Sometimes people say that water is removed from clothes in a spinm wxr9 kvnr*ztx q0x:,(wj q93 dryer by centrifugal force throwing the water outward. What is wrong with this staxm3,(n:r z9 90rwxkq*qjt wx vtement?

Will the acceleration of a car be the same when the car 9e:7yn :ub48 mrbx ldwtravels around a sharp curve at a constant 60 km/h asr bd 4b:m7xn:eu lwy98 when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speedq9mij4kbs k7;-lp0z ofs) so nff+ q/: along a hilly road. Where does the car exert the greatest and least forces on the road: fs)kb-m n ql /skj9os0:oipz+f7q ;4f(a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a mrt1qc,tchr ,ws:(5 bhorse on a merry-go-round. Which of these forces provides the centripetal acceleration of the ch5: b( ,1rhcc trqsw,mtild?

A bucket of water can be whirled in a vertical c-bjr4yc wwe :ef 47fgyo2y;t,r5 gf)mircle without the water spilling out, even at the top of the circle when the bucket is upsiderj 7,f5wef 2 tg:)g4myw-;or 4cey bfy down. Explain.

How many “accelerators” do you have in your car? There are wvx 1z(*t /p t,;*dpn:thhvogat least three controls in the car which can be used to cause the car to accelerate. Wv /h; t1z*xt p*np:hto gw(,vdhat are they? What accelerations do they produce?

A child on a sled comes flying slnez 793-s1i f42,cbmjrfz atg 9jv/ qv7zx +over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his ch z77 z l19 x /bag-4z3,jtfms9 qvvfesj2ic+rnest 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 roundinzxp/*(z h xj d3 )cym)j)pbg*ug a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angld0bopx o9,y fe.zk1r+e given its speed and radiuo+e01 ,dkp9z .yxbfor s of the turn?

A girl is whirling a ball on a st f8).r a4+syleu)zd djring 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 shoull .j)8 yzed+rfsda u4)d she let go of the string?

Does an apple exert a grav4s0tb.: 0puj1s mydfrk 6v)xe itational force on the Earth? If so, how large a force? 1eb6 0)t0.f ss4muyvrdx:kp j Consider 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 Mooac7 gdvfd jw.(:oo,del t :sdy3(z;6k n’s orbit be differeco dlew;z(3k(:7 a:s f doytv6j g,dd.nt?

Which pulls harder gr (avgumm qb5oi(cgi) o37 do8*avitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerabav7mi* uog dg83o(o qi()m5ctes more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yo:ur fohmid 6r(f .ghf4*iv 98et the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference idm:f*f g4 9 f6.ih8vuhoo ir(rn gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What k:1n 8zle9pyytwo effects are at work? Do 9 8znkeylp:1 ythey oppose each other?

The gravitational force on the Moon due to the Earth is only about half w b2x2 asvr icy6,01uathe force on the Moon due to the Sun. Why isn’t the Moon pulled awxa2 6v1w0a2s cu,i yrbay from the Earth?

Is the centripetal acceleration of Mars in its o iwhn sth*02b;rbit around the Sun larger or smasihnt*wh20 b ;ller than the centripetal acceleration of the Earth?

Would it require less speed to lacvcgs4 ;*.vw vs r(9raunch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotavcs 9cswr *a(.r;vv g4tion direction.

When will your apparent weight be the gred uj ( 5a5*xjd0kmhu9aatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) uk a(d5*xduj5jh9 0 mais in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely afh 6*v8r v(m*qir3gxdt:sln k9 weht :8s1sw8g fected 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 mtdih*681gg9 q8 w rsx(v :k3n:8*sevl srwht (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 yxnugo1i7qizzc p:b5+z87 82 gdr.rr weightlessness” between stepsipb r277dzn z5r gu .zg8xric1y8 q:o+.

