Sometimes people say that water is removed from clothes i45 wbbvcyhhg.:(bof6n a spin dryer by centrifugal force throwiny 4 h(.b hgfwbvocb65:g the water outward. What is wrong with this statement?

Will the acceleration of a car be nf6)ag0f.kxv 6 i+ni ie3zx; qthe same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle cuv6iz)a+k6niixg .n3; exq f f0rve at the same speed? Explain.

Suppose a car moves at constant speed alo/ldbjve+/ f*w+ev *mw ng a hilly road. Where does the car exert the gre+ wvebjd /**m/wlfv+ eatest 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 near the bottom of a hill?

Describe all the forces acting :ancr9e yf) p3on a child riding a horse on a merry-go-round. Which of these)9:a p3rfc yne forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cirto *qp35ur 6nxcle without the water spilling out, even at the top of the circle when the bucq*n 6trp3oux5 ket is upside down. Explain.

How many “accelerators” do you hav 7yylydt5s4c0e in your car? There are at least three controls in the car whiyyct5s 7 04dlych can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shownhfl0abp*5qgjlvau: 7 ;w 6/q q in Fig. 5–31. His sled does not /*qq hu7gap ;fqajl0 v6b: wl5leave 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 decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speeo , qm9cp3unj.d?

Why do airplanes bank when they turn? Hoa o8v7zd)..yagwy gi48k;z p ld7n-efw would you compute the banking angle given its speed and radd wnf d8) .48zgpy-z7ka vyegi .al;o7ius of the turn?

A girl is whirling a ball on a string around her head xz4zry ;;+gdjin 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 ojrd; z;gx4 +zyf the yard. When should she let go of the string?

Does an apple exert a gravitatioo6*yhh6)lql0 ru a +ttnal force on the Earth? If so, how large a force? Consider an applh0ly 6tuot+q6*a )l hre
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s or95ak:wvvdv 5lbit be differeak55 lv9vvd w:nt?

Which pulls harder gravitatirbb dbde 9 */fy6t1z8jonally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more6 rzt*b9fjdd/ bb81 ey?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet fy*n 2e1(u gzuthe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull y2*g1(nfeuu z from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? W1*gag8e jchj5 5 e2)k0 5/m bbrkqgnschat two effects are at work?k21)5 g8g jb barq/mc 55h*e0k necgjs Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the l-)2zhw4jobyu4 6cw4o /66uqqitxy b force on the Moon due to the j4l)xyo6woh6qiwu-ub6 zb42t c4 q /ySun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars ,ckx.h 043d ntedgf+y in its orbit around the Sun larger or smaller tha+ x 0d3gtfykced. ,4hnn the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towar+0b)bytb *y eqd the east or (b) toward the west? Consider the Earth’s rotation direte )bbb+qyy*0 ction.

When will your apparent weight be the greatest, as measured by a scale in a:-(*i-u m7 mj za ejp,lkul)tq moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? Inj7ze-) j k:lu -t*,(mlpiam qu which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods i:ckhaxcp w y3ic:u ;w/3bkd .)n outer space could be adversely affected by weightlessness. One way to simulate gravity ic:;c.kc ak/)uhwd yb3: wxp3is 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 gravity you can think of.

Explain how a runner experien 8 fe;itc eiog(;)wo;dmh 5x22 2kycdr r/gg(aces “free fall” or “apparent weightlessness” between mk g((d;x2h; re co )frgdcygwi8/i t5ae;22osteps.

