Sometimes people say that water is removed from clothes in a spin dryer by cegqm5*6ev: hth ntrifugal forctghq*:6h5ev m e throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around aj (+by octgm-2 sharp curve at a constant 60 km/h as when it try+bm go-jt c(2avels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly roao 5 a.- j3( xe)xefbpp+xtj1ccd. 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 bottom of (15 . pjabxef3 x optx+)cjec-a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round.fetmp3m z2 p34 Which of these forces provides the centripetal acceleration of the child?t334mzp2mf ep

A bucket of water can be whirled in a vertical circle withlh 4-zp jn,*hpout the water spilling out, even at the top of the cirj4*-h,pn hp zlcle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leastc kcjekzen4(e 71cz+) three controls in the car which can b1 kce+kc zez47c)n( eje used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying overzs/ox:18qh wu 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 usiwhu8xs:o1 /zqng Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high spey0w2uweldeg50, gylvw26 9 kued?

Why do airplanes bank when they turn? How would you compute the banking a59p(8fcshb lj ngle given its spehcb598spl(f j ed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. She xem:)r+cr bkf/ mva35 wants to let go at precisely the right time so that the ball will hit a target on the other side of thef:a)c e/v5+m krm xbr3 yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how larhv/ 6accx -0ncge a force? Consid-06hvxn cc a/cer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would toll3/ -ehk m0 yqgg,f(he Moon’s orbit beg,/l(-ylog0mfh q k3 e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon o;iw(77 6. jt 9fzgt.rokveia 04nl lson the Earth? Whiciz jawn4k os797r0ifg ;v(. et6l.olt h accelerates more?

The Sun's gravitational pull on the Eartzu7cb7 wc b6x ds7;5f mj0htt;h is much larger than the Moon's. Yet the Moon'scbhf stxdt 0;77u z5cwb jm67; is 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 more at the equator or at the poles? What two et/(fyfd x9/- md alo8lffects are at work? Do they oppose eacxf8da yd 9f(t-/o/l mlh other?

The gravitational force on the Moon due to the Earth is only abouus; 4u wt-k4o4 tsqka4t half the force on the Mokt-o4uw;ts uq4k4sa4 on due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its n qlz 7l/i;hw,c+ gl9iorbit around the Sun larger or smaller than the cc;gliw9l/+i7 qnh ,l zentripetal acceleration of the Earth?

Would it require less speed to launch ali9yww ww2;6cf 9allv 84q,2jyk tiu 0 satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dirc t 0ifyj9w,2q2lik6;w9 awwl8 uly 4vection.

When will your apparent weight be the greatest, q b i 8rw53pr7n(rxk1fas measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in fre3rknprx 8b( r75qwfi1e 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 adversely affe tmuc ffbk-muz -jj;:0a)4-pb hxv0p4cted 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 force we feel on our feet, and (c) any other aspects of gravity you can thin0-40tmapm k f- z vb: )-4cbjpu;fjxuhk of.

Explain how a runner experiences “free fall” or “apparent weightlessn-. 0h3lz 9g*extvas pqess” between steps.v-qhagp. t9l*z0es3 x

The Earth moves fast4l cl:ddvh*1i 8 )oaoa4ti t*eer in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in Jdt418*ic da li)tolhevoa4 :* anuary, 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 until it was discovered to have a moon.xa)w vkltwv4o)wmo*3r l 7(cy0c /rw8 Explain how this discovery enabled an estimate of Pluto’s mass.ky8rvm4 cr3)c)ao7lw/ w *v0 l(twxwo

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yi*r28 -5b sqic:q4f sfjhbk: xet the Moonxi:f f:-5 jb hibqs8r4 q*c2sk'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 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 1mq( b etc h;mc;qg4v bn9fi;;;980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 v0c sml)jkg2ef5ze8gs-h ,d .around the Sun, and the net force exerted on the Earth. What exerts0klsc z.,5 2dgeefgh-)mjv8 s 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 210x x 57fje.(fuj N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of j7fe j5u (xx.fradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is ina 8vgg;.3s kvlmr *a)tx +z4td orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find tal svr3 zv+ t). 8;gkmta*dxg4he centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck o-;-5k re-kgq xutji2 if clay on the edge of a potter’s -uji; x5 qg-t-k2eirk wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vert19 3 g,on,hgft;0ecep3xs *bfj e d5duical circle of radius 72.0 cm , as shown in F3j, 0o1fndbh,gu 9;* 5 gxfep3steedcig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn ofg gxx akd9 y2e/z+ 9r+6 tyo-qr8ikk/t radius 77 m on a flat road if the coeffic+rkx/xzg6q9y+9 gydea82rtt -/io k kient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of stat ga 6zizku(-c.r (cmsvo(u,g2bbu;:r ic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km ;bc6. :uumi(r,zvsb u(-grc (oza2g k/h ?   