The Earth moves faster in its orbit around the Sun in January thay b (8m3peyhl/r;*pvl l)(u jq9sk- frn in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not 8(k- rf (h9pb*yyv ul/j3 sp;merqll)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 pc ed-q*bqw0 /it was discovered to have a moon. Explain how this discovery enabled an estp/qqc- *de bw0imate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yehq wc+.d8;sf f.utfr e5v3:xvt the Moon'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 o3sh8cw xf;fvd: f.q+e 5.vurt f 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 198sg)t +h66 o1udmq9p ax0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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+q6 xuhed w4+i shj2xaz3zc.0 acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this x3ui wqsz+ja24 . dx0e +ch6hzforce 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 210 N is exerted on arj6 :0db,grf3h7zbskq x.hy2 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of thekjyzgs7q,b0.dr23x : b6 rfhh discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's suropev70 / nsus7v 2x-ktface, and circles the Earth about once every 90 minutes. Find the centripetal ap-ot v27 s7/v0nsx keucceleration 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 specu4)s+gwr2e25d or8seip:b bhp j wn,2k of clay on the edge of a potter’s wheel turning :sn8i4 5+jbr22 se, bphg2w)p wreoudat 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 vertic / hd3x:jnyvx:al circle of radius 72.0 cm , as shown in Fig. 5-33. If its s xnd3jh:vyx /:peed 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 3g*se8i: 1kwbvvz l xo3*o;tn with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of stati1kzo e*s* v;3lvwxtbin83o : gc friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between tht1 ,zd udx5et2e tires and the road if a car is to round a level curve of radius 85 m atz,ex51dt 2du t a speed of 95km/h ?   

  A device for training astronauts and jet fighte *ad.pm ,bli7mr 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 wei7. bla ,*dimmpght, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable-qb+ gpl4 kes-ij.yf7f,d,tk speed. When the speed of the turntable -ijpgkbl.f74y q-etkf ,d+s, 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 whlop7,(,dty ( uhulwoy2-vpy 8en upside down at the top of a ciryo(hv7,d2wop, lyt upy( 8lu -cle
(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 (inclu(z seajs9:rlmi 8 ea40ding the driver) crosses the rounded top oisj4r9aa zm0( : e8elsf a hill (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 v3nlol0f1 a11 vk,ol ca 15-m-diameter Ferris wheel need to make for the passenc 3 v1,ola nl0f1kl1vogers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle c to15/ da4blqof radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bu5d a 4c1obl/tqcket 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 r)/n, o ji tesz9(hixc-otate if a particle 9.00 cm from the axis of rotation is to experience an acc (xzci,tio h-ns/) j9eeleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricall.a, ;b hmbjzh.y walled "room." (,ah.;. zmb jhbSee 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 on a frictionless air-hockey ta+g;jmgr0vg 5ue( 4u robletop, and is held in this orbit by a light cord connected to a dangling beovr4g;gujg0(+5r um lock (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 b:0bq+:rhot;e -jd xkweight of the ball which revolves on a string 0.600 m long. hq;+t-r 0:dkjob :bxeIn 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 perfectlu zsw8jv :; gfvro;8 84cktbr.y 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 massey- 4rv*t-k xbhs $ 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,w hdv9 bpp0e/ by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of thed7xv-ad, f)g,h.v +hvpcs; br net force exerted on gvfh; ),+ar s7-bv xv,c.dphdthe car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acceldzo ,np-f: abwp97bv /8+o lw cldt,wvv nz500erates uniformly from the pit area, going from rest to 320lw8o+ vn, dpf vnw- c 9:dl7p5bozzt00,aw/vbkm/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the 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 particular iwh :9qe; ttrf+nstant,er9h+ f t;t:qw 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’n q9 2m1qi 1w;(p xzj-d:uragms gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if itqmjzxd -n(a pi:2r9w1u m1q;gs mass is 1350 kg.   

  At the surface of a certain planetpilj+t y/;) la, the gravitational acceleration g has a magnitude of a+pllyji/t ;)12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity o e e)ewd-gn8i+n the Moon. The Moon's radius is 1.74+ n-8 egwedei) $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hai-3arz a 6bna)m e6pg/s a radius 1.5 times that of Earth, but has the same mass. What is thb/gz 6a3a-nmirae6p ) e acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiu8r sn4 br/aqr6shsn74s. Whrnbs4 r/n6hsq 48ra7sat is g near its surface?   

