Sometimes people say that w/91 +y1v6cl on: kefbwzmves 4ater is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stayve c6 b:/9 fke4wsmv1n+l1zotement?

Will the acceleration of a car be the same when the car travels around a sharpf /tmdr)la m9;2v i)cg curve at a consmrt)f 9acim)g;dl/v 2tant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly rofh p6c*bct3:u24hk c+4 k1a;hz vqp 2xftce o4ad. Where does the car exert the greatest ankh:cxh+p4h2 tao u1q pzf*bec2cv36;k4t4c fd least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acwop2xtj g;.ptfv(o4zr9 4g* vting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratiogrtwg4pvf92zto 4x(vo*. pj;n of the child?

A bucket of water can be whirled in a verticaljn 4ztj: :u9c4b9cajo circle without the water spilling out, even at the top of the circle when the bucket is jcojj4n:u a4t9z : c9bupside down. Explain.

How many “accelerators” do you have in your car? There are at vzcvm* ; 00 f2qdad3w,)sgucx least three controls in the car which can be used to xf 2su3*agz; d 0vv),wqmdcc0 cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest ofgu(k. 9o9/0 damld lbg)tg yc7 a small hill, as shown in Fig. 5–31. His sled doektd b 9/y adgm(l g.ulg7o9c0)s not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curk f)x/xvxbp9x95ri 7 hve at high speed?

Why do airplanes bank when they turn? 4s;+hmk opwy8How would you compute the banking angle given its speed and radiw kp8+;oshym4us of the turn?

A girl is whirling a ball on aq kl3yxm( a+x5 string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target xxm l3ka(5qy+on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large 5of,gj sv0b0-3 xl3;qwobvy q a forceb ,0-sq0vg 5 ;lq oyfxv3bjw3o? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbw0 / 8w-:xr7cclkkmem14nbfyit be differen8- 4 w:fc0ewbkcn1mky/ 7 rlmxt?

Which pulls harder gravitatiop w;()*m 3im54liz nxw./cyeexg z cp*nally, the Earth on the Moon, or the Moon on the Earth? Which acceleez*5;pi/gmwm)(w.*cenp yz xx cil3 4rates more?

The Sun's gravitational pull on the Earth is much larger than them; copg-d;1v: nvurne /72lqe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from onm:g ed;n2-;vpren7uv/o1lqc e side of the Earth to the other.]

Will an object weigh more at the equator or at the poia/:kb -3ey lvibu 93)uqlg 16 6mamlsles? What two effects are at work? g6l)l:byu a39uimvb3s -6l eq1ia/km Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about h-,(z,kfp s2b8cbdw wxalf the force on the Moon due to the Sun. Why isn’t p-z2wb(f8k xd bw,s, cthe Moon pulled away from the Earth?

Is the centripetal acceleration of8wc,; u +qsgyllun ;b. Mars in its orbit around the Sun larger or smaller than the centripetal acceleratio +lqyc8u;s ;,lungwb.n of the Earth?

Would it require less speed to launch a satellite (a)n1;xj u9k3 b-3*kxp-r sw ups9qmk q4(rvsn /u toward the east or (b) toward the west? Consider the Earth’s rotatin runur-k/q99sx( qp3 ;mw4v bsj-3p sk1uxk*on direction.

When will your apparent weight be the greatest,bux g;s32l:a r 5dtom3c ,wll* as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves updu2 ll tgaxlo mr35;3s w:,*bcward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodrjo/ zlfvl3 b ))rfd8vs 4isq(py6d25 s in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotat8db4 yf lol/j3r v2s6fizr)d5q () psves, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experienbn 57n vpqoeo./oa8t6 ces “free fall” or “apparent weightlessness” between stepsoa/opq67.v8b eto nn5 .

