Sometimes people say that water is removed from clothey8emz 5d2f9ra s in a spin dryer by centrifugal force throwing the water outward. rf25zya89 mdeWhat is wrong with this statement?

Will the acceleration of a car be the same when the c sb ;ee 1f5ptoju,7kh*ar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explaine o7uks;jbt* 5p1f eh,.

Suppose a car moves at constant speed along a hilly road. Where does the car exw,p *a vs(dyr/ert the greatest and least force ,yvs (/rdpaw*s on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hor 7phwks.(i(my h af8k; 9sl,gcse on a merry-go-round. Which of these forces provides theykflh;sc. p9ag7mwih(8s k , ( centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withou j ,nd:wz2:rll+a (sgat the water spilling out, even at the top of the circle when the bucket is upside down. ,l :granad+:(ws zj2 lExplain.

How many “accelerators” 1lp1vgpx5vfmv: xkbf3n;3d vz- /n: jdo you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are thef3v;bjmnx 5lvp1- dvxz k:1 vfng3/p:y? What accelerations do they produce?

A child on a sled comes flying over 7oq2 ,drcyvs.the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease2yr.vs7d,co q using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high spv h2-av,ey*mwav j2i 2eed?

Why do airplanes bank when they turn? How would you compute the bankinghj )dp.r :jb *qxa6ts-8dws* m angle given iah*6 -ws.srtjq x*ddb:)m 8pj ts speed and radius of the turn?

A girl is whirling a ball/p1h;aur,ou.jm-k*ut zo g 3 l on a string around her head in a horizontal plane. She wants to let gou/kulu.,jz3pa o ; tor-*mhg 1 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 gravitatioml7 e1y)mwa+q8 twte8 nal force on the Earth? If so, how large a force? Consider aym l8q7t) w1eew8tma+n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wlhkm2 ). 9wolxp07i gzays would the Moon’s orbit be differkhl )w2 io7m.0l xzpg9ent?

Which pulls harder gravitationally, the Earthp, u.t 5li.gkq on the Moon, or the Moon on the Earth? Which accelpg qlu,.kt5. ierates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet rg . 3(hfxs1vhthe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the E xvh3.fg1( shrarth to the other.]

Will an object weigh mobe 9ph w88rg/c-pyzr7 ,plqw-re at the equator or at the poles? What two effects are at work? Do they oppo-y 8g b/qhw-7rez prpwp8cl9, se each other?

The gravitational force xffk 3+4sv2yrr 1vu 2t0skxn,on the Moon due to the Earth is only about half the force on the k0uxrvff21 y,s v ksrn3x2t +4Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around tdwnm8e j12te8uya. wf :4pp m.he Sun larger or smaller than the centripetal acceleration of the Earth?2p.8twemnfj m u.yep8 4dw 1:a

Would it require less speed to launch a satellite (a) toward the east or (b) to4oaw pt y+y f 1qng2/c*nv3i7fward the wes12ova f c+q7piyfny/ngtw4* 3t? Consider the Earth’s rotation direction.

When will your apparent weight nqct sxo95 v)nhd,nq( pj6b7e6p/j; rbe 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 upwar,/;hbq7 vnxc)n6 ( jpdsnet95jq por6d 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 per6o.bxfojh p*0rtz j/ 2 ;tvs4ziods 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 surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of grav/tp0*; f z2 zbsjrhxojo4vt6. ity you can think of.

Explain how a runner 6iog4 zk6+ 74w1s)2cicziwbb8lsmsqexperiences “free fall” or “apparent weightlessness” between step7c)qzb s 4l4gsz6m iwiwbcs 18i6+2oks.