  A device for training astronauts and jet fighter pilots is designed to ro g;eemdp6;h 4ctate a trainee in a horizontal circle of radius 12.0 m . If the fo;chg ;d 6emp4erce 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 axi/ob. o;+qfa-wsavx x;s of a rotating turntable of variable speed. When the speed of the turntable is slowlyb/v.ws+fx;xaa-oq;o 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 ad8 f f:wly(4ai hsd)t+ roller coaster be traveling when upside down at the top of a circl(dti8+dw l:4 yh)fsfae
(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 driver1c54 krqk zhc sk)yg5:) crosses the rounded top of a hill (radiuskzr hkk)5 cqy 15g4:sc =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 pe3 clq9qx-) levr minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlesslcl9vqxe 3-q)” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m8,u o9 knyyigi9*r8dcv(v +dgkq5 ;nz. At the lowest point of oy ig8ur(*cv98 5 q9+kyk;nzidngdv ,its 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 if a particle 9.0w:z t /;k1dt lq.7oa8qcl-kjf4u5fqc0 cm from the axis of rotationk/dwqfoq 1;zfl -k ta7tu8jc ql5c:4. is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrz3wcgs9x :sxans1 / s;ically walled "room." (See Fi9;swssn:s z 1xg xc/3ag. 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 ) i3 +p2b bakvx ;xopqe iq2m2-;c:( ydccs rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig2k- q3(q; ap+xbdpvi2;:bom2 cxyc ec. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisd aldn+2km)0s +m *ie7abf +bkely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In0l skdaf mbn +7+eib*d a)mk2+ 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 perfe wih4e2uz,d xe5c c(,ictly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massen4 w :/hyoofr ih2g7.gs $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 31wmg,*rj u /lh/0 $\mathrm{~m} / \mathrm{s}$ . 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 ceo.h / .cwdkd3ontripetal components of the net force exerted on the ch/dd ook..3 wcar (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 :ae u7jnt*qo ng*7qe1w+8 8 wt:egxsv, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangentiao8q *t8e7w*xgg 1vsenq:nt uj aw7e+:l 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 pxk q zzk8s *asd7vu4e8ww1zrx b17c5;articular instant, its acceleration1zsb8 rzx;8e5a v 7usx4 zw17 *kdcwkq is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravit*4 1tsv f3qr )mroc3afy on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350mt1o rs3 qc4)3vrfaf* kg.   

  At the surface of a certain pla aq 4zx4 5uiitq-mme(g* 56urvnet, the gravitational acceleration g has a magnitude of 12gmr x*i zu5tqvq 44(u m-ai6e5 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 Mo rbzjdcd, qs4/2)b4 kjon's radius is 1.74 /skd jjb2)rzcqd,4b 4$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that ofk:nrr)hj2 q57 p4mq jq*mz2rh Earth, but has the same mass. What is the a2mqkh25j pr7mjr*r:q q4n)zhcceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of21 h u-8qu.xrf7 cji1i)ii )/na jtyzq Earth, but the same radius. What is g near its .i27iy 118j)i)af-z/uji rtchnq q x usurface?   

  Two objects attract eaclj.6i+ 1h rjqoh other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of graj(uwcih d eh,;-g4t 0svity, at (a) 3200 me,j(s htd4ig;cuh0w-    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the *t ;r)zedb5djEarth’s center to a point outside the Earth where thegravitationalbrte;5 *djd)z acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hv m/z4h7g5e374(wr htyqx9wc l hr; muas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface grawexw 53hvr mtl 4/;zqh(ry7cgm h9u4 7vity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our S.jj exk4gdvh//dh /7eun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfakhexeh4/d.//j gd 7j vce gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whilh4qk l)0 z2pra/y iy+se orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms ofyz )kih4+p0 ralsq/2y g.   

