Sometimes people say that water is removed from clots 8 9cg 1kgspugt 3bgq3;f*ca,hes in a spin dryer by centrifugal force throwing,g;t3g guck*cq93bsf8a gp s1 the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car t*-i5wnxzmu fr v+*d* travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the sa*rf mwv+ xdztn** -i5ume speed? Explain.

Suppose a car moves at constant speed along a hi;vah 2rer i/q+lly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of 2rvr;/ haiq+ea hill?

Describe all the forces acting on a child riding a horse on a merry-go-room- 4 i 1sxvvbyop.)-jund. Which of these forces provides the centripetal acceleration bov x.j- m-v4sp o1y)iof the child?

A bucket of water can be whirled inj j6mkd)bkjq b82v 4:i a vertical circle without the water spilling out, even at the top of the circle when the bucket iv2bkb )i jk4d jjqm:86s upside down. Explain.

How many “accelerators” do you have in your car?a jcz .nqwliut r9g s)oe):x 5-w3e0c( There are at least three controls in the car which can be used to cause the car to accelerate. What are they? 5(x3ce0w-:g.j qw)zucna9)orie t ls What accelerations do they produce?

A child on a sled come gnh w9u8nw(hbz0 +1pvs flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does noh(vwbnn9+hpz1g8 0 wut 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 law.

Why do bicycle riders lean inward when (yr)q;bp 8oij rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bank, 9 ++hu lynqogab+g.:56x 0xhlzvzteing angle given its speed and re l+ .gxgzu hh q9xv6+zl +b,ty0:5anoadius of the turn?

A girl is whirling a ball o1mp*e 7hgn65bwshy-z n a string 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.5zh6sy1pnm7h g*-ebw When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If *p5zqioo f p4/so, how large a force? Consider an ap5 ip* fo4pz/qople
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublekw+vhr*u5ti5 igganus)55 i:vp4bs; what it is, in what ways would the Moon’s orbit be di t a55in gh4spwu+rb uvv)sk5i*:i;5 gfferent?

Which pulls harder gravitationally, the Earth on the Moon, or ;qz)zhnx2fe 8fw)l(r)pu a/p the Moon on the Earth? Which accelerates more?z f lq/fuh(;)nxp2 a r)w)8zep

The Sun's gravitational pull on the hqh; (vjsp -strk)4qi714voz 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 s71k zqj pt vh4-sq4i)o (;vsrhide of the Earth to the other.]

Will an object weigh more at the equator or at the polqkn2j, .kq; wves? What two effects are at work? Do they oppose each otherqw2 ;jkn.qvk ,?

The gravitational force 4o;h4isk2 r48mbb m qron the Moon due to the Earth is only about half the force on the Moon4m2 4k;r8 m r4obqhsib 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 largev.t:5gqtq1hal3yo*wzd u o2 l 0w)m,wr or smaller than the centripetal accelera 1hw,50)d wqg.t3qayu:omt o 2*lwvlztion of the Earth?

Would it require less speed to launch a ji44tl(i1oh tro) p q:zo; +odh;6teisatellite (a) toward the east or (b) toward the west? Consider the Earth; t;di:)i+6hth o(qo tjo4plez o4 ri1’s rotation direction.

When will your apparent weight be the greatest, as measured by a sc2+, xa4bl plp kx:d3c*.izgogx0 0phpale in a moving elevator: when the elevatocbg h20zdxp4kl.lp xgi3 0p+ pa :,*xor (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 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 l/j.rptd2w c hl 0m*lu*ong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with tlw l r2c.dtj 0*uh/m*phe 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 think of.

Explain how a runner experiences “free fall” or “apparent weuknr, f9kdnu)4 c- : u.kknah7ightlessness” between stepskku. ucn-hk n,f)79uand r :4k.

The Earth moves faster in its orbit around ths(ff9z rcw y 8w9ezr.1e Sun in January than in July. Is the Earth closer to the Sun in Januay z .9we(9rf8 1szrcwfry, 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)kq2y fg q9kc8wn until it was discovered to have a moon. Explain how this discovery enabled akf)2yk 98 cqgqn estimate of Pluto’s mass.

