Sometimes people say that water is removed from clothes in a spin dryer by centruqd rsgh;y91 7ifugal force throwing the water outward. What is wrong with this statement?rgd;9uhs71 y q

Will the acceleration of a car be the same when the car travels around a sh8y f q2:j+tfcu/ym5 g3az ahc:arp curve at a constant 60 km/h as when itcmcg+f:a2q aft58 u/hj zy:y3 travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along avwe 0 i.hszru; wak2)4 hilly road. Where does the car exert the greatest and lea0ra)4u s.e wizv;kwh2st forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on ydhg mtgwls3 h,a70 ;)c cic/8a merry-go-round. Which of these forces provides the cd hg8it ;cyw,l7 c a)h0/3sgmcentripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the watefq+/z5;jzc y y(wtl3 lr spilling out, even at the top of the circle when the 5 ltwfz;/ 3+yqy jlzc(bucket is upside down. Explain.

How many “accelerators”w i2cng .y u5 9em)c,9puar)du do 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 they? Werwpg,)nu yu .mia d5cc)992 uhat accelerations do they produce?

A child on a sled comes flying over the crest of.*jy iqd5n txec/j 8fx54mqb5 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 *xxj54 j ceq.5it5/qbydfn 8m the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding wvg46e)0lzkd a curve at high speed?

Why do airplanes bank when they turn? How woez;d(p+wb.i;, lbh pl uld you compute the banking angle given its s (piz ;.;e+l,hwd bblppeed and radius of the turn?

A girl is whirling a ball on a string around her h vo9xr2nix )o6ead 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. W2 n6vo9o)i xxrhen should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hoj x)cjy:i87 it(jn5xaw large a force? Consider (j xj)x:n y7ait ic8j5an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what r3bvoqrqn44 xv/u os(l+l))vit is, in what ways would the Moon’s orbit be disv )4rvooqubq+l)n v( 4/3lxrfferent?

Which pulls harder gravitationally, t7qu7hgy j)q a,he Earth on the Moon, or the Moon on the Earth? Which accelerates moru ghq7jaq)y ,7e?

The Sun's gravitational pull on the Earth is much larger 4f6036l ,:ujknxw dzsp:u tmnhqn9t /than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull frnfn:pq:kt63,ud 6 j/h9zxtlsm u0 w4nom one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whaf2 lak8/) uhyit two effects are at work? Do they opp/h yka)liu2f8 ose each other?

The gravitational force on the Moon due to the Earth is only about half the forco1 vk .yjk.mg(z.myo-3za n d964acdce on the Moczo. 9v6(4ad. dy c-j.oaym3nmzgkk1on due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratku:jt1 8edcm(j msz bj1* v8s6ion of Mars in its orbit around the Sun larger or smaller than the centrip8jm1ts js6jbu :me(v1dcz 8k *etal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towa.5jquf5y7l g y-z kd2zrd the east or (b) toward th qyk5dj. -g5z7yzfl2 ue west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest,z:2ifre a*+ po as measured by a scale in a moving elevate:rza*p fio +2or: 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 perio)z8 sf*e bjoc/ds 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 walk)zs8fbe*/o j cing 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 gravity you can think of.

Explain how a runner experienc9an me :03s;ag 7cmlz /inci8bes “free fall” or “apparent weightlessness” between;lin/i9e c sb7c:8ma03m gzan steps.

The Earth moves faster in its orbit aron2 3n e6kood6ca)6md nund 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 mai6nmck26d63d anno )e on factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discod,uxf l**qd0pqj2fkffq pg)gkx)75 )vered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mafg2*,)p5f ffjxq*kug))0 7dlk pxqqd ss.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Y ych(8zykv-le+4p5xv va *o n1et the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 +vo1-a8y5nhx kplv* ev(yz 4 cm 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 1 29;+inrvn fq2o vgw-y,.9lzb/muir7z j9n xe980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accea(o8 cr)1xqwy /pi0/x, da+zw9 ijpcqleration of the Earth in its orbit around the Sun, and the net force excw9j iyr) piq xz8p1/ dq/0,(+ aawxocerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus a8 u7bb xc;tk*ls it rotates uniformly in a horizontal circle (at arm’s ;tkuc x*b7l 8blength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eart:mi idad ycih+4zbvz t 1*3*w*h'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 of g , the gravitdmih aiy zi3* 4 z:vdct*1+b*wational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of3t4ujcxi opq)k3s(4y q.tf u * a potter’s wheel turning at 45 rpm c )s4433 upqiujfx* .ok qtyt((revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string i ly1-ewzb6dwfwof) 4 2s revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. I 4 of-1ldw)wy6f eb2zwf 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 5/tgb1iie g5.,sr zrd car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent/rg sd.b ii,tz5e 1g5r of the mass of the car?   