The Earth moves faster in its orbit around the Sun in January than fds;qoe. 9 .pp+mj ae+ bu-lw)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 a dw)p+ -.m;euoeq.s9j+f l pbof the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have+ ck7,ky3e wdt a moon. Explain how this discoverkek 3 cw7d+,tyy enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thaa8 cbbxcftfm.v22:3i(l 3 bvvn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from onx2vb cc3 bvi83: ta.2(mb vflfe 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 x+gxdfq lex2 .:7;px i 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal accev vx90cxeu 7cg5ya4f9leration 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 thx 4va7x9c0u 9ygfv5cee 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 210u8qu59zg 8z lh(s8ipk N is exerted on a 2.0-kg discus as it rotates uniformly in a horizont 8 zspu8l9 q8kzui(5ghal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fr7n d-vawwk9j) om the Earth's surface, and circles the Earth about once every 9)w9knavjw 7- d0 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceler qlzh;u4f6v;sko; jf-ation of a speck of clay on the edge of a pottfjzf qk ;v;4-olus6h ;er’s wheel turning 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 in a vertical cir fgfud3c.+vsu ;o *733gd nsbicle of .3s ucongi;d*7g3fvb+ f3sdu radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of radiuqom(/o l1ovo)q*4 vfzs 77 m on a flat road if the coefficient of static friction between tires and rol1()fqoov/zv om4o q*ad is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of st7ibw6fb- u z6zatic friction be between the tires and the road if a car is to round a level curve of6-zwf6 bb7 zui radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desig: aw:tkgjfah (,d tuxu 29k.v3ned to rotate a trainee in a horizontal circle of radius 12.2,:f xjuk :vak at9g.du(3h wt0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of 6ie;kxq) ;,bj c4.k,fqhbkcpvariable 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 of,k)pec b cqixq;f6kb 4,khj;.f. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside )u kadcvat8nu,d iz l)uc8h.m-1dr )6down at the top of a , dvc))mza.u8d 6n -u daihl1t8kurc)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 rounded todbl*;fy5yr q/sav+ ,o.knx 7jp of axs /; lkqyaonrvjd+5,b f*7y. hill (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 p8g i2hbs0qa .yer minute would a 15-m-diameter Ferris wheel need to make for the pasgsb 2 a0h8q.yisengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirledpk ,4o/jm7 bvw in a vertical circle of radius 1.10 m. At thwm opv,k7bj4/ e lowest point of its motion the 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 particle 9.00 cm from the a7lwbjy u fgfm54lgf nj;bi z(j cv2b48 ::w.,exis of rotation is to experience an acceleration c8, ;bj54wg y: zf2:7guj(m.bfbv4lfnil jw eof 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatedag)x s)b - z9uz*ljzx3 in a cylindrically walled "room."9bu j*zzx3 x)as)-zlg (See 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 rp iyx,.wz6 s*zotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to y,sz6x.w iz p*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 ignoring the weight of the c oos)k0 3gw-pzgbe9w+6.lhs/jvmg; ball whic3 ovhs e/m.gkl+6ogw gp cjsz-9;0w)bh 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 perfectly banked for 2ja. y.gkxsa nj+;0cha 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 massesayqw,8, +o55ctwhtdo s7n 1wj $ 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 map) xkwz9si-kcn i wulx1.3p1;neuver 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 components of the net force eadr86eck mx46i t9d) oxerted on the car (by the ground) in dc8rt66o9mk 4eid)axExample 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, going fx 6mx7aoppl0sh4 i(b8rom 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, wha87 4 hiaxbo(p6s xm0lpt 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 or4 o38;o jlx.gxsbrz 7* qfg(tf radius 2.90 m . At a particular instan*3;x .g48o(ot7sb rgjf q xzlrt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force rm 3l0y rpwoh/:svj86f ys /f1of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) lj68 0/f wysp:rs1/3h oyvrfm above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a cz6 j4bkmx7/rzertain planet, the gravitational acceleration g has a magnitude of zkz/46 r mb7xj12 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 Moodwytq7 dd )no(2td f9f/e :cn.n. The Moon's radius is 1.74 w)q(td7nnf cyd.d9 / :2f oedt$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 c*u mo:s/k8tptimes that of Earth, but has the same mass. Whmcpt s* :/ouk8at is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,ry 8gq;+ :prhz but the same radius. What+8q hpry;gz r: is g near its surface?   

