Sometimes people say that water is remo2 uk7o4a qi.mcved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with thiik.uc7q 2am4o s statement?

Will the acceleration of a car be the same when the car travels arou4w vi187hnvt0lb pbg)nd a sharp curve at a constant 60 km/h as when i h lipb48t7)b gwn10vvt travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does 2,*umuabnfrv) +in+ dumb:j0 the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hij+ 02vadnb,: *ifurb+mnm )uu lls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on ak;h yvrx(j .3;*gzyeg(a jcdwek2po 7ji13x * child riding a horse on a merry-go-round. Which of these forces provides the cex3j e vag2kd((*ypkiz1whj.org yej73x ; ;c* ntripetal acceleration of the child?

A bucket of water can bejoj:we d +rm7b ufbb(i*meun:f3 z(*3 whirled in a vertical circle without the water spilling out, e* ( ued3*e +ob: mbb zf3rnjifjm(u:w7ven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cont5wry wopr4m8rz+l 7q/rols in the car which can be used to cause the car to accelerate. Wyr7mz+l 4r q 5ww8p/rohat are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as show,4-jwil rwjeig 5axl 2enm 5):n in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal foxl2j g:4wne5i,ai r)wlem j- 5rce 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 (2qrb4.xett g; ky bu.lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anlj+qb0s +0cp+lfd)z sj- :vgggle given its speed and radius of the-fc+jl gjs+q v) s0db0zp:+lg turn?

A girl is whirling a bgmx pp7a *b6 1z4,rsigall on a string around her head in a horizontal plane. She wants to let rp zg,m1b47s6*xgpiago at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitationrf* je9(1xi*q1kh;rd1 2h2b jhb cvog al force on the Earth? If so, how large a force? Conkhxh**doecg21b 12;hbrfj r (91 jvq isider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways2- sm0; ejzlycvt,*qx would the Moon’s orbit be diffeqzy2,- vs;lje*x0 tcmrent?

Which pulls harder gravitationally, the Earth on the z.pxs(-axmx/ - doy4b Moon, or the Moon on the Earth? Wxb-/ m y-x4d(soz.apxhich accelerates more?

The Sun's gravitational pull( r h0(ywat/dq on the Earth is much larger than the Moon's. Yet the Moon's a tq(wyd(/ 0hris mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effectsx gni4 1y)zi*f are at work? Do they oppose each othe fizyn4gix*)1r?

The gravitational force on the Moon 5 jdmr1:d0plcdue to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pc1j0p :rl5dm dulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around then4j0w o,.bnj b Sun larger or smaller than the centrinob .nj,wb40j petal acceleration of the Earth?

Would it require less speed to launch a 2 nm0e ,nh/kqbsatellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation,0m hbqnken2/ direction.

When will your apparent weight be the greatest, as measured by a scale in a mo2lk v;-xd5a0ylrs)u y. rtcg6ving rlty;d-5vlg0 yar.)k uxc6 2selevator: 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? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely 7ro1kfz5kkj z18u ll7 th0b.waffected 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 z rl08w1.71ho jkl 7f5uktzkbthis simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” be lzhu lp71f w:u/ jf( qi+;rua8dtx33gtween sq; p ai j:wuh3luz 71trff g+8/d(3lxuteps.

The Earth moves faster iou02p)sg, ffym m mhrtj8iet7/ , o2-rn its 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 tilt of the Earth’s axis relative to the plane of its orbit.]uhps j,m -t8trriyf)f 27g omo02/em,

The mass of Pluto was not known ;sxr5 lnf)l )ountil it was discovered to have a moon. Explain how this discovery enabllx5r))snf;ol ed an estimate of Pluto’s mass.

  The Sun's gravitational pul/vkp w b ukunak24t6w(vsw: 2:l on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Considek4: sp:ab2kwwtkv /uwuv 26(n r 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 1980y tgx*g(f (vo/ x* zt;jps+r0u $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbit around the Su64gp 2 .cbxptb4nmw 9zn, and the net force exerted on the Earth. What exerts this for. zw6gp4bcbmpt492n xce 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.dsmvaigo -v(1w a 5b6 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. Calcul( md-1avs .o6gi5wavbate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfaceqdt :4p;-(hchzmzr o6 o;/saj, 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 /hq-: sa ;rmjcopdz6;thz 4(o , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acj- ts8d9yg5grp c -x3kceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diajy ts 8ckxg-p5-gr9d 3meter is 32 cm?   