  Two objects attract each other gravitationally with a forc ;* egvhp( h;jrcvc3)ee 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 gravityb,d69 bw4topfws *i q 2wj:8my, at (a) 3200 m w :j*s tw,9d6p4w qfb8iybmo 2   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eart ke0xk /u*rw wv4e,hkp:o55t vh’s center to a point outside the Earth where thegravitational acceleration due to th4 / r ox0*,ek:uv55ekkpwwvh te Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed inwxca5nhp)x /;to a sphere about 10 km in radius. Estima)5whca xx/np; te the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun bu9w cmnav:ob5kdg;,5 nt is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is t5b m;,kdv acn 5:ogw9nhe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the sp*)txr 00suzkmace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Coux)0rk*s0tz mnvince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square .ma)hl ; fkf/bof side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on /fm.h fkal)b; one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most o a;,n8d 73ay;a6 tuetza.jld,.g -zwth7 ftbf f the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are bt fg;..,f-a;36z7a,dt j nzuay8ha7twdl et$M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 ofhjnre )(wuu x6rqs6,; Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detrunsr;e q6jxh w,(6 u)ermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthlu +4u8w2+b .wk5tyzg vr pr;h and its dl2r v.wr zbu; py 4uhw5gk8++tistance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about64xodf6i b /wg6dcyq9 the Earth at a hei/gcb wx yqfo669 46ddight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite bjdcg6ywr:2(c- s -:es w6mdg into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the reg- s(w: crwe: bymjdcs6 d-6g2lease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa)*vawbw2h a 8ynts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameh*w )8ab2va ywter 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 satellite t:5ur 7yzp46:g;xyne ye6 oo sao orbit the Earth in a circular “near-Eaz5o6n ye r yya:p4s;u6x:oeg7rth” 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 of the satellite?    s ~    min

  At what horizontal velocity would a satel504 c:u zhgmoelite have to be launched from the top ofze05o umgc4h: Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo luna 8 *r8d(gldrfyr landing mission, the command module continued to orbit the Moon(*f rd y8l8drg at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chug 8xw ub)wh.9 k nre2(yo*9p5iunaj e(nks of ice that orbit the planet. The inner radius of the rin 9)( u.w n(bxoy aj*gpw82u5ik rhe9engs 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 1 w7s iw s-,xctc-g4xv75.5 s (see 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 bottom? s wgvx7i,xcc7w 4s --t
(a)    (b)   

  What is the apparent weight of a 75-kg ny; a,5ozs5pe( s gxx42u5nzbpq+tv2 astronaut 4200 km from the center of the Earth's Moon in a space veeq s 52oyzu+svxgpx4tnbp2; (n,z5a5 hicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of twi c7xge3z.h x*t oz.f0o 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 icxhxoz fz 0 e.7g*3.tthe mass of each?    $\times 10^{29}$

  What will a spring scale read for trf2, j+cuu92o u pmk7zhe weight of a 55-kg woman in an elevator that u9uc+2mz o2,pr f juk7moves
(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 r3, i,y2m(fjlq*aev xan elevator. The cord can w ve*2a(jfqx3,r m i,ylithstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite o gb6 3y quf;gq ;wxwpx6vui7)3rbits very near the surface of a planet with period T , the density (mass/volume) of the planet is guxu )wiw66fvby73; g; qxpq 3$\rho=m / V=3 \pi / G T^{2}$ .
(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 1eu*xr.gi.h hmq .a* bthe period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s *be .u.*q 1i hhgx.ramsurface.    s

  The asteroid Icarus, tho -31 w+cdl ktpfmzdu+9ugh only a few hundred meters across, orbits the Sun likedmz+cw+u t plfd-1k 39 the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist h,g:hn)au-tj ance 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 every 76 years. Itr 27tjf0(v/0ckmlrks ++ vw xl comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the g ktl7k2l/0 v0jmsrx+wfv+(rc reatest 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 Galax:2 bc)ma+(a zc 8adatty $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 largest mo*q (nz;em aelcio7yuo(x8yz1 b y4s*4ons of Jupiter (those discovered by Galileo inyz74soibloq*c(uzey4;xn1 (y ea 8m* 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 Earthxn gr60 qfj2.wmms8* p from the known period and distance of the Moon. xnpr*2 mf 6sj 80q.mgw   $\times 10^{24}$