  Four 9.5-kg spheres are located at the corners of a squycpfh y3/dd/2are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spheh2yydp //c3dfre by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on te1c1pop -( qmbhe same side of the Sun. Calculate the total forcpqecm1 (p-bo1e on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of g7 8vs6o6wfz3ul;qqpa2 *nxl i ravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius3 6s2p q 7l nq;wa68*ivuzxlof is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the ptfv*37st,9 , 3dm-v*bsmxg-z 8ynwbb-yqgozeriod of the Earth and its distance from the Sun. [Note: Compare yo-og xmbgztv,yw3*- zmv 89*qdbf bn3,tsy s7-ur answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellit 2v70gdey c*e ed dlg1g;x9w;ge moving in a stable circular orbit about the Earth at a height of 369ecyew; g x1edd*vl d7g2g0g;00 km.    $\times 10^3$

  The space shuttle releases a satellite into a3w t t56afiwys)kr -(ev5 y9m,,rbagc circular orbit 650 km above the Earth. How fast - ,s,wm3fbt (erc 6ra)wikya95ty5vgmust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceso f gdl8kuuk; g;w1)-nhip rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spac;w1gk8dl )fng o u-uk;eship’s diameter is 32 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 satellitubu-5v;y 9gi se to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass yvu;g su59- biof the satellite?    s ~    min

  At what horizontal velocit*n r/nnge v6x3y would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?6 *rgnv/n ne3x   

  During an Apollo lunar landing mission, the command module continudg w7/,t x9l x0cpv:mled to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once?p7x ,d/:llt gwx09cvm    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The ins0 m1rgl nr; gij/g;f1ner radius of the rings is 73,00 imfgng r;;/ 0rlsgj110 $\mathrm{~km}$ , 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 evec(oo04umj/pn+d .uhd4:kx hpt8cs( y ry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent w u4dt:0 ushc8((pj.o /h y+n4mxkcdp oeight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg muzhl.qs. ok/u7,uz g9qg*q6 astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving.qu7muusgoz9q z g 6*/q,l.h k 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 twok)u gaqwd7 kac( os+6r*; mv9i stars of equal mass. They are observed to be separated by 360 million km and is 9*k)ouqa7cdvawmg(;6 rk + 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 womanbi ag5r4n bdy4zhc+iz yyk-d-u59 7(n in an elevator that moves-u 5 drkh4b+zzya-cnb7iy 4n y i9g5(d
(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 ceiling of an elevator. Thc/v+2 /vuj+gq/gen9 vx vn 1 p*oo(zbte cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitudev/ x/n(2ve*vqou 9c+go gzjtv1/n+b p and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with xf v tcp.;,f;zperiod T , the densi;tfvz f, x;.cpty (mass/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 theij463xu +g *din+tzdo period of the Moon (27.4 d) to determine the period of an artificido xizunj6 +*4ditg+3 al satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred truw m* q/76c7dl.v-wqrv:me meters across, orbits the Sun like the planets. Its perioddluwem:./7q-v m6t c* 7rvwqr is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagzvpk+ odf w/g5o9 (9vae distance 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 the3 +su muyp *z8b0t/kbhfmd ((y 4fop.d Sun roughly once 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 planet’s orbit is nearest when it is out there? [Hint: The mean disto4/ 3bm f8+dt pusbpdym0y hzfu( .k*(ance 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 cente +8ou z6uqspjh3 gvo7a0nf-rg,,x so9r 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;+8 h:sgyt (vst0i8jhqgn4 oz, and mean distance for the four largest moons of Jupiter (those dish:oqt+g(shs8t yn4i g v8z j;0covered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period anduroh r54 )k:n1 d cdu,efl7iq6 distance of the Moon. r15 nu74u odhl,:i6e rfk)qc d   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s s9n 2kjf 4r4xlmoons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3.x 4jn k2rfls94 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 Jujlnpwyr3* dw bj31+o/ piter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but wasw r*3w+l 1onjbjp3dy / 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 fx sh; /*bse dly8cwc-1orm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that th/swl- 8c; b*hcyx1d seis sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hangi8psp (uf) b4 a6+ ffbfqmshl/,ng vine (Fig. 5–41(b+fa6)m,f f qusl p/f 8hpbs4). 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 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 gpbog ++ /8,ooqbsn/yrravity be half what itrq/ +bo8 ,ob /+npygos is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin2u0v alwfafk3*d l wrx;12j6jt04x)l3fgm g s in a mutual circle once every 2.5 s. If we wvm3* 3l4klxsa 6jg rwdlfu )2 gf1 0;a2tjfx0assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatej9* iuq28 ;m bpj6ulan:,qurb s once per day, the apparent acceleration of gravity at the equator is slightly less than it would be ifr2 m9lpqa,jub8*6b i quu:;jn the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance fro dc9 bsx wq0)-:wyil-xm the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with 0: sww9iyq-xb c-dx)lequal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,:jy2:mv1j ody mq:d: tguta j6 jm5b,9 but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevq9a16ut,b:o2 jgjmyd j:my:m5tjd:v ator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circul) 3 i zof 6 fbvk.ovsg+70klejgsps+35ar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What mugo7ov+le sp0f.jkg3kb) 6v fi 5z s3+sst be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43).v)/qgf( syo /mho9v7-pa , f)awqeob0
(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 amlesp1y5lj,vk,8 j1planet in terms of its radius r, the acceleration due to gravi,ap1sjj1l vm ye 5l,k8ty at its surface and the gravitational constant G.

