Sometimes people say that water is removed from clothes kc2g*g8h na1.,80p feg wirflrs: ee;c nh1d:in a spin dryer by centrifugal force throwing the water out newfplcg,i:. kgs;8 e*2ae1ghr8:cfn1hrd0ward. What is wrong with this statement?

Will the acceleration of a c;: u8el*e h kwfvw:;wnar be the same when the car travels around a sharp curve at a cvwhk;fe l;uw :n8 e*:wonstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at col mq5c:yib0 pv6hi(z v88gq g+nstant speed along 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 twozyhpbigc0(m v8i+5v8gql 6q: hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merfx0y6c +54ctqhqih1q9fp;m pry-go-round. Which of thyq 5cqcp6 txi90m p;fq 1h4+hfese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sm .7n/f(jjljwsb v rcn,8j *r7pilling out, even at the top of the circle when jv.*nn8 bm7 /r,cs7rljj j( fwthe bucket is upside down. Explain.

How many “accelerators” do you havejb m/skj u.32okjq;rs+2ok 7x in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prrkju; qj 2jkooxs/m2+ 3sbk7 .oduce?

A child on a sled comes 6 bbo.gs1o fj(flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second j1 f(bs g.oo6blaw.

Why do bicycle riders lean inward when roybk/i6wdtl:/qt40m nunding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the ban8v)v nbmrm63j king angle given its speed and radiu8vbjmv mn6 3r)s of the turn?

A girl is whirling a ball on a string aro tk2 pton5/,s2npqogi+ 9priv(5sv ; rund her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shou;ost ionqik5vspr5 pp2,t9n(g2 rv/+ld she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a fo;tlffi;ta ,zkc;up3 -rce? Consid,-f utf3p;;al z k;tcier an apple
(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 orbit r i,nn9kwm(6ns5zru/ f,mwiu h8( .cjbe different zr ,,rf.n ih5 i8ujn(n/69mmswcwuk( ?

Which pulls harder gravitationally, m1ww7l2otm:yypf5vufur,./the Earth on the Moon, or the Moon on the Earth? fl yuu: 1f,/vom7ypmr25tw w. Which accelerates more?

The Sun's gravitational pull on the Earth isrc0gi 2 )l; 4gm2 ) ma96zjscn(vlxfac much larger than the Moon's. Yet the Moon's mc; ) 0cv24)a9c(m nxl2 gial6gfrzsjis mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh moj nmuvla+j v70(*sta )re at the equator or at the poles? What two effects are at work? Do th *+(aj0 mu vtvsj)7lnaey oppose each other?

The gravitational force -dsagw5750kvp; kr 0vaegz 0e on the Moon due to the Earth is only about half the force og0p d0ek5 v0eav gwsz7-5kr;an the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or m 5x.esmv+dd)smaller than the centripetal acvsemdm+x) 5 .dceleration of the Earth?

Would it require less speem9gjgh6im1p5 g9afsr:2*jk2d7 fxtk d to launch a satellite (a) toward the east or (b) toward the west? ixgg t:9*khdm1rmagf9 k7 jps22j6f5 Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale i - twf9exxfoy7r:xo6, (3lechn a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upwaxohl fr7fecxo( ,w:6t 3 e-y9xrd 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 adversely affecbcs pd a 8cn(9tyu*0g,ted 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 objects fall, (b) the n 089 (ap,s* gtdccyubforce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weigha h-bmm4bs+6 z5t*s gctlessness” between sz-h*smtba 5g+6b cm4s teps.

The Earth moves faster in its orbit around the Sun in January than in July. Is p 071n7fz2tfmbtqee xaa) 5l01yg y g:the Earth closer to the S1tyax)g 17p5gln zetm7f 0qb2fy:e0 aun in 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 kno 6o.i4m ,ypjmmwn until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’p i,mjm4 6om.ys mass.

  The Sun's gravitational pull on the Earth is much larger than t1va0fd7 p lju757rtanhe 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 5 ljt0nfva7r 1ua7pd7the 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/ kp83skgm/m o $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 t2g0,+xn 7inu08 cvajm d7lptacceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Eartm7xlcn7u8 2t +gpj 0d inv,0tah'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 i.r*o4swh q1co4 fygn,s exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle qo,fr*h 4c n 1wgo4y.s(at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttlekt5q7i*ambcp**c 0u,x n:u0xp k8 gtg is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelert ,* 50uig0bg*ck7x*ncpxq ka :mt u8pation 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 9xnf tul4 * e:b bge:wfto;5+eof a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s d ne*tf eglob45ub9+tfex:w: ;iameter is 32 cm?   

