Sometimes people say that water is removed from clothes in a spin drdpiyxwiq(ly5ph 95q*+ b wx( r x7/mf(yer by centrifugal force throwing the water outward. What is wrong with t7 xd((9w5xpqilwyp+ 5rym(/ *qib xfhhis statement?

Will the acceleration of a car be the same who3.+kyb uip8p en the car travels around a sharp curve at a constant 60 km/h as when it travels around a gen3p.ou+ 8kpy ibtle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the c8d (jorou0gkyz-f 6g -ar exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch n(-8krdo0 yo-6ggfuz j ear the bottom of a hill?

Describe all the forces acting qiv9rxb )rj/ ;on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelervr;j /ixbq)9r ation of the child?

A bucket of water can be whirled in a vertical circle without the o 8drq zhbmg- mz- w-,u-c55ulwater spilling out, even at the top of the circle drb -,5 zm -z-uqg8-wohcl u5mwhen the bucket is upside down. Explain.

How many “acceleratorp.vz0 pn3v9e2c3pc v ob2x v)fs” 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? What accelerations dovp3 p2cvz x9.c0pf )b 3nvev2o they produce?

A child on a sled comes frra; py+4;a).g fr s 3mmvbe9mlying over 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. +9sm3byv;eg rr)fp4. mar am;Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hilr d o,vp5,x+bgh speed?

Why do airplanes bank when they3txt8,v sh3 fx turn? How would you compute the banking angle given its sp3sv8thf3x ,x teed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontk,2 *rm8rbx0fno3mw z zt u9.bal plane. She want9u03,z 8.k fmm nrwzot xr2*bbs to let go 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 gravitational force on the Earth+g,unc+ek 3iii8 l7zh? If so, how large a force? Consider zleui g3+ni 8i,h+ck7an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it4avq s(y f9j*l-ox6dz is, in what ways would the Moon’s orbit be d-fo* j aly4xvs 6z(9qdifferent?

Which pulls harder gravitationally, the Earth on the Moon, o6-i2r,sz uqjo* rj7r) jjj6l)w:bw ffr the Moon on the Earth? Which accelerou)s7 f liwjj z,wj6rrjj2)bqrf-*:6ates more?

The Sun's gravitational pull on the Earth ity 1y x hr;tkp,; +4euqqu8d-us much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravita;1+4 q ,ruq -udhyxytutkp 8e;tional pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pgoo:zf .bu 7t+i8 kzr/oles? What two effects are at work? Dt/u8 gziforbzo k.+:7o they oppose each other?

The gravitational force on the Moon due tgc 0 0.8+l4a xcctehhz v,4q2skl5m clo the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fromglh 4ml4zt.0cce 8a h2cs c5k0vl,x+q the Earth?

Is the centripetal acceleration of Mars in its orbitj 1t2g:ns:*3b w;a crx,brhsi around the Sun larger or smaller than the centripetahsti cxbgr3,2nwb :r1 ;:* sjal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) tebqpy+21 y pm2oward the west? Consider the Earth’s rotation directp2 em2y1p+ qbyion.

When will your apparent weight be the greatest,qn-1 jfep:+q t as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In whip q+1j-q t:enfch 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 adverw9 z u)5b s,,lvxpyss5sely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that )l9 vsywps, u5z x,sb5rotates, 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 gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betweez:5u brr3 k:xen uxe:b: rr3k5z steps.

The Earth moves faster in its orbit around the Sa0.jy3*fx k 5nc zo;uuun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much oz3 .0c*nuk f5xaoj;uyf a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was ner hyj+*g45bjau(; h /ptquy 8ot known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s e;8 y*tb (hj5pyuag+ hruq4 j/mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tk1jk 8ct0ebv29+lgzpqb.j/ hhe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center 08/l2hp.cjzg t9bq vkb+ek1jof 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 lm( ;j)ph mq yryls51yic-+ *c 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 acceleration of the Earth in its orbit around thecaw9g1(v+k k j Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbitj 9cg kv1kw+(a 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 as it rotates unifor;; shpmjd ,f1mmly in a horizontal circle (at arm’s length) of radius 0.90 m. Cal;dps mfhm j1;,culate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's su1eipa5zmw s(*b+l-pr. 4 gsg erface, 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 gravitational acceleration at the Earth's surfea m (5 bes+l4r1gg-zipsp .*wace. $\approx$    g

