Sometimes people say that water is removed from clothes in a spi nid (1e8ehxeax*1kyq3d x-9dn dryer by centrifug* -1iedndaedqxk exhx81(39y al 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 sk bzz1zg 73psk+)g vv;harp curve at a constant 60 km/hgvzks k1+v)3 gpb7; zz as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does r nu. d. )hq,8fy-gob 3tgb5fpthe car exert the greatest and least forces on the road: (a) at the top bt)5-ffhg3pg.ob yr8q.n d, uof a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a ho og.3bufjb 9 uzhx4g5*rse on a merry-go-round. Which of these forces provides the centripetalou3 j4xuf.5bg9gzh *b acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wn/ c. m2g )xkyx:8znia/n0ca water spilling out, even at the top of the circle when the bucket izwk/x :x.g)n aim8 0/ ncany2cs upside down. Explain.

How many “accelerators” do you have in your car? There ,cygvq1d()ot+ajsi:3vr b aas1b / b5 are at least three controls in the car which can be used to cause t ib1,(oaa1jsy:bq+ a5dc g bv3v) t/rshe car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying 2v1pr (lc bk8eover 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 (kb12pv rlc8e 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 roundinqp2(7c-h+d :)rj1 o: hdhjz6b yzbawh g a curve at high speed?

Why do airplanes bank when they turn? How woul (r(qel0b8wruq5y;ca aw ;a;9qq6nxpd you compute the banking angle gilb;e9qcr5n;pr w6x (y w0ua(a8q;q aqven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pd3 t(/.rs hx*5t ywrbflane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the ya5(xfh3t *d/ry trw.b srd. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? tvrn- n,hc 00n7s 5owa2og v*+bv nvc: bv98okIf so, how large a force? Consider an aph sw08 0,5oao b*nv v2v:rb +c7nc-nv v9gnoktple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tcf8(67 ayvunsg 9kl3fhe Moon’s orbit be differenlc 6fs(f9v8 uyan7kg3t?

Which pulls harder gravitationally, the Earth on the Moon, or the Motj.ne4 zow -)gon on the Earth? Which accelerates more.e-o)jgt 4nzw?

The Sun's gravitational pull on the Earth is :d(tqzriu6 xn )ytm):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 theut(q:z)dr m:t6i n)y x other.]

Will an object weigh more at the equator or at the poles? What two effectgj.23g iz .lvxs are at work? .2gi.l vjzxg3Do they oppose each other?

The gravitational force on the w7z9u qia89wgMoon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moo899wag qwz7uin pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit ajaquh lhzk) a-a q6fp*l5x91 0round the Sun larger or smaller thanqq x -*9phal6jalu kz50fh)a1 the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the ea)60+kruyjs vp r9 2nmbhx;pw4st or (b) toward the wesxvpsuhw6b2jkpn+ ry 4 ;m9 )0rt? Consider the Earth’s rotation direction.

When will your apparent weigh,yo i/zcy2y e.t be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least?e,y2 .iycoz/y 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 ,e6*d4ibvb cl fb h*l3periods in outer space 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 sud 4 ** 6e,vlbfcb3bilhrface (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 exp qp h9 2a38+)ozp aoq/0ihevvreriences “free fall” or “apparent weightlessness” between sv8q +ah) 0 p9rqzhip23/eovoa teps.

The Earth moves faster in its orbit a 8*dbt ).kpwewround 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 ) pte*w8dk.w bis the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. f uw*-+ rfubg/Explain how this discovery enabled an estib*wf/ugr -u+fmate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mdx+8h,gwlq: qn /n5kboon'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 fromw8,5n q bnx d+/hkg:ql 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 1980 db9 ypn.tr z0czry/94$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbritsph+v 0;q8:.:p r pgh v5wgit around the Sun, and the net force exq: 5:hp8g ps;.0 tivrgw pvhr+erted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.mgbls0* mc(bkr- m/r20-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the 2r/r*b0mm k-c( sblmg speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the5 kt ;gi;k9ezx Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the st5;;k gx9i ekzpace shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acccdu 5;ld/ud tn5)xgu)8.s p nteleration of a speck of clay on the edge of a potter’s wheel turni udtpx)dt)c .dgs 55 ;8nn/luung at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate i08vv rffkhv esi17 /:in a vertical circle of radius 72.07rsi1 e/ vvf: vi8fk0h 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 witwc7mzpj 8(,/ff:dn rzh which 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 resulzzfrwd7m/c( fjn8p, :t independent of the mass of the car?   

