Sometimes people say td .wq)(08i twn eqbem:hat water is removed from clothes in a spin dryer by centrifitqd n:ew. m(qw )8e0bugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sh3 ey0p*29en k:, mzwwogy l:ybarp curve at a constant 60 km/h as when it travels around a gentle curve at the saglop:ey k0 e*wmz3yb:ny,9 w2me speed? Explain.

Suppose a car moves at constant speed aloni7av9chx,+k (lfd/vng g qlqdy330.ng 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 betwee9qh7 cd iklyvdg3l0,nang+ v3(qxf ./n 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 merry-go-round. W -:/,umedfztrhich of these forces provideu,re/f-t z: mds the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillim .mu4yx:b5 pung out, even at the top of the circle when the bucket xmmy54bu: pu.is upside down. Explain.

How many “accelerators” do youpeeyc w 20fl1 tdkb4gem5t;6 1 have in your car? There are at least three controls in the car which can be used to caufcdlg2mk5tp1 ;1y04wtee6 e bse the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over7xlq(5u1u*; g5j fpl3 7drrnw3m pdqw the crest of a small 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 hil7w ruwpdrm3(gq3pfn j7 ;51 5q ludxl*l. Explain this decrease using Newton’s second law.

Why do bicycle riders lean s,en1/hwi wps f9: tw2inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gdd)f s,/nyau ++ sx.-mv rkkeko:z -6liven its ,k6sma/de -kd k:or+)zns. lvfy+- uxspeed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. S(3 aogmug*.ze+l mic);x-gj xhe wants to let go at precisely the right time so that the b u* 3egilxo.+gmczg(- jxm);aall will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravio /hqta2 ia )jpv,p0r1tational force on the Earth? If so, how large a force? Consivrop )aqh t01ai p/2,jder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the M6vduhge; ;nw l2dr5 v9oon’s orbit be different?w2 9 egl;vnvdruh5;d 6

Which pulls harder gravitationally, the Earth on the M9os*8dytpui tt*hp2m5 z+ icbsz5m *4 oon, or the Moon on the Earth? Which accelerates m28i5*mbsd pt+cz5to u yt*4* izmp9hsore?

The Sun's gravitational pull on the Earth ii-p1m q-k zmi;s much larger than the Moon's. Yet the Moon's iszq;1 -mkiipm - mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh m d+l r) pv:o7ma cqrbvsrc28.8ore at the equator or at the poles? What two effects are at wov88+7cb. )2rscrom lqa p:rdvrk? Do they oppose each other?

The gravitational force on the xv2t)0g9yka san / dq5Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pullydx gv/qt) nak0a 529sed away from the Earth?

Is the centripetal accelerati0dmi( it26f o :qbe2reon of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the2b 62oqr:df0iiem te( Earth?

Would it require less speed to launch a satellite (ai*u9nxn 3inft x5adzve0hn/ - o7v.)r) toward the east or (b) toward the west? Consider the Earth’s rotduxo)7n.nfirai vvzn0-h9 3e n5*/ txation direction.

When will your apparent weight be the gr 6 0k9 b02xmauxft;wl+fjeunh9.y )iaeatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in freuam; t)a 0f9l 2f6x9.knyw xu0 ib+heje 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 space could be adversely afm gv bf47;oy.3tum j;gfected by weightless;g3bvt4 7gf;omyu.mj ness. 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 gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” b vzmvrpa:cq7d (.vzg* goy,b 5:*pv3ietween stepp.zc5*:mg* aiqv, o prv yvvb3(dg:7zs.

The Earth moves faster in its orbit around theegph tc.or8b 9u02rr6 Sun in January than in July. Is the Earth or9hrgc2b0p r eu86.t 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 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 7uxqaixs48 cwz0p +.:qiw mo;moon. Explain how this discovery enabled an estimate of Pluti +z.q aw8;s xc47wuxmqp :0oio’s mass.

  The Sun's gravitational pull on the Earth is mv ct irrqjvv:gh tw7(j+;h19/rb4r2much 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 wjgrtjrvv q r4bh 2tc/+:vr;(h9m 71im 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.qz lea7a 4ko t,xu57r 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 centripetal acceleration ,(esa g-bc46 8uk hjquof 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 the Earth's orbit is a circle o eg-8s6ka uujcq(b4h, f 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 discusu8x:k,4j9bbawx a ;zx as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the spb4 wxxxkau9;8z,ja b:eed of the discus.   

