Sometimes people say that water is removed from clothes inl yih7hv.-xk /0hjv y+ a spin dryer by centrifugal force throwing the water outward.7+xvh jv0-hhlk.yi /y What is wrong with this statement?

Will the acceleration of a car be the same when the car w)blab u0u3w +travels around a sharp curve at a constant 60 km/h as when it travels around a gentulbbu a+)w30w le curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exdln2 5rw4gy2 yert the greatest and l nyr24y lg52wdeast 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 for0vhdt 4z9drh *8:b/ph svp5 0a we,amjces acting on a child riding a horse on a merry-go-round. Which of these fophpvh*h4m0 0 wdja5, ezs:dr b9 a/vt8rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sw )rir:cu t.ay08c6k npilling out, even at the top of thetr.i:)0rya8 un ccw6 k circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Theriykl-bn6d0 b)cky 7a :e are at least three controls in the car which can be used to cause the c:y)b k0cyknid-6 la b7ar to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of awj+loga(g b,657j8izf fwv kk2cu :j8 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 hill. Ef(ij go 5:z2 bujv6, g7cw8fwla 8kk+jxplain this decrease using Newton’s second law.

Why do bicycle riders lean i /:xrx0j fx,djnward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankizd evt-c18fi * tresotsm i4*c0td;*0ng angle given its speed and radius of the s-*z e*0i4i 0stft*d dcetomctr18 v ;turn?

A girl is whirling a ball on autk73 dm fy6xbjq.,p2 string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When sho y.bmjk 6ud,xp f7q3t2uld she let go of the string?

Does an apple exert a gravi8 a-)xo0wspyrkj5 qx2tational force on the Earth? If so, how large a force? q2k)xsp0owxay r 5-j8Consider 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 Moogg1 :5tq q-(6nvtdjirz. w;vxn’s orbit bq61j(itnz:vrdggw ;-5xv q.te different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the e1gprthrll9i4 27rj- Earth? Which acceleratei-tj 9h lp4rle2 r7rg1s more?

The Sun's gravitational pull on the Earth is much largeemkls1fcs9r c fmon5 8*rw9r97,mm p2r than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side8m729m9w9f5prmknerl *c c 1s sfmr, o of the Earth to the other.]

Will an object weigh more m0f3d 0jax ij5at the equator or at the poles? What two effects are at work? Do they0xadm if 50jj3 oppose each other?

The gravitational force on the M bm1y+p saf+1loon due to the Earth is only about half the force on the Moon duelspa+1f+ b y1m to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger-z+) tb*pc- mwvfvji 7 or smaller than the centripetal accelew )v f-i+pj *m-vbcz7tration of the Earth?

Would it require less speed toa *0rokf3 ljo7 launch a satellite (a) toward the east or (b) toward the7aojf 3lrok* 0 west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatevyujo2d y xs -7+npi)4st, 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 upopdyxiys-)4j2u +vn 7 ward 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 adverselr;vqfh7e4 u+iihxc9x+ 1 4hxhd1 0upni ;yo*py affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates pdyeh4 hhno4v1x9i;u;hi7cup x 0 1qf+ix +r*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 exper51wj .cg7 pzhziences “free fall” or “apparent weightlessness” between stepz7 h5gcp .j1wzs.

The Earth moves faster in its orbit arodpj(ua .u:rr8s3n pp3d9xj4yund 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 tilt of the Earth’s axis relative to the p3nsu4j.yd( ur9 px38p:dja rplane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explaigw xwx ym.j-s6-sd xs-3( 0yiin how ti xmwysy(.x i0 -s6-sd-jx3wg his discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much) nl g6 e8yx/4iv0ok-y;hyqo k larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cox8;/4y-yho0 qloiygnkevk )6nsider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19mnot8 8vcu. 5z80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripex- skd 5mo q:rmmbj/2;f 5a8c8c pl)oxtal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a cko 8l5oq8)r m/a s5dx- cf2mjmpc;b:xircle 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 N2b j(fo870, y aul)dfe1mhk )ggf0yhx is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m.yfug)j d 87ym(2 efgol ,0kbafh1)x 0h Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4j c cjpanmixf7;/t8a w2s6s.400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms p8 mfc xsjwc ji7.2/ta4s; a6nof g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay oe0teq/b(. /0ffsqgwnk- g 93 yrd +kdwn the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if thy(w.0 q d/qw 9esk/rebt+ kd3g0gnf- fe wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vepbu u dxxul4z6xsl q33(bt(f )mji53) rtical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spep(l( l3jfx)dqzis3b3uxu u6)45t mbxed 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 wi4j 6k8oef* k96mazhvdth which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficief6ma*dk jeo h4k9v z86nt of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffi.h e. gtiuphvg+l7-v0cient of static friction be between the tires and the road if a car is to round a level curve of0 - .7hepvihg.g+uvtl radius 85 m at a speed of 95km/h ?   

