Sometimes people say that water is removed from clothes in a spin drd5dw cf ;/b60sjp 7yhcyer by centrifugal force throwing thpc0s yj;cw/6dh5fb7 de water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car traveliujfn)c48 e /ioy4yy,)wc fiq3i9ac) s around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spe, eiq4/f384)9cy)y)aucy co ifwjiined? Explain.

Suppose a car moves at constant speed along a hilly road. Wherhf;kx q uko4rqz+(iimhr b/mid:* p;8spn, -5e does the car exert the greatest and least forces on the roadsh:qk*qi/+kd z(;x;pnor m84 r,5mpu f-h i ib: (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 w5d- b ufpe4r.a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerat5 -fwepd4r.buion of the child?

A bucket of water can be whirled in a votz k 7 0,h7p di+g/ 6johbqb9:rpmdv.ertical circle without the water spilling out, even at the top of the circle when t09i, zgob6hkpvbq ddpo/.jth+ r77 m:he bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least ti5gxqe wu33c) hree controls in the car which can be used toc 3 gxwu3eq)i5 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,.x08l 3ym;yyuda+) ddn0 k-f bpts1ik as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), xk1)- dysl3d aufb i+ y;ntkm 0d.p08ybut 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 highgruh( t0( kcd5 speed?

Why do airplanes bank when they turn? How would you compute the bct/d.mqtia k 09ax:;7oq/qf rs2qdo5 anking angle given its speed and radius of the 9q7tofq.20;/:i5ot dxm /aakrqcqds turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Sohxo3 sp8e.(qhe wants to let go at precisely the right time so that the ball will hit a target on the othes.xh3 (q8opeor side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the E0gpqupua3 5t a5yd(*ca 1ys 9garth? If so, how large a force? Consider a1aud 5y3 q puat5* sy(9acg0gpn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is,yq;i ;v0ez ie2 in what ways would the Moon’s orbit be d yieeqz20v;;i ifferent?

Which pulls harder gravita5m3bpfadb/ f:2cvl c +tionally, the Earth on the Moon, or the Moon on the Earth? Which aclb 25vf fpmc: +db3ac/celerates more?

The Sun's gravitational pull on the Earthh(vktqrelr2r +5r (6 d is 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 the ot( tev+qrh 6r2r(dk lr5her.]

Will an object weigh more at the4y agsz x-9jii*u 17b7rslfn6 equator or at the poles? What two effects are at work? Do they opposg1xb syn f74i7ij-za 6 9l*usre each other?

The gravitational force on the Moon due to the Earth iswrshc90azp4g)c l ox3(l fw +9 only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fro)gazc0r9ophs+w fl4l3x(w 9 cm the Earth?

Is the centripetal accelerationlresswhl6qkdlb)vt +- -5f)f 29 g o5t of Mars in its orbit around the Sun larger or smk q5s9tw )lt+5sf e-6gll-rod v2fh) baller than the centripetal acceleration of the Earth?

Would it require less8hcpzp ech- / m5,n5bo speed to launch a satellite (a) toward the east or (b) toward the wchp-e 8z,b5pohmc n 5/est? Consider the Earth’s rotation direction.

When will your apparent weight ,79 xio7e b 0d 3otpi0x5xt y8kso1bxobe the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weightxxi08keyx0 5op9o idb t3 s7o1b 7otx, 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 periocsc q40j: -pfids in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objejfsq:ic0- pc4cts 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 /4udos (i/ a5qqiqe6fy4q1 qf abcg/. “free fall” or “apparent weightlessness” between q i.ff/6 (1c 4iq/buo4sgqqday /5eaq steps.

The Earth moves fasterxm0 (js bx otm* b+3cgk6rwn1( in its orbit around the Sun in January than in July. Is the Earth closer to the Sun m3x +x o1j0(k6bnrwm(g b *tscin January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known d-+pw ltu k(/ko -o0gtuntil it was discovered to have a moon. Explain how thist/d0 o+(ol g-k ptk-wu discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on theqepoi:( fnsp0n7lw. u(+mff* Earth is 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 the other.]A child sitting 1.10 m from the center of fpi l(o f.mpns (w 7fqe+*u0:na 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 c, ce9ic;)vuzxo4ulll f07*i 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the npg;,f x(cmxyjwf7r,hn .k58 Sun, and the net force exerted on the Earth. What exerts this force on thx5y8wf pg (hxkmfn. ,jcnr;7,e 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 is1es9 zv5ag6: +deg lev exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circlegv51lagz e6e 9ds:+ ve (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ciu .l3ushe,be 1rcles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer1,behsl uu. e3 in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a specn dpfq5 v4zillo8 8+d/k of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter dfllodqpv8 z8/ +4i5n is 32 cm?   