  A ball on the end of a string vqi :mal kjh9u iymn,) -q1iuu976m2yis revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. -uy:n)qm qa 99vuy mi2jkm7i6 h,lui1If 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 caq4c4wp: ak7rr e-r:esr 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? k7e:q4re r a4wr :cps-Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the zsfhg y-01)-sb oqrnmt0v9)ztires and the road if a car isbzg)s9ty)nzs -hf1 o00m- vrq to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauw7z:c - g:ilyfts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by thezcf7 :g:iwly- 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 bo3g xe,fw )wrlky.5( 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 ()ybgxwr k wef53l, .othe coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at orloqx524i i,thei,oqox rl i524 top 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) 38gh9omdwhna o0dk2ct7 1, pbcrosses the rounded top of a hill (radius 3bo t9mwg0 h,ad 2hoc87 1npdk =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 min5bm y.bs14 l uy5esos+ute would a 15-m-diameter Ferris wheel need to make for the passengersb+.slu 154yo5s meybs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled inj-i l+)t,hyeqg8w h.a a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting e8h.jqw)thi a-l ,y g+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 centrif ql8:) hpqw*bxuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelera: bqw*)8h qplxtion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a+i*.z7 mbd zaa cylindrically walled "room." (See Figdi z 7amazb*+.. 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 on a frictionley9y.pxt t- 0igss air-hockey tabletop, and is held in this orbit by a light cord gytp0 -i9tx.yconnected 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, by not ignoringk -s0p ; -vemflh/gw(b the weight of the ball which revolves on a string 0.600 m long. In particular,sbk -lv(g;0e/pw-mh f 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 /l b,uz1fu0 eugt2u(/pr4kshcar 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 masse+j*.hg jgox :a5l ;dcys $ 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 maneuvf4m2. ra::p (usxh.8evom jwuer by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compo gtpr 2r ,i vpth*xe.k,:(ih0lnents of the net force exerted on the car (by the 2vtriit, * ,e0hlkr (gp .hp:xground) 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 from2vvri5; (xwgx:5ueispdpjj59fj f: ) the pit area, going from rest to 320km/h in a semicirculapi) 5e(5i vr2 vjdf9xjjsgf:5w:xu ;pr arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of 2 1(uurfzp/3w:;0g5jhe v4 o imx dusmradius 2.90 m . At a particular instant, its acceleration vo(mzfmus ru3 4ei5/p:x;w0 uh1gjd2is 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 (g8h 1+(c+ eauquotxu/2 Earth radii) above the Earth’s surface if its mass htxaog(u81/eu++q c uis 1350 kg.   

  At the surface of a certai;fsikn0 / bp0rn planet, the gravitational acceleration g has a magnitu00;kbn spi/ rfde of 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 dx gjn*.coi +nhw lk-;(q6s::dq4:tylp ez t ,radius is 1.7sng-j,6k(:q o+cpe d*:tdyqnh ; z.t4lwx il :4 $\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 ofm9l)yixwdq0 ( Earth, but has the same mass. What is the acceleration due to grwqm 9()i yxdl0avity near its surface?   

  A hypothetical planet has a mass 1.66 tim b qvyf,(rwi(+2x hfys;fk22ges that of Earth, but the same radius. What is g kff(gs iwbr2f,hy2xq(+2 v y;near its surface?   