  Two objects attract each other g;9i3uoyu9quz1 a5ko 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 g , the acceleration of grbxe6r:ct,;6 ghg u6 :kcj* prqavity, at (a) 3200 m t g:6:erh6x*q6;kbpu jcg ,cr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsidff9rpk. pe (t.inf2 :xe the Earth where thegravitational 2f tk.pp:erxn( i.9ff acceleration due 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 Sun packed into36yzhh 5y/ u r0x9c lm:s4sh0 s8gv1acbau- jo a sphere about 10 km rxc lyjmhh: 1h0u5au0b8v sz- o43/ sga6yc9sin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average stax;xv su1: rqu.ry 4pv xbzd/:7r like our Sun but is now in the last sdx1 r.u: qyu7v ;/:px4xrvbsztage 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 th v vl.hv+8ge wln5 -)mnqv9k;je space 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 calculating the accelerajvv k-e)+mg 8 l;nw.vlhq5nv9tion 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 sidel 6wpb 03s72zjc6mc15z a/yh - smpxsc 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thrcwscm62/p cb a-pz50h6l 137x ssymjzee.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sit) 2 sr;sn/9yahlz y)mde of the Sun. Calculate the total force on the Earth due to Venuynl ); tsrh/smz 92y)as, 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 is 0.38 of wusbz1s*vo)k-g 1* rik hat it is on Earth, and that Mars’ radius is 3400 km, detk-*vr1us 1* ig )bsozkermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knaevnhw9t.;br25ve ;m ;w sst)i;ze.ium 4ip 3own value for the period of the Earth and its di se;.pwu ;iti;inv w24) ;tmsee9.5v3hb zamrstance 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 satellite moving in a stable circul6o i2mj0ac y;lar orbit about the Earth at a height of 3600oca ;jy 206mli km.    $\times 10^3$

  The space shuttle relea44fy (gkr vv-)br :fi1 ;w hzbsx;6ckxses a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occursfbsr(r;:vv f)z6gik4-k cw14h; xybx?    $\times 10^3$

  At what rate must a cylindrical spaceshiv9z 1fws+g.i mp rotate 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. (Sfs+9.wi1 zmvg ee Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the E:d a-wspyk 84bl+u8cun22pv oj9cdgvy5p0) yarth in a circular “near-Earth” orbit. A “near-Earth” orbit is one ) 9o8uvb y8cv2 ckjy5n 0ds2d y-pgp+ul4:wpaat a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be dq3d. 0akce ,elaunched from the top of Mt. Everest to be placed in a circular orbit ard3 acee.0q, kdound the Earth?   

  During an Apollo lunar landing mission, the command modulug c r.gkx5l7ruv c)t(l5 04z;gpyt: qe continued to orbit the Moon at an altitude of about 100 km. How long did it rgut:p5z0cy7)llx q. ;t4kruggcv(5take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. 7fbik h5(xr4ua0l)x otr3 z uruax/;1The inner radius of the rinu4/h)3x ub7;(a rx ix rolak051 rfztugs 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 s (4tc 9anc ei(gg3/j)uto. (fncsee Fig. 5–9). What is the ratio of a person’s apparent weigh c)/o a4t( cfg9ien3.g t(nujct to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from te/znx0i l8i;d he center of the Earth's Moon in a space vehicle (a) moving at constant velocitye liz x/i08d;n,     ----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 talle2 h 3q4ozhu;n5 q9n6f;n jwo stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth ynl zn4;faqj 5 lh;hueq32 9n6oears to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman /y j o5pr+zn.min an elevator that moves y/+njr opm z5.
(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 coudjt- hbt 0+vygn( 5o1rd 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 elevator’s minimum acceleration (magnib0+ nhjty(gvdu1-5 ot tude and direction)? a =   

Show that if a satellite orb k ,h iu098e4zm)gi g-0j(6ibw dtktiaits very near the surface of a planet with period T , the density (mass/volume) of the planetiim,8e9t4jd- k (k0ihiwz u)g6a 0tbg 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 th )k*;x) bzsgrhe Moon (27.4 d) to determine the period of an artificial satellite orbiting very nes; z k*x)ghrb)ar the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun o q+joo:8c(awv+/ 14y ytsgzblike the planets. Its period is 410 d. What is its1+yvo w8 y4az:(c qojb gs+to/ mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis0m2 s0e)8bckx lyw l4mtance 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 every 76 yearsy y,8sk b2v 9xf+icha1ye ickl 0me.:6. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest y8l 9h sk0ce bya1c2.+yxke:ifim,6 v distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center 0y,y+e1m.4cp boh bih of 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 distan8pwn n0q.jh1 fvaj.,s ce for the four largest moons of Jupiter (those dis,nq.v jsf0j. 8hw1n apcovered 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 distance2bt/sxx m 9t-9bw2-ukngdfi6 of the Moon. 2 9wx/mfib26bu9g -sktdn -t x   $\times 10^{24}$