  A device for training astrop1:5sw0 x rilynauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . I5xw:r 01p siylf 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 from the axis of a rotating tu3mn+7hp alcl8,c l*f*o3 ttyirntable 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 coefficienf,ty3lp* nc37h +lmal*ito8ct of static friction between the coin and the turntable?   

  At what minimum speed must a rollerrk5 s mimd wc9)suk2,5 coaster be traveling when upside down at the topkks5 drc,mm 2w9 ui5s) 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 (zm;/akh (xr2hgw v;klnyy/ :+syw z*3including the driver) crosses the rounded top of a hill h3lvzsy ;n *w2y;g+r/hay :(wkxk/zm (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-diame9 zewq,t4bcroz :5s j5ter Ferris wheel need to make for 59twzo j5er :czbs,4qthe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled iyco jz0be+7 g.n a vertical circle of radius 1.10 m. At the lowest point of its motion tybe c j0.z+go7he tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a part5w5u1s je hq4oicle 9.00 cm from the axis of rotation is to experience 5uhjq51s e4w oan acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people arel7r4h cf+9 ul4ighx quafe1 q0 6l*x:f rotated in a cylindrically walled "room." (See Fig. 5-3fq 1 09lufac64hrfue4x ll*i7xq :gh+5.)
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 M0.-,,xqf revp1dv o mt ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this10ovvtq e-x.rmp , df, orbit by a light cord connected to a dangling 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,egvja -c1qe3)oe 1 dt(-b-zyv by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partic j -ec-e1vtd(ey 1 o3-zqgb)avular, 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 perfectly banked for a car traveling 75 yd;/ks/)g2 j2i0mt0a ym8csh g wh 7qt$\mathrm{~km} / \mathrm{h}$ , 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 massesw;l(m37c zqxi:hc om, $ 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 r s:9ng 4heat02kw nl0vertically 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 cenqq 2ucbw xw(znua(d2tjs /.13tripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its spee2xqb3sc/j1dwu a( z.qw2 (tund is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acceleraty; f,h/j*jwtuyr 2 zx.es uniformly from 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 cur/yxyw hz*r2 juj;,tf. ve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circlef7 0zkqkjy8m6t 7 gn7k of radius 2.90 m . At a particular instant, i777 k6q kfm0kgzt8nyjts acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km lkg * t)lmgz)+(2 Earth radii) above the Earth’s surfagl*+)kt)g m lzce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnbfq obp2z-*7nk n3mk s82gf0ditude of 12f-skqb0 *7bp8dzo2ngnm2 fk3 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 o57ytvc54 4hxxif pwr0 n the Moon. The Moon's radius is 1.745tcwif4 yx0r p45xhv 7 $\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 same mc9s-4ghjq /h yefc r0,ass. What is-gsq9/ychc r,h fj4e0 the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sa;t e )0iepm:zxe92uus me radius. What is g tme)i u 29x:p 0;zuseenear its surface?   

  Two objects attract each other graviavy/;t)h aed+2j/ mk ftationally 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 accelerationdma.gfnr cx8/ xfxi 4jj)5/i pp/3gt, of gravity, at (a) 3200 m/dtxcfmx3)rn8 i igppxj /5g. j,4af/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to rdh4i vumm0ajd; 7(fh*)h-vp a point outside the Earth where thegravitational acceleration due to the Eart0 7mv uddjhp* -4 rf;ivmh)h(ah is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the masshnh qqasp0 *yr:8e2 9k of our Sun packed into a sphere about 10 km in radius. Estimate the s:09s hkyeprnq2qh8 *aurface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was antz m2k-(kol 3c average star like our Sun but is now in the last stage of its evolution, is the size of our Mo-l3o mt 2zck(kon 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 space4tb6v kw5rwa2o;5 7hz dpu(sl0rre8 w shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince de;w8r soh t (27pzvlkur55b aw64wr0them 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 square of side 0.60 m. Cajdu*9puak c+clupj8m3tu.f ; +k.a9jlculate the magnitude and direction of the total gravitational force exerted on oneak. u+a*dujufkl 9ump8.;9tp3 j+cj c sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mos/ m,yf1bge(8d i ph+qveuy8 )lt 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 four planets are in a line (Fig. 5-38). The masses afvil1+88,e)qybe phmg d( yu/re $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 surface of Mars is 0.38qkbe1z:5a:kw 0ym r 9u of what it is on5:0 we1yam:kk 9zb ruq Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perior jeb no4u)v:05b4d4n;;jslri x 7wi ed of the Earth and n0ned i 7i orjb ue;b ;s5xl4w):v4jr4its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellitrr,jwv irond:/v/:: f e moving in a stable circular orbit about the Earthrrd,::v rnf/v /:i owj at a height of 3600 km.    $\times 10^3$

