Sometimes people say that water is removed from clothes in a spin dryvu p/db .ahk4(qxxf. *er by centrifugal force throwinub.xv(k4.fa*hqpd/ x g the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the ca6 pfx+hbx5(yh wc cy62vs ob7;r travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at thehh+ vsx6bxc6;bp 7yo 2wcy5(f same speed? Explain.

Suppose a car moves at constant speed along x-l8r.q9 lpg w)d 5o;pgcir7tpu,xq.a hilly road. Where does the car 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 near the bot.p7 uxqg 8,lpg)li;xor.rtwc5-p 9d qtom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rouns+f8y jrab:/b d. Which of these forces provides the centripetal acceleratiobj/fb: a8 yrs+n of the child?

A bucket of water can be whirled in a vertical circlj swrzu0zv3sw: ib*5.2z;rcq e without the water spilling out, even at the top of the circle when the b*;zrbq3j50:zs c rv ws2wiz.uucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least lk asn(/;2 3mdbk+ws2.b mofbthree controls in the car which can be used to cause the car to accelerate.3bd b2/mslwaks .okn+2;f ( bm What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill* 4gckp l0w0(zaq0zp h, 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 the004c(*q0gzzlhp wkp a 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 sp::1c61 6jr gbqmfcremb v8(aw2g8mkp eed?

Why do airplanes bank when they turn? How would you compz/hsli5:i j x( zvr*8cya(9quute the banking angle given its sp(cjxi :/z9 yz85s*urlhva ( qieed and radius of the turn?

A girl is whirling a ball on a string around her head in a hori8 d 0j:jj8mxs4j2gjivto9gs:po ++pu zontal plane. She wants to let go at precisely the right tojjgds2xj os :mg9:80iup tv 4jj++p8ime 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? If so, how large7 )xl(xa nc/6si oy7rz a force? Consider an/ly(6 7s xc7 xozr)ina apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass g v2f7t jj*jvvy8) s69/dnu nvwere double what it is, in what ways would the Moon’s orbit be dif j* 8tnvvsfnvdg /j7yu)vj692ferent?

Which pulls harder gravitationallybi y3ek b6rujusiws 2o6(57+r , the Earth on the Moon, or the Moon on the Earth? Which 236w(7 kb6ejbyrrus +uosi5i accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yetno68/gt.5oj ukub(( (efko ge the Moon's is mainly responsible for the tigku . (fbk6o((to egjoue/5n8des. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the eym.dfw9 c;;.y xmavm *quator or at the poles? What two effects are avcyyd.af m9mw*; m.x;t work? Do they oppose each other?

The gravitational force on the Moon due to the Earth isffs/ .g ibbxsw2/t7c( only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from tt/ b fcwis(xs/g 27f.bhe Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or s z ,()p m1i21qfyctpkkmaller than the centripetal acceleration ocpk1y) 1z2,p(qtkm fif the Earth?

Would it require less speed to launch a satellite (a) toward the erz/h4/*iyraw ti- ) /bw kf(qhast or (b) toward the west? C bif4zkiq y )r/a-ww/ h*r/ht(onsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as meas 4fxv+su4vq 1cured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b4+uvxcs4 1 fvq) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adve mb-.x (dyidk3otmun (tk8.4rrsely 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) ho mt4(-mdt3 .dkk(oiu8xn rb.yw 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 : td(u/0d:yjzij6pm q experiences “free fall” or “apparent weightlessness” between :dmi y:0 dp(/6tqj jzusteps.

The Earth moves faster in its orbit around the Sun in January than in July. Is r5rm8(h z8jd cthe Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons rj8dc rmh(8z5 — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was notz)lyh* px,bi, known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s malhz*y p ,,)xbiss.

