Sometimes people say that water iqu- x3bhw3 h7/g6edka qc/w n1ltg; +ms removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong k +3 w6am/dbw7;xg3ch1q/n geqt l-uh with this statement?

Will the acceleration of a car be the same when o y zp8y96f co4om,bb+t cn/l)the car travels around a sharp curve at a constant 60 km/h as when it travelclm + pb8, ocy 6/tnoo)zy9f4bs around a gentle curve at the same speed? Explain.

Suppose a car moves at )yv,mvzka t. s3ce/c +constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of v, sm eay.c+3 tc/z)vka hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridiq7xw9wmo8kxok eg:ywph 4 ,21ng a horse on a merry-go-round. Which of these forces provides the centripetal acceleration k 7qwm pwxey:g8h,4wk o9x2o1 of the child?

A bucket of water can be whirled in a vertical circle without the water skax/+- d4(hx,agrpes pilling /,gx(r apxadk+4 e sh-out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? aw6 shxae*3vzl t13ql- z*2 soThere are at least three controls in the car which can be used to cause the car to accelerate. What are they?a v-xe6*3wqs*llzah21o3 zst What accelerations do they produce?

A child on a sled comes flying over the crest of a sma*9vmo g0rmd-fll hill, as shown in Fig. 5–31. His sled does 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 gof r9v-*md0m law.

Why do bicycle riders lean inward when rounding a curve at high speewo 2f+p2(4 ncdz(e mcvd?

Why do airplanes bank when they turn? How p9w wy0 q1t;zo3uf w6gwould you compute the banking angle given its speed and rg 9qu;o60 f1 wwpwyt3zadius of the turn?

A girl is whirling a ball on a string around her hehkg 8-y d(0qqhad in a horizontal plane. She wants to let go at precisely the r 0q(dh-8h qygkight time so that the ball will hit a target 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, hsuvt 2;c8kyme 680r ggow large a force? Cos u8vy6g rmk 82gc0e;tnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wour nyl 3a93netg0opsx+ z8c9 p*ld the Moon’s orbit be differnp8yt z9pn93ocs* gax+l 3r0e ent?

Which pulls harder gravitationally, the Earth on the Moon,p7rbcpli:z )+ or the Moon on the Earth? Wh7 :l)+r pizpcbich accelerates more?

The Sun's gravitational ,;v00epqw4dvyzy7nvv q :4uiy 6pqq (pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for thw,eyy;zi6ynd 4qq 7v( p:4vvq0v0uqpe tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equat:px 05hdzk4 hqor or at the poles? What two effects are at work? Do they oppose each oth:d5 pzx4k0 hqher?

The gravitational force on the Moon due to the c ew2,ecap-q6rom8jymw-n; 3 Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled ,j8nrw- yqm3wc ao2ecm;pe-6away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun c.1yb lz,g0nr larger or smaller than the centr nrzl0y.b1c,gipetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towh .e8m.o)beyc ard the west? Consider the Earth’s rotationboc.e8m )hye. direction.

When will your apparent weight be the greatest, as measurj01wv3zxa1t 16 yrr eted by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be1wj xr a et3yr160zvt1 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 periods in outer space coul ka,xt.96yv d7 g*swg8zf dk,rd be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (rz8g9 w.d,dv6t7 ys *f kx,kagFig. 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 experiences “free fall” oryse;2x+yq 4 8,zgz 9gyk)i/zvdgkov : “apparent weightlessness” between steps+qysy x9vkk8zg:zoi2g,edv; 4 gz)y/.

The Earth moves fasterplf uxyjp:3/ b8x6 wu; in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: Thi /w:ux3pyxjp blu ;f86s 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 discovered to have a moon. Expyfr0 gjv o0hg0v5/gph :q:vn,lain how this discovery enabled an estimatev oj pv5 hn0ghr/,y0:g:vf0qg of Pluto’s mass.

  The Sun's gravitational pul.ag.b(f v-xqgi*n1 upl on the Earth is much larger 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 other.]A child sitting 1.10 m from the center of a merry-go-rou a(.u*bxn.ip1vgg- f qnd 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 198nyg-l i-jx0if3ncy05m m/ckv 1* puk90 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earthaplla /d1 36rj8yd3h y4(e nub in its orbit around the Sun, and thbj d8hl6yy3/u a(1np ad3re4le net force exerted on the Earth. What exerts this force 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 2.0-kg discus 4qti v,b v.qf9ayp,.w as it rotates uniformlw 4i.,atf q.vvyp9 ,bqy in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfa 2ed)z/ygdr(;/ iqby ice, and circles the Earth about;)2qgr//biddey( zy i 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 surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of yyf,.v cj ,m+mu 1r+zxclay on the edge of a potter’s wheel turning at 45 rpm, z+1 yy.mumvjrcx f,+ (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in ab;e(l kp, kgao+. pk9u.vmf 4u vertical circle of radius 72.0 cm , as show(u ; b, ku.p+.ogmvl9kfaekp 4n in Fig. 5-33. If its speed is 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 with which a 1050-kg car can round a turn of radiust:a7o6cl:5p) j m xduj 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this re: mjaxpdt)7luj 5o:6 csult independent of the mass of the car?   