  How large must the coefficient of static fricpclr y ax6028stion be between the tires and the road if a slcy2 a0rp6x8 car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pwd ker8 q h+ *4+qcj-dwezv(2bilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fastj r8wdv e+qq+4(*hwk 2c bedz- 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 xjb13rr mb.q* the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction betwe mb*xr1.bjqr3 en the coin and the turntable?   

  At what minimum speed must a rollev4i:o3u wsx4c+t b u*:6topmt)) t xtqr coaster be traveling when upside down at the :it)p+ms3 ttqt4co* uwovx6 x)4tbu: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 th0y1n5 za)cdqhr 8cz qmjt+-,*h ssu v6e driver) crosses the rounded top of a hill (rac, 1ucq)+ m hzdz5h 8n*y06rqvt-as sjdius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferrkvs*) z(cfgo( ;h / 2tpc;pxfnis wheel need to make fsn2 (c/t ck()f*;px;gf zvoph or the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirle (vxas m*j1iq6d in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bu vx(qji ms16*acket 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 ax54osih-mhz6 x is of rotation is to experience h46 sh- iomzx5an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplzd m:zkj*g62te are rotated in a cylindrically walled "room." (See Fig. 5-35.dz6mjg:z* k2 t)
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 circlect gr 4/+by3 ryp+mch. on a frictionless air-hockey tabletop, and is held in this orbit by a light cord c.cg+y 4ry3h r/ btmp+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, by not iahj/f+6-iyvc gnoring the weight of the ball which revolves on a string 0.600 m long. In particular, finchva6 -+yfj/ id 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 isy1imdub cw+:)gq: t 6ak sgp25 perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massez3b:oh2o9o ud2 2dztls $ 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 vertg-mt6a0qkm(,u8 al.qqc +l txically 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 f a8(oi*y8fnd-sw yp)worce exerted on twofwa) (8y *n-y8ipdshe car (by the ground) 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 from tn4k f-bv5 v9bs(9iln0gwqn 0 ehe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration s05n(q0 b9gbnefw k4lv 9i-nvof 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 radius 2.90 m . At a h+jm xy)e * mn/kr0h6jparticular instant, its accelera)h6 /yk 0xr+nejmm*hj tion 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 m8 k 1)sv,qul 3zhoh3espacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass o3h3 uvsqezk 1)l,8mh is 1350 kg.   

  At the surface of a certainy,a kfk:v*n,d planet, the gravitational acceleration g has a magnitude of 12 my,: *fvkkd,na /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. *cnsi;q sj)4z The Moon's radius is 1.74qzi;c4j )nss* $\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 -wush)a(g8d7mo ,gofhas the same mass. What is the acceleration due to gravity neog )-um,8sa (7hwofgdar its surface?   

  A hypothetical planet has a mass 1.66 times that of w)n7oamiew) 0Earth, but the same radius. What is g near its suaowm0) n7w e)irface?   

  Two objects attract each other gravitationally wi0ahy(0*kbq vgth 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 smyv510r ums )dy o5y8of g , the acceleration of gravity, at (a) 3200 m rysm5d s85o )vu0ymy1    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cente 4gue7(nwbdtam ;em() r to a point outside the Earth where thegravitational acceleration due to the Earthm4) mt7gwd(;eub( n ea is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five ti lr:(dnq4 yzp-mes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this m(prlydqn 4-z:onster.    $\times10^12$

