Sometimes people say that water is removed f tvwz8 /g;6z pt koryurl.w. ,4xj6;xmrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with thi/ 4lkmw zv,.tg6 u;6py;8 .zx wrrjoxts statement?

Will the acceleration of a car be yaqit* lbi1 g7mr dan*t:sx a*+ 4*s2nthe same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speeix*tsra**:tg 24a +n b17siaqn lym d*d? Explain.

Suppose a car moves at constant speed along a hilly road. W8klb) z ;wd43ezxdo0e here does the car exert the greatesdxeweb8;)40 dk3loz z t and 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 acting on a child riding a horseg. zl,t/6xko i ++fdht*fcyri 9m.k3 n on a merry-go-round. Which of these forces provides the centripetal acceler9km+gk.yi*ncz t+ 3ol6d /,f.t hixf ration of the child?

A bucket of water can be whirled in a verticays:oak h-x1+ cl circle without the water spilling out, even-hso +a1cxy:k at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leasa5pop ;4m-ck )xgp7+ ;wyrot0agr a-o t three controls in the car which can be used to cause the car to accelerate. What a;yao0rxgpto4 5pmc;rp +ag-ok)7 a w -re they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shownw( ++zaimr g 8knxep*- in Fig. +wzp+*8 geri (xnk ma-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 law.

Why do bicycle riders lean inwa 07juepf;d/ o4ex8texs .h:dyrd when rounding a curve at high speed?

Why do airplanes bank when the hwe7j1.88rwhcznz 1xt:1 qavy turn? How would you compute the banking angle given it8.w1 1r1q zea hz wx8tv7hjc:ns speed and radius of the turn?

A girl is whirling a ball on a string around her head in/ ikp d ow58 n:fyrg0poy. wk,y1t7v8t a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When sho80tpn/owv,.ywtkfg 1k7y orpd i5y:8 uld she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, h / 0.pzupd0ixdp x7g.aow large a force? Consider an apple0x p0z7 .. pxgpa/iddu
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would th zp fevm/f5.g9a6 bkf5; j4brde Moon’s orbit be different?5.zb bd/65 f va4mrpejgkff;9

Which pulls harder gravitl( 80udv nm-.p 1hpzbgv zcw4:ationally, the Earth on the Moon, or the Moon on the Earth? Whib -4 (1 dlu.pw:8vgzpv0nmc hzch accelerates more?

The Sun's gravitational qc 6rjq;-u ah1imd 3l03 h6uoxpull 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 t 6 hm3ijqa;x3rc 1qold h6uu-0he other.]

Will an object weigh more at the equator or at the poles? What two effects 83lz;4irv gy p c4)5s j6nung8e .ntbxare at work? Do t4u46pz8evct;35gg sjxn) nyn 8rib l.hey oppose each other?

The gravitational force on the Moon due xs:jh3m bc bc5tu. +p*to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earthcj*x+: smbh35u.pbc t ?

Is the centripetal acceleration of Mars in its or1dv*sy(rlvyd-xc .j 1bit around the Sun larger or sma.j(*r-1vcsld1 yvx dyller than the centripetal acceleration of the Earth?

Would it require less spee-rzet:jp )r pcs;)s 6cd to launch a satellite (a) toward the east or (b) toward the west? Consider the rcpesptj)6r-: zc); sEarth’s rotation direction.

When will your apparent weig l2qd np 1mdy -d):)fura((p hgsf,g8cht be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upwardphcngdq sfy d2:pmf1-,(glda 8 (ur) ), (c) is in free fall, (d) moves upward 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 periods in outer space2cfuna x. *+ 8vvye6xj could be adversely affected by weightlessness. One way to simulate gravity is to shape the spacyxfc jn62x u8v ae+.v*eship like a cylindrical shell that rotates, 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 experiences “free fall” or “apparent weightlessness36qv3 v(iawen ao 2 u1y8vvgj/” between ste1 v/o 2ve 86va ajqwguvi3yn3(ps.