A plumb bob (a mass m ngqa( z -bq.e.,ekc uu,;4r wf hanging on a string) is deflected from the vertical by an.bg euzkq.w (-q ;e ,,c4urafn 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 forwq4ilys3xc i9v 0/ 1zg zy,mf.l:v 7tv a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handleyvvfzvl3ii7q0t:g z. my4l 1 /wc9x,s the curve?

  How long would a day be if the Earth were rotating so fast that objects at p jsf .-yw y.n78s2rewnc0;2/g fzalathe equator were appareyfw;gl n802sae7n-.wcr /2 ypz jfas.ntly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant u o04f.rvef3nh 9atx0distance 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 speedps( e*0 ffzyd+ rounds a curve of radius 235 m. A lamp suspended from thefsz+d 0y(*fpe ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mass7t1*duf3f o-qeoj (y qive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such o* utf7-31deyfo jqq(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 d(y ;o3s3 -uqpbvsq5 e sz-nv.5uo/lqof 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 by measuring 5 v-.3q-5qso z y3uqvsdb;l/(ensupothe 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 ixjcs 1+: sfw 4xrd)9tcn7xgw 9o*3ljot 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 sg+9cw7*tn wf:os1j3 x l)x4x9j od crlargest? Smallest?) Explain. (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 satelq+98 tyjsb6fk(td 4bp lites 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 accyt6kj +(tps8dqf 49bb uracy 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), afte:2ws*1qkj hnxiwxh lduo+m jr::. ;i5 r traveling 2.1 billion km, is meant to orbit the asteroid Eros at a heighoh2m 1u kxh:jq +r.xdlsw;:w:*nij i5t of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repa tm.h:ou2vzx8ir. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km be2.oz:x v ut8hmhind 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 meb ;4vdhiiu,, n.n6aqean distance from the Sua;ei n,u h. 6q,4vbdnin?   
(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 "feelw. 6qwbxuby5pu* -6wn" yourself gravita-ub6w6wqb5 uwx .*yp ntionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distap-j pk 9ksoxj)p)y,/nnce of about 30,000 ljjpks))o p/9kx-, npyight-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 locod1v-luc8w+wzl11 h wated at the corners of a square 0.50 m on each side. Fwhdl81+zov1 u-c l1 wwind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass b04psl gz0/ d0(md;hffdlghk,p* m *g 5500 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 by the tip of the bd8uff;t+9adwff ny54 m,vdf vh7* x9p4ndw*1.5-cm-long sweep second hand o;f vxddynfm + u7b fphw5* 9dw4,fta8v *4fdn9n your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arouk nyw(kq :3.mxnd in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. Whak y.w (:kn3xqmt is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R 6fhf,wp0 (hfgin a new highway is designed so that a car travelinf(ph 0wh6f,fg g at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of 70mj ,mgftb4ethe cars when negotiating curves. The angle of tilt is adjusted so that the 4m07 fetm ,bgjmain force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 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.$\approx$    $\times 10^2$