Sometimes people say that water is removed from clothes in a spin dryer by cenxu,/)rs jbe-sm k d:5jtrifugal force throwing the water outward. s,exu/kj5r d)j -:msbWhat is wrong with this statement?

Will the acceleration of a car be trac,*zb; d0tjkm)2ur59wtm w 3u5*cpd/j gu xhe same when the car travels around a sharp curve at a constant 60 km/h mutz 0 )dr35b g/;*p,cam59 djck*wuwjrx tu2as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alonm 7fqg*f, 2cxeg a hilly road. Where does the car exert the greatest and ,gx2f*e 7mf qcleast 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 cub,de4jv.1mh69 jko m hild riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the childojhb9m eud46 jm,k. v1?

A bucket of water can be whirled in a vertical circls)ctq kz+ c88+ e k,7e2ldzkfce without the water spilling out, even at the top offzcd2k8+8zk7 cl)t kes cq+e, the circle when the bucket is upside down. Explain.

How many “accelerators” do y w9r q;m3i.bej7f ;jqyou have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What ; e9.73;yrbiqmjfwqjare they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in.eld/eh-)pan2b rq s( Fig. 5–31. His sled does not leave the ground (heee2h bal-(n rs)/qp. d does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high ss4dpj1 (dh9gsv2dv45y0i y rdpeed?

Why do airplanes bank when they turn? How would you compute the banking angle gz0z m+bnf28g41m kvjm iven its speed and0kmzzvm281+4 bfjnm g radius of the turn?

A girl is whirling a ball on a string around her head in ,fdtl5n(d ze9u 6w+fd a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on thedf5ewfd(l 6+ du,t9z n other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force ko 3ivx0-g0llh/ ki2t on the Earth? If so, how large a force? Consider an applikox03t0i /vl-k gh 2le
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s; p7jpif0 gkfb 70grx1 orbit be differenkp0g7 gfb0ip7jfr x1; t?

Which pulls harder gravitationally, the Earth on qh z 9/p(j1 gwik0w-icthe Moon, or the Moon on the Earth? Which accelerates i01(wp hwkiqj9gcz -/ more?

The Sun's gravitational pull on the Earth is much lbdz:sgt1ev)9v 547,zydokzcf) + jl barger than the Moon's. Yet the Moon's is mainly res9d 1 oygs74bz)ldczzfje)b+vvt 5k:,ponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two efxuivtn)o)*+t fects are at work? Do they oppose eac vtx +i))ount*h other?

The gravitational force on the Moon due to the Earth is only ab h vt h*;ykxm9umd+ 0qx)h55arout half the force on the Moon due to the S*m+ m0dr ty5u9hvk ax5;hh xq)un. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in ite0w2ibuu3t-3a 7cg gmsofzu/2;j ms 5s orbit around the Sun larger or smaller than the centripetal acceleration of the Eus3om-iu wg7tjaeb2um2g cfz0 s35/; arth?

Would it require less speed to launch a satellite (a) toward the east or (bux3k7utdadbzyyfn1 - 7ke,5, m8y tv:) toward the west3u :7 nd8dy,7z51k mxuk-yebav,fytt? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measurejgeo emaa.d+17 skj qrbf9*;8 d by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In8b jaoq7 .+rgksmd9;1 *ejefa 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 spaceherl7l7o s3n* 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 h l3s *7norl7ethe 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 “freg n(m wyxf)u:6e fall” or “apparent weightlessness” between stmyx6w)n ugf( :eps.

The Earth moves faster in itsbhf s8iy+(h vqr/ 45vv orbit around the Sun in January than in July. Is 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 the tfvs( hvr58/ +qbih 4vyilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was dn5+kiwxm)y1 eiscovered to have a moon. Explain how this discovery enabled an estime5)mn1wxi+y k ate of Pluto’s mass.