The Earth moves faster in its orbit around the Sun in January than in July. Is4e,: s6 acpag pbu2x5d the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is th p,xp5agu:bd 4esa 26ce 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 moox3mc+oqw/ eox/(ux 0z-q(tetslji(- l : l7qon. Explain how this discovery enabled an estimate of Pluto’s mas lot( -o etmcxull7qz (jsqx3eow/x /i-(+:0 qs.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. ;.dzs.kgv, qv- *b4;cp2j hrvlg6onpYet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gra 6osb;zjhdvg .vn q2; ,-c4p.gk pvr*lvitational pull from one side of the Earth to the other.]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 travelinkt, )o u whof xw6wm.+:a-wa;yg 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetalnhaz3 ;gxfcs/70 c cl4.vm6xa acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that t aag3./vzn4f 06x;smch clx c7he 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 cn:ezk9d i q9 tjpc xp+,xegh+7;e-;xas it rotates uniformly i7ej- p9+,xig;n; h:k+xq cde ctepz9xn 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 surface, a: crc t jg,el,gw6p:o85p ilv3nd 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 accele iwo 3p,:ltcg pce:vl5g8jr ,6ration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge v uc/ozdqx3g gs7dm0g/wt5x;7*c6 qrof a potter’s wheel turning at 45 rpm (revolutions per micc x*s7domzvwxqg ;05/ /rt36uq ggd 7nute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a iiq)aq 3l5v*-u2 wso xvertical circle of radius 72.0 cm , as shown in Fig. 5-33. If i qi3ai-lxqwv* o)2 su5ts 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 fo*bpdrm;a2 +of radius 77 m on a flat road if the coefficient of static friction between tires dar+2 p;*bfmo and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fr3s*xfp ney+ b5iction be between the tires and the road if a car is to round a level curve of radius 85 m at a sp y3 pef5bs*xn+eed of 95km/h ?   

  A device for training astronauts and jet fighter pilots isxzd q:ro u(2p5 designed to rotate a trainee ( o5z prduq2x:in a horizontal circle of radius 12.0 m . If 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 oqk 9;d0lec4-iq b.dm cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntablq;0clkb.9 doeqid-4me until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rolle.q9/vfc7er1 sj n rcf/qn 6ry6r coaster be traveling when upside down at the top /n / 9srryn6q1q6frf .ecv 7cjof 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) crosses the rqwd2( +m*lkxbounded top of a hill (l d(kx+mq*bw2 radius =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 Ferris wheel need to make me3v.rs6vk s7 for the passengers to feel “weightless” at the topmosv r. semv6s37kt point?    rpm

  A bucket of mass 2.00 kg is whirled inu7j4z7+r5kp.o c3 xo-z t9ftikxspy 9 a vertical circle of radius 1.10 m. At the lowest point ofo k5+r.z zty k9p9 7p3cs4txxui- 7ofj its motion 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 centriqi:/n( )h hrm40h1 -ysk*cqandi g(jgfuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000igkgn:qnmdq h)y hi*js (/10( -hc4ra $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopl6t3ghg10 v lgze are rotated in a cylindrically walled "room6z0hggg1t l3v ." (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 rotated in a circle on a frictionlesv u7pz0wpb;drst( -i/s 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 zpuipsdv t- b(70;r/w shown in Fig. 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 ignoring the weigher14 dd0,chnb64 8jrkw -locct of the ball which revolves on a string 0.600 m long. In particular, rojk40wrlcd-1dcc n468 eh,bfind 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 giz(.ki lc8b 188 m is 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 massesf 33n0d xnu(+yk ejm3d $ 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 maneuve 0 p/kwdbi6 8w-2oxmav-p9 devse18( hy yes3sr 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 cz**eqmx:zi8components of the net force exerted on the car (by the ground):*imx czq*8 ez 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 5*0rvv xxn;rs3 00 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc wn*v0 ;xrvsr3xith 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 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 horizontal cinkdkzpz r7ezq: 55+-brcle of radius 2.90 m . At a particular ins edk+5zkrz bz7pq:-n5 tant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 gravity on a spacecraf ;wd(worwn g 3h0q10art 12,800 km (2 Earth radii) above the Earth’s surface if oq3w1r(wa0 wg ; 0dhnrits mass is 1350 kg.   

  At the surface of a certain planet, g yrs2:bxb(+ ki:wcg .the gravitational acceleration g has a magnitu wr2.gcgb:si(+xk:y bde 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 Moonq8x n5wt.)it eckw39h. The Moon's radius is 1.74nw3h ekwqx 9c.5tti )8 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a 7 .xcni2gp ydz5 (d(pzradius 1.5 times that of Earth, but has the same mass. What is the acceleration in yz2dxdp(.5 g7 zcp(due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ea j844nxpt/i mrm)95z(doew ep rth, but the same radius. Whatr p)jitx4 4 e/zp85wdn(emo9m is g near its surface?   