  What is the magnitude of the acceleration of a speck of cx9y:zp f2-dcv lay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dy -vcf2x:z9p diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verh)s* /r3hoe g1u3y kmvtical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp*e1k m3h/3survyo) hgeed 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 v9okaoo0nf * y58d uo4can round a turn of radius 77 m on a flat road if the coefficie o9uk* vf4no0oda 8oy5nt of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient2qw(l:pzs 2 +espl( yv of static friction be between the tires and the road if a car ie+vzy22((qls :slp pws to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet f+g37 5gpe0 c.y3tilgzcp uj,highter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weige cc70uh3yzgpj. ig+tg3p,l 5ht, 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 ttw8+,0yrgy pp if i y*2 *ofhci8j+n2ihe 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 the coin and the0 j fici* yi+2tg+woyp8 ,pr *ynf8h2i turntable?   

  At what minimum speed must a roller coaster be 0 2zk(vbzt g+bgobwmm .2k+v. od) n-0csgza/traveling when upside down at the top od0v-2g+.bz. c(obk/ z+ b) gwzmo02gastmv knf 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 th ef.)mc 2(lpype driver) crosses the rounded top of a hill (radius =95ecl)f(pm2 p. y$ \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 minuteozqvump- azvd6i4j9 qd ya667ca2 .e5 would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmosaqa65dq 9676 juz2zdveo imc.-v a4ypt point?    rpm

  A bucket of mass 2.00 kg is whirled in a verti kz)1ve7l *li:lm5nbccal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportingblz)iklcel5mn*: 1v 7 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 axis of e(vg9g3lgrb+6t,gc5s ;p w mf rotation is to experience an acceleration of 115,00l,gv9c gb gr ;gp3+ftw 5e(6sm0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival,54dx dxw2bm .v 1fkhvu/.kbq 0f be64d people are rotated in a cylindrically walled "r qbuv4dd2/. kfh x 1fme. xdw4kv56b0boom." (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 rotated42q/f6mqdap;+dipgv p g. y o6 in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through amq/2ygpv 6;pi4pg.d f+doa 6q 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 , preca4kf.ecek6lpc u/s6 z.yck7 fg0 k12 uisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In parti/pk2 kc c1.uez6y fega407 6kfcl.kus cular, 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 perfectlc xh6ku 9hfb*;y banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses 2b k4umgd:hoc7i +c1e$ 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 divingsp+75txxhtkj rxq xy7xm*3 )b,v b*h0 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 ne vk9, 5arexg4q34jspl4tlmnd4 p73vw t force exerted on the car (by the ground) in Examplelnxmke74,p5g4pv 4t3 j4 a3q wrsd lv9 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 d8c/a( x,wvdithe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assu i8/c ax,wd(vdming 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 . Atb*2atdu 2wwc43fn vp7jfe gdx7p .)i 1 a particular instant, itsg7 fu nd 7dwe)apwj vf1p*.tic23 2x4b acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 0x:u)j vlq9lu9) n tqdEarth radii) above the Earth’s surface if its mass is 1350 kg. 9vuju0q) xt )l:qln d9  

  At the surface of a certain planet, the gravitational acceleration g dji)x7j6 -h 4rp2cqs;tqu eg3has a magnitude of 12 m x6i7ursh q3c jgq-dp4;2te)j /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 grav i8bark,b+kj2ity on the Moon. The Moon's radius is 1.74 a2 8bji+k kbr,$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5: ni ulkm d,qrxn;9fq h*)6o-v times that of Earth, but has the same mass. What is the acceleration )urh x*vlmo9k-6 ;qqn,f n:didue to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samegyekd t d7udn f)s 3zpk+p/w,nfq5+, 4 radius. Wpu4q,fe,ngfdydk) d p +k 3ztn/w5s+7hat is g near its surface?   

