Sometimes people say that water is removed fav/se+ dk6j,s:urn :nrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrosnjs eua/,r6+:vkn : dng with this statement?

Will the acceleration of a car be the sam si2wlc/-a95 j+ufi p7y nv+qae when the car travels around a sharp curve at a constant 60 km/h as when it travels a2iu57iavqfs9nywj p-alc+ /+round a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly r6vdxobzks:tj , ;q+eitu7n1 3oad. 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, 36tznx uieo:kt1q +b7; ,sjvd(c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh3 g9;kkwvjm kd dapw1 :b0 pmt::js9s9ich of these forces provides k:: p 1pwgjd;dsts:90ajk9bk m3m w9v the centripetal acceleration of the child?

A bucket of water can3 6ki f fujhsm*t-5f(m be whirled in a vertical circle without the water spilling out, even at the top of the circle when tm5mijk futfh-3 6(*sfhe bucket is upside down. Explain.

How many “accelerators” do you have in your car? There arl/ zt6 8lgv2are at least three controls in the car which can be used to cause the car to accelerate. What are theyr8alt26 l/vzg? What accelerations do they produce?

A child on a sled comes flying over the crest of a small ht0ft-xl n4+n7vb gj m06fsmk0 ill, 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 t m0 vxltf7km nbsn4+g0t60j-f his decrease using Newton’s second law.

Why do bicycle riders lean inwarvr l+0nf/cy0cd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle m7d7f,r v) .*(efav)ah agorzgiven its speed and radius of ha7rvzg.,(f a 7o))v mefd*rathe turn?

A girl is whirling a ball on a s;ro*wb1jv q00 os2jk9 b ,xkmdtring around 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 should she let go of the string?k 90vx;mwkb rj0sjdb*1o,2 oq

Does an apple exert a gravitational force on the Earth? If s8tr(akly qq:h/ mfmiz 8 zf:06o, how large a force? fktz:yl6frq(qh :ia/8 m8z 0mConsider 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 tlfqflj0v 3xt1(c( 6hbe differenttl0c hvtjf(x6l f q13(?

Which pulls harder gravitationally, the Earth on the Moon, g*yw 3)wlw,v hor the Moon on the Earth? Which accelerates)*vg 3,hywwlw more?

The Sun's gravitational pull on the Earth is much larger than the Mooe:cz ( lt*dzj314leocn'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 tc4jto ezdc1 l:(* 3elzo the other.]

Will an object weigh more at the equa(5hz m)jpo v-tav*zm6w /t1dmtor or at the poles? What two effects are at work? Do they oppose each other?561tv)tj- *mp v/zw (mzmahdo

The gravitational for 1)eu 32yx9 pij.jmf+joiq t6ice on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled aoje9 . pxti)31 2fuii+6jjqymway from the Earth?

Is the centripetal acceleration of Mar bbg-z;60ldp4zgm8 m ms in its orbit around the Sun larger or smlz;-gm b8 0g pzmb6md4aller than the centripetal acceleration of the Earth?

Would it require less sp0xqkc2ppch6 5v nh.kle;az08 eed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direch.v8pkccz2qk; n60e a 5xhpl0tion.

When will your apparent weight be the greatest, as measured by 1uqc mf18 wpl5nyqe4)s9m6joov 1,k ga scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When wo94osvm)p 8, fjk15ygqn6we1qcumo1 luld 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 :jwh9l;ctf/j c9cukta yc5 7-adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravihy ctc j5l9-f /cukwct;a79:jty you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessne*ho6nqnp+tc2sn4r x) ss” between steps.)oqp+ nnxh r24 c*n6st

The Earth moves faster in its orbit around the Sun in January than in Julyqk(fnz9c6)kv f93kpjfdg- 4-c3 wfho fwd /8h. Is the Earth closer to the Sun 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 itsnjdf fdqcw -wg 9ohvff/zkhckk6)3pf49(8- 3 orbit.]

The mass of Pluto was not known unti;* gs)4 1:,pjtnjd -xtteg jhol it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s map; t1x jgtejt-nsdg) j4 *:o,hss.

  The Sun's gravitatiotv0l +r6h p 9bgf7+sziz/1 f.qqyjid; nal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to th sfyjg+bztl 9 q1+ pif6hqrzd.i0;7v/ e 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 .d .9nnkm e t(vy:0 2f//dvkn jbwnj-m1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ik)s 0c8p mceo9n its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the E08 )mecksoc p9arth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg dis r onld-j*g;v g*gn,0.rjtsd* cus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate thetrggsnj 0d-,gjvro. l*;* n *d speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circli *th0nxp ub :k*yes86vhtx*0ia*po8es the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms k aitb8 *x8t6 e:so00ppix*u*nyh*vhof g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on theod7safp/u nf7n,s 3m( edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32u3,/ nnmop77(f dssaf cm?   