  A ball on the end of a sn8t ag5xhj:f3p:uk5ltring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its3p5f jg:uh8 kt xan:l5 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 can rou5z ch;jon( n+tnd a turn of radius 77 m on a flat road if the coefficient of sta;ochn(z+tn j 5tic 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 tikpmn 1 ,kl*uomrn46c+res and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ? nu6okm c, rkl+1n*p m4  

  A device for training astronauts and jet fighter pilots is design6fid7y bm0gsnh3 1 0wled to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the tr6y0f 3im d701w gnhlsbainee 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 tu rsksrl( 4e2yn,zi. 9arntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpry9e24nr(zk.sl , saim 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 bnnw 4:c; el2+hf 5dkase traveling when upside down at the top of a cirn wn2s +45l: hdfke;cacle
(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 rdn8 c t8ad j*tq+;i4w m0j9kdthe rounded top of a hill (radius *4ni m+q k9c;trdd8 jt80dw ja =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need togt9k( p)b) w )fam i;nkdmlhm( 36gk)a make for the passengers to feel “weightless” at the topmost bwi)mthg9 pkmnkka )3la;fg d))6 ( (mpoint?    rpm

  A bucket of mass 2.00 kg is whirled in a 4ae cnrg7s(+yi6 ozp6 vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the ro+y ci6( n4pz6 sorge7ape 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 cm friqp()nun)6q90ktp nt om the axis of rotation is to experience an acc0)q)6 ptun (nn9 ipqtkeleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrica+mht5sfa hp 2 y+,t1nmz ;z9nslly walled "room." (See Fig51a+y tmsm ,+nzt2fp9szn; h h. 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 mh tr+uf 26 c-;7ggzkscircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord con67t+ kz;g2 fus g-mchrnected 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 balln) w r g.u.z0f-qu*rva which revolves on a string 0.600 m long. In particular, finu) uzr0gaf. wn q.*-vrd 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 travu4:xcx/.fih /g yge7 meling 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 67;m,zq trsr,la ; hfv$ 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 a7yp15n8bh iq ot 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 centrip9ew4hnpy*q1 id yh (m)etal components of the net force exerted on the car (by the ground)4q 1y *wdnhy9( h)pmie 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 areacws0 5 a9tzeg5, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curvta50s gecz 5w9e 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)idyilegb;vf5su w55z ihm /,8t. -zd of radius 2.90 m . At a particular instant, its acceleration is .lef/yz dtb;i5izwh5v gu,i 8m- sd)5 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ear2/qhnm a c+q2ybt f2.bn;rgzx ejh899th radii) above the Earth’s surface if i82.q h/ft;n +jr9y29gm beqnxzha2cb ts mass is 1350 kg.   

  At the surface of a certain planet, the gravitational actem6g 3tl(.h aceleration g has a magnitude of 12 .th(e63tg l amm/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. Ta.arv f,fowf / /srn-9he Moon's radius is 1.74 , as//f9rrav woffn-. $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1 3h):.kxozltm .5 times that of Earth, but has the same massk)m . 3hzlox:t. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but */g esxvv*(3t v;kmjs5uv73 r/ tqxlvthe same radius. What is g near its surfact;/lvts7*sqjeg5u3 vkm* xvx v r/3v(e?   