  Determine the mean distance from Jupiter for each o sdg75 .(vr tx8jgu.kdf Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compj(.5 d.7sgd8tr g kuvxare 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 64l) axx l+vybhc vks6/9sy2-sxb,cpy3 k6 ggfragments (which some space scientists think came from a planet that once orbited thxl/bxlvy,xvk sk6s64p)6h c+sgbyc-3ya 29ge 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 f9 q s/,;pqp5 jj:pdacan artificial "planet" in the form of a band completely encirfqq,p:d j9 cp 5as/j;pcling 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 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-yruscl,rn:.g kdi:nf93 2bbil i, p ) gorge 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 hek, )p ls:.-dcyb fili: b nung9ri23,r can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of graviopkb94hix9,h3ws j qbz 53b- zty be half what it is on the 3,zq3b 9 hbbzjh9w-i sop45kx surface?    $\times 10^6$

  On an ice rink, two skaters of 01nc oqy4 yfc.7vz9cv equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume thycc1qo 4c0n7f .vz9v yeir 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 rotatesqt/8l2cgyuw,.hqid)ek7 i- c once per day, the apparent acceleration of gravity at the equator is slightly ltc kye.w 2l7q ,u/)cq8-idhgi ess 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 spacecrfn0tq:qs cb-)yj5( ;j ne+pgkaft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moy :q+c-0pqfk nj ();5jetgnbson pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in3sw7 j8 yuy,w u8jgmh6 an elevator, it says your mass is 82 kg. What is the8wg uh68jys mw3 u,jy7 acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboaq+ 6tk fhz;v1qcrge 5dk 24y+ut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per h k+1; efczq4qt+v2ga6dy5rk 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 fw;cxiu*hj0 a/o;jw2 (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 m, 6(2pv8mr8l zvnp+wuxw nzh7 ass of a planet in terms of its radius r, the acceleration due to gravity at its sun7z rvu8lh, n p vw2m6wp(+zx8rface and the gravitational constant G.

A plumb bob (a mass m hamljg6my. 0v,4k k,ryrwrb6n/ nging on a string) is deflected from the vertical by an angle y4 6r0jgkb6, k nvm.wyr,rml/ $\theta$ 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 9pecjk.ijez+n06eh om+u uq p/5ds 3. is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a capdmepz3uj /c+jk .un+q09 eseo5h6 .ir safely handle the curve?

  How long would a day be ifz0 zvl8*f )a-gd5cj zr the Earth were rotating so fast that objects at the equat rzj0-a*fd8 vzz5 gcl)or were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant disl)0i9 o;-hhm6khhl 5ncy9cgjtance 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 (m0frx xa8bvuk:ad79 rounds a curve of radius 235 m. A lamp suspended from the ceiu8x(f d90va rx7k: mabling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it h2m qhkg;4b7lgl n:x0 has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a pq 7h:lngk h4 0l;2mbgxlanet. 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 Hub48 vyjxlbqqq-l97 u *v2l b1yxble Space Telescope deduced the presence of an extremely massivubxlbl9 qvl7-yq *x48jv yq21e 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 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 xy ma6e,a is/1speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley haveas/ miyax1 ,6e 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. (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 savpa ,8rg b1hjf tg/.a/tellites orbiting the Earth. v/8phfr/a, gg1 b.t ajUsing “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 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 rmqlun+: r/d(2z wi/hRendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 4/z(2+ mdqr i:wrh/ul n0 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 *(q6ffvk us1q in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit ofsv16f uqf( qk* 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 yearsu)ygrt3 :.ei96s 98r bvl5 o(iewagrz. (a) What is its mean distance from eeg8 .obv9:3i96yr g wsz lrta)(rui5 the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the val uoy9vx 3ef)z;ue of G would need to be if you could actually "feel" youzoyx)9 3uve;frself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around wxko4c qc4drm2,u7j 6y 7d-ha the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center c74rwx6qj od4c m-a,huy 2kd7$ \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 sql3*+pze bgll.uare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of g b pll.e3l+*zthe square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth 6) a3lmnsyn5 q$ \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*d.gr8yisyo4c2)t o6jd ew )l ong sweep second hand on your wrist j.wyd2yo8g d *terlc)4 o6si)watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wejin (atrr1sj h.e8hm85sgm -y a cm:b/)q9ib0ight 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 with. mh1h (msrmseji9nc8aia50/y tj8 qb:g - )br the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwayzowq6:fpm+k+ bs m *6x is designed so that a car traveling at x *pbm6+q+ mwsko6f z: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 wzfb,gz1 s i4 :q(a8vvmhen 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 t1 vgfimqa sv8z,z (4b:rack 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.$\approx$    $\times 10^2$