  The space shuttle releases sikbb byzpnl6xb,9/) 53 9mrva satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth)by9 bn5 l,x vrskm)9bi3/6zpb when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshipki i2 qyt8htg/c8u8d6 rotate if occupants are to experience simulated gravity of 0yth88i / qducg k2it86.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eh0 ;8wk6 d+fxq zxuk+ 2xuuvb;arth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a heigk6b;x0uv2zu8 ;x+xfwukdh +qht 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 velocites+t1zmo5- a ny would a satellite have to be launched from the top of Mt. Em+ao zt1e -s5nverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the cwnbi4 ca1cntd++;t gr9t ay7,der.l3ommand module continued to orbit the Moon at an altitude of about 100 km. How long d+glw;1br ,t. t ccaa34 eidyr+t7 9ndnid it take to go around the Moon once?    s

  The rings of Saturn are composekw:kd;)-sshy+p vr7 uj(om0g d of chunks of ice that orbit the planet. The inner radius of the r js +ywdok)prg0vm: ;h7sk-u(ings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 ;r;w91hwzq i8x.l hk-fzri..r vnik0s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the botto8kix nzwiihv; 9.qr1- fr.0l ;rzw. khm?
(a)    (b)   

  What is the apparent z (;*fzf vk/8q)gwo+o.tekmvweight of a 75-kg astronaut 4200 km from the center of the Earth's ) of*wz+;vk. t g/vf8q(zmkeo 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 binary-star system consists of two star 8zke8, kqrtcu2bmjs/k ;6on0s of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit e2/8kknkj; rz bos,ucm 08q t6about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevatordu a1jkh6d zrus0ntra);- 5n7 that moves ua)rdjd 7nsk;n1 5za0thu 6-r
(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 susmkwjyu6gr;no .8lt+ 3pended from the ceiling of an elevator. The cord can wi 8u+kt l.mwgr;j63oynthstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet/sghd;ng 8 oja6 k5t0ic+2 mzp with period T , the d2kz o g; tn5/is6pcmh0+jag8d ensity (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 determine the perifz 3wk(fbzkm;ut2a c2 wd5a; 8od of an ark8 wz2(;a5 a3fd2k;uz wfcmt btificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus,6dkgo uov0 k;h6ipq*po v(.o, though only a few hundred meters across, orbits the Sun like the planets. Its perio6.0op(g k qho; vk*d6piu,voo d is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancivh3iwx p;4m 5e of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once evef i/e9ly9 (f:suee.x ze*do g8ry 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 n8ye/fx.d eu9ioesg *lf9 e :z(earest 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 cf+ mr)7phhdczp nw )589yh3bthe 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 largest moonxhakj mm;e .b2sa ((x*s of Jupiter(es*. (k;2bahjax mxm (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moo8we n5 +g493x.z gnfdu hu0nown. 4wgn. 3fe5gh 0odunz8x uw9+n   $\times 10^{24}$