  Two objects attract each other gravitationally with a f- )akc 5n3bobeorce 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 acceler)5iwr7 k jdoi(ation of gravity, at (a) 3200 m o)7 dwi5(ik rj   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point out- zsds c;m1wn;side the Earth where thegravitational acc swc;;smn d1-zeleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron stari cbrp56 ay) sr20ebfv95bxr1 has five times the mass of our Sun packed into a sphere about 10 km in radiuf56sb2 0cx)byb1 5piraverr9 s. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun c.) ell b 6.ksg8e;jrettiezbu3ba 672ogi19 but is now in the last s.8g2it k9bro6 ie lecbj1l)e ze ;s6gb.3 tua7tage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spacv 6j3qgh.uf2ie shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculj hivu.qg362fating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locar;tx ay 6q-h;mted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted t;ry-axh6qm;on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of nq:3nw .t.3o n7y z4lctf 8frrthe planets line up on the same side of the Sun. Calcu3n7rf8tn.qr 3z4lnoyt w .:cf late 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 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 surface of Mars idp3.mv b* , b/*kkfyqis 0.38 of what it is on Earthb/dfkyp ,3m*k b.v*qi, 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 n9-uyeku65e vthe period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained u5veu 9yn -6euksing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving l*v1o9wbr z2vin a stable circular orbit about the Eart vrw2 l*bovz19h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km a1n 6/b ,ymrmmqbove the Earth. How fast must the shuttle be moving (relative to Earth) n/ym b1mrq6m ,when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceubq ,(0m kw47nfve q6uship rotate if occupants are to experience simulated gravity of 0.60 w,qn6f eq0v4u7k(ub mg? 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 satellit4ik o kk8;ht)we to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared h8kko) wi ;kt4to 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 frk/9fz4u/y ugvs t8p6d7 wbc.n om the top of Mt. Everest to be placed in a circular orbcn8/. ku7fgbuwz4t d96syv p/ it around the Earth?   

  During an Apollo lunar landing mission, the command module continued tl 4 )szq ybtf-pxj32(0uqjg+do orbit the Moon at an altitude of about 100 km. How long fbt p40g xj)u3l2qy- s(zjqd+ did it take to go around the Moon once?    s

  The rings of Saturn are dqd 1netk 9618kgl/jw composed of chunks of ice that orbit the planet. The inner ra k6g w9qnk1tdj81le/ ddius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in ,,*n r:ygq ck+1tvu7frr sp 1tdiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to hgyks*1,7urtrqtf:v r+, n 1pc er 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 t n+lh w8**u cjt)g3vgthe center of the Earth's Mow n+lg*8hgc ut )*tvj3on 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 stars oa)), snu: kamlf equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between thema: )k,slu m)an. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the;m2ez6 t; b*lsysj sn6/itz7t j-gxl6 weight of a 55-kg woman in an elevator that moves i s2gzt; / jjy-t6elnbx;mz*slt6 s67
(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 co4. qo8w zu,j:5bsp/4 sn* kxgeb(f qvard suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eqbe4b, 4z gs*5o kj:sp.x/ 8nqv(ufwalevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelqw81 j.s9p*utya5. (:vh yjidu(y wvjlite orbits very near the surface of a planet with period T , the deny8j puvt.( v(a*ud 5ywjiw91hy :s .jqsity (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 detj2/gqi21 jxg permine the period of an artificial satellite orbiting very near the Earth’s px/12jiqjgg 2 surface.    s

  The asteroid Icarus, though only a few hundred meterz/(5uluy- va cw6 7hgfs across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the S7/-fw z5uc ga6uvhl(yun?    $\times 10^{11}$

  Neptune is an average distance6u. v*crbb 5xz yl;j8uiw 9ue5 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 oneya +z5g-uv-;sby s 2yce 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 neares;+sz-sau v2 yyg5b- yet when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy +7 a07dojozfc0p-qeb $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 moo k44hfz 9kjr9bd fnzut:4f03sns of Jupiter (those discz9f dht 9f340z4nukjk:s fr 4bovered 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 ag vs b3-13ynrdnd distance of the Moon. b3s 3v rg-1dyn   $\times 10^{24}$