  Two objects attract each other gravitationally with a force of 2. p4q-p+kqg6dt pvmh98. ,kphn5$ \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 acceleration of gravity, at (a) 4+gy9ec c aqf:p 54vf24wfrcq3200 megc 4c2+ryffq49w c5q:fvp 4a    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’y tm7 n bnnno)tl;g81( :1qukl/fcoa:s center to a point outside the Earth where thegravitational acceleration due to the Earth) km1 q/1cytnfbo:glno8;nl7(u :ant 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 intoqzpwb x u.whip*. l53, a sphere about 10 km in radius. Estimate the surface gravity on this monster. lzx.5 b*qh3u pwiwp.,    $\times10^12$

  A typical white-dwarf star, which once r82rxhd rvdc *v3lq- 3e+i0* sfu yce3was an average star like our Sun but is now in tfuxr*e *cqd-0s23il38 h+vv3y ec rrd he last stage 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 orbitinv e9f18f62cn co)ara rg in the space shuttle. Your friends respond that they thought gravity was ranv)rc6f2c9e 1 aof8just 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 of g.   

  Four 9.5-kg spheres are located at the corners o r.t7 )msb+yrnf a square of side 0.60 m. Calculate the magnitude and direction of ty)s+7r.mbnt r he 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 line up on )9k2nzch 04f nqa **6zbwcefsthe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming allcbf 0 wc4z snhn a*)feqz2*9k6 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 accelerati.sezt9 e89l d7 /4rvm-dys wgzz2ezud n q5*:uon of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deter2rl z ssetyd/e*z.denzuw95d4 q9: m7v 8 z-gumine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the mrj yk02)pn-j;jf7nbqt 6 :og known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using :gj70fbk qnm;2p-r 6y) jt njoKepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about theuhcvsrp1,b+ 6 8.xbuj Earth at a h b+ u8p,.1usbchxjv6reight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite intdh4wmfy awbl*/hdq tv7(:. +co a circular orbit 650 km above the Earth. How fast must the shuttle be mom7qwf( ca4 +* dhtv.hdl:w by/ving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if 3hlf3 )okr ts3g;h9,xtv4m1bt p1sgtoccupants 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.ts1),k l ;3r13h tmtgp9x4gb fosh3tv (See Question 21, Fig 5–32.)   

  Determine the time it takesgs b8 3x:q5-er+g kmbk for a 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 very small compared to the radius of the Earth. Does your r5es+qgrx mkb 3:-gk8besult depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from2 +cewpe;;*bi/ 2cg ayiz/upfkxz h). the top of Mt. Everest to be placed in a circular orb; .ixp*cw +y2becfpg2 ziz)/hauk / ;eit around the Earth?   

  During an Apollo lunar la9 vq6lwk rqih(e,usd5,g, j7f nding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How7,6( h e,jlgdfikq uv, 5rs9qw long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orcm)) .b+aiu nl :)ijdebit the planet. The inner radius of the rings is 73i)ne .:)+ jimcadlb)u,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 every 15.5 s (see Figpkma +y24bde9q d08yj*s1xu l. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the t 19j a+q8d2m ux4s yyk*bdl0epop, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg a-kgez v: jyt63stronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant3-g 6jzekytv: 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 consistl uns42lpd+8 ns of two stars of equal mass. They are observed to be sepaudll +8npn4s2rated 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 for the weight of a 55-kg wom0o.uhcm.sra (j /cquu z(i2t0 an in an elevator that move2jm0 us/ac.ti c0q(uhr (. ouzs
(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;d w z if:.alpi-7uw.wy+y+ tljbo+.o suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Whauw. ;wlp.l.y+itd7w az-:i+ojbof + yt was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wpo)/9p9k o w.q8ka( gl ,iythuith period T , the density (mass/vo/ap 9 ,otkqw9gp u.l8io()ykhlume) 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 th u*yy3(cpmr ,we period of an artificial satellite orbiting very near the Earth’s surfacecu*ry, 3p (wmy.    s

  The asteroid Icarus, thoughtqkhoqk8d9r8*- h 3b v:zq vn) only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its m8h zq3 tboq)nv :9rk -hd8k*vqean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dip07 jdjko .4xqstance 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 orbits the Sun roughly once every 76 years. It comes very close wm s 6aazt6x6 i* i p9h.jm4em+n;xta2to the surface of the Sun on its closest approach (Fig. 5–39). Estima4jnxap *maa+ztx;i t.2w e666imhs m 9te the greatest distance of the comet from the Sun. Is it still “in” the 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 t) xo: m,d1 p8xlolbxkw/-t0n Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, perioctxaifp/a8zk+6 f sfh6buw 9)b:in6*d, and mean distance for the four largest moons of Jun9 ubc*it ha6x:p 66 fb8w)szk+f/i afpiter (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 the Moon.,w+rq ,emav u +(fez j,*bvkf3/o(mfe ,bvu eokmj(e+f f3(rz wm /a,fe+*,qv   $\times 10^{24}$