  A ball on the end of a string is revolved at a uniform rate in 2)qgt9n:r npnc9rnjprhl( 7,a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed i :cnp,(r2)tl q9rgh7 rjp9nnns 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 w86d.je;qi d4d rw 9lqw; x.dfqith which a 1050-kg car can round a turn of radius 77 m on a flat road if tdd w8j.qfqe6d4wrx9 l.qdi ;;he coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coe7h7d vt;8ctgev4i 7v bfficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed o7e b 8dvc7th7vi;tv g4f 95km/h ?   

  A device for training astronauts and jet fighter piml4.oj c+pt5mlots is designed to rotate a trainee in a horizontal circle of radius 12.mo l.5mcp+ jt40 m . 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 rotqkzd1s1y5:+a3 -pi7mveda z+p hrk3 qating turntable of variable speed. When the speed of 1p q+dm +73 krdq3vaek- 5s:hiz ay1zpthe turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a m3iy tv3j5f;h fz x*n(vm. )aqroller coaster be traveling when upside down at the top tqhi(fv. nfz a)*xjm5;3 ym3v of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of masatw.0nws i:/ ypk3j3z s 950 kg (including the driver) crosses the rounded top of a hill (radi 3y:jt0k/wzsi w 3.anpus =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 needi(ao:oj b sy./rgi )/am5e: km to make i a/gk:oar5b sjoi/.(mem:) yfor the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cirlt42rn6 tq,hwnv,xiq9q / 6xjcle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buc q jit6n6 hv2nr9/x,l4 xqtw,qket 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 fromlewp a94 x5sx8 the axis of rotati8 s9pxxal54 ewon is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated/y3p+yzax.z8notfzlld;m + 0 o, 2kxt in a cylindrically walled "room." (za,z2x/.y0 yl ++ft8d om 3lzxkp;tno See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circ( +ec( kpauh1 fqb t4us*-m3lile on a frictionless air-hockey tabletophe u ql*1(kb 3csaumfp (i+4-t, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the bvua;qk7*x. ) dthslaz8c yv.2all which revolves on a yh*zkvt a d x.lsv7q)c a2;8.ustring 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 75 )rn9(kjzv00-(rvyo z gl+yxf4qse +e $\mathrm{~km} / \mathrm{h}$ , 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 aa-z)a)k:jpx $ 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 verticallycb d xr1sb84uk k97-o46dbm se 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 components of thebh/k:4;jzaxtq oqn +g 7z8-ur net force exerted on the car (by th t8 /q4q u; bz7onjkga+r:-xhze 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 p8:z6xjeyr5pbl89lydp8q qg k*p 9otmt k f; +1it area, going from rest to 320km/h in a semicircular arc with a ra5r 8zp;g 8ky j*expt1lotp6mqlb kqd:y+f989 dius 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 p4wy* ieu-3 /t2 hhzzhm . At a particular instanz2-tui3p4eyz hwh/h *t, 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 Earth’s gravity on a 5 ok-g.zy)8cl1ozk a /vi5mdgspacecraft 12,800 km (2 Earth radii) above the Earkok c.8m5 vlg oyz1-5gd/iza)th’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratsp ;vwmhnjq 7 9g(40wlj-2cqd 1pcv j l6zly)-ion g has a magnitude of 12 m/sm26v1- pjqn( q hw)j9sl;l0vz7 py lccgjwd 4-$^2$ 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 grosg*m8vn 7w+w9yfvpp7 pp,,y mn: u8h avity on the Moon. The Moon's radius is 1.78s9+ v7,g 7n,w:n hypp8ou* pwp vfymm4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet h4en y a)c; w1uojl3nz:as a radius 1.5 times that of Earth, but has the same mass. What is the acceleren3 c);w:1yoajz l4unation due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but w8sd 5ab s*ss(the same radius. What is g near its surfaadbw8s5s s* (sce?   

