Sometimes people say thaiptwysi)508 k ;ehk 1nt water is removed from clothes in a spin dryer by centrifugal forp;ts5ky1 k i 0iehwn8)ce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroun)mbdter 72g s-9 0wrtxdy.vz-d a sharp curve at a constant 60 km/h as when it travels around a gentle curvs br02 yz 7.twvedr-- mgx9d)te at the same speed? Explain.

Suppose a car moves at conlq7-xff.1(tz7 myiek stant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretc.7i-t(xey1qf lz7kfm h near the bottom of a hill?

Describe all the forces acting on a child riding a horse on ay l 80 o0(cbzwhr fengwi+b wys1n1;)0 merry-go-round. Which oblo ief0 c swwy yr0(+n; 0hzwb)18ng1f these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withourd)pl0br q4 pje6y+2et the water spilling out, even at the top of the circle when the bucket is upsiqb y4 rl+2p)jper ed60de down. Explain.

How many “accelerators” do you have in your car? There are at least th/ y.0t,1dnq aodi ra9efnq/i-ree controls in the car which can be used to cause the car to accelerate. What are-q/0i.qr9yd/toi, f n1a ndae they? What accelerations do they produce?

A child on a sled comes flying over the cres5,ozx 1bu5d 6paejnd2t of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s secone1,xnjz 55b6 po dd2uad law.

Why do bicycle riders lean inward when rounding ah tn( a*,yt,fm0jlz9e curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankinghm yy.v)s,v q/ angle given its speed and radiusmqv.y,hvs)/ y of the turn?

A girl is whirling a ball on a string around her head in a horizont vm-sdu w7s9i,al plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of t,v7s -mdu9iw she yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how larg(vdub( 1qq *toe a force? Consider an apple vo (q 1qutbd*(
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what 3l7fa;lm:4 ce4sryr n it is, in what ways would the Moon’s orbit bn3e;: y7lma frl4src 4e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E;u+ 4 s7l gjy/7kapfeaarth?ausgef;y/j lk7+ 7p4 a Which accelerates more?

The Sun's gravitational pull on the Earth is muchnd:z luw .-bd4 larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fr.u wdn:4 zb-dlom one side of the Earth to the other.]

Will an object weigh more at the equator or at the p6oduunym-g9:*9 sn cpoles? What two effects are at work? Do they oppose each odo n*u9 :s6uy -gcm9npther?

The gravitational force on the Moon d 6 2ozlk -gc1rn5-oj tabx9d(jue to the Earth is only about half the force on the Moon krb 6j-jlz (2-5 x9t1oacon dgdue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal ag )4cugf. lr)qcceleration of Mars in its orbit around the Sun larger or sma)gf)r.cq 4 lguller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (+jwx j tz,k9 jorni6p-a.y*6a b) toward the west? Consider the Earth’s rotation d, njzo t6a9w+-rjj y6xaik.p *irection.

When will your apparent weight be the greatest, as measured by a scatb8ymek6(s-2 s +1e ,t 2d 2osfu:en l/gwivdlle in a moving elevator: when the elevator (a) accelerates downward+tebi f 1etd( sl8y 2 l2:vs,md6s-ugko/e2wn, (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 long periods in outeri r 4vd9xkl9o- space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astron94 dori-klx 9vauts 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 faloe c(m3 xrg3e dnj6x;)l” or “apparent weightlessness” between steps.(crmd) o ;ejn x3eg3x6