  Two objects attract each other gravitationally with a force of 2fj/m m-gqmyi-v 1 m+u..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 ohxcp, c*9/ r hucoosl 8.)2sxjf g , the acceleration of gravity, at (a) 3200 mljso h.uh *8ccx/ )p,9oxc2sr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ewza dji0q l9y,z*hx /7 miuy.j6u;eh-arth’s center to a point outside the Earth where thegm /izh 70xwh9leujd .zq*,y-i ;ju 6yaravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star -y1,gwd1kc /:w-cnfbqm w e-r has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the sunfg y -,c-m/w1k-qw ed rcb1w:rface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whic n;cgrua rf6av9,wl82h once 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 a; v c9funra28rg,6wl Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weighpqgh g;v ,sakyna4d 9b.jcuy.a;-r86 tless while orbiting in the space shuttle. Your frienj ks9.pq. h4 a; g6b ,dy-y;ucag8vnrads respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of ai37 w28mp(d yfl m+qr i*fvfj*na++ua square of side 0.60 m. Calcu +uamni+*(jd8fy+mqr2 7li aw3f* fv plate the magnitude and direction 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 t5n fxmsrs( c+.l 7,a(rbfsps,he planets 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 planets are in a line sfpss5 7m f(+s.n,xrcb, r(al(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 surfakm;.da qi6(pl ce of Mars is 0.38 of what it is on Earth, and tha 6q(l;.d pkimat 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 lj8a:d hyx w 4y9uk/d3x/ oc3.z3xlgbperiod of the Earth and its distance from the Sun. [Note: Compare your answer to that c3yd /zka yx.ou:8gh33l9 xxj 4/d bwlobtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in f:/a)52 bsy*pk9 zktsrd+ gne a stable circular orbit about the Ear k ns)/5* rty2azkges9fb: d+pth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a spd- g2s.vcxs 1atellite into a circular orbit 650 km above the Earth. How fast s vg- c1spd.x2must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylinx.pxp3a3 5.; dlorm zbdrical spaceship rotate 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. dlp5.ma;zprx box3 3 needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it tak1n )ph dvipu*hhn6+ o/es for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend o1hpd +*onvh)u n6pih/n the mass of the satellite?    s ~    min

  At what horizontal velocity woulvj:11ze3 scob le dvjb+a2/ m-d a satellite have to be launched from the top of Mt. Everest to be placed in a circular z2/bjevsajb-oe 1d+ m: vl1c3orbit around the Earth?   

  During an Apollo lunadfja3d ,ihj-mm..-* i s8zjaa r landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go-..8im jsdjzdafa3h-a jm*, i around the Moon once?    s

  The rings of Saturn l:2el r+dedfa8du4xa( eue 5 0are composed of chunks of ice that orbit the planet. The inner radius of the d0l(uae8fld r4:+xdu 5aee2e 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.*zq/9rm p+ gg- d.*kwp0bgbrv5 s (see Fig. 5–9). What is the ratio of0pvzwgkp.*/rb*-+g gb9dmr q a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a,k:0163h lkdlwmt p ob .zzd/.s qg.gjqx)l-y 75-kg astronaut 4200 km from the center of the Earth's Moo/.lz 3kxm ,.1yqqk 6owgjt .)l: zpbhgs0-d ldn in a space 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 staa6br by vjl86cv 91yh3rs of equal mass. They are observed to be separatecvyvby36 a 8brh16l9 jd by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weir* 6,hdnosb.yoc+fa.xa2 gx- ght of a 55-kg woman in an elevator that move-oo xc+db6aga .rsn.*yfx ,h2 s
(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 ce-1bpn(0f4jp n i83u(pwxl5 xrv2rvn qiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator 1j-n3(xpbrl4p f un(i pxvq 208vwn5raccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelw /b a+6*zwtkp 6gxj ol4ie/t5lite orbits very near the surface of a planet with period T , the density (mass/5zi+ oxlb*gkww6jt 4/ 6ate/pvolume) 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 Mo. 05ek:jmbg4sya3s he;0b nwc on (27.4 d) to determine the period of an artificial satellite orbitigscs0e ;.0e 3knwj b :5yhb4amng very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters ac8r8xc5mwa5 -vdqqg3 s2r,yd hross, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from58qv a3mycsxdqw -rg,5 hd2r8 the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4tm ox-rlu7.4xyhsr5k k,k 7 4h.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/h3gizyoe :m9 once every 76 years. It comes very close to the surface of the Sun on its cmy9ez:3i o/ ghlosest 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 b 7w; 4rvzd0d rgn3ie --ejq-dthe center 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,fe21d*b ndb 8h and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 160h1 *nbbe 8dfd29).
(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 Eav9un 5i011j qje*yivnrth from the known period and distance of the Moon. vj0y1un9e ni5qi*j 1v   $\times 10^{24}$

  Determine the mean distanctsq 1ddeaf/x+i3zc6g 050 olke from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the T/edo t 36l50xdfag0ci s 1+zkqable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments ()n)v8az .r:f wlfs bd8izs i/:which some space scientists think came from a planet that once orbited the Sun but was des:f:si8sflwadzi))n8 .r vzb / troyed).
(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 ba8tif an(aj 0m-nd 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 th (mafn-jt08iae same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swi2z,ky2 58 qyijby1mbb 7g jiq6nging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowe25 bib7ijb 28 zjqym1gqyky, 6st 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 acce tm(en8 n5 sm(za7of3qleration of gravity be half what it is on the surface? 8mo q3sn7tazf(5e(mn   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in ax+7ci+4uu( ; kffvm mq3gz ul) mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling(cg f++mki7) u4v3xmlfu uqz ; on one another?    $\times 10^2$