  How large must the coefficient of static friction be ;6uzvv5;op 8v4yt j;2ck pnqb between the tires and the road if a car is to round a level curve of radiuspc2 kn v 6p;vujvb8o;tz;q4y 5 85 m at a speed of 95km/h ?   

  A device for training astronautsb-tkm h2m(zuv /(g:me and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . g2be(k mm:tu (hmv/ -zIf the force felt by the trainee on her 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 the axis of a yf3z( :c9eyrkl)t .j srotating 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 the ct3j c(e 9:y)y rkslzf.oin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rolleu) 0 ujuu))oajr coaster be traveling when upside down at the top of a circle uja )0u u))uoj
(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 )5 h.y*okvpvc nn- 3s;p styeb8gi;o8 (including the driver) crosses the rounded top of a hill (radiush;p.*ky ) 5-o npgi8yvoecs8t s; bn3v =95$ \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-diameter Ferrisa2,igwb 59sk +nerj71 umgm6h wheel need to make for the passengers to feel “weightles raksb 91e +m5n2gi,guj6h7m ws” at the topmost point?    rpm

  A bucket of mass 2.00 kg.xbsk w:dc2 r4 is whirled in a vertical circle of radius 1.10 m. At the lowest point of its moti. 4:cbx2wsrkd on the 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 c27e6:ui.wzy-i: g3cp+yteu f s/pt ezm from the axis of rotation is to experience an acceleration oe:/ftz3y2 .g tweypz-+ spe6:icu7u i f 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindr,3k5 patbmyc (5fv-n,ld y n,qically walled "roo3(aky ync,,fpldt,-nq5mv 5 bm." (See Fig. 5-35.)
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 rotat)rs1. q*+dmr(l8 l.xhhlrtv qwu 5xg4ed in a circle 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.r(5lqd4h tgl xqwmxvrh u) ..* lr18s+ 5-
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 not ignol:yfnd20jhj w .exp+,ring the weight of the ball which revolves on a string xe:p2jjfl+n, dw0y . h0.600 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 is0tai4zwv51ws n: 1zts perfectly banked for 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 masses lt*:bt3: vqmbsr*m3p $ 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 maneuv ndp9xs0v0uhktqj o * ah+v46 jl,oq./er 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 centripetal components of the net force exerted on r1a.h6yjk (jev 3qz5a j6wf3m taya6qejfjk 33r(.1v mjz 6h w5he car (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 accelerates uniformly from the pit area, going frod4l.+a+ (cceouumhzufg2)1 f m 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, assumuomfcdhl+g1 (zec 4+a2u.fu) ing constant tangential acceleration. If the curve were flat, what would the coefficient 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 ho1 ib7wk,g lv: omldz07rizontal circle of radius 2.90 m . At a particular instant, its acceleration is iwg01d o7 ,l:bklm7 zv1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravitytp;,1-5ed km i8fjiul on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if itstdl;e1-m,kju5p f 8ii mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hahffh*wxmdbgieib i :+s*d-96 jd 2 n(7rh-h 7ss a magnitudeh:bf(sdhi 2n-*-67 mhs 7 ihf*re9wdijgx db+ of 12 m/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 gravity on the Moon. cf6 r7l p9:yqkThe Moon's radius is 1.74 :k7r l9 cqfp6y$\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 hw eeq*6ovq3*g q, w3awas the same mass. What is the aq*o,6gawqve3weq*3 wcceleration due to gravity near its surface?   

  A hypothetical planet:q4 ,z unwss/o has a mass 1.66 times that of Earth, but the same radius. What is gzw/: 4q,o nuss near its surface?   

  Two objects attract each other graviz-s +j1s fby7jtationally 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 value of g , the accel:c we*, eynuivm h,60neration of gravity, at (a) 3200 m*ew c:um ienvn,06 y,h    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth t8kyhb u 636zk4 idpi5where thegravitational acceleratiy5i kuz63 ib4dth k68pon due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spherkb6pydsh-9e.k .mw u 7e about 10 kmk7b e9dm. wp6u-sk yh. in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an a27td/ 2bntkbeverage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfe t k2bd7tn2b/ace gravity on this star?    $\times 10^7$

  You are explaining why avl60p k9mii/estronauts feel weightless while orbiting in the 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 gravity 250 km above the Earth’s surface in terms 9k/0 em6lvipiof g.   