The Earth moves faster in its orbit around thi.r0h/cf2yq) -n p ihie Sun in January than in July. 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 a f.rn )hc20yiih iq-/pxis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered*puje 3( up0p po5: xifcm8i2h to have a moon. Explain how this discovery enabled an * u im08icxu pf35h2:poej(pp estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thb16a1nc gef5c xn/fpxm cg p gd5;l(+5an the Moon's. Yet the Moon's is mainly responsible 55ne(dpglx 5 c b/+fpcx1 1g;g6nfcam for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1) zufezym- h58980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eartcjtjrf (ix )3arn4.r7h in its orbit around the Sun, and the net ()fx7r rja ricj3t.4n force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exertece s1k5-,d zwt axt87jd on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the spek7ax dz,s tecw-1jt58ed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfao21x;tkwvt0 h6k-hg2p/bjg7fj sl 4ace, and circles the Earth about once every 90 min/f 0 jklgvst4kh2w;xpbo -gt6 a71j2hutes. 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 on the edge o bh9vgk0.6zu+wac6 ppivs+n:ud x 5o4f a potter’s wheel turning at 45 rpm (revolutions per minute) if the u9wdiv knpc:4hu6gp o+06 5azx+bv.s wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at qij/t4g hlr8h9;c4 pm a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3 ig /tqhmj49r4pc8l; h3. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radzo.(aca*t 7mk ius 77 m on a flat road if the coefficienc.za ok7(mta* t 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 fsz/f hj( 5)quyriction be between the tires and the road if a car is to round a level curve of radius 8j/f5s)q( zhy u5 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots 5ixj f0(r. w.iv /oj0 oq-j9flfx*xin wu/:yeis designed to rotate a trainee in a horizontal circw fjfi(no/5 joe 9 x r0f/uw*x0i .l-:iy.jqxvle 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?    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 i bb7d7v4fq 30sy( lmj0hn/lxof variable speed. When the speed 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 tuyhl(3nd047mb 0q/i lbjsvxf7 rntable?   

  At what minimum speed must a roller coaster be traveling when upsidebfd939i6u q:ny2aljumyu5:ad0 m0y i down at the top of a circlm9:u3amja ldqyui 9 6520niydy uf b0:e
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crossa eyvl m/+56 v/fzqthw 1gmx lt4/9mj/es the rounded top of a hill (ryqjmh/vlm4 wtlgt1/e5/6/ am9z+xf vadius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to make m4tjix869 z*nxv ;5 xyrda3oa for the passengers to feel “weightless” at the tva*xx 36doy an8m ;5zxrij4t9opmost point?    rpm

  A bucket of mass 2.00 kg is whir42dxj1 xc n.khled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket isd n1k. 4xh2cxj 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 from theox7djt,y9 b4 y;8ouba axis of rotation is to experience an acceleration of 115,0oa , o8u 9y7bdjx4byt;00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" ati;0hzi 7nrx *d03*i ic h:cprn a carnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) ni0n cr i:p30i;*rzcd*hi7xh
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 fricti g6ui-olwokjg+, :xafb4zoo v+01l0 r onless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) t4oo- flr gg,u0b6+:j+w0ia1 lxokvo zhrough 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 webq i;kpp5wbbi80h ,f9ight of the ball which revfpihqpk 0ib, b;b 8w95olves on a string 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 forjif816t,m-lffi d kk* 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 q4, adx;dq9o g$ 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 ):ubvwr1pzw8ede5 b ,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 centripet3y9u-3-wqn4qtf f :agq : lbimal components of the net force exerted on the car (by the grou3w:lqgubtn i3 a-m94:q-fqf ynd) 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 ed:jz qs,lm:7 /9bgxvq 7wpf0 accelerates uniformly from the pit area, going from rest to 320km/h in a semiq/9:zvds 0: fmx,j7 q wep7lgbcircular 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(wk6rga1 i6w8. k gkop 2.90 m . At a particular instant, its acceleratiokg6w ki .kr og(68a1wpn 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 Eartwi23b v8do g9th’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. ivg39wbd 2o 8t  

  At the surface of a certain0o1bb uti9aq 7d-/fq ;a5jfd;) wyylh planet, the gravitational acceleration g has a magnitude of 12 ybd0qd7f;/ t ho9 ;iywaqul )-jf15bam/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius: .zalp3bo7ekdm9q s. is 1.7lm7.eop bak:9s3dz q. 4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a r d99xm -8c.ezbhnwb(wadius 1.5 times that of Earth, but has the same mas(8 9 bc.xmw h9-nwzbeds. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a ;- v7qe:g wx ru r3;ax2jt0emm3u vzx/mass 1.66 times that of Earth, but the same radius. What is g n/ex0;w 3jv;7e:m qxtx muu3 r-2azrvgear its surface?   