  The Sun's gravitational pull on the Earth is 72obth2(s 1df7yl6in g:dfrf much larger than the Moon's. Yet the Moon's is mainly respon1bd yf:fh o ( tig27s6r7fnld2sible 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 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 0.8krsvjac v4kr25 zg 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 Evc*d3- ,urs uvarth in its orbit around the Sun, and the net force eursvdvc, *3u-xerted 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 i9 j6+up z9vhh210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at a+9hvp 6i h9uzjrm’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, a4xh7r9i 9vndjg3m 03sac-srynd circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space s 4shnyr 0m7 j9a3dsvrc3-ix9g huttle 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 th65 k**ilmrlmg(obm/:5 +aea8p flopve acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per * lmkl*bp6( / +v omiagrae:558lmofp minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvedethi4+nl 1dwb; u ;u9a at a uniform rate in a vertical circle of radius 72.0 cm , as shown in wl;4u 9hai;b+e1dtnu 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 carxfnt) w/-hxyb c24tg) can round a turn of radius 77 m on a flat road if the coefficient of static friction between tirex ngb)xt2/)wtyfh- 4cs and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fricti0prh bvcmml5z,p/65c. buw1 y on be between the tires and the road if a car is to round a levellmuc0 y /cwzrm.b1,p6 bhpv55 curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to ro9kr b.ope *7tzz fslu1w*d9,gtate a trainee in a horizontal circle of radius 12.0 m 9*w. 1t*bf7o s, 9repzuzdkgl. If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of 3 lhnzkr1; o7 iaru6fywhh. 0)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 the turntable?0wr7a.1 nuhkhr zi6;3 lfy)oh   

  At what minimum speed must k9a1a,dvhdmva9a(; l gyai* 9 a roller coaster be traveling when upside down at the top of yd1h,aav* ;dg a(9ai 9mlv ak9a 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 950fdqse5uio 7 70(gwgw-+p h i;w kg (including the driver) crosses the rounded top of a hill (rif0w -7hwq+wsop ;ge7 5 u(gidadius =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 perkv: rh.;pmk5r minute would a 15-m-diameter Ferris wheel need to make for the passengers5vrh.;:kmkpr to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticu9ydgyx(oe1bruf * be9r)6u *al circle of radius 1.10 m. At the lowest point of its motion buo1r(d9)ruyu* yfbgxe 6 e9*the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cab5 ahi unnzeo7b,9/8m from the axis of rotation is to expob z,uhn5b /a niea879erience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoi+ctfx mcms+c 0t uy2c 0v/m.16)mill ple are rotated in a cylindrically walled "room." (See Fig. 5-3m .liscxc) imlt vtm++602 uc0y/1mcf5.)
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 tabiz .wd,-8ryx j/s:dwmletop, and is held in this orbit by a light cor,i/. dsxr8 d:m-jzwyw d 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 bahp qd./w0qowl 93ka0jl bz)7b ll which revolves on a string 0.600a) k0wwlq zlq/h3 o.p0bd9bj7 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 t z,cl ,rujk rd5q.vq:0raveling 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 masseso ;qv7owv k+w4:/koef $ 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 est5*fze,9p/siuv-ihbn y(5 v vasive 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 component7gkr+kszo 2gvgv6 tzl1,* 8ow s of the net force exerted on the o8vzwok2v1st*6g7, g rzkl+g car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going frodue)pt1mh :3xm rest to 320km/h in a semicircular arc witt:)em3d1 hx uph 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 slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a par (ow1co/)f+j y;cwmd nticular instant,fcw)mjw +(y o1dc o/;n its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earthmrf8s/1x+ra 5kpvg z5d/ vow. ’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kvw xgo v+p1/85r/.dkrz m5a fsg.   

  At the surface of a certain planet, the gravitation85vk pg:v: azpxk: ) mgo/xf/sal acceleration g has a magnitude osov f)pzpa:x:g: kvmkx/g/58 f 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon+y5.x rm,iiqf's radius is 1.74 + .x fiq,miry5$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has theex( pvu ylsc5+77zk lx,l*g, r same masss*xuzep7(+7g v5ck,,x lll ry . What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radioj-a8,3ql vf2rl5bhvus. What is g near its surface? l-5, fo 8vrq2bvlja3h  