  Suppose the space shuttle is in orbit 400 kmu+fst /;5g/siene a p, from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational accelera tige/u5sfsa,;n /pe+tion at the Earth's surface. $\approx$    g

  What is the magnitude t .0wwu+ +dzw8-lpjmdof the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions +. 0m-p8w+jdtwluzw d 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 a verm f.q0yab;r f6tical circlemf0f .;aqy6br of radius 72.0 cm , as shown 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 radius bxh/ d7xi7dt+ 1 s)uih77 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 the cart i+ b 1)dxx/hhiu7d7s?   

  How large must the coefficient of static frij1cprt 14kf / k1pk9wvction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95j9rwkp pc/1ktfvk 141km/h ?   

  A device for training astronauts and jet fighter pilots is desigx qm.5d5cr2 nsry9v1ined to rotate a trainee in a horizontal circle of radius 12.0 m . If the y95xvd1cn.s2qri mr5 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 rotating turntable of variable speeg34+ ldoj,ou .5r dnjv8k0d cq1.ggnyd. 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 ofrd13co5y.dn 4jk.g0g+o g uv,d q8lnjf. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed muq,h 0dw3 c(( s+rczfoast a roller coaster be traveling when upside down at the top of a (s 3(rq,c0ozd+cwfa hcircle
(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 rounded jxix4 hyli0j. z8oa,nr )p( x/top of a hilpxjny,) hlia oz/x4x. jr i08(l (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 nee8,x6kql+y zpfd to make for the passengers to feel “weightless” at the topmost poix+q ,lpk68fy znt?    rpm

  A bucket of mass 2.00 kg is whirled in a vbio8s1 x /dj(hertical circle of radius 1.10 m. At the lowest point of its motion the tension ii h1s/b8d(o jxn the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the aktjz5yag,*wmg -y. t3p6mrd7xis of gd6- r3y yz.tp tj*a7kwmm5g, rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in ad :fmgyf ;ag,8mv-2ti cylindrically walled "room." (See Ftm ;f v:dy2,g mfi8ga-ig. 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 c8wol (rrmi; 1oydy1 j30k,) iz 6eiwewircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a d8i w )elwz1rje; 0 wkorm(63,ioy dy1iangling block (mass m ) through a central hole 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 , precisely this time, (uyw6s+3zakp by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnituda(p +zwy3 6skue of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for vh3qk(m/3su--k c ,(mrxc5cc2h v zvpa 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 massej 4nbjt 4f1ca7+y (gwzs $ 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 evx;y k4yg* 5ytfuyv u43asive maneuver 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 compon)jipihvf. *y;eggz0: bnd 31 bents of the net force exerted on the car (by the grouf*)db geji bhng1 03vy:ipz ;.nd) 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 a73(.fyyn8s qf/nt xtthe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to y 3yfat.8/q7(xnn tsf provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontai2xj3zwe5 yw 8g vis78l circle of radius 2.90 m . At a particular instan88ie w5 yv x2ws7ji3gzt, 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 gr0.di*pj d8/f jdzm( ms*pwri /avity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mfii/*(mp. d0jpsd/8 djmwzr *ass is 1350 kg.   

  At the surface of a certain planet, the gravi9bde oj-mf+ xf)3gff/tational acceleration g has a magnitude of 12 m/seg -o9 dfxf)jm 3ffb/+$^2$ 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. The Moon's radius is 1.7pj) r, 01g ,ohbcn0qbok-bxk,oq08 i y4kr ,b,b0x,q-0obhg)o8p 1kcj ny0q io $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the aj;gd deg4 lx/xt0+2psame mass. Wh0jxg x/t;add l pe4g2+at is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sam +7v rq(frd,p1dk .eyde radius. What is g +ef1, q.(d r pk7rvddynear its surface?   

  Two objects attract each other gravitationally with a force o6*tn q4r*phjd f 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, at (a) isu gle 3z-x8-3200 m x-u-s lz3ei8g   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ou-s)tkq kc d+z5tside the Earth where thegravitational acceleration due tk)dc+s zk-t q5o 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 packedla.j b+zsj*p+ into a sphere about 10 km in radius. Esti*+lb azpj.j+s mate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an ary0 m4 gy3/uliverage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but hrmy3 l g/y4i0uas the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while or f: aahs7jtve 9-0mz)gu j1sz7biting in the space shuttle. Your friends respond that they thou tum9j-hgjsav1zzf)7 a7s e0:ght 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 of g.   