The Earth moves faster in its orbit around the Sun in January than jn4v:4rfsbvcq(b ((; sl0ujz in July. Is the Earth closer to the Sun in January, or in July? Explain. [;s ub(rzjv l(:0q (fjsbv4nc4Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knowd1wt9 a;:pb(0vj e- itq kaa4ln until it was discovered to have a moon. Explain h(;v4-0dlik q ab9awta pej:t1ow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is)2ia 5cz .xz83vyzdna much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to t3c) .zda xzn285 vizayhe 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 1980( qxg7 h5/2 e-;vm42z1lu uudhhjgfe b $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ot3u +ljr ocq:qa4 f3c2 /vilw*rbit around the Sun, and the net force exertedcqvjl to*l:fc/2q+3 a4iu3r w 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. 13lggpjq1* pg0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 01gjgp1 pqg *3l.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is ins1wpr(i l8g pvh+,v ;taam r.6 orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes.w mls ,pg;8va1a6 v.r(pr+hit 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 acceleration of a speck of clay on thed.7tr86 qh; -wjiya cj edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is ci76j hqt8;w- ajdy.r 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cir( 6it4plewgv b*m,5 kkcle of radl ,t mpge*(k5v 6wi4kbius 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 -99 pf8pmb9k1jei w lican round a turn of radius 77 m on a flat road if the coefficient wmp8bj99i kf-9lipe 1of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tirgz.nek0)t4 efeyqfk1urf/ *9c b9.ka es and the road if a car is to round a level curve of radius 85 m at a speed of 95km/fze)0n9.*ga f.k e 4ftqyb/krk 91uech ?   

  A device for training astronauts and jet fighter pilots is designed to .a/c x4 b /0mum7 wym.8kexfksrotate a trainee in a horizontal circle of radius 12.0 m . If the force fel7x4uemkfmcy0 8//skm bxa. w.t 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 afg-vzeb70m q+ rotating turntable of variable speed. When the speed 0egz7fmqb v -+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 the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at the-u 2*b,emawzoym;. gp top ofoy zp,m g-we;bu 2a*m. 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 (ig;+cdoxb l.+j ncluding the driver) crosses the rounded top of a hill (rg;o.j d xlc++badius =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 min;nk g72zfe mltn7 n.1vute would a 15-m-diameter Ferris wheel need to make f; 1n2g.tmnn lk7 ev7zfor the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle +im65cg:j ft)hi jj y*of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bu mg fyhi*5:c i+j6jj)tcket 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 fro8k;yrpz u2* yqd*x 5kkm the axis of rotation is to experience an acceleration of **dzx 8kkyry5qk pu2;115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled y x ssc85ect/x4 cklz(4* ay,k"room." (See Fig. 5-35x 4kc*x/8ka y5 c4(ytcsl zs,e.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tvnl+j2 mvpk5*abletop, and is heln+lvmkv2 p*5jd in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely t i mndc huo-4x 3b;aee,b 86* 5llls;z,pjmu2nhis time, by not ignoring the weight of the ball which revolves on a string 0.600 m lon5ix4;snpu8mb;- 36*2o l,l lhbucaezd m,j eng. 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 a car trave8 oni(( hoo.jeeilus 8 b)42)ohx+rvcling 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 massesxpg:i 7 y zfu-iv j;j8t48cv:o $ 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 vertically at 3 m8+ yg gt.ti1jtxsb1(10 $\mathrm{~m} / \mathrm{s}$ . 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 exerl.lmzc zw3:p3ted on the car (by the ground) in Example 5-8 when its spwzc l:3 mz3.pleed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapo( nez qww1;yikkmdq0twr: fx+*+n( e.lis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car whe+dk.m1yxwfq(+wnt( :*0reke z iq;w nn 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 radiuh66xl(ecl;18os ygr gs 2.90 m . At a particular instant, ith1(;g6yl c8x eos 6lrgs 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 ongol 6cxc2yd 06 a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1352l66gcdcxo0y 0 kg.   

  At the surface of a certain planet, the gravitational acceleration g has abq) cp70woa(8- yt/nen a 9qky8k; gmz magnitude of 12 t8a g8;ya)ynbwco7mp kkzq/0 e9-n( qm/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.vcmz.ht,zxj0mg9 s3,,/nte r The Moon's radius is 1.7mg, .thsn9z ,zx 3jvtmcer0/,4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tim p-.7tke e5yde9rcg.zes that of Earth, but has the same mass. Wh e r5-p k.ce7t.gde9zyat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the s19ybh2i qcb 0:de mpfqyp*f db, /3d(wame radius. What is g near its surface? 2bmd9i/ep*cdyb3h1,w bq p:(yf0qfd   