  How large must the coefficient of static fri;33xjye -l57g jsib wuction be between the tires and the road if a car is to round a level curve of radiue; g57w yjx3b3l-jiuss 85 m at a speed of 95km/h ?   

  A device for trainingca4s c/m68 wtcvxcp.- astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast ixm-scwc6 8/cv ac4tp.s 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 var 2ceny jqy-:sbis;/7eiable 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 bs n/s7:;iq yjbc2yee-etween the coin and the turntable?   

  At what minimum speed must a roller coastp uqc:nt* ti;5er be traveling when upside down at the top of auc:t* ;5 qptni circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the round4)k5mpot j+r3adaz)red top of a hil zo 3mja+t4d5)kp)rra 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 mrx-2udi di-b+inute would a 15-m-diameter Ferris wheel need to make for the passengers2ud-id -x+b ri to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00*omok q p85t19b4filyh azv*y:-ejn; kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tensio -p ybn* 5 qv8eiof9t1yh:a ;4zoklj*mn in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle oz -mb1xh9xc3 9.00 cm from the axis of rotation is to experienc9hxx31z bm- oce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyli;htpg xlus*(:33cqw bndrically walled "room." (Sextl;w: 3 bu *gs(h3qcpe Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle svj hb.p y-p0uw-o -d0on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a d-.pwuj obvdh-pys -00angling 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, by not ignoring the weigh* - bzrm2vwfv5mjulra 2i89m9t of the ball whichj9m8m2l*v5zb-wmv 2riraf u 9 revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfeqvg4 9.d2i)(ivu(d i;zrx1i,wmtvut ctly 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(d 0;t jnwn5n7lg2p cr $ 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 by diving vertically 1i, kn+o at6lkat 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net fuk duypgpsscex .24v. 7116o korce exerted on the car (by the ground) in Examos 7kd4 ypg up2c1e.vk.16 suxple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goininbutxry603 xwz5 55 :mwyz4 2;s ecrfg 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 wewsy6i20zx5 xt n 5;b c4rm5ywzu3 :rfould 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 circlen6klh.6u)z; 6qq npjl(dn 6iv+yv2st of radius 2.90 m . At a particular instant, its acceleration is j 6vpi tv2u;6nh 6)n(lz6+q qskld.ny 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 graif6mo/abw6z+ fwl0a 3vity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is a/zf6+ wlbfa 06iomw3 1350 kg.   

  At the surface of a cer d m3raldz)-fhg51p*y -jl*enwpab 0,tain planet, the gravitational acceleration g has a magnitude of -*y p,j *-apeml3zl0)r wnadhb 1gd5f 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radw+l je67n ibf-c b (l95yln;amius is 1.74 5bjnamf679nyl( b;- cwleli+ $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiuse6mudsy;z 3h2p 2s/vioic w; n4j0f q2 1.5 times that of Earth, but has the same mass. What is the hyj;dp 04c we3 2uz2m6sqfon/ 2iis;v acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earthnfu w;a7kii n7hcn:4 3, but the same radius. What7anu 7;cin k3whin:f 4 is g near its surface?   

  Two objects attract each ot0,apmv 12ntj lher gravitationally 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 i1nlva( zku k; *i;o(t g , the acceleration of gravity, at (a) 3200 m n1;o*azkti uik(; (vl   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frk u4mixyz-h3 nj;9eu 5om the Earth’s center to a point outside the Earth where thegravitational acceleration due3j; iy emhxnuu4z59k - to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Suw ygd,b1 lx2w+man:a az6v(z(n packed into a sphere about 10 km in radius. Estimate the surface gravity on this mons( gvanz m a6w2,lb1+yzdwx:(ater.    $\times10^12$