  Two objects attract each other gravitationally wit,w) e4pu,;ris /(qj xci(wotth 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 gc+0x i3 )8 ;ymykp h3+f)ahitr exib*j , the acceleration of gravity, at (a) 3200 m y xmh+ i)eif;0)jb8ra* ki yxch+p3t 3   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point out wt( af-/jucc*c5,hxsside the Earth where thegravitational acceleration due cc(*ctxw hfj/ u -5s,ato the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fi5- ozh6p/eh 3zn0g g)lgy:mvlve times the mass of our Sun packed into a sphere aboulv3h ) :eg60zh 5gon-l/ gzympt 10 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 but imm3yz/b ny/ 2rs now in the last stage of its evolution, iym/b r/ny2zm3 s the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel we;cs8y vh/,kdjo)n(d w ightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and8/d,j ;ykchnod sv w)( 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 0.60 m. Calck .14 eux4nph pv0m/exulate the magnitude and direction of the total gravitational force exerted on one sphere by the other4xp.h nk/xu 1 4evm0pe three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most j/8)i nos4zcaw e46bbof the planets line up on the same side of the Sun. Calculate the total force on the Earth dbaz4c)6j ine 4bw o8s/ue 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 tcl4fb)hu c *4khe surface of Mars is 0.38 of what it ikcu fb*lc 4h4)s 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 per9zyd y))vv;x(xrs dp5. aeg-oiod of the Earth and its distance from the Sun. [Notox (g .ed);yy-5 psv9zr ad)vxe: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelq9u.v1+k jk; ffhi7n 3z k8gqplite moving in a stable circular orbit about the Earth at a height of fn; 39f7.8iu+v hzpkk1qjkq g3600 km.    $\times 10^3$

  The space shuttle releases avy4 f-dfe/y3cq7 d mb2 satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs4 f-3 /dqycdm e27vfyb?    $\times 10^3$

  At what rate must a cylindrical spaceship rod: uzw1le)g3 ttate 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 tim1ge)lw td zu3:e needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the tjhf/uu,t tw06o k9 d.ra4p , exp--dzEarth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a zu.two6rth 0dd-9ap- 4,/ex jkpu ft, height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hab :02.f(fbl,uj dw qiove to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earthwf fobb0j.q2d ,i:lu( ?   

  During an Apollo lunar landing mission, the t(qr33z , y5diiyz*yk command module continued to orbit the Moon at an a3ziz3, id*yk( yy 5rqtltitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunkuckv1y*+ .brm s of ice that orbit the planet. The inner k.1+vm rcbu *yradius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (a ii b(m0fk6fc6jb2t +see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) ai(fb26 am6b j ctfki+0t the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km sqa 9 qahhq3)6from the center of the Earth's Moon in a space vehicle (a) moving at constant velaqh 6sqhq3a) 9ocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of fcw j-t)0;151uaxivjceer5 k 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 eacc1e r)jj0 1-uik c 5t5f;vxaweh?    $\times 10^{29}$