The Earth moves faster in its orbit around thw75w iy.sij dk+ pu+mg2h9)b xnu8+bwe Sun in January than in July. Is the Earth closer to the . mgw2+bswj5xii)b7ydp wu+ku89+nh Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was d 7j 9s 9lfz45t6e py(cx6d5llxfgzaa/iscovered to have a moon. Explain how this discovery enabled an ec a 5x4y9 eadlst5 fz6j7(gx/p6z9fl lstimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largr1 u0iei5ic*t er than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the otc uiie*r51it 0her.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19jq yy )2v. n*yzr1x(se80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around th re(;* fb 5l-ntnudn3ye Sun, and the net force exerted on the Earth. What exerts this forc e5y(-d;r 3nntul nbf*e on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.h8 .-d qmykr-uhig7 i40-kg discus as it rotates uniformly in a horizontal circle (at ar.8hiq-k di7h 4yrm-gu m’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 v1-89 .h jkwctlkyt /ckm from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surf 9y8tj./-vk w ktc1chlace. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay z i15rm :7tdxqon the edge of a potter’s wheel turning : qrd5ti1x7zmat 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is6) g8 zaqteb1bpn))x s revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed ixn1gepabzt)) 6b)s q8s 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed wit zct4nd. m;p b+ q j3:hez7hyo/x fr6/pimaw18h which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction bet6f:hjnpp dzi3;/ byr xc /wmoteh +a74z1.mq 8ween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of :px9gkl;):)p bibq scx q52xf5i eu9astatic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h l q )buxq9b2 :x):c;ek 59gipsixaf5p ?   

  A device for training astronautay-n g8+g b+i0x/x wzws and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on - gi/wbxyg0z a+w xn+8her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from ulrgdp:7h x4:)exg2jish)s - the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and t: hersl:)xghi 2uxdjpsg47 ) -he coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when uvg3 z.81k rbbwpside down at the tovbwk1 g38b rz.p of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) cro2 - n e; nfvfuqmop3m1(y,t1wlsses the rounded top of a hill (radius =95o21l1p3(yfq- w,mfnem ; nvtu$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-di);pm ktrgu2v;g 7oqj2 ameter Ferris wheel need to make for the passengers to feel “ k)q2 gro2mp;u;t v7jgweightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vqsd 3kiemulvsrc(5 ;*dg;8xu-c 9kb , ertical circle of radius 1.10 m. At the lowest point of its motion x db,cuuc qk(r se 3;l sg*-5md8ivk;9the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axis ofiof1f; 66y0)lhs hd qmy 2i5bf rotation is to experience an ashf2fy qf1)5lmbd0h6y;6 i oicceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotate*nta4byq,q 2rou7 :wo d in a cylindrically walled "room." (See Fig. 5- 7:qt2*yonq,b4rw a ou35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circlegk:trab f1..k bf t:8lb79q rj on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-k9 r:fg lt.brq: f.bj7tbak81
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by noq)txhvqg*2+re :y 3f irnurigg),3.p t ignoring the weight of the ball which*xq .hue rt,)3piyg irnfq+3)2: vgg r revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fl,pnvyo wcy p,34sv, ,or a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masse2+oe8pzf8qw4i hsl0 1nze5 kma.h- yfs $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive e)sq vm-py3g f8 g ga:+pid ti3b4-f9dmaneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centriz8gokcbp5f k1 p9hwh*oaqu-v;/pgfj8- r; h 6 petal components of the net force exerted on the cah arc h;;o- pj-kkbfv86f*9u/ggo58zqp1 h wpr (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 a,k4 1:f w7py9ei sw7p,qouq we1bb*kh ccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the cf,yw1b h91q bwoi:k*uw ,p7eq7 ks4 peoefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a )gbh871 mm)pku9yqc ihorizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05mc ) ku9hqbg)ip8ym1 7 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecrabhz)a)/+o 1ic -tmffpkf .ua6ft 12,800 km (2 Earth radii) above the Earth’s surface ifbif )/+u1.tk-a6fhfzm o) pac its mass is 1350 kg.   

  At the surface of a certaio mtkui,02zjz e8w067)7 9fa xkmmah ln planet, the gravitational acceleration g has a magnitude of 12 m 0lwja9 )7amt ui ,emf76 2hk08zmoxkz/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravitynq y.tkp b:ns8-s,e+o on the Moon. The Moon's radius is 1.74,pq:bkno8sst+n-e . y $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has 2 s 6o p 2b+c2ve.ash.wjrqwa,6mszf, the same mass. What is tm 26evb,.w.2pjscrf2s6oawzh a,sq + he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ea jh62 c5oewa1grth, but the same radius. What is g n61whg5j2aec o ear its surface?   