  A typical white-dwarf star, which once was an average star3qcoafr,h(pr8 hm7)pzo q3,a4 oaj ,,(x p omv like our Sun but is now in the last stage of its evolution, is the size of oujar8,p(v)3,,r3ax4 (qqoo mpa mo fchp o7h, zr Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feelwksgi z5c18i q(x7. vy weightless while orbiting in the space shuttle. Your friends re kzsg ii(.1 5ycvqwx87spond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners hqe+s.5z5dqic98:5e z rzp0dudts74ooix z4 of a square of side 0.60 m. Calculate the magnitude and direction of the totale pqz.ddzsto5 ezi5c5 o +u 8d 4qh4r9zs:x07i gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planp+ .v*nynd p;-xc ke3kets line up on the same side of the Sun. Calculate the total force on the * d ky+pevnc3-xkp .;nEarth 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 ofmj-ie r5wq +b, Mars is 0.38 of what it is on Earth, and that Mars’ raqwrmi ,+-5bejdius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the .be fy+ l5*jemknown value for the period of the Earth and its distance from the Sun. [Note: C*el.j5m +fbeyompare 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 cx6cfsg)- p mm2lzz (r6qrhq d2(sf7p.ircular orbit about the Earth at ad(frm2 qxss. mzfcpg 2zq( 67 6rplh)- height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abov7/nf t2 m+f(tqpcoq y/;7oqwke the Earth. How fast must the shuttle be moving (relative to E tyo/qt q w+fcm;nok7(q/2fp7arth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshixl g - 8jwiq6wzygpwhnsvb cn 5/bo12,32 (8zlp rotate if occupants are to experience simulatx5 8cbj1n/woqp2(l-g6w ,sw2zb3 zhviy8g l ned gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takesvda1a g46 3e(x rij s uli694 yq3kk4l-ftjae) for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellus3k je9q6l 6f(j ay1la4 i3vtd 4)-4iarekg xite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top ovi;22qy6uh y6wkdlg z;f p((-erv8 sxf Mt. 2gi(lu-rh;6 2kzs (qdyxfvpw 6e8;vyEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, tht9ym t *tm 3c,e.f.1ym3 bb*hokgc1 lve command module continued to orbit the Moon at an altitude of about yhg1e f b.mtcbvt 91.kl3o3, ym** ctm100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are cqpbf 7sr kwa-ek/ ijm;a ;5/3uomposed of chunks of ice that orbit the planet. The inner radius of the rings is 75-3jk kr uiba;q/s/a; mpe7wf 3,000 $\mathrm{~km}$ , 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 (see Fi8um7kbn(:;2 w5tzrncqcbss1p b ;:hig. 5–9). What is the ratio of a person’s apparent weight to her real wsqtbsz 7 1b:phuw 5:2imn c;(bn c;8rkeight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a0; nl(nplbhp , 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) hn n;l,(bppl 0moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They an0jtk*zy;tey r4:q6a re observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass ofe ytn*z ;0t64qk:yaj r each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an ezqjhd jm3 zv6 /b;s*6ylevator that moves m36qjh b6v /zzj*dsy;
(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 suspendyzz4okrkk 0+ 6ed from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acceor +zz kyk40k6lerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pe*txnj trhw )g)ozs,t0 8.+ mbbriod T , the density (mass/volum8gt.tt*m0 owh) , xj+zsrbn b)e) 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 /r; sgvs iuw-6bu. /jmperiod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Eart/6jm. sb-ur v ;us/iwgh’s surface.    s

  The asteroid Icarus, tg8brm);n(cvx hough only a few hundred meters across, orbits the Sun like the)mrxb( ;8 vgcn planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanceczem ldjq6 pdk54h8, wz*fq -+ 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 years. It comexdymn 84w vmw:51mv, mkw8wt ;s very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the ne1wm8m4mv;yv m5 kd8 wxn,t ww:arest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the jg7 s ;z;ww.z q4ylg+b9tw4yncenter 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 dii b9s03o1f va,1nbt 1ajaih1 xstance for the four largest moons ofv itiaa,0 1a31hs1 9bn1xbojf Jupiter (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 knowpq.. iqfc8np r +c8y2xhgfn7) ny 14/jdd klp(n period and distance of the Moon. p7+y p1 8cfkq xqcd2 .(ld hinjgnn y/84pf.)r   $\times 10^{24}$

  Determine the mean distanceo5d5zf1 k2 0zh;o oloc from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distan1 o ;fkz5c52h0doozloce 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 betweeng5iyy8 +u0fep5+ehe j Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was de8e+5 +uefyipehj0 y5gstroyed).
(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 au;e8+ 0qaa1 obkydv0akr)k /h 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 apparent gravity of g as on /qoh u;0ea+0k)dyak brv k81a Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge b p 3j-(2xpil:gvzeej2y 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 lpgz(j3:-e l2 2jpi evxowest 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 a d gbf8,8go1pytj4 )yfcceleration of gravity be half what it is on the surfacyf1g8p f,4ob dtjy8)g e?    $\times 10^6$