  A ball on the end of q47cuq* 2 sknja string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in 4 unq* cq2jsk7Fig. 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-f/ 0rngpk: k02rm(xljkg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tiref(m 0:/krlr nxjkgp2 0s and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be bel-64fn m8*mfh d) xexetween the tires and the road if a car is to round a level curve omnf4emxe * 8fl) x6-dhf radius 85 m at a speed of 95km/h ?   

  A device for training astronautw +)2qi hh k)pnpdl2b8s and jet fighter 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 l )p2kqn h8w)2pbd+hi back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rote: z 6oh,qo)myksbt04ating turntable of variable speed. When the speed of the tursqhte0o6):o, z4byk mntable 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 coastsj 5ha+gn3ms(7pjg 2z 3) sdyger be traveling when upside down at the topps3ngs5)d3ms7g( jy z 2aj+gh of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top v;bg hujg0 7d01:t rsgwt jln9 +s3;m9 jsksv6of a hill (radius =sb3;0nldu+w6v 9s; v719 sj tjs:0jgrgtmgkh95$ \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 Ferris 4;0qcrr 7hf,pur0 zm- e g6oq/owvlj (wheel need to make forewc0rfo7o r ( 0-/ 4mh;z6qvrgqpu, lj the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirledjhg ,-:iyr) lsur9r b0 in a vertical circle of radius 1.10 m. At the lowest point of its9rur j i ),-yrg:h0lbs motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate fntgjr*e obupjj6no5c4 s(29,;p1o b if a particle 9.00 cm from the axis of rojoo (fnb51*juo;4r 6p 9ejnbgc2stp ,tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a5y)hd ziaif(0 2zvd:oi-ahg 1c/b gy +re rotated in a cylindrically walled "roodagiy/zgc iyohhz15 db-i: ) a (02+fvm." (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 rotated in a circle on a frictionless air-hock0ye524fd4y0gub jo pk ey tabletop, and is held in this orbit by e0fu4y2j5g o40bk pyda 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 this time, by not ignoring the weight of the balk c98 9ly*2w*bapaz1ur8ec ull which revolves on a string 0y8c1u bal89p zau w2lk *e9*rc.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car tr*., w+j+cq :yi dam/amskqh f59gvcb 1aveling 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 xw*ul wb+9c i6$ 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 ev75) 3fbtkeks/q ct z5xasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal cur6rl.cvsh y0t.;a j. omponents of the net force exerted on the car (by the ground) in Example 5-8 when its speed is cus y6tjh vrlra..;0 .15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, glug(kuyisl) x8y7 zrc/p 12m)2 dyv*doing 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, 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 slidpmyk(y/2) 8u dl z27uc x*iy1vgl )srpping or skidding? $\approx$   

  A particle revolves in a horizontal 20.ovmh)wat fpakw h) 67 jf4;u d2rarcircle of radius 2.90 m . At a particular instant, its acceleration isd )aw4;hjofwr hu.m2v 276ftk)r0aap 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 suog15s ms*on+qsp g1 ua) /gqjzc+4n2(8ysugravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfa s 4a/ gsg8qgp2jn uyu+)qn15o*zs+ssou1c(m ce if its mass is 1350 kg.   

  At the surface of a certainy weqav9iq7d;76t 8,v c4d xek planet, the gravitational acceleration g has a magnitude of 12 qd4vkede9, i8a67qw;v7cxtym/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 Moonm-3swv) nu8 r7/vkyued *xb6b. The Moon's radius is 1.743wbvs/u-6e v)* d7bykrxnu8 m $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.m3 mygm.3x x8 0tfmb,.m 3xtxe5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its mtf3m m3m xm,3yt x.ex0.xb8gsurface?   