  Two objects attract each other gravitationally with a force ofo4v +tph 8k )fkk9gp.9lp:y ll 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 g.fh +t5np0 lpzravity, at (a) 3200 m. f+05lzntp ph    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside l xmgzlb+0ii8uf:79i1b7w . o; oyelpthe Earth where thegravitational acceleration du0: g lb. b1iuley7m8;pfoxi ozlwi79+ e 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 into sw-3gx49db,h q/+ol k6fzezla sphere about 10 km in radius. Estimate the surface gravity on this monste -6 x 9qkz,bz+4l /sdfwhe3glor.    $\times10^12$

  A typical white-dwarf star, which olifcvijw/ 8jtvq/, +7nce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity onqj/jv wi8,cf/ l 7vi+t this star?    $\times 10^7$

  You are explaining why astronauq, iqmptiy 275ts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince theq,y5 i2ipmtq7 m and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.e *v0-fps:ioz60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othe*szfpo- ie:v 0r three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years06v a ; ute-ti0(ri srz/njw-y most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, w-/ 0ret zr ;ainyj-06sutv (iand 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 ofk4ji*4lh2 wl0-p abhn what it is on Earth, and that Mars’ rahjk4hai*n0lpl b w42 -dius 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 daqzr j2p24bbe:)pf 8Earth and its distanbjqb :)2aedpzr24f8p ce 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 circular orbit about thejky q .mvto *pv15q (2iqhdnx5l3+r+i Earth at a height of 3600 kr12i .v5+3o(xk+hndtqyi*vlq qm5pj m.    $\times 10^3$

  The space shuttle releases a satellite into a circular l9v tpp3g ,zfpc03s*f orbit 650 km above the Earth. How fast must sf9lfgppz v 3p0c*3t,the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatbl9c. s4;g ;u0,xq ggcom-zwp e 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 onzu0m.lc wo gcg,9qg;4bp xs-; e revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes foi7ci+l9 yhgq 1r 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 9c lg+y1hii7q of the satellite?    s ~    min

  At what horizontal velocity would a satellite have z3tidt ;.w0fe8z br/ hto be launched from the top of Mt. Everest toiwed3t;/8f.tb z rhz0 be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit vxgjt ;2pu b py5,:k)lthe Moon at an ajlu)tx kg2bvp,y : p;5ltitude 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 that orbit thevgsdx*:y n5fmgp(5++ ky -wdo planet. The inner radius of the rin:sv* -mxf o+k 5 5gdnpyy+dg(wgs 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 jze4rkdja*f 6.klj,0diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a0 j6l,adj 4zj*er kfk. person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weigdlscd9j2c m,30qw 4kg)(aj ceht of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) dlqcj4s,0 a wd jcg32m)9cek( moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consis402i:j 2oi nv.q0ip* jw 7jkttwdzuk,ts of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each? ,pqt:.ijdnjk 7iw to02j wu02i4 zkv*    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an eled45(5 ioznegg vator that moves gzei5nd (go54
(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 cori )+rwd*2ikp wd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as ti+ ip2k*)wd rwhe elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very neu7y:hqy ci55. bg k cdz,8 vxq7-s)uxhar the surface of a planet with period T , the density (mass/vol b5x:svqiguc yh8d7yx.q7kz )uhc, -5ume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to ybt/ q )w)( m3pg(gsqndetermine the period of an artgybq ))s( 3n(tmw /qpgificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mettxtk uy s1h+/wwrh-;.)b:ijo ers across, orbits the Sun like the planets. Its period is 410 dyr.;sb jh o+wit w/t)h1-x uk:. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance mm83;v.jph kvof 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 9,mc mjqfn+(c comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still n,c m9c(q fjm+“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 cezg8grr v t *5*ri3:an7iwium7nter 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, perio7mb1m7n1f brd1+c mx hd, and mean distance for the four largest moons of Jupiter (those discovered by Gal 7b11n7m dc+bmhx1rm fileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of1ai qnlb s1x5k 8 l:r2nue(g/m (ni1vs the Moon. v8( ial1kmuq:1nn egs2n l(irx5 /bs1   $\times 10^{24}$