  The Sun's gravitationalzwq*q p+ bc/rpi9xzc0 m9qk7t az,:9 l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the cent99 xz qcb:c*/9lapt+ 7 0rqmzkpiqz w,er 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 19 /oc) dabbjbria(90k980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 okzkmg;k- )dz.udac.f:.b w t,rbit around the Sun, and the net force exerted on the Earth. k- ..,z:tgwk zkbum;fcd.a)dWhat exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates udp9a)ai *rwd3 niformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the did)rwpd*ai a9 3scus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's so9*ns9; aevb*(mr 3 l.rd omy n7pm/ecurface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surb o(n3om payc9e;7ds lrm*er/n*.m v 9face. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on 17u6djrje3.2+n2an vf h qrz 2qlw;vv the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the w+vvzj3wlh2aj.q1 rfn u7;d ne62v2 qrheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vert,c0r exm) qic:+p8 0h sbxao(qical circle of rqihm:0pe sxc8x0,rb aqc )o+(adius 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 radi up 7dd41dll7xus 77 m on a flat road if the coefficient of static friction b7ld7d4du 1x pletween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tiqhk7 61 f,ev2vphlag3;fcwa )res and the road 1a3w; 6 v)hqfk,7feg h clpva2if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training a1 o e ;dq qgizyim7-80c m.i8w(cd/dfnstronauts and jet fighter pilots is designed to rotate a trainee in am 8z0e8y d/g1;- qiwmcq7do( fc iin.d 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 cm frou yrnzi4 9x;+0:je :aliyu qm(m the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntabeqi:n+zj: u;ayl iu9xr y04(m le?   

  At what minimum speed mreo)f:v) hpx4ust a roller coaster be traveling when upside down at the tep4xvho)f r: )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 3 o-3q5e xghmd;vj/xs) crosses the rounded top of a hill (rh5gmo/vj3 xex; q3s d-adius =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 wvr4 sxyt m7tz)j 7;g3vheel need to make for the passengers to feelvy 7st 34xz )j7rgvt;m “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius svrbd,k.zy cv4iv o)+ -bet+ lg*w/8g1.10 m. At the lowest point of its motion the te8w*yslvc 4k++ d v v.gi-t/gb ,zrb)oension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particlen9a7 3 cp:lbxg 9.00 cm from the axis of rotation is to experience an acceleration ofcb7xlp9a3: gn 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a 7o2k3eopfa c7carnival, people are rotated in a cylindrically walled "room." (See Ficep2ko a f7o37g. 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 c3q:9mgqf 7hnmircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling b3 q7qmmf:9 nhglock (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, by not ignoring the weight 2dq2vg-o)lp*ot h eb1:n3nc vof the ball which revolves on a string 0.600 m long. In particular, find v onncb*g2 td1:plq)oh e2- 3vthe magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly bankessd /s3vb kp0u 73eiu.n x9vb*d 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 04(isjm+ ghx7a xi eh9$ 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 eva: 4c1+6xanh2ib awmfextk7m0sive 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 tangenex;5 bmsv; rd/ o+fidv8p ni53tial and centripetal components of the net force exerted on the car (by the ground)mn ri;+v;vo 53b5ef8p/ id dxs 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 fromexr78yz3g leg +h8jz8 the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have8g+gyjx8ze73 8 hlrze to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizojhng.z6 btmn577:30-a uzqby ziii/d, uxxl :ntal circle of radius 2.90 m . At a particular instant, itx 7 :j0, qnzyxb tn/:bl 3iai.ud-zh 7m56uzigs 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 spacecra+wv4k3y3 e*vjc u.x/ sgnxkt )ft 12,800 km (2 Earth radii) above the Earth’s)nkwx4ev vkc3y x* u3js.+gt/ surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has4vxfr88/(p jbzdsu : yllb:e) a magnitude of 12 m:v 8f4yb :bpxjs)(l/del 8 ruz/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. (i)5a5py a51dkrlqq qThe Moon's radius is 1.74 5 rya1) dqp(k5ql a5iq$\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 ha08peiiptk 6 t/ ( 6e rc6q+hdkehvx-(ms the same mass. What is the acceleration due to gravity near its surfaemie td/kxp 6-ik6+ ep6(8 (htcvrh0qce?   

  A hypothetical planet has a mass 1.66 times that of Ee sfk1c* f:n5uarth, but the same radius. What is g near itfeu fn *c5k:1ss surface?   

