Sometimes people say that water isi3g4wl:o1(0kalqif,utw v+ c removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wil0t1i4 wu aog3w+cfi,k( q:vlth this statement?

Will the acceleration of a car be the same when the c9cg e9 aa36k2j7s +rle jesbc,ar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Exple 9ekg92lcar 3je bs+s6 7,jacain.

Suppose a car moves amla+a:tri1 pqf3b . 9zt constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip qipt1 : m9az.b 3+flarbetween two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a 6a8 dffj*cg0ih1 hfgt qv /e5;merry-go-round. Which of th f/6d0*1hfi gcjvq5;gahtf8 e ese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a ver 2bu5by2; myrsxjy)0rtical circle without the water spilling out, even at the top of the circle when the bb2 0sjy )yb5rx2urym;ucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leas m p-e*udm,h5-bdi(kbt three controls in the car which cad*iuhbpm k,e dmb(-5-n be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hk6a7e1le b s ykx;p;0bill, as shown in Fig. be;y70ke1a6 ;lx kspb 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 inw: b f)*jd69voonnpsw 7edj-o(ard when rounding a curve at high speed?

Why do airplanes bank when they turnm(l:1z8d8xhphv b ybh-ok3 6z? How would you compute the banking angle given it z6hz:3phk 8-m(vbo 1d lxhyb8s speed and radius of the turn?

A girl is whirling a ball on a string around her heaf lgej:-xi)60 hc+7nff* pqz.jn n vu;d in a horizontal plane. She wants to let go at precisely the right +lhju-7f jz: n nfe.)p0 ;x6qnc*vfigtime 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 fiegxu 8 ;qy 4.ls+,oda gravitational force on the Earth? If so, how large a force? Consu.,q;+8yxo4ies g fldider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thermlk ne /i6t f6bil3.6li88na Moon’s orbit bei.l8brne3alt 6 f8/inmik 6 6l different?

Which pulls harder gravitationally, th+vtr +o xrep*m 4w9sj3e Earth on the Moon, or the Moon on the Ea+*xj3w4 t+pr emvosr9 rth? Which accelerates more?

The Sun's gravitational pull onehn9;uo utc (1 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 sidncueot9; 1h u(e of the Earth to the other.]

Will an object weigh mou) gl/jp9e e*u) nbh:ore at the equator or at the poles? What two effects are at work? Do they oppose each other b)9 eu/lu*:heg)opnj?

The gravitational force on the Moon due to the Earth is only about half the f/fm9 nxj:ad8moj a f;z8w6sj0orce on the Moon due to the Sun. Why isn’t the Moon pulled away fra: ds/j098n 6m;fojam8jxfwzom the Earth?

Is the centripetal acceleration of:kyd 9aaso)+8 fw 9wzam*ss 9f Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eazfkwsywm9 ofa)sa9a9s:8+ * drth?

Would it require less speed to launchxhb+bq)d.bu0,qs: ed a satellite (a) toward the east or (b) toward the wes, uh b):xbde.qsb0+dqt? Consider the Earth’s rotation direction.

When will your apparent weig7sa1aci *b; jmg j qqo;w9pt+/ht be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, +*awo7spq1 ;m; jgbqiactj9/(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 spscwsuio) igs (3b* 43oace could 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 (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 gra o3uo*sgc4bs) wi(si3vity you can think of.

Explain how a runner experiences “free fall” or “apparent weigheopp:0j(7c.i (y 5kkondp4 pztlessness” betweekp 47pz.5 onp0ikj ed(yp: co(n steps.

The Earth moves faster in its orbit arounb:c u38;qg eqc:d3q ord the Sun in January than in July. Is the Earth closer to the Sun in Janua3rq3o:qg db cqecu;8: ry, 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 discov3k1.(/b.z iytw p plncered to have a moon. Explain how this discobp1c3l./ zywitkp . (nvery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lary. z3ic7laq.ovw 8ee6ger than the Moon's. Yet the Moon's is mainly r..oeewq8 a iz3y6lcv 7esponsible 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-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 1g8e5e/+cjj p j980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbfwou0e gt:rjf roz nh-i6-(a147 3+(mxxe uadit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radium 0rjtoiheneg3x4( ( :- uaa+1ofuzr6x-wf7ds 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 z gu)s*v a2ru7x3njf5a 2.0-kg discus as it rotates uniformly in a horizontal circle (agzr23 f xvnuj)a57us *t arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shu0 9xg+fd osr,tttle is in orbit 400 km 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 ,xftg9d0osr+answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleratg,nnt7 q94zyg ion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32ntg7yn ,gq4z 9 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verticalx q660vmrv 8+ i u2bnnv;)plpp circle of radius 72.0 cm , as shown in Fig. bn6 ;ilv)pp+x68pmqr nv0v2 u5-33. 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 wh,m qrgxkq inohf1u d15*..x7 jich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of thn ,fo xi1xhg7qrd5q. k.jmu1*e car?   