  Two objects attract each other gravitationally with a -.0 lcomjcnrz 2/ro5nkn r,* ss-j k)pforce 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 , tp/2rfc7cti: , oq0 zcehe acceleration of gravity, at (a) 3200 m p7cc/fqc et0o r,i:z2   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsinyp*1a7noc8 qde the Earth where thegravitaca7p *yqo1nn 8tional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thxj z830q mt6que mass of our Sun packed into a sphere about 10 km in radius.qjqum83 x z60t Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avbp0g3a-0f9negpwcx 2r: bms4erage star like our Sun but is now in the last stage of its evolution, is the size of our Moon b-0w0nabp ger 4pg:2sfc39x bm ut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel wd xjkzeryn/6- j;)d (e90wegei5ll b)cuu7i 0eightless while 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 ti nd/erc 0kl-5 gljx u6()yje;0e) ubwi9dz7eerms of g.   

  Four 9.5-kg spheres are located at the corners of a square fc 9xol8b;em 9xvc+x1of side 0.60 m. Calculate thf ;xb e1m9xv cx9c8lo+e 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 the planets line up on the same c8u *cvrnz4o1 side of the Sun. Calculate the total force on the Earth due to Ven nr1vc*4oc 8zuus, 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 the surface of Mars is;uy-jfx 4ct8b3lduypnh 1 26w 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of;l8yf 2u nhywcjut1p3 6d 4bx- Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perj 2;abw/ge)ju iod of the Earth e;/)jw ju2 bgaand its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed o-.-sx v d4yakd av1nz*f a satellite moving in a stable circular orbit about the Earth ata.1d*4ka-y-svv nxzd a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km 1xyj/u ,mrh k(above the Earth. How fast must the shuttle be moving (relative,/ h(kxju 1ymr to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan7- 9kh( b4ix- ejja/;k 2lf7beqfgl gqts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 2l-7ea gklk4qifh2f x(;7j/ge -b9qb j1, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in-+k7:f rsh8j,um fc-sd1g f ck a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfa17ksfhk 8:g-,rc +f uc-fsjmdce of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the t j3 8 tyteqefo)sb93 /d-+dudcop of Mt. Everest to be placed in a circ9tjdo3 us/d+8 bqcd3 )ye et-fular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module w r. ;1jscvenab )5ta8continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? jaweabtc85r .v) ns1;   s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Tht(ox hkzvrws ,war uzyop.u2 r5:7.()e inner raz.( .aw)kxps ovyt,wu5zo7hr2:(u r rdius 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 (se r3o+,l cufrbp o5e 3/9wrur)qe Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottomfqrr,br+u3puo el9c3wo)r5 / ?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center o arz6;ucb q7v+o(kb) gf the Earth's Moon in a szc+(kob ; q bg)arv7u6pace 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 ozkz+09okw9p)/kmf /1 pm fdowtv *)hjf two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of e1f k9ov/+pdkz owpfw9 t z m)hkj0)m/*ach?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman ke6 o8qb h-(8 m/rb z ta4ar,bubcbb9 l.s;8wwin an elevator that moveswzqb,e84m8-bbl(aa ks8b bh9; rr otw/ucb 6.
(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 59h+xnria4c 4o+o nxdy (6prpfrom a cord suspended from the ceiling of an elevator. The cord can withstand a 5xpa++oxr4icyh ronp ( d4n69 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 satelli7 3paqo1z8dnc8ez4y -c7 apaste orbits very near the surface of a planet with period T , thncs7y-87ao 8ce 1zp4dpqa3 aze density (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 the period of the Moon (27.4 d) to detery:ss./uf vkx+ :s6zvi 2ysvq5mine the period of an artificial satellite orbiting very near the Earf s.u:sys 5 x6+svvky/2vq:zith’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lir2wr4e7gxm,fs3 e/ hbke the planets. Its period is 410 d. What is its mean distance frh g73m er,x2feb/4wrsom the Sun?    $\times 10^{11}$