  Determine the mean distaonh ,bgm; 4wvt0 cctctd*ti h(3 :0gr.nce from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io a,cnh0t*hrmtd:;g( b4cto0 v.i tgw c3 nd 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 betwz,7:h is/ t..jcax ikjeen Mars and Jupiter consists of many fragments (which some space scie 7kjzcish/ xtaij.:.,ntists 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 artificial "planet" in th, qizt4m:*2tb xqf1xi1yj s5lj, ,lioe form of a band completely encircling a sun (Fig. 5-40). The inhabitani1xlzj, jiq1lm,5,f x tt*2b4q yi s:ots 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 Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gje fwdwahzk fwntgtvs8 :( pf+ 46/.28orge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can f8stt w4 p6whgv(n8+jf: kze2 fdaw/.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 weug)h wse(3onjf17: the acceleration of gravity be half what it is h7gwfn1oe:s je3)w(uon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spcq /m nd6.-ix 3 iye:elwdm0d8(dky )din in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses aryyd .mdwcem80/3n (d)l de6ix ki-dq:e 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, th;/ko1gfw4;l a(sh il2 hkswj8e apparent acceleration of gravity at the equator i hwjoaisg 1(k s82/h4lk;lw;fs slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Em-uqfb5s vit:11)q q aarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth asaq1tm vuq ):qbf1-5i nd Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you -gpfj:ithhb(( rd,7 w stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelera ig -(,wfjhb7hp r:dt(tion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatirqg-.gah vxu,cwga9:7 a21j3 gh m0k e 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) if an effect equal to gravity at the surface of w3a.c 1r7ggakhg2g: i qvm,ja 9u0hx- the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a dbc9c/a *+y*z b wemo+..qyzb vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius 1/ro;hufq+eiirp (k(0za p m +r, the acceleration due to gravity atrkzo a1i + /r0qpu(;f+ihe( mp its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by7s ek/,15slb) kpvvar an7klp1 v sr5kev /as)b, 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 speed of If the coefficih3w5j* 1w;m) kax qstnent of static friction is 0.30 (wet pavement), at what range of speeds3)w1m xj5nswt;hka*q can a car safely handle the curve?

  How long would a day be if the Earth were rotating /:yez t8u4 ikypn3gr4qh9d q,so fast that objects at the equator wd4p :/kuit 3h ny q8,4yzrgq9eere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a const66y x9vcm q9qzant 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 e/k 2,ie:/y-ahj m )k7jiga wqconstant speed rounds a curve of radius 235 m. A lamp suspen/aey i kwm-) kj 7ei2gja,:qh/ded 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 massivegykynx 6; )ly0y-h5zk 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 Jupite hkyy 6z;yy0g5n )kxl-r since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telesc z4 u2 qv5va4qfofdf6;ye06 ayope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it cou 6vaq; ofefqvzy04fu625ya 4d ld 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 speex5qazuyfpqb83-l6i)l2kw d: w s/,w md as it 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 p5uz3 ) lqlw,i6x 2d ysb m:8k/ww-fqathe 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 (GPS) utilizes a group of 24 samz8 n3y1mpvy: 6b0cr dtellites 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 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 ea1 8 ycrnm0 z6b3:yvpdmch satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid R vv9qsrcw(mqplam d /37zb 3/,endezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Erosqv vw/(3q3sm9mazr/b7lc p,d at a height 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 n)m; iz3hcs7prepair. You are in a circular orbit nzi;)sm pc 7h3of 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 a period of 3000 years. (a) Wj7w4uv/j ku:2* o: 1hkydsjkehat is its mean distance from the Su7wk2j 1d:su *j/ :jvoyhkek 4un?   
(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 actu as7t,mfb0/vv*ptlzo*z5 hhiw y7: y7ally "feel" yourself gravitationally attracted to someone near you. Make reasonablw/m7i7zly*vsvba hof5:phz70* t, ty e 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 a42 ; rvl3oix+mhm-bi l distance of aboubh2m-o+vmr i xil l3;4t 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each .1+z fkgr5 ondside. Find 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 squar1ndgf.zr+k 5oe.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the0n:i1tj ayct 3 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 exphq05+msh7;g:jf :gxej qdc k0erienced by the tip of the 1.5-cm-long sweep second handjh :xfgq sehckq0;gdm70+j:5 on your wrist watch?    $\times 10^{-4}$

  While fishing, you ge6w q7c;*adkcqg jll4hm)x(l 3t bored and 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 isql ad4jw hl(7q;g*cxkml3c6) 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 desb9zw wlu :m,z:igned so that a car traveling :9wwlz mu,:zbat 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 cqt2 q-0( duuhb1q8sdqu g:m5the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience lessq 0gqcq81htus5qu 2:bu(m- dd 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.$\approx$    $\times 10^2$