  How large must the coefficient of static fricr(6 ad;* wrj9tug1t7fp8zenv tion 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/npdw;6gv z1*futjt9a rr7 8(eh ?   

  A device for training astronauts and jet fighter pilots is designed to rotaf-xh6fd.dc 7z te a trainee in a horizontal circle of radius 12.0 m . If the fo7 .xczd6-hf dfrce 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 rotating turnt,.z( se2v(qs s+el-cw galvm*able 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 coin slides off. What is the coefficient of static friction betwl,v e2ael vs.s( wc*zgsq-m+( een the coin and the turntable?   

  At what minimum speed must a roller coaster be travelin*9de+f mn90 k oewoyi4(s bkj9g when upside down at the tneow990e*y kks+fdi49oj (mb op 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) crosses th rp: 2 .u5n2l teq6kuujha65gle rounded top of a hill (radius .gutj u:2e2ha5uq5 nkrll6 p 6=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-( 7 (;gnjk9ldx 0e i7.bmjtvuxm-diameter Ferris wheel need to make for the pa9 g(7b ixdj n.tkx;em0j(ulv7ssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00c6e9u+ng5ya:)xm tyo kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its yacx+6t) m:59geonyumotion 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 rotatemyoq dbzw 1y9twehk14+7m j- / if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 11 zj9 h7wbt-11o+me ym/y kd4qw5,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnipx 7nb((/)lj58mm:wk) xg vqpx ws6ub val, people are rotated in a cylindrically walled "rop:qwjx)8 lwsx( /bx5knpm g 76uv ()mbom." (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 rotatedce ea+t:zb8*,zf w,08gdd sos 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 f+,ade :0ebzto ,*swc 8gsdz8hole as 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 , prfkrtt3f 2srhee1:q 0 xr1 u/1l8 9jhrdecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particuhrtl0x 9h1rfrk1 j3/edst12r:ef q8 ular, 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:w,kva( 1y, uuk o+z qa9zdji+ 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 masses 0a2d8qfm5t wzo x r:8n$ 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 maneuver *zt,bk.xvfw s1sn m 0cf/*dl;kde6t , 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 tangen utb+ h.vc3f ()*9kmnkpd+bjwtial and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when itb(+ k 3wtnpdjmk) v+bch 9.uf*s 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 fro/3 hm,kqvykk r- pt5 h+xr25vvpdo(6 dm rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radiavypr2( 6m3tv-hdx+ ,/odkph 5k vqk5rl 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 circle of radiuoe2dkf+o; t ():ptelx ;r: xyds 2.90 m . At a particular inetdf:xxlpe)dr;k y t:2oo(;+stant, 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 spacecraft 12,800 km (swz) 3dbf)*p z5pgwbi;)lw x82 Earth radii) above the Earth’ssld)wiz)* w) pfzg xwbb58 p3; surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g ham s 9tm7 bxzg-o0pc,r (ftf:;us a magnitude of 12 msb9 utcg7rmt, fox:-z(p0; fm/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 acceleratiojbf) 21s h;b/nhqps:p) ut c(bn due to gravity on the Moon. The Moon's radius is 1.74 cqfb2stb( ;hb)/pj) h1u :psn$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has bc9:/xmbolyh.c:0o q a radius 1.5 times that of Earth, but has the same mass. What is the accelerbxlb0oy:ch cq/. 9m:oation due to gravity near its surface?   