  Four 9.5-kg spheres are locateaz8q: z qnbla+z81t *ad at the corners of a square of side 0.60 m. Calculate thz+zz*qnat qab81: l a8e magnitude and direction of the total 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 lign l-yp iyxw (0qm41q:cmqc72ne up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assucqn: q2xcp1mmgiwlq7y-0 ( 4 yming 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 grwl;u wt)q0*- j egydfdu3:w/ravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass ofeuyf l:*3-gr/w;q wtd d wju)0 Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periefhu:, nan5kdimb(w 1y))n o8 od of the Earth and its distance from the Sun. [Note: Compare yodyk,ah)n:nu (oi 8wb) e15mnfur answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite t-t+8tzkyoim5 c( nz g, )gmw/moving in a stable circular orbit about the Earth at a height of 3600 m(zn/k gi ttywo 5mg+,-ctz)8 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abov u2yai8s; kf+mmy-e4,zcdj. ve the Earth. How fast must the shuttle be moving (relative to Earth) cy vmim,zj;8fs2kyu+d- .e 4 awhen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshipn(ahjq 78 oh bdezo :w*ouu eh(339r2z rotate if occupants are to experience simulated 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 ujz38o ezuqr3o wh:h7dn*( oeh 2(b9 aQuestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ne:, wrsf zx.uiku,*ufr5n9s4kfs jk)0ar-Earth” orbit. A “near-Earth” ojk495 u*rri0xss: n,u fs,fwukkz)f. rbit is one at a height above the surface of the Earth which is very 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 satellite have to be launched fr 4f sj y/,yerng/m/1npom the top of Mt. Everest to be placed in a circular o4fps/nmyygr,/j1 / ne rbit around the Earth?   

  During an Apollo lunar landing mission, the comma hhgy2ta6k6c/nd module continued to orbit the Moon at an altitude of abt g26/ya6hchk out 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are compo)2oa1r n 6j2/h. uff ks5((afm(o jfvo 0hgrqwsed of chunks of ice that orbit the planet. The inner radius of the rings is )6mok w/(j0ro(sr2 ao (uv.ha51f 2gfqnfhfj73,000 $\mathrm{~km}$ , 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 eve* fui6: g-lpdn7sg 9yfry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight tyg : 76nul9fid- sfpg*o her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg a ro.rwk92a- sastronaut 4200 km from the center of the Earth's Moon in a space vehaso9ra2.r -k wicle (a) 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 sysnsdo 9 g,bh2w.tem consists of two stars of equal mass. They are observed to be separated by 360 millioob,s2h9d.n gwn 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 for the weight of a 55-kg woman in an elevator t ny30t ;up.wq(xbcew ): ,tln 6vcwt(ohat moves : tbc;o wnel (cu30nwyxqp(6v)tt.,w
(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 thi:m+ujf 6ydk1ff,(hi e ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elei6 fudfk:,i f+j(1y mhvator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits ve m+tq9)42 uk*f4gnkp sbh(oxbn h.1xiry near the surface of a planet with period T , the density (mass/volume) of thegi 4xh*uo)fq1 tbbpm2+nh.9sk4knx( 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 de1(*(e nuau gwstermine the period of an artificial satellite orbiting very near theauu1(sg w*en ( Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Su af4i vly*in)6n like the planets. Iv ianf6*iy4 )lts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag03g-*(cu.u m kqxwxnfe distance of 4.5 $\times 10^{9} \mathrm{~km}$ 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 orbitg3gf0,rg,5+bdkn+ktkzwf9 i s the Sun roughly once every 76 years. It comes very close 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” th+, +gzd tkn ,g0395rffkg bwike Solar System? What planet’s orbit is 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 Galaxy(b*h+c4 vp m-3zd zr6isfbtl 0 $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 irfobej a qmw2wea(v ud.(;1v t,f:;ets ;,(h, and mean distance for the four largest moons of Jupiv((;ist w(1;.ej hu dfq,b rvwamefo2tea; , :ter (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 period and distance of thb9fbe v/y.wo+ 0io0oxc*,b8(9 twj irtlloi/e Moon. y 0b9e8ol/b,vjof o(rw/cti . wobi9 *0+ xlti   $\times 10^{24}$