  Because the Earth rotates once per day, thek4m,0njr j)v m/miv 1x apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. E1)/ nj40jrmxk ,mi vvmstimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the E6by p +e.c)f;: )u;mc akdpoq(nl)noparth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because) lup6:fcymn(pq bo ce.; k+) d;ap)on the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wxxokhy /6z+w 3hen you stand on a bathroom scale in an elevator, it says your mass is 82 kgko/36w y zhx+x. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate ab-ra m 0srq:byjs+43s3vn zjn9out its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 43 3rmzsvsr:j0s n+jy a- n9qbkm. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4 jx 5+ f/+opjug,x3p t-mezkfwo2,ly (3).
(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 9 d9 hnilildkte)37y7e 6c4kv of its radius r, the acceleration due to gravity at its surface and the gravitational constdhe79 l97lvc n4ki)6 3kyi tedant G.

A plumb bob (a mass m hanging on a strt5hrsu7 dm-r8 ing) is deflected from the vertical by an anglr8 d- tsmu5hr7e $\theta$ 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 spee5-bm) sjvks fwfw5. ph,h w .7(2fzpzzd of If the coefficient of static friction is 0.30(,.z 5 w h7fpspf mwhv2kbz)5j.fzs-w (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatintrnx3x s yan/brz;8aw85b+ j5 s9azb9g so fast that objects at the equator zzss8x j9583x+ nart /bybab5w;9 arn were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of pwnhr1:4 i g)qz6a7ak 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 speoy )y-jgxn4vv4 hlhsgi 39 8di2e1l: bed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an l oy ib4dg: 8sl1n)y xiv9he-hj3vg4 2angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has bsi5n(s mv0/qx-+lj1lcx1 :th gsmpn;een claimed that a person would be crushed by the force of gravity on a planet s10x1ltmv c /+snx5 :(pmqn ;jl-gshithe size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for 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 p su 5fdnccg,jc.af:m 0a.4zh :resence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this b,zfcgcj 0u45amn.scd:.:a f hy 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 and vad 8- b*:wx j4-kfihmaf+.o yrklley 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? Lightefoi+a:br jd8w k4-h- m*x.fy kst? 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 satellites orvwzq xf8h5 :)jmo zcfm.73r ax9x 6pu-biting 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 fewrmz wf h-3a5:of6 7x8xqm.z ) 9pvxcju 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 meh;ky4ozwyf)c0j k , xw6.xzw2ant to orbit the asteroid Eros at a height of wxjy.4xz k0y wz c2ho;k6wf),about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the spact3x/3lcsa lo+ ilb)s 7wmf-y9 e shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abovl)3o7 /mc 9fbx y ilaw+-3tlsse 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 v4vpdm-b je,, a period of 3000 years. (a) What is its mean distance from the mb-pdv e4 v,,jSun?   
(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 of4,gpa( icbt zrk6)d e/ G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Md6 ck r(4za etbig,)/pake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mil nr+5.i3e2b*g0 dkob.zy z qmgky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-ye*rbo3m gz2i0znbe q5 y.+.gdkars 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. fdsm +)*ig8nyFind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass pdg*mfs i8)+ nylaced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 l:0hv tg+hk(6cdk w+wrl. cb:k 5fex;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 acceleratmt2-k ,an gmrm 2*dng9ion experienced by the tip of the 1.5-cm-long sweep second hand on your wrismmngdmt 2 * rn,-kag92t watch?    $\times 10^{-4}$

  While fishing, you get bored and start t/ycbo rsy7- ue4 t )r- -jowol2uab7;qo swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the ver yrbu -re-/7ow-7ocs)2o;q utyjab4ltical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a no;527 zgg7/rx2bm aitaxg(d fa8tc)wew highway is designed so that a car traveling at spee bxit xf;/z2oac 75(a w8a gggmtrd2)7d $ 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 t x)5qjvfk :ie+qj :j1urain, the Acela, utilizes 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 j)i qej xjk:f5q+uv:1train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$