  A hypothetical planet has a mass 1.6 az5z;4v2omz pim7s9,hjupo06 times that of Earth, but the same radius. What is g near its surface? 25vzmos j ; 9z,p7um4zioaph0  

  Two objects attract each other gravitationally with,(jo cnm +emj(9p c7sm 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 acceleration of gravity, anr3oxr6 kp/c7t (a) 3200 m x rpon/37c6 kr   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr s)ozeiw3a4lb2lw1 z- om the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Eartazwbi14)e 2lsz - owl3h 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 ;d7cby pkk4lfxkw 53 8sphere about 10 km in radius. Estimate the surface gravity on this m85734dxkk ly cwkbp; fonster.    $\times10^12$

  A typical white-dwarf star, which once was ab-cx7,b0k3y il ze7i2uy wr 3 cpe4ve,n average star like our Sun but is now in the last stage of its evolution, bp2eirz0 7xuve3yw34,clcb e7, yi- kis 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 astrozal/ 4 jaza ww0cvx 5mta,b+e6t(af3 8nauts 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 wz5 8,4abalm3+ xz6e0 jc (tfat/a avwkm above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of 0 du(4evt2ahn side 0.60 m. Calculate the magnitude and direction of the ta4 udnvh (20etotal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years cu)fiucr4qr *3*xj mn-,/pbq most of the planets line up on the same side of the Sun. Calculate the ti)b -/pqqxc *,u nr34cr *jmfuotal force on the Earth 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 9a6g tpr71px4(igl h jgravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deterghax47g(i6 p 9rtj1 lpmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knownea3yex : akut e4 3;kf;vt.5zn value for the period of the Earth and its distance from the Sun. [Naxkz5f;n.u3 ek4aetvt :ye;3ote: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving insxpr* nrh/: rc+vs i )ti.6c.n a stable circular orbit about the Earth at a height of 3600 /n sr i rr 6+:n.p*.)hcixtcsvkm.    $\times 10^3$

  The space shuttle releases a satellite into xok/n/y0 i(,r ba am4ea circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occur(k/ni/ xr,baae m4o 0ys?    $\times 10^3$

  At what rate must a cylindrice nzfy 6flm2a61et8:e al spaceship 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 ez8n:m266 ytl1f f aeeQuestion 21, Fig 5–32.)   

  Determine the time it takes fords1fp ur)3 77kp.up u0t*fs by a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfap)7u * b7s.30ppfrsyt1fduuk ce 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 vel +e3nud q/ dso36-gdsyocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbisguoq ed-3d dn+ /ys36t around the Earth?   

  During an Apollo lunar landin) bqu tb 5ge8;;gh-roox1mzd*g mission, the command module continued to orbit th;-g)hub ;z5xom 8g*be dq tro1e Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. g*r1y 1:, t.iy8nb+a zxluoezThe inner rad teayiz.8 z lbounr*1x1,g y:+ius of the rings is 73,000 $\mathrm{~km}$ , 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 6dq4 xam,.c*jm0 na haf4jp4j)h ,vihFig. 5–9). What is the ratio of a person’s apparent weight toa64h fmh4v4i0 jhqnmxad j,* ,.pajc) her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wqib aije;( c3:0l8hvf eight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving ata3 j;fl :ve(q8i0cihb 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 equal mass. They ajcjqc606r a r,re observed to be separacr,jcqa6 0j6r ted 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-kg6vwq:a3, wq)s rdo0lj woman in an elevator that moves aj)o d,:0v wrq lsq63w
(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 ceiling of an eleqrgsu2 (z w)0;+do lzgvator. The cord can withstand sr)w(l0gdq2 uz;z +g oa tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellitf3 5 qx 72+sai,whmq2qr8lljge orbits very near the surface of a planet with period T , the density (mass/volume) of8, qhf2ql mwr2+3iag xs7lqj5 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 perioikms-x 6je d3.d of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface.d- sixme63k.j    s