  Two objects attract each other gravitationally with j1 qn);zu;q jga1p/r1petac, 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 gravity, at (a) )amgzge 5q(hchr tfv 20-/f.o3200 m a/hg mqtfzc e v(f05ho.gr )-2   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center 9vn2k o4ac5bl to a point outside the Earth where thegravitational accelerc492vb ko5alnation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times jbn(n(d)vatgq1b ; :u*bp z+xthe mass of our Sun packed into a sphere about 1+ np1 v*xq;a(: bjtb)gudbzn (0 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun burb p3wt0o9-fehp 6mwir ep2 0l;n3 ue-t is now in the last stage of its evolution, h 3e-2eeun 9 0f6wppop r0-;btwimr 3lis 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 astrongjaq noglg:q p* ft2i+e3y13- jyn14dauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t sonltqaj fji+ydg1 1:gn-pq2g34 *y e3 o by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Cal2q gg1;5ys edcculate the magnitude and direction of the total gravitational force exerted on one sphere by the other t5yeg;sd 12qcg hree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line upyr3:x; rph.xc on the same side of the Sun. Calculate the total fohx ;yp cr3rx.:rce 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 is fjmzlq2 236y-x:ob+l,e jyj x0.38 of what it isx2x j2jjyll3qy+eob f-m:,z 6 on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earl vdsib *s*3zhl 3.b9qjfp;3zth and its distance from the Sun. [Note: Compare your answer to that obta.;is j3lpzd3f3z *qb*vlbh s9 ined using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in ajerf-x /j;a*t stable circular orbit about the Earth at a height of 3600 kmj/fea x j*;tr-.    $\times 10^3$

  The space shuttle releases a .es/;3 yuiqrwou s9d/satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the ry;u/rsqs93 ew.iudo/elease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to exo9c51zmcg b*sv5i 0h0 oo,e zaperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your mzc i1z9 vc* g 00aosh,o55eboanswer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a4jp fke5l38j g 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 toj45fk3 p8g jel 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 f1/gavb0l ll*orom the top of Mt. Everest to be placed in a circular orbit around the Ela/b0llg*1v oarth?   

  During an Apollo lunar landing mission, the d(+j og1-qp;o jgc+bv( exz:h command module continued to orbit the Mv p o+czoh -; 1g(jg:+xqdb(ejoon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice . 4vbiw/1 ekmxthat orbit the planet. The inner radius of the rings is 7ebmw.41 k vx/i3,000 $\mathrm{~km}$ , 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 mj1 jq7e:v +r 0ox xs6:0wojfm2/ yjnj(see Fig. 5–9). What is the ratio of a person’s app o2jjm:x+ 0o7w/jeyjr s0x 6qnj:f1mvarent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weighrcsmrgmrqg 1; rzf5);e) .sw *t of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, r5f. ;;zgr rs))c m1segm*r wq    ----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-stara+, bb(qu;t+tur. z am system consists of two stars of equal mass. They are observed to be separated by atbrum(z+b+q .ta ,u; 360 million km and take 5.7 Earth years 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 weigh6om)qwzwm0ljqsx 6;c wn d9 .r-, 5krmt of a 55-kg woman in an elevator that moves ljnx wco6q mm- mws)z,r5 .kr 09;qw6d
(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 suspendno+t pz .0toim(lj6;cp r;zf4n2m3jged 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 minimf;trm6mcpnj0 nloip 3z;t( g 4oj.+ z2um acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a4db zxpr8/vra yvi 58vc(ae18 planet with period T , the density (mass/volume) of the planet i1eavc a8(brzy i8r8v5x 4vp/ds $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period.+l-9(q zjgcnsqnfe+ ,n u*g/hx- xa b of an artificial satellite orbiting very near bshj*gaq.- ++ qfu9nz n-,/nlxg( cxe the Earth’s surface.    s

  The asteroid Icarus, though only a h0h lcgi;zk6 2rn)pj+ )odkmz4) juo(few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from m) nr oj(k)2d6ohh;zligpzj4+ uk0c)the Sun?    $\times 10^{11}$