  Neptune is an average distfkl+wg3xf+m wh 14 w5gl /ksn3ance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once eveldused1 f 78ka0n,( chkm ixirz2-)0qry 76 years. It comes very close to the surface of tdx l7q8kzim i0210h-dcf (r)sunk, ae he Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga8gy qxux 0rh3n m:mn eb8 6jak6.92bmvlaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distancefiansgvv((voi 957m) zku 6 z( for the four largest moons of Jupiter (those d6nuv5zoi (g(vmv(a i s k97f)ziscovered 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 and di6:r*osj8bm qz /*rksg stance of the Moon. :rqmb /**szo rs6g j8k   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter ;2lg 4///sdn* kc ahadzmu hp*(o6pte-j3wwq’s moons, using Kepler’s pjmk/( z2tl46wu*qs w //c* a;onphdedhg-a3third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter co+br xo:3 3zbn( mf*vgvnsists of many fragments (which some space scientistsbv* f( x:ovnmrz+ 3g3b think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artif.enxrpl+(r( z cfi33micial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earn( (x33prfrz+.i mel cth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swingy:tvks 5do. h-ing 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, vs-:ht5.d ykowhat is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be h4/d:)t hde zs se1u+hlalf what its zuth le+4e:/d1sd)h is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equalx f.ky 17o7msv mass grab hands and spin in a mutual circle once evefo. 17 vxy7ksmry 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 on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra;2wv ndyv5ry.vity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this efy.nyd2;5 wrvvfect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth an1 r jhu10 fehfe08s/will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth ae1 /nj0r s1h8he0 affund Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whgu5gmueuew bw j6:t;-8e34 ok en you stand on a bathroom scale in an elevator, it we-u3um k;6g85 bjt 4egueo:wsays your mass is 82 kg. 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 zpp0q ,t + 0dmh6 pcixj9s+tz0will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) ix,m9qpzspi ch+ jtzd6t +00p 0f 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 (b2)o-zysyu8 kl*0 krp(dj ,vkFig. 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 planujrtc8 ;(py so(m; :u ,9f0 j.bbgkoqret in terms of its radius r, the acceleration due to gravity at its surface and the gravijc m,skrb p:j8(gq 0;yr(u; o9u.tbof tational constant G.

A plumb bob (a mass m hanging on a string) i14s. ijl qdh mmz1jv:*i:c)yis deflected from the vertical by an anl.4q:: djh 1i m*1c)imjis yzvgle $\theta$ 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 fx fr0h;jfl wvh-0m*(jor a design speed of If the coefficient of staticv0jw (hrf0*-lxh ;mjf friction is 0.30 (wet pavement), 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 objectsvt22c0z,kl)c c k2llf at the eq2fl2 2vlc)ckz tlk0c ,uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of . omk0 hlo)yfist1 g.+9kjas+ 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 cury3scrw0.u ktpb 2aobo1e.e7/ve of radius 235 m. A lamp suspendebeso 1ut3y .2e.0pcw/ rabo7 kd from the 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 massive as the Earth. Thus, it haen7( dx(ryusg-7 mk l l9 wukw(:ko2y)s been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the followingl km(n )9xlu2:kd( 7row- yk(wy 7eusg 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 toh6(0 po/g4bd+n umyahe presence of an extremely massive core(m6p oo/a bh4u0yd +ng 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 0t.i6 bsdq8kjh )eh rq30x(-jxz f.tsbc,k9e and valley shown in Fig. 5–45.bjtf i8(3k.s. e x0 kce90jdhtx ,z qq6-shbr) 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 road at A?

  The Navstar Global Positioning System 85z- f1zmhj 7nlysj0i(GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a y0-s8hz57nmzf ji1jl 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 Rend-w(ap/*lqu,ka 8sg x -i fou+rezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15sf/- al8rqx,up i(-*g a k+uow 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 repairt1z(- x7k3xlw*tnf7qog jcxer v5s65. You are in a circular orbit of the same radius as the satellite (400 km abx5w61kvjoc 77r3e-tsqfx5 tx*gn (lzove the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (az9uy(d7c2l d5 5ch sce) What is its mean distance from the Sun? 2zuc( c9 l5sde cd57yh  
(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 w5omz ztvyaqyb7.o(oz* zy2g 8g4(1 qdould need to be if you could actually "feel" yourself gravitationally attracted to someone near yo bd(z( o4qzyq81a zt*zm527vyo. yoggu. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-4c89 y5aqqg g9r6) at a distance of about 30,000 light-years r958q9g a gyqcfrom 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 cornerd.a7m-z, sxk ew8u.sis of a square 0.50 m on each side. Find the magnitude and directuam.,8.esx7w z kds i-ion 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 5500 kg o aa91e10vp8ql62 xuowul0tni rbits 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 expzdzz(4hnh-7yk idx9, erienced by the tip of the 1.5-cm-long sweep second hand on your h -9dd4 inz,7zhkz(y xwrist watch?    $\times 10^{-4}$

  While fishing, you get bored lovl8os 5xk6++us *weand start to 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 vertical? [Hint: See Fig. 5–16vsxo+l 8+wlo *5 eusk0.]    $^{\circ}$

A circular curve of ya:tw 3u yanifhx/tv,795(kbradius R in a new highway is designed so that a car traveling av an7f/b3 9y 5ia,ywxt:u(kt ht 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 n+qedav,v 2 8dtrain, 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, tovneqd v+,8da 2 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.$\approx$    $\times 10^2$