  Two objects attract each other gravitationa-mq b;8bqkga avn,j0xymn2h5r951 wa lly 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 effectivb;dw (-yy.bg;fuqlw 4 e value of g , the acceleration of gravity, at (a) 3200 mb(;u4ly-fw .;ygq dbw    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cey4 tqk)g tps*zf 5xd g39x:bj:nter to a point outside the Earth where thegravitational acceleration due to the Eaxg:z 3g)sdt:4*p tb5qx y9kjfrth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five time ldf5 s-f).sda-.fumsev-2jwc m-c b)s the mass of our Sun packed into a sphere about 10 km in rad cmd5u w.vff as.) b-j-dscmefs )2--lius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Ssec4 wls/m3l5un but is now in the last stage of its evolution, is the size of our Moon but has3s sm /l4wc5el the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weigkyg :ttlw;zf, 1wrkr whcj((i0i36 8x*esy6 vhtless 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 8*jlw(xytk 1f6twe icwi 3(y;z rk:hgv0 ,6rsby 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 of side-7 */rr yje9qmqk 4mwd 0.60 m. Calculate the magnitude and direction of the total gravitjr qm dqk9e7mwr *-4y/ational 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 side of yh( z;6m+crm:cbytr . the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, asst rmrcyy+ mzh bc(6:;.uming 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 accelee9)ypq vh tz2zp* v :qe/td0)dration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’edyd9eh*)v zt pp) z2/:qt q0v radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using thayv5a, 3w mttnq+;g9ne known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to thangay53 9t;atqnmwv +,t obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed exvuo(c +n:c -9 doilgtr tky5)y9 ;.one),idof a satellite moving in a stable circular orbit about the Earth at a hei+ xdc ;9( -.o5 rt9:nl)iyk yvoo,gni) tceuedght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th ytl(5+f e0roll, s.kle Earth. How fast must the shuttle be ms+ylt5l l( 0,fkeor l.oving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ f.rdirm2g4./m ed:)9z/natp 5 b ffvpupants are to experience simulated gravity of 0.60 g? Assumem.r fpnt pib2a4)5 vf gem: /dz/r9.df 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 satellite to orbit the Earth in a n;8rcay g7 8uxcircular “near-r8xn;y8c7ag u Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top : pv92v.i0 e4sh*elibipy k3 wof Mt. Everest to be placed in a circular orbit around the e siiv 03pvp29l:ih.kybwe4*Earth?   

  During an Apollo lunar landing mission, the co)pb uc.v(p2 x l9+eb3m/ebacymmand module continued to orbit the Moon at an altitude of about 100 km. How long did3le9aeubx v m+b2pc .(/bp)cy it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plan,a nzqa94 3vufq*eta.7mw v4d et. The inner radius 3 9vqm.a nft*vq4aae47,wudz 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 (see Fig. 5–9). Whnm,-epjxji u q+g.9l 9at is.jj9n+,u- gleipmq x9 the ratio 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 kvg, 94( lb+v exbiv9wzm from the center of the Earth's Moon in a space vg l9v b,(4iev+ z9bvxwehicle (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-sttf;cs. 5 ynwq3dn 8f:gar system consists of two stars of equal mass. They are observed to be separated by 360 milqwy;nf3f5 .n cts:g d8lion km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weighr /bgitf ) sei.d:e17st of a 55-kg woman in an elevator that f sgde):ibe1i7/. srtmoves
(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 y q ck*by8:hm;from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks a:qmyk cy bh8;*s the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet dcveg.v0ew r.t9af;(with period T , the density (mass/volume) of the planetfavcvd. (ew0; .r9ge t 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 o4rhlk z1-y 0qrf the Moon (27.4 d) to determine the period of an artificial satellit yr4rqh0- kl1ze orbiting very near the Earth’s surface.    s