  The Sun's gravitationalts* s*t )vao)1kcvkc z,l3u2u 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 gravi2vz tv ),)* u tso*a1ulckskc3tational 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 5q7/rezhl c2wmy:.a w1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 it aui6l )rtqlvn-l70cls6 in+.s orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radiunvcl lusi076 qt-.ra+)inl l6s 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 7ci)t(8,nsworj v2kps exerted on a 2.0-kg discus as it rotates uniformly in a horizont s8 ,tkn()7rv2wj cpioal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's so-g1 v91ht kcc*-b : xbybyfg8urface, and circles the E9 ck1byygghtb-:co*fxv -8 b1arth about once every 90 minutes. Find the 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 of clay ozfz-devx1b-( djjf(-u+y 1 ki n the edge of a potter’s wheel ty11vib jjfukxed z- -+(-fd(zurning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strivtb;y :+ 9pwrkni4,ojhzt7 i.ng is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. kw+4v7 p,onrjt; t9.y:bziih5-33. 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/ ;b2uf drvbo; car can round a turn of radius 77 m on a flat road if the coeffi rfvoud 2bb;/;cient 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 static frictionq7nwe5lz9a 0 w6yre1k be between the tires and the road if a car is to round a level curve of radius 85 m azy n6a95kwerq10lw 7et a speed of 95km/h ?   

  A device for training astronauts and jet fi2r3xhbq/ jtcde7,q 6 ighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?id,qx7brh 326/te jc q    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 *f d3 5cwsmt)y55;fufgwe1qk axis of a rotating turntable of variable speed. When the su)g; 5q ywfsfw5*5tfedkc1m3peed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at thx2d ;ewc 2qmxv-u,f9we top oxfcvq;ww 2md9e, 2-xu f 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 qn( w4e.;u 9n2fria opmass 950 kg (including the driver) crosses the rounded top of a hil(fn 4pra2n9e.uw; qoi l (radius =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 np 3rp8uymum p,r/yn 7h(5e9ubt: mjj2eed to make for the passengers to feel “weightless” at the to:u8ytj5n he7(p/r yrb3, jpum mpm29 upmost point?    rpm

  A bucket of mass 2.00 k x8w viip93;bug is whirled in a vertical circle of radius 1.10 m. At the lowest point of its i9uv 8bwp3x;imotion 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 pa5u1;m8d f e/( jmscmzw(m;epnrticle 9.00 cm from the axis of rotation is to experience an acceleration of 115pjme/wed (u8 ;s1 ;mcn mf5zm(,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" atr )uh w*j,sr)ahw 4uc; a carnival, people are rotated in a cylindrically walled "roowjwr cu,hh * rua;)4s)m." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle yu p3/cip,z j26:ezyvon a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to y je/3pvzyu p2c6z i,: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 igmz ua-yx1ctpw 7 wf5 bsntp7 dwxv :+0vb5*d+4noring the weight of the ball which revolves on a sttwm0 +x tpyb17*nw -5abpddvs 4zcv wu x75f:+ring 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 perfehr(:0gznru f3ctly 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 masses p uk 3j1mb(o/s$ 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 a3p*h( nuvbpm /t 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 gcid8f3/xxw 7np ,9 uv y4gou7of the net force exerted on the car (inpc 3uy xwgd,7g7v 4u9f8/ox 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 acceler/,g h ecys8zfkf:ad09ates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Dg ffz8s9heka:, 0c /ydetermine 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 2g-,cj. fed+0j.axtw 7 qgl-pk.90 m . At a particular insaxckjq.+ -dwf ,ge t-07plj. gtant, 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 spacecraft 12,80 n(bqox (j6+,m 3psuzp0 km (2 Earth radii) above the Eart( x,o mnp3qpu+bs(6j zh’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g uzl*+) rc8q gihas a magnit8r*uzl) g qc+iude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravit yctb/pg ;j6fk1 y-r-wy on the Moon. The Moon's radius is 1.74g-jcfrtbkw /;y6 1-yp $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ty*oahk k)2o s w.tq57pimes that of Earth, but has the same mass. What is the t2 q.k7y)*hwpsoo5 akacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eeu3t it;uul 26arth, but the same radius. What is g near its surfaci3u62 ut;ulete?   