  Two objects attract each other gravi yfpo(ilirc/r/j5 z:4tationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleratiov),, eq2cr6k 6l ze ooqb9r5qxn of gravity, at (a) 3200 m qeo xq2,9k),l6 v roc65 ebrzq   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a *7eg.p.bc ,x7 fccpxl point outside the Earth where thegravit 7pxc.cb*7x,ce p lgf.ational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star cp-vko ji5hf5s+yxwh3 8ja: 9has five times the mass of our Sun packed into a sphere ab-kfoyswpv3ih 5h59:x+ jj ca8out 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likej-( 92 s r.ah8yw8w569 fykyrohjdhx m,gr4su our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass9y6h8 2rgosrjyu(4f,w s . jwxa k-r 9d58yhhm of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astrona juqf(z1, dtr6fm0x5 futs feel weightless while orbiting in the space shuttle. Your friends respond that they t1zm6tf 5dx,jf(uqf r0hought 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 thqe05li1jop )1gm tdmmv 3rl/;e corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted o)jp iml0gqv3l rd1 5mtm;e/1 on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mosrx+ w ze*k4r6bt of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fou*e+6kz 4brwxrr planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfacerahd 3i hnjy(-1yvt5 p:ts+w) of Mars is 0.38 of what it is on Ear+dp35 r atyi()j-vyt :ns1whhth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val4o2ixw- fmh ,6*oipj zue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kw,i joo*2zpm4 fh -6xiepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of-lq jhct s7.1o kjx 3q2b.oo2c a satellite moving in a stable circular orbit about the Earth at a height of jkc-2h s3xt1lo2bcq7jq.o o. 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ed)7hbku*s0m garth. How fast must the shuttle be movu0*sd )h bmk7ging (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate io4kjsb4ql k( 0y 8xh5m9,bhhvf 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 Ques( hqh948k5xom4b0 kh l ,ybvjstion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eartu ub;xwz;fi6f.h a 5(q 1imh0uh in a circular “near-Earth” orbit. A “near-Earth” orbit fq0b1uf . zwhah(56umux;i;iis one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal vas zug,k79e*w5u sgj 1elocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Ear1* s wguz5a9e7 sj,kguth?   

  During an Apollo lunar lan*8 ofd3n8x, hinnc+nw ding mission, the command module continued to orbit the Moon at an n83+no ,8 *fwhx dnincaltitude 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 ic);g0eha g5kim e that orbit the planet. The inner radius of the rings a5ge im0gk)h;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 0i q,/ow ntd3eevery 15.5 s (see Fig. 5–9). What is the rwt 30 nioe/qd,atio of a person’s apparent weight to her real 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 fmo0 2u.ju-2yg-cdrh wlh )z.center of the Earth's Moon in a sp y zl )h-0r-fom. ch.gdu2u2jwace vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They arew+(ai xw/9 ezx rl2 st-khsu02yr;2dl oz-u +/riyhd ls 2s 2k9;r(eax2ltxww0bserved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of soa ms/+9 a5fja 55-kg woman in an elevator that move5f9 aas o+sj/ms
(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 a2s-;yn xdasoj8 hd5;m cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N an2 ; sd-yjom; h58dsanxd breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface ofdt7aj8)se9; ix ur(x,9 xdu kk a planet with period T r(iuk uxedk ,8;9j7d xt as9x), the density (mass/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 detrnur g-8m7 1bwb;*q crermine the period of an artificial satellite orbiting very near the Earth8-b;u nmrrw7r*1g bqc ’s surface.    s

  The asteroid Icarus, though only a few hundred me m(xu5n wr+sze4dh,y;ters across, orbits the Sun like the planets. Its peri wu,5hs+nz4e(rx yd;mod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancetoxvv w-u4ou2lprcp 7z6v-a )7wd(r; 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 thtw z;*;a 0pnc:lpt3 mx:5sycze Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” 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 l; zs3:w50 xnt:ay zc mt*ppc;the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the /6:,aknry i7mxm-z dw 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 distance for the four laa;4 p iodamd.*.:m/ya1 klhtlc2w*w yrgest moons of Jupiter (those discovcwa;.m kad/**.2a4iw 1ohl yyl t pdm:ered 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 nu8qm r q84+5f5 bqb5rxbfi+dfrom the known period and distance of the Moon. bqbf5u8b 5iqmn+qfx485dr +r    $\times 10^{24}$

  Determine the mean dis2 ,e9(j hba8 kkh-drlptance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table k8-(, j ar bh9pk2eldh5–3. 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 fragments2(+ltvtfd0uxmv :gcf2a m-,f (which some space scientists think came from a planet that once orbited the Sun but was dest(tgxf+-t cf0 da v2vuml2:mf ,royed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a banoxaqmglz, v8) bc02k*a x( io:d 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 th:zolaqak 8, b*x i2( 0omc)vxgat 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 arcg3/m xsf8q ce v(r;;j(5th5r vbl)d kx from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force jb ve; mxcv) g(xh3 qtfslk8rrd5/5(;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, and the vine is 5.5 m long.   