  Determine the mean distance from Jupiter for( 9b5zx dldsex:+lwke760jq p each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the peq0jx xds5deewb + k96(l7lzp:riods 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 betni7bvx ojo5fu./ sf ac+2qwe/5eak/fpz3 a 41ween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbitedf o./ 7ebo/ sf ef ni2u1awvzaa/q535c +jk4xp the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a b:2c.jyw8ca;;kl uwlzv 0 tf/gand 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 Earth. kwwta.c2 ;0ly:jvfz8 l g;/cuWhat 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 qg w 0jo,1vy(c(Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maxc0 (oq, vjygw1imum 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 wovmo .6) dff+will the acceleration of gravity be half what it is o.+ d fovo6w)fmn the surface?    $\times 10^6$

  On an ice rink, two skatexl xcw3hv lr.* *k( seof5y.g0rs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indivi v(lok3crw x xs *yl*5e.0hg.fdual 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 gravity a *lpa4r p,xn :w2vgu g5-c(wyet the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. 4a2ewvp (r-:glpg *ncyw,x5uWhat fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eas;ny 0vp2o49qb 4dtyxrth will a spacecraft traveling directly from the Earth to the Moon experience zero net 0d;o y s4pyv4xb2tnq9force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,90ab 6n lp0lb,9ely/)h ;s zw6wmh wxm but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directiozbhl9 wb6xanhw0l e); m,pl6 m09ys w/n?     ----待选择----upwartddown 

  A projected space station consists ox(crz ( q:p8vwf 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 day) if an effect equal to gravity at the surface of the Ea p(wqz8:c v(xrrth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in 4ms/t c3j6v g 8z c4wj,zgebr5a 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 in terms of its radius r,5l +iiyi mvl,; 8;lpi 3wdkl/k the acceleration due to gravity at its ;53li8+/ miv,dll ywi ip ;klksurface and the gravitational constant G.

A plumb bob (a mass m t du+4 -ocx-.sje,jvu hanging on a string) is deflected from the vertical by an anglxju.v-, s-eu t dj+oc4e $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of 2vnwb mp/in6 .static friction is 0.30 (wet2 / mb6nvnpi.w pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatinc :0lj:asl6s ng so fast that objects at the equator were app j0l :als:scn6arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constantfx k2-9pn( c3xz )3n daamofep(54ebd distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of jiv p p(e,i3x5radius 235 m. A lamp suspended from the ceiling swings out t(p, eixpvi 3j5o an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times wfv1je/ 0.n am0xite m*f/ os5he g+n1as massive 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 followihfx0/wmm faov1 e 0/.n e+ s*ejt1ng5ing data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremel9f6wzow ed f*6y massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did th 6fod w6fw9ez*is 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 speed as it traverjoy: 65 gzg39( sxqx /tqxfq(rses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Wher xys5q9/xqrq((6o ggj:xtf3ze 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) 6ener8*w6gm .2f q 1wq4db 3rtjy /tcjutilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determin gcfybjr rd 1246/.qt6 ewn tm*j83qwee 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 :01te ;scfept billion km, is meant to orbit the asteroid Eros at a height of about 15 k:psee ;tc01f tm . 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 sh )-n,xzvl y/s gc3.vdouttle pursuing a satellite in need of repair. You are in a circular orbit vzgn d yl-3s/xc.v )o,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 period of 3000 years. (a) What ispv ymreb. oa13 n6b(1j its mean distance from the Sue3 n. ryb16b a(vo1pjmn?   
(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 o y,km)a7qv 9l42l 8. gnxnjxjneed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like F8)a9 nxnly jkj x,.l42mgoqv7 $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around txr0n/(hcavk . qhv,- xhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of abohnv cq rh .,a(xx-kv0/ut 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on ypm.bg0h3(2vi fs0qvx,i no 0 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 the squar0f0b i vhmoi3x. vs(n0,y pq2ge.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the vtvihb thy/3+le* 23m7erc* qEarth $ \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 sweep seeo c+dsxcfo iviw0;;f uq1,+9cond hand on your wrist waqc1fi +x0; oie,v9d +cuwfo;stch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a : r1s j3)yotb0, beszncircle 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 fb): 1,nz toyj0besr3 sishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed sop5 diy: ,gpuj jx8w6q- that a car traveling -jxg8j 5 iyqpu,pw:6dat 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, utilizesc an,v+ h-*u/ri4cc8s) t uwbv tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75c8u*c-i/ vu+wtr4b hs, )an vc 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.$\approx$    $\times 10^2$