  A hypothetical planet has a mass 1.66 times that of Ez 70vwqd9 eg,i/b*uhoarth, but the same radius. What is g near its surface? zvwo iqb9h,07/u d*ge  

  Two objects attract each other gravitationally with jvw-se u+2w)omuwpj5nqnm9 m0 l97f1a 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 pu-c au+zs5s3 lq)j:h, at (a) 3200 m s 3lpcsh+uaq): -5z uj   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tc rdd)q -8onnu7l *v-ro a point outside the Earth where thegravitational acceleratior-cn7ron8d d -)lqu*vn due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hasg/rprq c p3w*ez4 nv78 five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity onrg7 z *w/4p3vr enqpc8 this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun x1zzlzm 2 :1qrbut is now in the last stage of its evolution, is thxm 211lrzzqz: e size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless wh tke5ae-amm6+y9/mr yile orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker uyem96ktra+m -my5 ea/ p 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 locateddc9b b0ao0y3v at the corners of a square of side 0.60 m. Calculate the magnitude and direcyd9c00v a bo3btion of the total 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 planets:lev 3p():7: jcxejqo8tiz lb line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planetsqxv8bi to 7:(:pjzl3 j) ee:lc 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 surfaceqe2a j g;miz4sf1+o;d of Mars is 0.38 of what it is on Earth, and that Mars’zmeo;d1i fj+42 ; sgaq 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 Earth 5i d:a)ectd t7;3clw jand its distance from the Sun. [Note: Compare your answer :te7tlicd; jd5 3 ac)wto 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 the uvk0ak0cela6icwdg+(2 .p (kEarth diav0gwk+ckl6a. (kc(0epu2 at a height of 3600 km.    $\times 10^3$

  The space shuttle relo6 hd/,dgo8t leases a satellite into a circular orbit 650 km above the Earth. How fast must the shutg, odd/loh 68ttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan/ zbm:nzleqw.c.m/r/se*( ip s* ikf.ts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m,nw*zrzk:ie bqs.ls.cpm/i/*e.f( m / and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellil dt)n05bvo o-a1e5i/b.xa wz te to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a heigh)d / x5nlbbe.aa0-ito w5z ov1t above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top pbvfuaznpv1 h4 k,3x0u sb+40offhpk 4bx0n0zu1v+ 3s 4pu,b va Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar lymt3,jgg/ 5 vnanding mission, the command module continued to orbit the Moon3jg tv5gn /ym, 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 (u fz 7p:egsy-ice that orbit the planet. The inner radius of the rings is 73,000 u(ge:fp y-s7z $\mathrm{~km}$ , 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 Fig. 5–9). Whak sm *qm1k:k-ofzky,)oq(h5yt is the ratio of a person’s apparent weight to her real weigs*y5m,h:k(ykkzq ok)mqo f-1ht (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight o;i q93k dfd ) c0ktm7btjx/6tzf a 75-kg astronaut 4200 km from the center of the Earth's Moon in a spa63z tqtjdb d/xmt;i c0kf)k79ce vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars ow)9 ss2rmket2f equal mass. They are observed to be separated by twrsm )ks 292e360 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 weight of a 55-kg woman in an el6 lf10rz*l brum,9gjhm1pxn 5evator that mzj *1hm5,rlmpr b n6u9lfgx10 oves
(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 suspended fro )lwoynw 4wssmg bav8yj x.:e-u:9 02um the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the el -ssbw 0wu :gmxl)vj wy8e .9y4a2:onuevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nea++ h9 9vfvall/1/ivk dtvo .vor the surface of a planet with period T , the density (mass/volume) of the plald ho/9 . v1tovvv9 liv+k/+afnet 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 anp ql / x,b2q,3bxxo(msd the period of the Moon (27.4 d) to determine the period of an artificial bx sqqomb3(pl 2xx,,/satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits3)h vcuk 4c;cl wm45wg the Sun like the planets. Its period is vcw4c 4h 3;klwc u5)gm410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance s,0ox-ec ca/c 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 7;8q.vn wlqjt*p25v lqx mof0(6 years. It comes very close to ;jw 50v8n qqvtf* mlx( o2ql.pthe 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 nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center8c ,n35glr rlod ;w+v ymc4m) 7)ldttm 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 distance for the four largest moonsr)g w (0zyv-bg of Jupiter (those discovered by Galileo in wbg)0zv(y- gr 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 of tszjh)v:ee wg lp( h (:e:)r9+dtdyf)zhe Moon. sde (zl):wvthepr:ez 9g fy ))jhd+:(   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mooncftqp8d4)p*l phn6.xw h: ,css, using Kepler’s third sqpnc,tp*.6 dw) hf lc8:xh4plaw. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter6sv9rb z5-p q9zaz*ah consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destr phzzbv9rq6a9 *za-s 5oyed).
(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 a,i/-hr5*rr /vl jj nedescribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an appa,ieln- v*hr5r/ j/a jrrent 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,*;jhj+b5uiukqw ; 7xc(ywno by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, whatuquo y*(wc jh; k,ib7+nx; w5j 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 acceleration of gravity:dpjd: i(ia4mbs ei a95 /n3jfb n-v: chw//ai be half what it is on the surfacejidbnf: whd/ 3/ebi:4j(:-p5i a ana scmvi/9 ?    $\times 10^6$