  A typical white-dwarf star, which once was an average s4gm 51 i 0mjxczx5jdmjqp/a5/ tar like our Sun but is now in the last stage of its evolution, is the size ofg515mq j 0m4x jizp/x m/ca5dj our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sksns (zfriq*i n8k:0w h08g .)/gkvjh huttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above/ 8vf8nki .sn )ijz0hqs( gr k0:hwgk* the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side jar5i2k:(xo)y f(tyb 0.60 m. Calculate the magnitude and direction of the total gravitational fo) yy(:fk(a 25xr jbotirce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pfrsb +im hz2.3wcf1*6wn l*nzlanets line up on the same side of the Sun. Calculate the l1w zc n2wh+zif*.bfnr36 sm *total 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 gravitqtzhi41d5t( w y at the surface of Mars is 0.38 of what it is on Earth, and thatt1i(5w t qdh4z Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using th1: n7,17jnk8nq5chcd nrz jo:wrj 8au e known value for the period of the Earth and its distance from kznj7n,j8:1 w:qc8rcrd5o 17 uajhnnthe Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a zqwvd 0gu4 6;r6v1 mzxsatellite moving in a stable circular orbit about the Earth at a heigh0;xv6d mqvz6z4ugr w1 t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circuwlt/ e na90irfucu 3dc/-x g v+l)2)uylar orbit 650 km above the Earth. How fast must the shuttle be movin ecl3x9/wl frn/2-t iyu0+ud)au)gvc g (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate2yuwu4 dsq(. r0i3c giy t-z+e 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 Question4dwcrzu3(i0e + qgus .-i yy2t 21, Fig 5–32.)   

  Determine the time it takes 2rulma9 .oaq.;:e(wa.9oxp-)ej l jmsfx4 e rfor 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 im f lr:xlu.e)e woxaa; m.p 2orj 9-sj4(q.9eas very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from tr,x+ ax21) )/ itamjuej o (hxers)h)the top of Mt. Eve ,) rhsao j+ret1axtx)x uij/m2) h(e)rest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missiz(3z hja iku-j bv4eu:ecd)9) on, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once)-ju3kceb9i)z(d j :4u vh zae?    s

  The rings of Saturn are composed of chunks of ice that orbit these2as+sa*1ary ,rmlprh0 w,lp nm( 05 planet. The inner radius of the rings sea lpp* y1 mr0r(aws0,+an52 l,rs hmis 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 my.s;ty wz( nj 82(xqpevery 15.5 s (see Fig. 5–9). What is the ratio of a persp .qy mtsj(y znx82(w;on’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of 94-7 opp8r)7efxoli ,gqpy ila 75-kg astronaut 4200 km from the center of the Eartq)fpp7yr8 oplo,e- 4 gx ii97lh's Moon in a space 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 binarkec. l pj qj2:yf..id3a0i/cgy-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yj.dce.qj0 :c/iyklpga32f.i ears to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scalex3l16b(6rxycyes - im read for the weight of a 55-kg woman in an elevator that y(mib6rlxe1y-c 6 x3s 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 el0 x;qb e;fgvk9ln0 0awevator. The cord can withstand a ten;xqelw0 ;bv9 fn k00agsion of 220 N and 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 of a planed1+ir- ocsf ugoj7(ral/ .o;jt with period T , the density (mass/volume) of tsu1ag7(dio; ojo+ l/ fj.rc- rhe 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 perdx q.ycw)2q x1iod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting1q)w.dx c xqy2 very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits 2j*wbfs1.9 xm9sa fv wthe Sun likw.f a*1s9xwjmfvs2 b9e the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ozyt 6 tfow0lkdd; 9jvn,e+*s (f 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close k)ey 6pnfl5m.bw/bj6 to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun y l 56ekjm.nb)/pfbw6. 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 oyg2) / 3bmau1akwx :myz9etc; f the 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 largestap;2v*dmx/*juo8nz r moons of Jupiter (those discovered by Galileo ipdm/ j* *uvr8;oz2naxn 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 thjy+4lj *d .viwe Moon. i+*j4wdv. lyj    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiq pd93)dfsch37myodjokx:/ 5s/ s yb1ng Kepler’s third law. Use the distance of Io and the periods given inypdf1h 3o5):c /osd dms/ 7q9jxsb3ky Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of 6y,n h:- ojqk3l/.amqh4g y vjmany fragments (which some space scientists think came from a planet t:,yqkjg-/q lnv64y3hah.mj ohat once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" im,i 036q, 7gsemtmxysn the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that thei6gesyxm7 ,q3tm,0 sm 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 - dv3nf( az, 1sam t0y.)lgluhin an arc from a hanging 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, and the vine is 5.. n0d fztvyhal(us 1gam)3-l, 5 m long.   