  Neptune is an average d pkhd;t mq(blt*si: s2tw/o03istance 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 comes very close tcyoe7f 4b4rp xk6u6ng4 5arna 2u0c5oo 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 Sac g5rn o7 knf4 eoubyrp 5662acu0x44ystem? 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 cent22xlbyp9/mqse-xp,f l5e mk:er 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, an-0 mm8,pv xwvci sqxw)z-4i .ud mean distance for the four largest moons of Jupivx cuv-m)x qw i,.w4pz8i0sm -ter (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 k ioof 4,epq/v)bf b20mnown period and distance of the Moon. v/f q e)mpb if24ob0o,   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupit* t-xdy r*2tfeer’s moons, using Kepler’s third law. Use the distance of Io and the periods yt*-etd x* r2fgiven in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frawt yh,x5ur1 ui ro.s, zf/9v(xgments (which some space scientists think came from a planet tt.,/i ru uz5rhsvw o,x9yfx(1hat once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the fowm3t5s,we:2wgcz78o/ed n/ vvhn g;g rm 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 7h/ esgwwzm /g;evw,g32:dnv8tc5on the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. ;wxgx34ahq)d1/bl c s 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what al;4cxx1d g/ wq)sh3b is the maximum speed he 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 kad+* ga4 +6sozjead7 acceleration of gravity be half what it is on 4adza+joda6 s* gk 7+ethe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in apm b x*r0ybz4ziw3omt6uuj:7 bt ) (/e mutual circle xbpzjw my7m3t46u* t(o e:bbr i/0u)zonce every 2.5 s. If we assume their 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 gravityqua0n3 e6dsw : at the equator is 3nw qd6s a0eu:slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraq-bk m58h.)e0z lwxp6k rmp(u ft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces)-kmx580l m 6p (hk. qrpuwezb?    $\times 10^8$

  You know your mass is 65 kg, bu4/)fyk0+4l -, n p8ksynmoxell hu0c qt when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceler04l 0efm kp+k )qh l s4nn-8olu,xycy/ation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that willn aw,3. x.4wms p(cwiu rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circlp4w(icnw3ms w.u.xa ,e formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43).bt*ks(v;4g6:sh zjhb
(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 in terms of its radius r, tgj(1qvmme5i0 r:cx i .he acceleration due to gravity at its surface and the gravitational (e5q. v:gc riimm1jx0 constant G.

A plumb bob (a mass m hava:w2sa t +j5inging on a string) is deflected from the vertical by an angls2t :5ajia+ wve $\theta$ 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 speed8w8cis .t2k fusd; v2 sf-t*oi2l r9qc of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safe t9 s2;.ifowsl-ivucfkr 2qst2*8 d8c ly handle the curve?

  How long would a day be wx)m,t8 u ,li dad66tjtokcd/-zv- y :if the Earth were rotating so fast that objects at the equator t dtw y,xia-vdt : kocm l,z/u)86d6j-were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constc u kke ue*r4m35s9 *qpl:xkglhx759bant 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 round0 .s26*p/.phtcw6uod v, vcz ss 9eifxs a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 1s2h wu .v9c,ps/p6fxt.iec6 *z vs0o d7.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eawn0 hza7dgo,jix/l 6(6dcz .zrth. 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 /6o7lzz j h.a60dz ,(gnwxc difor Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremub,c 9 3 6x s7lqoqoc8l-(ebunely 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 orbiting the c,lb3-s n96 bc7qxc8loo ( euquore 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 theun b:9w/wln9 ipl /ut5 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 drivei ll/9w/ptnbun:u 59 wr 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 s1za 3ws;6b2. qcwn59cbd gk asatellites 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 sat3 wq9 bn a2k;wd6bc.s casg15zellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, es2cw4c 7dr d*is meant to orbit the asteroid Eros at a heighed*d7 2 s4wccrt of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in neenz; /*i; w-bhtys0w ued of repair. You are in a circular orbit of the same radius as thbez swn-yhwi * t;/u;0e satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is b 7 xa(erhdsv a.19n bsn/-u7hits mean distance from the Subv7nx1 r-as7/(eunb ha. dsh9n?   
(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 actually "fedncp z)or9nvy +)5z6bel" yourself gravitationally6vzcyb5+o np)9)ndzr attracted to 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 Galaxy (Fig. 5-46) at a distez c i1v14ms5gance of about 30,000 light-years from the center g mz 1svie451c$ \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 on+os2p8on/q corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass plaoonsnq/o +28 pced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits2( ees b(mc,ys 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-long s*tv) xfpqbz t ok909s+imriu6 )jt;9iweep second hand on) zktqi ;urx0 tb9miv699po stj) f*+i your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinusqg1mo i-fszs *q9+ 7ker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the a-u1 qs*zig+79s fsqmongle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius s5. y 9:dugtvsR in a new highway is designed so that a car traveling: y9us.d vg5st 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 whe ;/rttahd2b ar3,i,x jtlq h*.n 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 friction3 ,;qalht2xrh i*tt ,a.b/djr 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.$\approx$    $\times 10^2$