  How far above the Earth’s surfae +sl96yj; v 5wmydgh.ce will the acceleration of gravity be half what it is onwy+dj lg;ysm ve56h .9 the surface?    $\times 10^6$

  On an ice rink, two skaters of equal maefdan+5b z hs7s9 hwbz2p*)+fq, )shgss grab hands and spin in a mutual circle once every 2.5 s. If we asfa h5)hbfwnp,bs +q g2szs 7)de9z*h+sume 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 rotav5 ;(o0mmew; nxns d*mtes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the ;*mevn wsnmd5 ;0omx(Earth didn’t rotate. 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 et8s(ipmm1lso + df+ -directly from the Earth to the Moon experience zero net force becausp1-esmsi ( mt8f od++le 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 bathroodga:yx+if v 4 +8a6 xxuu jf)3-ymgy6um scale in an elevator, it says your mass is 82 kg. What is theidumu+:yffx6ga4 u+ yax yx gv-8 j)63 acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circupuwfxx - vd- r(j,b)a+lar 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 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 fxdbfax)r-,+wjp(v -uelt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a v0les oo(1uo 0gertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius rxlm ta7 9,b,bf+yvc9o, the acceleration due to gravit 9xvy+bm ocbf,at l79,y at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fr3q l2gq0 uq0ghom the vertical by an0g0g qhq qu3l2 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 mhi2 cz( 3f),+ phjcy xah5k/uq is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavemenq/ z2hc3)ai(c f hxjyu5p, k+ht), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rot+bdph .f* z-tjating so fast that objects at the equator were apparenz .jhp -f*td+btly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distax()q vf 2x zgf7nm3t8zgz)s9unce 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 p +oh/xw4 ;crh7x8zrw speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 1rrw 7z+op8/h;x4w xh c7.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiveif( /i3kide+ l bwd3+e as the Earth. Thus, 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'tiek/dd3+b(eil+ fwi3 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 ij p fvfb c8-:wl)6ft3presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They -jc3fv b8lp: )tf6wifdid 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 constantnx 2mg -t+2d49hygsin 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) Where would the driver feel heaviegn gt2dhyim-x2+n4s9st? 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 ac(f8bnuep /j;,aegjp/yrxj63 /q+ rlrb(s1 of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined ,j/j(flbs6 a8(ecr1+yp x; ebnrjgp3//qu r ato 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 Renx99 8ympuw9o)u kfhq,dezvous (NEAR), after traveling 2.1 billion km, is mem9o9y9hk8qw ) x,uupfant to orbit 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 pursuing a 1br m yo;ertmrjq w6 3a9/p2o9satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km bep2arretmm9o/q; or931y w6 b jhind 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 mean dist-;eva ckw+v x;ance from tvaxk;-e w+ vc;he 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 f)k in.,t0sodof G would need to be if you could actually "feel" yourself gravitationally attracted to someone n ,t.kd nio)f0sear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at g:yxo-uhfrr/ yo77 m* a distance of o*uyoyx7-7fhgr :/ rmabout 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 corners of a square 0.50 m 2f;u:cvxvm hx- az 9v*2/e nwzon each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpef: m/-xh2*uz n cx9vz2;avw voint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitsux6v+qf2 6l :vno q;bv 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 the88dy bn (ccqw; 1.5-cm-long sweep second hand on your wrist b8nwd( 8ycq; cwatch?    $\times 10^{-4}$

  While fishing, you g, az 523d 9uweam5usfiet bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complm fedia3ws,ua59 z u52ete 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 soz+;b.yfoqpw w3+e)4v)n- kak vz9 nfn that a car travel vzz ; k.3fe+ f9nnnbw)+o-)aqvpy4kwing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when tr /1x,lr3apqujd2omah 2;m - 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. Themdp1 3u2aa xmor/rt,lh-jq;2 passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$