  The asteroid Icarus, though only a few hundred meters across, orbits the S+63s0dkv k ffj kb76tfun like the s v67t3kf+0d kfbk6fj planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofl:ghp04a:u )a zrd 1s 4n5fqow 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 closew glo6a5w7 -vw 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 is nearest when it is out there? [Hint: The mean distancev l6w awgo-w57 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 qzogq0 7k4dp5$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,f4k8hex6 5e/ 9b xmo8 cgj+wpp and mean distance for the four largest moons of Jupiter (those discovered by Galileom +w89okx f /ehbe6jcppg58x4 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 --py2 v9vs d;bt7 gkkvthe known period and distance of the Moon. 27y;-vdsvkvkgtb - p9   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupit m.z,0fp 2fijkk yf,y2er’s moons, using Kepler’s third law. Use the distance of Io and the periods0ykfi,f2m.,jzpk fy2 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 betdyur/unv;*hq;+;9 dvx8 sx p uween Mars and Jupiter consists of many fragments (which some space scientists think came from a pl/dxunh x 9q+8v;;y spdu *;vruanet 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 artif+nnqred:hlg xxl5qj.s /u o-2n5:-jw icial "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 exactq :r lun2xox- 5lghqws5:je.d/n jn-+ly 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 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 (Fig3 sa0n+o n.lni. 5–41). If his arms are capable of exerting a force of 1400 onil.n+ s a03nN on the vine, what 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 the acceleration of gramcpw4bq(zh-d5 h wvn),:irm4vity be half what it is on the su-(cphmbd:hnv,z i wrw)4 qm45rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gvi+; m5y;mpvkhybz4- lr j)y-rab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m lo4i;z5;v y+py-j m bryv)lmhk-ng 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 day, the apparent acceleration of g) hh*c/4 ck)ppo uhw(f /b*sihravity at the equator is slightly less than it would be if the Earth didn’t rotat ch pk)*hh/c*o/wp)u ih( fb4se. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from t;9fil *.0xoyq:gvev uhe Earth to the Moon experience zero net forcevei0u . log*qvy :9xf; because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you st (/m21z5ir/shdj tzvt and on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acce ( t2/dzszhmrvj/5t i1leration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a ciqm8t 5gwyt: b)s 2ydbh52h -.z-ambxprcular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must85z b2ayx dh m2.:y)qt-pb ghm5tws-b 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 air0/b u.qcwuk6fa; r1 ercraft in 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 planetiuv6qkm 6e. s3 in terms of its radius r, the acceleration due to gravity at its surface and the gr.i6s qvu 6mek3avitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by w1b gbqx3y5f2es6 i ,e jn5ox,an ,fe1b,n6wx2ojigsey q b3x55 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 o 1gn:nv/qu9acoefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handl 9:anq nuv/o1ge the curve?

  How long would a day be if the Earth were rotating so fast that o crk)bvey.n,er +pnh( 6ti )j-bjects at the equator pen)-6+hcrjyn(ib rv ,)kt.e were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of f.g;jvl6 hb 8:uz0mb+9wh )n al um3am8.0 $\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 rounds a curve of radius 235 m. A lahkf8o-s3;o9.wxeeibj w 8 9 qtmp suspended from the ceiling swin- ;k8.xs8e9 wbfhejq9w t o3iogs 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 54z s.9tmw7tr tyh5vtlgp9e+as the Earth. Thus, it has been claimed that a person would be crushed by the force of grget h.v5trw9+ s7t 5zyp9mt l4avity 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 pres/ y; bcq8s1 a.nzti; js1tvwh6ence of an extremely massive co18/ tzaincsy61vs;t; hqbwj .re 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 const , ua0sv+ u2*b90hspo5pedlge ant speed as it traverses the 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)p9ld esh*s5+pov2gua ,0 ueb0 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) utiliv7 fln1 g3;oozzes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by thevo 3o1l7 zgnf;se 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 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 bil *my xfr/7ar1vlion km, is meant to orfy*1rm/v7 r xabit the asteroid Eros at a height 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 the space shuttle jw/7+/tkev 0jyx )r pcpursuing a satellite in need of repair. You are0e )t7//jcwjxv ypr +k 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 years. (a) What igi/ 7w j+l.je o:7zfngs its mean distance from the lwe zgo+jj 7ng/f:7i. 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 couldx*ebu: h 2:vl.hde b+/yvtl) b actually "feel" yourself gravitationally attracted :/:) lyvt*2b lvbebed.h+hu xto someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cenjlm:ni.6 /vbty2,ya+y uy w8vter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years /v:na+ 8 vytu lm,yb2y.j6wyifrom 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/q2smg svry- 8phjw kz59;y z*r(v9sy on each side. Find the magnitude and direction of the gravitational force on a fifth ;25s* 8vvyhs mpj/zs(r9ky q9gz wy- r1.0-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 th -tr,6eyj kz7ge 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 srk73r lt itc6:6bb9kal yc0t2econd hand on you c03lc:6kbk6atry it9l2 r7 btr wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a nihn/z735oan circle below you on a 0.25-m piece of f /nh357anno ziishing 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 sovku+-jzr wr0 x8hcp8yvx38l8 that a car traveling at speed w8-v jrrvz 3y0kl+888p xuxch$ 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 cars whe 2-ksu8x*sx78ctawpn n8k)kvn 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 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 o 8* 2 s cnukvn78skatw8x-p)xkf 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.$\approx$    $\times 10^2$