  Determine the mean distance from Jupiter for 6yw2kuq3 fia0d zg06)a 9re seeach of Jupiter’s moons, using Kepler’s third law. U euyk0 w6)3zqir09f2ads6ag ese the distance of Io and the periods given in 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 consis+jt2zf0n7w/cbj9qrni :u ip, ts of many fragments (which some space scientists think ca7j+n/ i9u02i zw nb, :cjrpqtfme from a planet that once orbited the 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 describes an artificial "planet" in the fos 0sxeqjtcqk5 7 8ogv:759x qdrm 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 rq kjc:q78v55s 90xeg o7xst dqotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vb slhg /jm*4u-ine (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 tolbjmhl*g/4 s u-erate 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 surface will the acceleration of gr d2. 7hmm maoff/p:xw6avity be half what i./ :fm2md pwm oxf6h7at is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin scy -jey9i3u* in a mutual circle once every *y9eyui j-s3 c2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per i-fn6 .3 s r;gvci:wmi+qd:ky day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magrii dyqm- i 6;:sw3fn+vgck.:nitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecracx b upo5plh cfk(,.c(f*1od ;ft traveling directly from the Earth to the Moon experience zero net forcblp cf(,o1p* dc hk5o( cuf.;xe because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scal c2y9lvp, ohlr3sy5c);9sog ee in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,; 5s9cg3 cvs,pyl9oelhr 2)o y and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will r mrh n df;2itpxpowd8/1p w;-*otate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 ; p nph wf2ix18ro tdp/;w-d*mkm. What 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 isf:f9r6n g6w yqqd.j4 9) fmain a 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 tkqrugpbppgzv /3b0 d,g2 9;8xerms of its radius r, the acceleration due to gravity at its surface and th3 rq0p/8kp ggb,g9z xuvpd2b;e gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertija9dl .fy 98sbcal by ay9 adf.slb8 9jn 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 m is banked for a design speed of If the coefficient o0acom-i8tg) if static friction is 0.30 (wet paa i c)m0o-8igtvement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so f;nt8ufu2 ahmh45kew 9ast that objects at the equator were apparently weighta8e5uth 94 2nwhf;mukless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan/b+upxlp3(:q*b adwb hc 3(acl. fsb;ce apart 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 rnrqhvd68*bs: kni 1+ a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceilinnksqh 6+n1ird: r*b8vg swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it hqlv-c 9mw *d9d *lhhx/as been claimed that a person would be crushed by the force of gravity 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: ma9hqxdwc*hvlm *- l d9/ss =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 Teles-wd93vkqs9pjzi z , base)a*6cope deduced the presence of an extremely massive9-a9skp6 ,aqjzei)s bvwd 3z* core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). 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 trm;6gtutjz /rqxi1-p))edh)k averses the hill and valley shown in Fig. 5–45. Both the hill and valley ) -z)ijq/kmupe;drtgt 6)x1 hhave 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 go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellitefbf06)l0ufe ns (vyl- s orbiting 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 Earth, 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 (nvu60f- 0ff)llyseb the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Aster 05y,eu9aqzxg:o-.yn: dp ua coid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of aboutxaen: u0.y5u-z, cgp :do q9ya 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 i, vu :a y,s4-oqo4ltzin the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behu:z4ovt-io yl,s qa4,ind 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 periovn5x8v4nf v) ed of 3000 years. (a) What is its mean distance from 8ne4f vvv 5n)xthe 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 be if you c4gz4q mn; 3 chnls7+ovould actually "feel" yourself gravitationally attracted to someon7 mlcv;+4qn4 osznh3ge near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galxk1qm9s6mr4tkw 0a5k s y uye)m1(2+axiwx* caxy (Fig. 5-46) at a distance of about 30,0 +axmi24xmxy0kt)1cm15 es y( ww6*r ksq9 aku00 light-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 0.50 m on each sbh96.fztrw8hphng 54m1 dc v5 ide. Find the magnitude and direction of the f g96c 8d4phzbmr 5h.5tvh1nwgravitational force 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 5500v;ec;9;hvwr00p5vh w( v9ynyr vak ,b kg orbits the 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 experyy3x6+-6vq jf(hnm1/ u y5vwxku5 kheienced by the tip of the 1.5-cm-long sweep second hand ( f3 + j6mxh keyuvknxy5/hwy1uq5v6-on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sink b -crkr2x*cpg0j.8k+2e n mfher weight around in a circle below you on a 0.25*g fkjb2ckn -2+rh.0exm8prc-m piece of fishing line. The weight makes 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 hi5mfzz/ 9+hvlk ghway is designed so that a car traveling zfzl/5h m+kv9 at speed $ 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, uti8e5:zunbjw ; jlizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the n j;:8u ewbzj5centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling 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.$\approx$    $\times 10^2$