  Two objects attract ey(s.8 m x,qqkzi/i .3.gboj jhach 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 gravity, at d+ rtci+on 15a(a) 3200 m+ 1t5d+an coir    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the z jxs/hav qr, ntvp;;068y5svEarth’s center to a point outside the Earth where thegravitational accelerays8x;shp;0qrz/v 6 5a v jt,vntion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h,q9f tq2if,( aihxk ;pas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate theikqx i(tq9h; ,p2,ffa surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like x(-/lrjs *xmbcc, 2gkg*o w.p our Sun but is now in the last stage of its evolutix,l *g p2xk/gcm so(-b rw.c*jon, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while oj6(fo jh(mlb*rbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them anj*(lf6mh(o jbd 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 locate3xl ;ciqm+uf hubxe +/4th1r2d at the corners of a square of side 0.60 m. Calcuu txq e ur13lx2f ;+b/4cmi+hhlate 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 the planezrf.q-:7xtr6cbk 9o ir+v4ikk2ob + lts line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all. 9+i7cz-kktbf :2o v4 rbr +6kolrxqi 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 0ctt/5*m0yx hx acj,z:.38 of what it is on Earth, and that Mars’ radius is :yc*z/c at0h,5xtxm j3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eart*7o v7puw; b)fgnenl2 7 5twtwh and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exgfweultow;t) vb72n75 *n w7pample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stab6nl0 *f6dz;ckbyjey5shn )+ cle circular orbit about the Earth at a heignsn6y kc6 hcz5) *0ljf+ edb;yht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65r o;syrxmj;-8 0 km above the Earth. How fas oj;yrmr-x 8;st must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants armnegsjo8: sp+.03idx5j p t0 xe to experience simulated gravity of 0.60 g? Asssi .mxpdo 8j3tp n0e:jg +sx05ume the spaceship’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 satellisr rv e4ues(upo:w 1k2j25 lg,af*7w qte to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is o 4f5rar*k1ev2q2sls(opej gwuw7:,u ne 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 of the satellite?    s ~    min

  At what horizontal veloci h8knh 1aiqjhqbhw 2:ndv63 -2ty would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around thn:i vhh1knd 2-q8bhq2a36 j whe Earth?   

  During an Apollo lunar landin u1c/iq b(h1lsg mission, the command module continued to orbit the Moon at anc( q1 1lbiu/sh altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed ofgs0w11lp-awa 7.d)s zk g-9jir vxno+ chunks of ice that orbit the planet. The inner radius of the rings -v s1 1wgdkagl7ipxsr)azn-w j0o+9. 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 (see Fig. g(:pgu f an)ggx49n f*5–9). What is the ratio n 9gxfg*(np: gau 4gf)of 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 75-kg astronaut 4200 km from the center of tho6ki: 2)y av.kwrv.iwe Earth's Moon in a space vehicle (a) moving at constan.voka riykw). v6wi2:t 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 t5uvv(2 eyq np2aknms93euhu+068h d swo 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 ms6neevu2ah +2 q(9vk8 5ud u3nyhp ms0idway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the wq0 ;nn, l/rd wtxv 8zr8n3vq le-/c4pleight of a 55-kg woman in an elevator that 3 -,rvq e8vnrlcp/ lx;08nqtzlw/n4 d moves
(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 fre2ymsfk 23 .olom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerati.yl 3ms2fo2k eon (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period Twk*o26zq cuuxq4)my 1 , the density (mass/volume) of t 6z*c ouqw4xq2)y1kum he 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 54:y,n *gyen csixgad o)7o-8t ml(ir) to determine the period of a4eyy8:x g r clo idonm(* g7,-)5sinatn artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun 3k zbk 5mqpoq.u7k8c7 3na gp4like the planets73q7 u.3 pbk na4kqgzck5o 8mp. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance *i v*d8zd26fc 4kp kevof 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 ex 4oggy- , uxq l5f.0q89fjyiwvery 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 distance s in Kepler’s third law is half the sum of the nearest ail g ,goy0xfw-q8 ju5yx4qf9.nd farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about3 b) xrcnx+so an7(yd iez;k85 the 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, and mean distance for the four largo9i8 brh.( plbest moons of Juhlbb i(9.8 propiter (those discovered 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 distance e;c3b e.g4yljof the Moon. ;jc4 .3 lbgeey   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moonsobp hj((r0i- e, using Kepler’s third law. Ujhobrpie ((-0 se 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 consistp;:xyjxd;ni06n/ h 4 pxv7ufhs of many fragments (which some space scientists think came from a planetui4h0;xxp vjn 6n/h7 xfpd y:; 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 descri-galm.gk8z - nj/ apt r82um+bbes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), /jat+l-288-nzmpu mgrga. bk 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 hanging vinea 5.pqgi7m r7d (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 lowest poin5 pm.a7r7 igdqt of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface 0wat k(6f(n)ov6ugk5wgo1 fq will the acceleration of gravity be half what it is on the suf6)5 ugwq k1( vwa6o0ognfk t(rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsh1erty:7f zr9 5jgsy. and spin in a 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 on one7r9ysz1f ry j 5.eght: another?    $\times 10^2$