  The asteroid Icarus, tho4/b/w i2hgfq hugh only a few hundred meters across, orbits the Sun like the planets.hhq/4/bfi 2wg Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distnlawxrl4xp8 ; c1+:xb 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 o(e;a/z6:p * xjwjklfrnce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39j*jwz/6 : pkel(xfra;). 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 +y hj..vrwcc l - lzh:5a-((vobail )qthe 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 large qlzbk 8bf7o; j5+fldcm(v*4a st moons of Jupiter (those discovered by l;zmv 87d(+bblj4fao *qc5fk 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; :g7(nhd z kax1uj9bx of the Moon. nu1 ahxz x:kgbd (j;79   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’so a:m2gexpup3 .- kb)k moons, using Kepler’s third law. Use the distance of Io and the perio:3po k -g.umka2bepx)ds 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 consists uge v 6(ers.yp;,4:rt 9hr xuuof many fragments (which some space scientists think cam p6s,h9g ue;:rut vx.y (eu4rre 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 the - rxzzk*/x b(bform of a band completely r zx-bb(/ zx*kencircling 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 Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by seg.wfg0/b,u4cs (nt8-lv fst winging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of/(0 w 48svfbc-t .unegt,fs gl exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface lsv7+wyli , 6uwill the acceleration of gravity be half what +6ywi,vull s7 it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsma45f l qd*:1sb pxe+obb:-sj 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 one another? xpsfq5s j+amlb-b*:e4:d bo 1   $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravityxxwuhzh8h) 4k+gfq* 8gw +6t n at the equator is slightly k 6qz* 4w8thhxg)8+h f+wxgu nless 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 Earth will a spacecraft traveling directly from the s i)lw hi+c2r6Earth to the Moon experience zero net force because the Earth and Moon+lr6 wh) ciis2 pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elsl8curo n*)8levator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directun s*l8 lc8)roion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotaq46hhox l8yo1)xjj 7g te 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 surfacg8yqo )xo1h jlx6hj7 4e of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertic(avfasjq2.ax16w-xoar, bi04h6 nhy al 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, the api4 bg)eq2 ob* n:k/rucceleration due to gravity at its surface and the gravitip/knq)4:*bo2ebgu r ational constant G.

A plumb bob (a mass m hangingm;xi g4;pzv u a)zoob(2;8nhm on a string) is deflected from the vertical by an angim;xgpbzo2; m; uonh )v4a8 (zle $\theta$ 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 coefficient of src7tpaqexr 6tot*3(b ,8)o(awg d1 axtatic friction is 0.30 (wet pavement), at what range of speeds can a car safa,o7dac t6awb(egx8tqor tx3) (1 r* pely handle the curve?

  How long would a day be if the Earth were rotating so faajvlxbsb l,y 67jhl+j6/ko 3gz 05bzy 7*mj,tst that objects at the equator were apparently weightlesy7t ka66sv jl0, *, 5lh3+bojjz l/bxbzyjg7ms?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartlm4 o 4 n)s59t,ob5mn qri7vdq 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 speed rounds a c fztf lbw,/0fo5iyy/ql7z40 i urve of radius 235 m. A lamp suspended froyfzf fy4/50i 7bw qlt 0l/,izom 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 sr4ndtx7 e+ 1mhas been claimed that t4x +erms 7d1na 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 following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extrem wp+w8sal(w ;.8vkoa a yf +:j6nijor7ely massi+o8kp: j6lo+vy .wf8 aw a7;(in arsjwve 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 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 t-5 uz3en7kk dv 8v0ydaraverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do 5y8u d-3vekvnk0dz a 7the 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 (GPS) utilizes a group of 24 sawj qkf(f+n -yqok1q-o/s2p5 ptellites 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.” Thefpq1qs-ok qf-+y2k(/njpwo 5 satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billif+ tbl vy-y(c u+rq0ayrg-6jckw ) /0aon km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 f-(kctcu gy awr00-+/6va)yy q +jblr$\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 r5z:igs,eu m/ tepair. You are in a circular orbit of the samm sge,u5t/:ize 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) What is its mp 4e)/mc)uzoi ean distance from the/)pizcom)e 4u Sun?   
(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 neeg- t1ks2, jd6v xdww;cd to be if you could actually "feel" yourself gravitationally attracted to someone near y dk-vjd2wwgtc61; , sxou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fi5cihi**h3 6gb4pf idg effx12 f41wes g. 5-46) at a distance of about 30,000 light-years from the ce2 ef1xibhfhfp4gf e i d5c3i1*swg6 *4nter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side.il5cmpl a71 5uwsgz .0 Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at theu15c0wll7as5p. zimg midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ori e ba k:yq9z:iu9cdfhv 77p5(bits 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 accelera6fuobr3n* 8cgtion experienced by the tip of the 1.5-cm-long sweep second hand on6f cg n8o*r3bu your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing .a)yl j(z3v2cq5gkf ye .+f+h,wil iia sinker weight around in a circle below yoh ya ize.fwqi+)l2(fvgi+kc. 5jy,3l u 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. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thaeaoh *15nxti0 ,b,l (ung zd.st a car traveling at s* eshdg5.o 0u(lbn, 1tiz,axnpeed $ 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 cars when negotiao4yujv4z q w+g9b+a4mv xit: +1a dwf(ting 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 train to 4vw1mazwaj ++u tx(v9 y4i:db4gq+fhat 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.$\approx$    $\times 10^2$