  Four 9.5-kg spheres are located at the corners of a squarewklrta se;v hpygqq/68z45p (uwy 996 of side 0.60 m. Calculate the magnitude and direction of the total gravitational 9wrz46vt9 6;g8ey hap(sqqup 5l/wy k force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thox ,oubitevz) s8* )gb ,n ovda2(pd79e planets line up on the same side of the Sun. Calculate the total force on the Earth due b dnvvaei o)7 budt,*)8, ox2(zp 9osgto Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at t;*w lbvmw8c j.he surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3*v8wmljwc .;b400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the tk 7id 6c 7 d4oruk8e3j58nddwde)s +e) x7aazperiod of the Earth and its distance from the Sus 77 3knkj8)t rcdie6)+eo d8wd5u4dzaxd 7 ean. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite dy l8pnj( m;gm8-z (mrmoving in a stable circular orbit about the Earth at a height of 36(ndm-mgzly mp; j8 (8r00 km.    $\times 10^3$

  The space shuttle releases a satellitp+1)rz zr ms2tbleq517:pmy se into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative l+sbp 27sy ):1rzq5m mpt1erz to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatp;f.5mjgz /h)h 1vtpp1zcg4eqz el*a9ep:m 1e 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 h4qz 1pgm;z/ pz .:1p jgeah1v9 *le)pcm tfe5Question 21, Fig 5–32.)   

  Determine the time it g sg vo: .-89ww4cdsjvtakes 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 wd. g9 84oj gsvsv:c-wthe radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a sate43 k6ucfv7fm5k q:n ecllite have to be launched from the top of Mt. Everest to be placed in a circular orn5m7ukc46cf qfkve 3:bit around the Earth?   

  During an Apollo lunarr.bkyr i0n h2v/vsl-5 landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it ta2sv rylir5kb nh0-v/.ke to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. zrd4kf0on4u -The inner radius of the ringouznf4 k0dr- 4s 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 evexv(wcpf jdb/woklqpql2b4i p +2/4,6ry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her r wq b4c, dw+vq/4pkio /xj2lblf26 pp(eal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of the y ymtm 0omb a6hjx/8f ;i5g4c3b,/rfbEarth's Moon in a space vehicle (a) movi 4g0t/ frxjm56by3mfc/,; 8obhmya bing at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consistsqfx .,ca ud(e0 -iore0 6xziv, of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What i,uixdi,o cafx00(6 evrz .-eqs the mass of each?    $\times 10^{29}$

  What will a spring scale read for the w+p;s89+u jjbcwn +qgh)p c nc*eight of a 55-kg woman in an elevator tha)h+nc9qjgsw8n++ *pc; cju bpt moves
(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 elevator. Thkq)en v)sr 7z8;4jjs ne cord can withstand a tension of 220 N and breaks as the ele )s 7v)kejzj8rnsq4 n;vator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with ,pyq*ux)r dfxgm.ni6an57 .v hx*m4wzv7.hr period T , the density (mahr* y xmvfvr)nzau .iqwd674.h* ,7x.m5ngxpss/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to detercy +ut6.nujp 4dvr39f3 4lcfqmine the period of an artificial satellite orbiting very near the Earth’s sqlf tj93v6 +pu.ur cc4 f4ndy3urface.    s

  The asteroid Icarus, though only a jzcwc68h p)irr6e9.h lk,(oqfew hundred meters across, orbits the Sun like tj, z.rhh96r6p l)8eo( ic qkwche planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanw(q,w6epfw+ecn aw ) 8ce 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 on c,rhh4;*l kiuce every 76 years. It comes very close toi4lk hr;uh, *c 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 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 m16fcrt1a .7 rnoah1)mlj1ju 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, period, and mean dimg (vg-) dibcm ka:sito6/vw4i k41c;stance for the four largest moons of Jupitg-magv6(;4kbd4 c/ tci1vo:) wi msiker (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 uyc/j*(b)a+ y/y +tip) tbqqhexjb3,the Moon. b)uj xeby*,+y3(/cjbha p)t+ qyiq/ t   $\times 10^{24}$

  Determine the mean distance from;v8s/l/vmjgw a4ng21wnx ti9 Jupiter for each of Jupiter’s moons, using Kepler’s thixn4jm/wv2/ 1;9gativ ns l8gwrd law. Use 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 betwepa:1 yekbg;h 4en Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited kbagehpy:;14 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 den* udw)w 1xljat 1g9q3scribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where i 9 ld3wwn)jqt*gu11axt is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a d tm0a8mnxsy28sgc2( diq g hx y;2.3yhanging vine (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 tolerate at the lowest point of his swing? His mass is 80 kg, d.y y ; 3y(gdmgx22a28hscniqtxms80 and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gh d)ogh58 av (mo 5)ujawkj6-u; be7fcravity be half what it is on the sure6k )uw85mua 7f ha-d)j;(5ovcgbj o hface?    $\times 10^6$