  Determine the mean distance from Jupiternv 48t j8alat+ for each of Jupiter’s moons, using Kepler’s third law. Use thel avj ta848tn+ 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 between Mars and Jupiter consists of many sni7 (ay8 lj2 2;h,(kjgwrqd ifragments (which some space scientists think came from a planet that oncejar,sk qn2w(8 d ;i7 i2yjh(gl 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" in the form of a bat4o3ap .n * lq3rbn.yqnd completely encircling a sun (Fig. 5-40). The inhabita3n3 r t.o .nya4lbqpq*nts 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 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 swing7z + gaxy26aumd3b vz u2/xis 6)wk;cming in 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 2saza w76vxu+ix/my)zkc326 bu;mdg at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity bhnowz ar +*i0i4b5l r. jlt3i5xdm+ h1e half what itzt0 rhlarl*5 +nij+d1h 5iwix4.3o bm is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutualk + g4;uivr 7we.g0ih5dj.rh8dop i9r circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.90kop. r we4v di 8urdg7+;ri5ghih.j0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratijb0ka b+ 5,bfnl d6nktz-fx73n)a ps :on of gravity at the equator is slightly tbn bx0p bsk,aj3 f6 5adnfz n+l:k-7)less than it would be if the 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 traveh)5 .v xxfo;pdling directly from the Earth to the Moon experience zero ne5p)o;.hf dvxx t force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when uj/ h:3vpj6 09 /xqlcopzcc)l you stand on a bathroom scale in an elevatv3 :pqc)p/jo uch09x/ zl6 ljcor, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboutg 4:e +qmlwuq73oy; cs 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 bmgluo3 7wycqe+s 4;:qe 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 (F phejzhp: 6 ,dm3(kzvu/ g86kmig. 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 nji-y9zm ojb-0)+axwthe mass of a planet in terms of its radius r, the acceleration due to gravity at itsjjyz9i+-o 0wxn)m-ab surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by asblgz7q0y .3/kc2 sx hn 0ygxc hl2s b/q37z .skangle $\theta$ 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 bayhrj6o) ;/kxpu n, 0tunked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely ;j)ku/orxnt60yu h,p handle the curve?

  How long would a day be 16vh.; oncjqrsyv1s3if the Earth were rotating so fast that objects at the equator wncv .v3o 6rh;1jy1sq sere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a coa.imc6au(;b6y s; xyenstant 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 rouc9y g 4 )zjmuta3h(ti)/ sku)znds a curve of radius 235 m. A lamp suspended from the ceiling swings out z utgh)k c/u))sm y jt3(i94zato 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. Thus, it has rb livf7d )cwruge 2a.jgf(w191i p0+i6gh4c been claimed that a person wouldw2b1ic61 0i dl7agp4g )iufwrg .vrh+(c9 jfe 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 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 Hubbl + cz :nlhboo :.v39w(4df/vq7m vpofh4)ezxne Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clou ozom3e(c474onqfv /:nvbpfz9h+ .hl )x dvw:ds 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 shown in)6i,-cha*t i imaib4z(h z 4lk 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?) Ehzhcazkm)i4(,ia-lt6ib i 4 *xplain. (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 of 24 satec skfiu (i(y0,r t5/sollites 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 each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11tiifs/0 (rs,c5 yuo( k,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), af :o-8vm:p jyrzter traveling 2.1 billion km, is meaojp:y:mvr -z8nt 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 satellite in need of rsorh 52 yj ao31mvm i1req7i52epair. You are in a circular orbit of the same radius as the satellite (400 km above the Eaivqy3i hj151om2 rr7m 5 os2earth), 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 periohw/lw2 /t wrof.x1w u9d of 3000 years. (a) What is its mean distance from thet wfw2wo r9/1.l/ uhwx 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 wohaeoqlbi.gs ibku9:)/si 6 fxn+- +,kuld need to be if you could actually "feel" yourself gravitationas.:sblak i+k + f-o q/x6 ,bgunihie)9lly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centerwcrl2ej b b: 4bfn6 ab9k4t9m2 of the Milky Way Galaxy (Fig. 5-46) at a distance of a r9n6cejmb: 92walb bb2fkt44bout 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 v 6ok ;6fbkb2k.ssp+j0.50 m on each side. Find the magnf+vjk6;kos26. k bpsbitude and 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 or v r.3 ghp;hv+je.t-mm6(zixibits 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 8.hsi r0o mepa ;7zu+xthe 1.5-cm-long sweep second harm ei7;sah8u. xzo0+pnd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and gq5v)fctyaq2d2j h87/b.vc x start to swing a sinker weight around in a circle below you on a 0.25-m piece of fi 7c.g8cfavj)/vtd qqx2hyb 25shing 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 that a car trah /jcqhx/. u;.v 4a.z2ignezqveling at spa4/ /.nq. ehv;2uzcqhz x. gijeed $ 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 thv5p9ua5a( uq y ;df9cle cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force 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 9pqdf;ycaa5 9u5v ( ultrain 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.$\approx$    $\times 10^2$