  Because the Earth rotates once per da8d 8n,,g7xtim8vmg cw0cc,j ny, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of8 ,xtj880 vwcm,ignc,cd mn 7g this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spa;q3)qgvec3 e acecraft traveling directly from the Earth to the Moon experience zero net force because the Earth a)q3eca g3 ;qvend Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stanpd)x,ofc,ve; b: : j;yarad3gd on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction? vad pr3,f ,yeoa)xg jb;:c;:d    ----待选择----upwartddown 

  A projected space station cohbbs6 w0o-,goj0 0e yyqw-d :onsists of a circular 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 must be the rotation speed (revolutions per day) ifh-b ws ,yq00 o bodjy0-:eo6wg 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 verticenz .ihao9b /1al loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, / .8apq ol-nkuthe acceleration due to gravity at its surface and the gravitational constant8/o -l uqnkap. G.

A plumb bob (a mass m hanging on a stri txa/64byis 5xng) is deflected from the vertical by an 6/abts4xxyi5 angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design s * yz:ca*)s,zxttvi 8npeed of If the coefficient of static friction is 0.30 (wet pay:t 8v) itacn*zsx* z,vement), at what range of speeds can a car safely handle the curve?

  How long would a day be ifkhi ht90s:p v) the Earth were rotating so fast that objects at the equator were apparently weighth:t sp0i)hv k9less?    $\times 10^3$s

  Two equal-mass stars mainta,vm1:,ovv oaw in a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant s6sdwt7w(.2 ap5ppzj5g1 5qtu v c ;ofspeed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angwopjdtpa;5uv t7.wcpsf5g s 2(5z1 6qle 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, in ;s3ck q,1oitf*l2pit has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can'qil1*otif 3c2, spkn ;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 mnnn * ml)p/)vdeduced the presence 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 by measuring the snlnp /n) m*vm)peed 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 valley shown d 0il :gjo;n3iin 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 Cin;gl j0 odi3: 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 (GPS) utilizes a groupxeoy )wbx/).kp76y cn of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can b exc y./)pxn6bok w)7ye determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1b9bl +;o wy6t bcgfxc) gz3;v3 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros isb;+6o wtg xc;3ybf ) 9zcgvlb3 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 repaiy 44brvtirwo*y r m-z2/q ;3blr. You are in a circular orbit o4wmq yl3v2r/;*rbr z i 4oy-tbf the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has ae0orqcj1:.*5dsn2 aag tpxt( period of 3000 years. (a) What is its mean distance from the Sun? .q: ag noa*(rt5p xj01sedc2 t  
(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 o a2n,,+rlqjd could actually "feel" yoursel2lodrnaj ,q ,+f gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around jt -(/vjcx6+q-nfuo jio-je - the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center u(-evo6nqj- -jjocfx/-ji +t$ \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 cornersa aa/cpf/ db2j)f /;1jg4p:ime lq)fm of a square 0.50 m on each side. Find the magnitude and direction of the grav4e fpg/);/1)j alpmijqa /af:2dcbfm itational 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 orbits the Ear; stf doxau1f-hhl* 96th $ \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 1.5-cm- d4s),y 1jjkgflong sweep second hand on your 1 y dj)g,s4fkjwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and 5zw1 s rsdy.l (ovw1l1y x6+eqstart 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 circwdz+qswlovr y(5yx.1l 11es6 le every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed sor 3d -a14wr/tkik;,; pm1d.l yttftei that a car traveling at sp ;f 1kak-p , d/ie;tttriytw.4ml3 1rdeed $ 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 the carcmws3kb8 9 znb67u +hts 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 trainw6 kbh8st9 nm+b7z3cu 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.$\approx$    $\times 10^2$