  Determine the mean distance m) ,x(4 qifdepe-w ma+from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the disx)d(m 4 + fpmqeie-,watance 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 Jupitc5b-.9ai ls bhf+8qprer consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but wc q8apshb+9-bl.ifr 5 as 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 uup k3x2-r: jk5lavm. artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is 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 apparevlk x:5-mp32jru ku.a nt 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 go- 3m l8lqdz7large by swinging 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 at the lowest point of his swing? His mass iladllz-3 8m7 qs 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be h:sarq2zctf h8ax14 m1 alf what it is on the surfacest:h8zq x 1m a2c4fr1a?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands nyg/orkh,r 1 8mq( r:mand spin in a mutual circle once every 2.5 s. If we assume thei8 /mmrkrr gy,o1h:(nq r 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 rotates once per day, the apparent acceleration of grae;79mmuu mqd-vity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate emqd7 -u;mu9mthe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelix; de h :+kpbq90(xjthng directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal a;eb:+ h9xkjp(xtd h0qnd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an e+)(;qmnh vz wgu h 3jzq z8n;*is9eed4levator; hnud +hgvie*(n q4 ;8)3zmw9 ezqjzs, 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 cs- c1v -chvo d(*s8p4ccqhp1 gircular 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 81d h*-c1hcv-gc4(s posp qcvrotation 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 n;d71n)u n *+ .4 mfncq0n8qsaulp foe(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 pukepfo (g 4.-e.jdhq0lanet in terms of its radius r, the acceleration due to gravity at its surfdfh 4(0g. eqek.j-up oace and the gravitational constant G.

A plumb bob (a mass m hanginwkg/)p,w, 4c - *v kgbmrs8gkug on a string) is deflected from the vertical by an angwg-sb gm,v *,48c/)wpkrkg ukle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of Ics9*6lwky u gm p/j;d3h-lzt0 f the coefficient of static friction is 0.30 (wet pavement), a*; w/kjpl9z0mdgult6- hsy3 ct what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were ro:/z c+qu,pcn :j kj*rntating so fast that objects at the equator were apparently weightless?+j:: /pnc,*ukcqn zr j    $\times 10^3$s

  Two equal-mass stars maintain a constant (jr1 fcgs2uj) 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 radiuszkmt5 1cr6* op+b4vwh 235 m. A lamp suspended from the ceiling swings cp6r51t*m4w v zhkbo+ out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as uq -: tljlm13-um0dqsmassive 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 Ju-jqd1m s-lu0mult : 3qpiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescopqa *(4ibw9c u kslv65x )uusc*e 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 gc l(ivc49u subu)k *sx*qwa65 as clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as(-6/ n,dgugt zovfp6(gk7 /zgek wdl bx :3nw8 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 heaviest? Lightest? Explain. 6ondfe6g3wg bkwxd: 7/(l t-(z 8,vzp/nukgg(c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili/5ud f(ve)zvk ,v)rxiq g(.avzes 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 each of six orbits, allowing continuous navigational “fixes.” The satellites o,vg/z(( qx ve5d .v)vfraik )urbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, 6 4y 0:rmwv/ozik) qnnix;.vois meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly k6vxo;0)z/v iyowmn nqi.:r 4 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 satelliterh 1zomh9 yc7(0mu,3wiceup: in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but phmuh1cuez7:rio w09 3,my (c25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance fv 4qa3dndx 6od,ju8 8irom the Suna8udq4,xvi 6dj3o 8dn?   
(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 wsp9c9xk b;:h0c u88q fjmte5u ould need to be if you could actually "feel" yourself gravitationally attracted touum8;:qbc5t p 8 0s efhxj9kc9 someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga*r 7qn +3o j56jkikwyz7pofg) pclj,4laxy (Fig. 5-46) at a distance qzfk)o,p* iyc5p rwl g73 jo7k4j+nj 6of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m kh+(l8 sqv)+q3jm 3v yd)zkdcon each side. Find the magnitude and direction of the gravitatiyj3h +(dsm zqq3kc)+vk 8lv)d onal 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 5504v eyc/wxzz8,8-t1 oxj4r 3o2qvik ks0 kg 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 experienced by the tip of the 1.5-cm-l;x x-- );igo2wq1 (nmnytvdlfg0 r8oih(izb.ong sweep second hand on your wristfr(- i8-gtmni)h(gdbn0lo.vixx2 1 wy z; ;qo watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wfwrfl /v kym5b.l+n1 3eight around in a circle below you on a 0.25-m piece of fishing line. The weight / .k5mnb3 flfwv1r ly+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 7-yle3 .xdmh ew0;o :9kekogda new highway is designed so that a car traveling ldhy 07mo wo.;9e:gk-edk3xe 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 negotiu ej gj.(-lqmz(m4ty- ating curves. The angle of tilt is adjusted so that the main forz-tjm4- e (u ylqjgm.(ce 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 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.$\approx$    $\times 10^2$