmn72wt+ w3thbvq8 static friction between the crate and the bed of the truck is 0.75v3tw+m,w tdbnh728h q. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has.tg 8(:4e0tdg1 nr p1sxh qnicv)8peim.eq. c an inclinrgv: xcenite (hpis mpeg.1qt1cn.q 8 4.d8)0e 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 auraua8s7n2)1 w hd..ke kpda; slide 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 lies on a plane tilted attk xtzy65x/h5, dr*zr2s yd,+d)vh z t 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 fpe7 jix29sc+ll)98e8tut lx initial 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 witj99 rbs p,;w;sy4oo tbh a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by someone pushing on ite a ;fx6x.4c 5w/-+vgqpxwsye with a force dire eecaxv +g4p.f xxw6q5w-;sy/cted 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 dange6 mq5k6)th ny*;gkgtqrous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch htt6 k6;*qggnm 5yk) qof $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at t l6i+x1li +*if gse,ospeed v is equal+so+lfl* et , 6gixii1 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+x pyl9(x 5obp forward on the dash when the driver decelerates from 45x 9 5px+lb(pyo $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initi y -1d2gr/nc5bhgkvqv7 x;z6wal 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 vmw /hhd 2 myv,l;mef:cg+3pvw5(q s7 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 if the belt accelerates for half the distance, then decelerates fom/v:w fg3lhv; 5m2dmve,7(+ wcsqphyr 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 coefficien(hxe sy8(d dtbtb22e, t of kinetic 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 coa - gsibieqiw)vj 1),8hst 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 eachg;puf ;0dd/t ess q)x:rznk,/ pulse approximately 20 g of blood is accelsunfzdpr;,sx : )kq/gtd0; e /erated 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 chaddz3es1 1nz 3qnce of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calcd1 qzedn31 zs3ulate 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 produced by an earthquake is a -y wu 6nw7ccmv)ev0* v, and if an object is going to "hold ic)w0wvv 7c yn e*-m6vuts 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 scenedj6otkq hm3 u*0 yh 1:n)5mq7hhxtz3i 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 z *j3m)qdtyut6o:q 1 hmhn7xh i5k3h00.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 meanskz:1mb ptv18tv4 yb 8e that for each 4 m traveled along the road, the elevation change is 1z18pek:4t8 vtyvb 1bm 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 p .zroam:*d/wt iv0+l Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air re/z. dp tlmro0a v*w+i:sistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy ye. 28gn82 pw cmnytgz96-dy ostretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lamtenn6p cwy9g2- 2oyg8. yzd8sts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redpet. 1oo*qno: 2,nt icsvp-w,esign of a hilly portion of a city. An imporitos 1-.,coepo:p2 *, wqtnvntant 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 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 likesel4p axr6m 72b . xlv8af.g.nq/cqu brm 3x--i 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 n2v xrbm-.q. 8cfx3a. -u 4l7rig6bmpaxl /nqeotices 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 supex05 jd;y me9qhm 5v8wkrmarket, there are to be several ramps connecting differenyk mjvwdq; 5h58m 09ext parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the fr8 m.fd. i;vrgh n0r4pulle4 r0 m .nhg8.rdfrfvi;y 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 accabyvhub-tu l*gdj/fb1k 2:+ (elerating 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 processlo h 3m oh*hcsv8+;7o0+n9)ppfe*ub8xz siob for a child-restraint chair, an engineer considers the following set of conditixzm;sb)i38ohp *co hpo+ 7 vbn8o sfh*e0+9ulons:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian t22h3voe tun2o rain 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 ropes of similar lenk/d4z +ckq+fzh 0l7 0 /lsix+ftd l9wqgth. 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 stretches by 30 cm only. How many times his weight will the rope pull on him? Wkli4/d/wf txdlsk+0z+ hqc9z q07lf+ hich climber is more likely to be hurt?

A fisherman in a boat is using a " 1ag0ovcp6 +3z f0-1 $\mathrm{~b}$ 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 r5 p4o 9w y f1odwoskt;*9opnf.each 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 cy36 bob0w6 drdh.c,m egpj9 4are roped together are ascending an ice field inclined9yg ce3,r06hmb pd6dw jc4.ob 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.