  What will a spring scale read for thedfptsxn+f zwsa3 b5u;u:8x9ro9 rs64 weight of a 55-kg woman in an elevator that movesf3s8 4r a nbxu s5x9o;:fw6dtz9sp +ur
(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 from the ceil rea 5dpk g05ovov)ye9 p/:j f0hf*-fging of an elevator. The cord can withstand a /god fk:5efhp0gevr p j5yo)af*v 90-tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very n)m *sye 03o*sh79s)q rfesiutear the surface of a planet with period T , the density ()es)hf07 osus3 9i*em*ryq s tmass/volume) 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 tw 6x0h/ dd5xemv )1eszhe Moon (27.4 d) to determine the period of an artificial satellite orbiting very near m5esd 6dxv1wx/ 0ez)hthe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orlh522r twr56xc r6yxfbits the Sun like the planets. Its period is 410 d. What is its mrth25 ryf r5cw 2l66xxean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of-6v/vz ,rwx,pr zl-vf 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 once5/drf77j pdg(i0yjw lxuh 3q9 every 76 years. It 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 “in” the Solar System? What pladu 7x/ iw7rg50j9q3 yd(hplfjnet’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 cel)ceaf m -c8wx9/ +rs vdi8ua1nter 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 lr gg is/ :j-/o/pqp6vnargest moons of Jupiter (those discovered by Gao-vps6i jrgqnp//g/ :lileo 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 aae2y6 /ml4t n8lyws n3nd distance of the Moon. s2/3 l8e6n yy4nlwamt   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using ok+n z( ;bqrh+lo)iw)Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.+i ()q wr+;zkhol b)no
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmenbf f: d)qhg09kts (which some space scientists think came from a planet that once orbited the Sf)09f d:bkhq gun 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 ho (ksif2dg )/c5zww0a 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 thef /2i)o0 hc( zgkdww5s 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 1iu9v 0nbe6x-g c lc*zan arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he e-z* bvug6xil09 ncc1can 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+fb) r5-9tyt-l 5yc. 3o bul0pkn)syvd lher/ surface will the acceleration of gravity be half what it is on the surf0 h 5t9-o) 5l ser 3rk dty-yc)llb/yn.f+bvupace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutualmg8v.5 sbsh 4iw89mg:0o v tgn circle once every 2.5 s. If we assume their arms are each 0.80 m longvom.g9sw b5s:ng v8m 84h0tig 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 a7ss)x ,n8 aaxocceleration of gravity at the equator is slightly less than it would be if the Eart)s 7a8oxnsx a,h 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 x(n vt9autj;* 3phy4e spacecraft traveling directly from the Earth to t x;hjt 93 4tenp*avyu(he Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, d vs;*nu-/ g15 qbf.o9hicf gibut 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 ivi; 5cfs9 qg1uo hng-.f*b/d which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate ast e1r )pr;ls:rx:0cr bout 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 speeelrrx;t : 1r 0)rscps:d (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 aircpp gylm v/m6-.raft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r,imm.a,joam:9 l i0alwq+g7m 5gdf x3- the acceleration due to gravity atx a7a- +mgm.,0lmo qfgiawl5d9m:i3j its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticaab y(y4p*2hq tl by aypb y(qt4* ah2n angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design ki6:kg eb1h k-hxlbx/0v m90c speed of If the coefficient of static friction is 0.30 (wet pb/g- l 6i0 9kcbmx 1kxevhhk0:avement), 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 that objects at the e jwobqy8j46p4 /u-s llquator were appq-/4ls 6wjo4plybu8 jarently weightless?    $\times 10^3$s

  Two equal-mass stars maintain 8:fl-zat7 h+1reot jka constant 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 ra;dmpg mf+tx 2+ -emw1.h pyin4dius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5;4nmp+x+y-g hmdew. p 1itf2m$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as thedj/-n*ywq -qv3u 1a gm 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 expeg-*/wj v 3 y-dqmn1aqurience 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 presencs orid-igtyp1)y1ml:-k6qf 3 e of an extremely ma-1tg)iy3 1sk 6pyor:qfmdil- ssive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill ant/ j/lo8yonj4 d valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the njt8yo l4j//o road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of u xlb* .gj2fz124 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receivl1 ujz gx.fb*2er on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is mea1navyb r+tk:a v 2uv-h2w2+zant to orbit the asteroid Eros at a height of about 15 km . Eros iwn: hvt+vka 2-b21z2ay varu+s 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 nmy g: 5r1pfnp)eed of repair. You are in a circular orbit of the same radius as t1nm)gr5py p :fhe 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 perix;azliy5-y z km-25dpod of 3000 years. (a) What is its mean distance from x;d- py2 a5 ziz5-ykmlthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" k :6ytchkzi 54yourself gravitationally attracted to someone near you. Make reasonable assumpkh6y z 45ct:kitions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wrlid:q 9aq/u 7ay Galaxy (Fig. 5-46) at a distance of about 30,000 l /iua7: lr9qqdight-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 each side.)ksw;8 r0 culbp3knr5 j+b mk4 Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sidk srp)m+0jw8ck ;unb5r b 34kle of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55x/fbs*ao pza5 .6y m(w00 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced r v+ 7sk2/c w02wwqs6 lsdhan(by the tip of the 1.5-cm-long sweep second hand on your wrisksvsn wr2 wdah+c/ 60s7q(w l2t watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circ15kwj9 t6xe axle 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 a1 ek5xt6jwx9 the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car rdi:mle.0ww6 r nvy(rph, 1e7traveling at sp,m0e vleripw7h n:.6d wrr(1yeed $ 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,6kmpub0 wo +tg/p mk- 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 neem-wt/kpb,kg0u6+p om ded 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.$\approx$    $\times 10^2$