  Two objects attract each o.pf +jq/ng;wk ther gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective va/cnr57-v62rqs aevlh lue of g , the acceleration of gravity, at (a) 3200 m2vh e65s/qlc rrn7 -av    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartmaw enfytuf2ffjyfh(u )sa 0)e,k*f26 (-z(rh where thegravitational acceleration uufzy 2 *2n fa t (f hf0(r))e,aysf(fmkjw6-edue to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star / btpkvd01) zmhas five times the mass of our Sun packed into a sphere about 10v /zk p0m1bdt) km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf stdhm6 bbh*tjadg.ali10hjzsp k.- w 4i(5 kb,2 ar, which once was an average star like our Sun but is now in the last sg jhks i-a..pb6dz0*t 1i4mhab5b lhjd(2 w,ktage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in th3m q,dszvaeix 4b; 085xx) nkde space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of k,i3bqx8ev05a m) s dz;xnx4d gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Ca 8p4x6spen,r ilculate the magnitude and direction of the tot84ensixp r6p ,al gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up ogjk)d9p53vy bed.6k wn the same side of the Sun. Calculate the total force on the Earted9d6gy53 j vp k)bwk.h due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars i5 *yo kdc-vm+v .ba.kys 0.38 of what it is on *.dm bc -y5.ovv+akkyEarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known va cobvv z322ikih*br,qj.p,b 2q +oo.c lue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lovkb+q3 2 q.pb oiobjihc,zc 2vr2,*. aws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abo7pq x4+jdt-n u) )w: zfgk)*/xhwqgp2 nps0fqut the Ext*qgwz fn2/f)): -n7w)g j0 qp up4x qkh+dsparth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circu03de mokmvj) 5pfz1ad1otc4 -lar orbit 650 km above the Earth. How fast must the shuttle be moving op1 dom)3f t1v0j -5zkdcme4a(relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate el0i6gd a zgry..jr /(if occupants are to experience /j6dy.g r(eazil.r g 0simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for 9hg1u.1oox;kag-:nbhl6 ab ua satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is v;1 g l o.9 gahb6hab-kn:xo1uuery small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitrdh-tb0+ekv93*v p h 36qjb obe have to be launched from the top of Mt. Everest to be placed in a cirj639hq*e h0b tkv3v+ o-p dbbrcular orbit around the Earth?   

  During an Apollo lunar landing missionibo0f;sy-05k+f sic; ggkxo :, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it txy;ffi00 ; kokgc si+5gbos :-ake to go around the Moon once?    s

  The rings of Saturn are composed ofl; ek/vo(r06 pd*n kuu chunks of ice that orbit the planet. The inner radius of the rings is 73,000 elko v0n;kr/*u (u6p d$\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once evsp4un /(8h/x dhyy ui*bg3vup *w4)zs p;2xzxery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottomu3)/ps/4(uy *v4h 8x ;*xyn2ppgb zsxduhizw ?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from ndegv) c)k n6/the center of the Earth's Moon in a space vehicle (a/gnv 6 cdk)ne)) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of ): 0 aym1pmhks p*5 puo0ag5ljequal mass. They are obayg*u)hsp50 :mko1 aj pp50mlserved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read f. 6fo q-q(su7kyf iiz mj:a f*v51(gggor the weight of a 55-kg woman in an elevator that mo z6(g o-ia.y gm*s vf qkguff5i1j(q7:ves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceilinji3si/+p* by jg of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accel3 sp+jii/ b*jyeration (magnitude and direction)? a =   