  On an ice rink, two skaters of equal mas )2; 1sbtg;rzb9z jslls grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg,9gzsl jblrz1;2ts ); b how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotat 6jv)qfssl,,r es 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. What fractionl,js,v)s 6fqr of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directl/en .y oxmyv8)2j,ea qy from the Earth to the Moon experience zero net force because the Earth and Moonx o 8,.mayv2j/q)nee y pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yo mwa1rwrm z b9do3f/.5onp9inv h2m12u stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceler1h3/brvm9minw.fa p9d2 1 52mozworn ation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a ci4hqunpffl.0dkx41v +rcular 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 abodqx h0f1 f+l nuk.44pvut 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 vertical loop (Fig. 5lymps/m *n a 81(pu66dim+d0 gl0rg)u*rtfn o –43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acs7qi l8)bzzns) 8 m2mcceleration due to gravity ssnl)8ic) z7z m2 8bqmat its surface and the gravitational constant G.

A plumb bob (a mass m hanging w//61qr4qrp qhyf9i yon a string) is deflected from the vertical by an angy4 /rpfy qi/6rqq19whle $\theta$ 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 desu nirbaffs tl9mj7/+14pu8k- kv81yg ign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speedsuybag8j k9ltfn7 u1+1vsmi8r 4-f/ pk can a car safely handle the curve?

  How long would a day be io 72i3skqun+f11,tfy icp:-9fly romf the Earth were rotating so fast that objects at the equator were apparenqmn -sc1fuf+ o:79 yrtp, 1ylki3 2fiotly weightless?    $\times 10^3$s

  Two equal-mass stars maintai nc,.s5wonva ()k(dgzn a constant 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 constant speed rounds a curve of radius 235 m. A lamp susc*9j-w-5 1ky: ddxff sesb*o56sbz utpended from th-oy 9 dss *scfk:xwez*u5j1b-f5tdb6e ceiling 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. Thbk 8dc5i- ivm8us, 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 g 's a person would experience at the equator of such a planet. Use k88viicd -mb5the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extre7 zl.h 7ropr-.(mg pnymely massive 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.r7 (n pg hlomz-yr7.p clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shf s1/ rf8x(pwvgy 5tru5g qkp1z3e*3fown 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? /gfswxy*f v1tq ruep k83p 15f3(r5 zgSmallest?) 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 ofzs+q xs b)vl67ljfb4: 24 satellites orbiting the Earth. Using “triangulation” and signals transmitte4sqlj)+ zb 7f :6slxbvd 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 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 billizg.dcp3ui4 4i,bef8 von km, is meant to orbit 3,bd ziu8ef pc.4vig4 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 spaxcgw 6e+ e(2m+cxm e-kce shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abovx+m wgce-mc2(x ke6e+e 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 31 xdqde* sxq9:000 years. (a) What is its mean distance from 1d sqd*:x9xqe the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be ifyxe awrh+69u, you could actually "feel" yourself gravitationally attracted to someone near you. Make reasax 9,uyrh +we6onable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig(qqtn3c4 yq it5;5oup . 5-46) at a dista3(;oq i5 tcpn y4ut5qqnce of about 30,000 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 corners3 jtqn)x) 2pvn of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of jt2)3vq pnn)x the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orb o))xtb1ii-qbv :w u4bits 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 j2:wq /sn-6khoh98zw 3g gkkwthe tip of the 1.5-cm-long sweep second hand on your gh8 -k9nwkw wk 3/:gh6qzjos2wrist watch?    $\times 10^{-4}$

  While fishing, you get b0u;:s.lb ct* g ufs(hbored and start to swing a sinker weight around in a circle belou:cltb*0 .s sghbf(u; w you on a 0.25-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 highway is designed so thatk7kn ( elxy*paghuh) /2 lie8+ a car traveling atn h)xlk/pul *8kg7 eiyea+ h(2 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, utilizes tilt of the cars when negoti d7u kw1+e.rtvzr. /nnating 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 mdt7r .znuk e+w.v/r 1n 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.$\approx$    $\times 10^2$