  On an ice rink, two skaters of equalk.9r-b lge2xc mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their a9r 2xk-.e lbcgrms 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 appare1vbnw:*2sy5 b fyyhv,nt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fracv2 :fy1wyhsvbbyn 5, *tion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly .t( zxj iikxxfu 8l-08,;hlqpfrom the Earth to the Moon experience zero net force because the Earth and Moon pull w h8jzx0 pl;8 x.u(tiq,fk- xliith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stan.gf96gv:f (dz/rvkqqh76 b tfd on a bathroom scale in an elevator, it says your mass is 82 kg. What is thev v ffgh9dg/kq :ftzqb67r.(6 acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thatovueo-dv; u3e m : z00/dp0sly 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 Earth (1.:u 0 0e3 ;z suompdlo-0y/vedv0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Figq l.koxfk o;w f6c68 r3/u(gkw. 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 j, wcw;(9q -2zzzjlcvthe mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitqwzz;-jwc , lj9 2c(zvational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the (ss3bbi9 k twru-6pkfg+ku9. vertical by an angle r39s6gubk b.utwfsk - (k9+p i $\theta$ 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 de7d u yahu,li ih7,u0z.sign speed of If the coefficient of static friction is 0.30 (wet pavement),.u hiduhzu7l 0,i 7,ay at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast tha90 ,bi.qh;c e1bie9xk1tr bx nt objects at the equator were apparent901n19ie b,bqt x.xc ;hei bkrly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constak :*lg3n9z hjyafnt6+p jgf dx.19hz+nt 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 radiu k(q)1/2fph5k/xxq kb* nnsrns 235 m. A lamp suspended from the ceiling swings out to an anglsqx nfn nk1)kbx( qkrh*5/2p/e of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. pw zi6mk(zl+7Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since pz7+mzw6p lk(ieople can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an epi 3a*j: ppcaqir6 d y)4*;mpyxtremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whic4p6)irjmdy;:aap*q p yp* i3ch no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant 69thcx:beziv f9ry )sh s4pf 7j6 c:1cspeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Ej67z6spsch1:c:9 bxf4 trc)ih9 vye fxplain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sa/t v tosx.2j6b5bs 8ib:5e-oxlwm-z ltellites 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 att. 5ll/i-bo6v wsbx: 2s em8tzj-5b xo 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 kmm.pa.z k sxe9o g/,y:lqp1. ei, is meant to orbit the asteroid Eros at a height of about 1q. ,i p l ypgke.zesm19./:aox5 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 pursuqh u*tnpz,wzjo:o1; )ing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abqu1:z)wptn zo ,j*o;hove 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 its mean distance fr1j6/ x +gev(4 bljf saamp5kv,om the Sun/f, pvg6 la1j4(kab sj vxem5+?   
(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 +0 lskcyt8wa6 G would need to be if you could actually "feel" yourseac8lkty0 6+wslf gravitationally 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 Mil4q be ilnv*)w1q3 ,abxky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-ye*14 xneq,bwv)l 3 qabiars 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 ai nlnsf8 w/h0fd+v3 q2t the corners of a square 0.50 m on each side. Find the magnitude and direction of/3ihf8s v0fln+nq2w d the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg feh. e87o. zauorbits 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 t4ci - x7tg g+dce7mejmizz/)*ip of the 1.5-cm-long sweep second han j7 4)xc -im ete+z7gcdi/*zmgd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in aayeg*5a*- kweibqh xf4061k s circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vexkh4y*wq5k0 1 ifsbgae-*e 6artical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travylzr/jx/+. jad k5y a:eling at spe r/lxjza+y a5:/ jky.ded $ 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 ofbh 7h5 (hjqc,tr 25txp 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 (approximatet7h5 p,h qj5rb(2xt hcly ). (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.$\approx$    $\times 10^2$