Show that if a satellitst*clk+t.o23n us(8 2p ut ztse orbits very near the surface of a planet with period T , the density (m8t+uol tsst.2k*zpu3nc s t(2ass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period otr laic sax.2v,f.j6)f an artificial satellite orbiting veri2a,rs) ..a6 vxjlfcty near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun li9i xlsh6 z.*/y:zoew w44o pqwke the planets. Its period is 410 d. What is its mea4z.e6 9wixho*o4/pw zysq:lwn distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.mi ,5m7/t wzr:v4efpp5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very closepe: dm6-.aac w to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit isa -:da m.wcpe6 nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga) 2w3askerh( wlaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the f.m:his au*,8qxp:lv4a *y vkkour largest moons of Jupiter q:v ahs8p *4*.:vkkyal ,muix (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known a0)7mo; m /m0 zg15ji neqwmpbperiod and distance of the Moon. qni7mowmz/m1 bj)p 5g0m0a;e   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moh mnibv2a2,xy8paa: 1ons, using Kepler’s third law. Use the distance of Io and the periods given inv8h,paxba m2y2i n:1a Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whichh6o s/xjv y.m1 some space scientists think came from a planet that once orbited thy1 vm/h6 xs.joe Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describesll /dvf:1 x8 jgzj/xfh3;dzy ; an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the f8x:/;dljv/zhyl z ;1f dx3jgperiod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging -jx,wv j 7zhhyd/w7te10p n4bnhp a-1vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolera 7wphb/7,4zhxahe- 01t-vn jdy wp1 njte at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s 2 sa,*ceuoor2surface will the acceleration of gravity be half what it is o2oreus2oa,c *n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and +7/ clx/q 23jy6p:s f tktobqbw3u u4espin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long anfbtuc7 qxltwo2 ep:k s6/ /u 43qyb+3jd their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent5 yv*h,j7v kq+,l pni6gr-n ca acceleration of gravity at t avl5 n*cvq-ygh j,np+irk6, 7he equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from they nl6-bb l(90dk+ ice.2vkhxy Earth will a spacecraft traveling directly from the Earth to the Moon experience ze +y(i xnlek d-v29cyh.l6k0bbro net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bu+ r0m zkh*n3l; yg:h+k8k sxmit when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceler* k0+8:nmhhy3rzm+k;xg s iklation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboubgyyyf0m6 3u86 usrv 7lcj6c rxtz, .4v-ik :rt its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. s-,jvl yky06x gc68 :bvyu.rmf i6zr4 u3trc 7What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in gv7o57ert0qxa vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r,,-tp v*day ix, the acceleration dxayt- d, ,vp*iue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectea o(sf,l/)y nflf* hm;i hbbi1w s,xi7inj6*2d from the vertical by an 1ii f*m2) nf bab;6ijnshl,/,7i ( whfoslxy* angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 ao a;ldabyd) j+,09qj m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle th jb0j9la,dayaqo)d +; e curve?

  How long would a day be if the Earth were rotating so fast that objects atbflu aq1;x e-5 the equatore luab5;xq-f1 were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparter vd34 cn:squ5x a zh;7nk;lq+j/ i:- bszju) of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed);,g no oosy:n rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5 ,ooy;n)og sn:$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been cg6b - sn(kh u,,)hje1gg+ h7huzg lg;claimed that a person would be crushed by the force of gr (h;)gnegg6b-71+ hglhh ukz,,jsu g cavity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extreme;tovqv+s cpfc+ 1h1t-1) simsly massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapeh+1fi t s)cqvm1 ocs;spvt+1-s). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley showna pu5s 5-d/ml2idmec1suk+d7,2 ,baf 8oaeqv in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car sd m /s-o 5,p8def,mbu7acu5v qaei1da+l2k 2go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites ofpc43 k cd:jod 7l/f7brbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Ea7f: ck4d fo7db3p /cljrth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bil8f 6qg ruc7i-ilion km, is meant to orbit the asteroid Eros at a heigu fi 86gri7-cqht of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in tht;:g0h :6d*es tf)t bpfh-z-n)o uxwue space shuttle pursuing a satellite in need of repair. Yot )*;pbwtfo fu txu-h)6n:h:ed sg0z-u are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 11p lsgp2niv*mw8 4htyears. (a) What is its mean distance frtg1w*s lm8in1ph2 p4vom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to it (oq o 9qh;91bktv3kpi:a 3pbe if you could actually "feel" yourself gravitationally attracted to someone near you. Make reason9; q3o9ap : 1kthvopi3 (tqikbable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroundzvztfgi:v 5 bmuax89f +o)9f) the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 liffa)5)xu+otz9f zb8v:gi vm9ght-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square; qm8 l6)k hww,z-emwa 0.50 m on each side. Find the magnitude and direction of the gravitational fo m;maw)-z8 l,ehq wkw6rce on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the .6-tgawa2 vj-l0yjzj Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration ex 2 ka)ka/fr/ctperienced by the tip of the 1.5-cm-long sweep second hand on your wrir /a2/k kt)afcst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wey)f qi+p24, q,st5zz*p b:.us o;gibye 6toul ight around in a circle below you on a 0.25-m piece of fishing line. The weight qupo+y; og* e 2pzu btl, i64qfzi5t,.s)ys:bmakes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a cuur +be b;m;x:ar traveling at speed ;u+mb x ;ber:u$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cao0snrb6l(7 l wrs when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus frolb(sn07 lw6 eeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$