  Determine the mean distance from Jupiter for ean mi.bjj56sx/ vxel;tgpf8g9 q6+6 jich of Jupiter’s moons, using Kepler’s third law. Use the distance o. qi8lt/5is 9jb gx pjjfe6mv+n6;6gxf 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 consists of many fragments (which):x*pz )tfbh m some space scientists think came from a planet that once orbited the Sun but was destfm)bzh* x p:)troyed).
(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 talet9o i fy zhqg7+2q2b0o s0;xya describes 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 thbsqf9q2 o2yo0atgi7hz+; 0x ye ring rotates 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 vine (Fiho,j:v+ubk.u9 npj6me*m aj/ g. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, whaa juk bm 9:.,/e6ho um*npjjv+t is the maximum speed he can tolerate 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+jzxinm0ru.k /o. :ji the acceleration of gravity be half what i . +jju.zr/:mkn0oiixt is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spi +ke/zo4rf,7b5p ) jr7 ndwkvohe/ 5osn in a mutual circle once everw k7 zrdknvo5b/oj7se pf/ 5 +eh4o,r)y 2.5 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 rotat/-p7cc9 f2.roj j3zcs1l4 jd;bpt px ges once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What3pg st l9bz1.-cd pjcr42xo c7f;j/jp fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecr 9v geo4a o)h+i s4216gn3h 3qyk3ysjqc sk3nuaft traveling directly from the Earviua34 31o 2 +k4ys)engn69k hcsqqj3 soghy3th to the Moon experience zero net force 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 ruafd 6g mjme+0q6x88bathroom scale in an elevator, it says your mass is 82 kg. Wda6xf0 mg u8+q ejrm68hat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consi1.5 6epsvs)r u*abu: rde yn+g3 co;dysts of a circular tube that will rotate about its center (like a tubular bicyclse3y*na ddurcvbg+es 6)5 o:.u;1r ype tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. 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 in a verticl,8jm)p i uch69, sbazal 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 rad gt)gu xlsig -./bh5c)e,(qam ius r, the acceleratio.t/g chg)ui( xqbga l5es) m-,n due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strqv0kffr )6s a5ing) is deflected from the vertical by an an0v5 fqa6)sfr kgle $\theta$ 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 coeffya0nco14 h:nmicient of static friction is 0.30 (wet pavement), a no:yam0 ch41nt what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the :ci,s+ kb91- ws rwx7oab a-yo*0gdifequator were app*b 1siafrc7x w9:,+d0-kog-abi o yswarently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a contz5ta ty1 :k j)owqcm 462dhp9stant distance 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 a zzlwxa +2:nt)constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling2xtz )z:wna+l 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. Thuswaloqwl /0 d(+nnq+x819cly w, it has 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/cq +oxqw 8l+w0 lnany9 w(1ld 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 Telesm;/gu7fk a:bj cope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light esb7j u;mkf:/ agcapes). 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 ty qtbpt79y(li2tr2 r, he hill and valley shown 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 crti2ptr yqlby7 9,( t2an the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orf2(u) (fep ltzbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receivfe2 p)fz(u t(ler 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 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 billion km, is kbmst99fryq ;unnqz0 r-u+ 4 bgo24x+meant to orbit the asteroid Eros at a height of a4u9 0 zybxq n-k qgt4r 2bmf9u+n;os+rbout 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 the space shuttle pursuing a satellite in need e/ *3lpjus/liof repair. You are in a circuels3*/ /pijl ular 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 years. (a) What is its mea xnw-x.*xg i6i5pg edxv */w2en distance from the Suip.i5g gw w 2xd 6nvx/*eex-*xn?   
(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 :m7s*ivkdm g7 G would need to be if you could actually "feel" yourself gravitationall7v:smi* 7gkm dy attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centh;e 5 (p -yq,mfz6tigrer of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-ye rft -gz,i;6e hmq(5pyars 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 sn4z /j)h jd kr:ze.nq3ide. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of th.z/nd4 qh)3zkr :ejjn e square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500gt wb+):w w5ngqa-hm9 w)enbj)ry- n9 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 experienced by the tip of the 1.5-cm-long sweep secon prazr8 nkhnlo r)6967kegy:/ d hand on your wrist watc9:ok/ky786nar lr6 nrzep)hg h?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkeruli:h k w2 (t(g*78ec dsotwg( weight around in a circle below you on a 0.25-m piece :o(w dtie w7u h2s8* tlgkgc((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 highway is designed pc/hm/eup(2e.w+yb -2*jv5qpj r cl g so that a car travelin w /+pb( h*pq.c-5ge/2eyp vcmjlr j2ug 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, (pj-h+kj9z mk je*94*zrlxy k9w 4e zbthe Acela, utilizes 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 centripetal acceleration, is the normal force. The passengers experience less friction force agkm*b l49z*jy(9zw-rk kj 4xeehp 9jz+ ainst 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.$\approx$    $\times 10^2$