  On an ice rink, two skaters of equal maq0aqcn*m*kb,; ochomd3+w h )u zo 0quo +s29sss grab hands and spin in a mutual circle once every 2.5 s. If we assume thei02zc wo h)os+ d*0quhm3cu o 9 s+obqqnkm,a;*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 grxir4+/x,xg3j b hgn1v avity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this efn3hxxg bji, 4x+g 1v/rfect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will jrv *s xee: s. f:puch5c+ma/u mq03)ua spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forcu fq)+u p.* 5mh:jm:cv a/30s eexsruces?    $\times 10^8$

  You know your mass is 65 kg, but when aoo6isk 8z5 ;nyou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and inaik8s n;o5oz6 which direction?     ----待选择----upwartddown 

  A projected space station co54tf qq+;+dk x +7mmsjiq iu;wnsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per daywq5i+tqx 47+sm;fui+j; md qk) 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 azfp-do . e0et;;y ts*a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet djb2 *+z kik(sin terms of its radius r, the acceleration due tzkd(2bisj+k * o gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from)va*w-a lv5 q vfwksm+21 ,mbq the vertical by an v,ws v15a+v2k)-lfw mq ba mq*angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked 5 a4m/e4y 2qz6,c7 jci zscsjyfor a design speed of If the coefficient of static frics /5y,y zc744amje26q jzsicc tion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were0)y(j j+kitju7bg;h g rotating so fast that objects at the equator were apparently weightless?bjkj0(uhgg7j ty)+ ; i    $\times 10^3$s

  Two equal-mass stars maintain a constant distance ;z*oc0rpia t5apart 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 rounds6l(inc *pc5sqk* uv n.1x id2x a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.dixi1c. (qn*ukp 5s 6lv2xnc*5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mafuj-r 9;l/ wu+pzfgx9ssive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't 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 Jupgfpuwlrf 99x+/j u;-ziter: 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 Spaiiva;r3bdwq rb3dif384fe/, p zf6b/ce 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 clouds orbirvr3b,3b63dpf 4q df i i;eia8zfb w//ting 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 th 2/5jpfg xu1a+o,f7vx rgeeo3 e 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. (c) How fast can the car go without losing contact with the road at fv13jg +g oxrf5a p,u/ 7e2eoxA?

  The Navstar Global Positioning System (GPS) utilizes a group of8ln.bfo 7v z4s 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earthfzn8 4olv.bs7 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 Rendezvous (NEAR),d qw+*kn 7r(da after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros iq7 adk+r( w*nds 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 y n. /nwmqzbdu/,3x2s t+3fr pneed of repair. ywd3nr./np 3 t/ qfxzs2m,u+bYou are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a 2o d nu)eg m xb*rfh:*qn+7.cz)uu+et period of 3000 years. (a) What is its mean distance from the Sun? u*+xebc* + hnf7eztnr).q mgd2 ):ouu  
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could ajk:5 *i,9zjygviyo7: kjz4 xr ctually "feel" yourself gravitationally attracteik4jj9 ,yo z5v7r xgzi yjk::*d to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milka+kyi+y t5 sg7y Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ce+t5k+7 yga iysnter $ \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 az -: emhhgn5+w7med q/ square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass plqzg/ wn7-hd +e5meh:maced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 q3rr1e yz))2k t2uxmiig5+ zmkg 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 acceleraw)36ptxa cl .ga gpv8*tion experienced by the tip of the 1.5-cm-long sweep second hand on your wrist watch? pv*aggpw63 tl 8)xa. c   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ww4rp-732l i(xr8 puv ry ho,jaround 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 8x rrp,(lvw ryu-i 3oj2whp74 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 tf :oc d)ry4j ,aca2c9bhat a car traveling at spee aay9c, )bd:2ofj4crcd $ 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 Acei m:8ikvyg,9cpi3;idf v b0)ela, utilizes tilt of the cars when negotiating curves. The angle of 8vciyb pivi90idf;)emg,3:ktilt 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 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.$\approx$    $\times 10^2$