  How far above the Earth’s surface will the acceleration(wz h0y/b1/mioyz81:0 xceabryq( f d of gravity be half what it is on 0:(/1obz drx/( a08zwqhfbiem 1y ycy the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutur3whw d; )o;x ne7ta:i4v-jawal circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual mass;wt j3i wd7ax r)v-en:4ahw o;es are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent ac-+4p*8 +yvrz0on4 tljy 5zfcljwp 75uqiq g/aceleration 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 fraction o/p ut*q5po0c 4fa+l4 ylnqz-v8jj7 gz w r5yi+f g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directljemx5h lpk8t2sh. z:xc,z/1k y from the Earth to the Moon experience zero net force because the Earth an2hm c: khxzj 5e.s1t,klzx /8pd Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in vk)v8y u y:/e3r .yiomr7vda:an elevator, it says your mass iyyev8a)73./ r: rd uoykv:ivms 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of aw a2e5 umel-x)nb-. dbc0at5x,l7lf y circular 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 abllace0)bynduw- -mx, 7fl. a5b ext52 out 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 verticaj:c6yogb0bowv7lxb44/jiq /n ) qad/l 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 plan0 oolg 6ng2cxa/x*2w2xlz l8net in terms of its radius r, the acceleration dull6x l2/x *28go0w g2zanxn coe to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bykx z0qmd /p q8wlw41+x anzqp d/ mwlx 0wkxq8+14 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 banko )b qa(0 3xfyh/yr,loed for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can)h /aof 3by,lx q(r0oy a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects oq5 9uoc (f.n5u +jhb6m kbn+qat the equator were apparently wei+f+ 9bq on.5 k5m q6uo(bhnjucghtless?    $\times 10^3$s

  Two equal-mass stars maint)x6gw e; lb3zlain 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 235:6jpm9zc z4 sss6 h5uq m. A lamp suspended from the ceiling swings out to an angle of 17.5 4 qs6sj z6cp59zh:ums$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiv.p 2tqbamd: nyc s38nkr5lo08e 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't 8 y2qopsn8l t kdc:b5 n3am.r0survive 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 presence of an ex60 8kl+a ebvqehqe+rn) /p +kstremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes)knev 0s+hq re68)+e+l/bak pq. 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 conj5 *mp+o3p mapiubm 9u4l9r1m/ )viwdstant 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 heaj /plvd irwm4u 95 bm+mappuoi )931*mviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Syvn iu5vvs*4,u;b*q wo stem (GPS) utilizes a group 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 to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in* s;vu nbi v*,ovw5u4q 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 xxdc d(z7 qb9b6 ij0yi990elb9x.jof2.1 billion km, is meant tl y9ox9.x z 60ddif 0xq9cb7j(jib9ebo 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 purdkhix80f t8p (suing a satellite in need of repair. You are in a cir di088phk(xf tcular 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) Whatfve,z hzs:5 c )sl3la+ is its mean distance from the Sunl3: svzhla ,zcs5f+) e?   
(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 nk9:e,7cec ,4n ryu bjveed to be if you could actually "feel" yourself gravita7e,c r e4:9 uvj,nybcktionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around1 ui y*+ncqiep ku;u., the center of the Milky Way Galaxy (Fig. 5-46) at a distance enpui+,1c uuk.iq* ;y 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 ar9ojb 7+fjd2dg (-td ;zosn ln+e located at the corners of a square 0.50 m on each side. Find the magnitude and9(+2onz j -b dndjl;7dgs+otf direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg/nep8ur z- p;2tdndf-j +r/i g orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experi qcb)*. jrux+venced by the tip of the 1.5-cm-long sweep second hand on y+)bjq*c.u rxvour wrist watch?    $\times 10^{-4}$

  While fishing, you get boreyp. ,j,( u-qrz..ex qctuir. pd 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 complete circle every 0.50 s. What is the angle that the fishing line makes wi,iru,xqppt .ur cq y-z.(e. .jth the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designe: j0bkiv1l 7gdd so that a car travel7:j1d i0glb kving 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 carpn ,);63a si.xnkramus when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the k ,n6ia a3n.x);pusm rnormal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$