Sometimes people say that water is removed from clothes in a s g8wj;kt n.h)tr e+-kkpin dryer by centrifugal force throwing the water outward. What is wroht-wkk8 ).jg nr;te+k ng with this statement?

Will the acceleration of a car be the same when the car travels around a*xbpv 1p 5+v1heailke+n66 * xm *kprk sharp curve at a constant 60 km/h as when it travels around a gebpex1 ak6k 6+e pv5+n1mlpv*kh *r*ixntle curve at the same speed? Explain.

Suppose a car moves at constax wmx y 943n qo,gh++*oym4usm30nb rint speed along a hilly road. Where does the car exert the greatest and least4bx+4qoy x*msnyw3 , g9mu3 0hron m+i 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 a hill?

Describe all the forces acting on a chidtj76xd jn/5e 1mqcx6 ld riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration6x/md d 1xnqj7tj c5e6 of the child?

A bucket of water can be whirled in a vertical circle without the water spilk )wr(gc ds-mxh4/5 tuling out, even at the top of the circle whetw)-5/x 4hmrk cgd(s un the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leastg )c9(xkjq0h j three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do kxjcq9)h j 0g(they produce?

A child on a sled comes flying over the crest of a small hill, asmrm 7eg /5( *uyj*otfs shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he fe* ut 75*(sgm mo/eryfjels 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 roundin9 h m/h3pkpugma+v0fr ohxx. 4)evym/)o ix+2g a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angqv-4x . tme9gg lp4 pxbsajv9(y*1n0xle gi-m9l. s0xe19bgjap(vytqx* gpxv 44nven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a hn4zc 12xst i;sorizontal plane. She wants to let go at precisely the right time so that xtn4s i1z;sc2the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hown 7p2z5jwu8jz a8igs9 large a force? Conuz8ajgiz pj85ws 2n7 9sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woumu 5s47npg uoqr(:u w6ld the Moon’s orbit be differenqnp(o :u7m546ugw surt?

Which pulls harder gravitationally, the Earq 1ci 4f7hmcr 0avvj.3th on the Moon, or the Moon on the Earth? 17.af qjvc4i3vc0 hmr Which accelerates more?

The Sun's gravitational pull on the Earth ( 0e-db oib wvt*ftz,*is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatiobd t wo(0tzi*, b-vfe*nal pull from one side of the Earth to the other.]

Will an object weigh more at the equatdorr e0jgr- 1u3g)d,kor or at the poles? What two effects are at work? Do they oppose ea3rjo10r-d r) d gegu,kch other?

The gravitational force on the Moon due to the Earth is only about 6(kns0b d:bb- n tksoq(/e) ethalf the force on the Moon due to the Sun. Why isn’t the Moon pul:(qne0bsods6nk b e )/-b( ttkled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger tp zzznb+m xdii(5nr/36y6, eor smaller thar 6t(pnin myb,/zxedi+z5 z63n the centripetal acceleration of the Earth?

Would it require less speed to launch a a(f. q :o8tim/ 5ukpkbsatellite (a) toward the east or (b) toward the west? Consider t:ok( k bmi/ afqptu.58he Earth’s rotation direction.

When will your apparent weight be the greatest, as measurewlqqwlg 4kq21f 60ow6 d by a scale in a moving elevator: when the elevato6w4qw2 qlokqgw f16l0r (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 long periods in outer space could be adversely affected by f - sl63jiz)zg2g n xj3y39zbtweightlessness. One wayg3-)39zsiznjly 2 6 z3xtbgjf to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessneaoi85y.va0o ppmwygks 9- :)yss” between stegys- m 9:w5p).a0ykya 8ioopvps.

The Earth moves fast8ulm/)u)lke cdb )v +s;h a:tfer in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much))d ufc ;/b+el:hk st)lam v8u of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a +y bi6t.7 zchdmoon. Explain how this i7 .+dbc6 hzytdiscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is iqrxk(cd-5n3 tx +g 2dmuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from oni(5kdg -+2cdx r3tqnxe 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 19809ml bbw 3fzi3x mbb*-; $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accele cla-1fvo c 9cup :0(ivrcz.+dration of the Earth in its orbit around the Sun, and the net force exerted on th (r.c1+povcv- a9cu0fildc: z e 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 exerted on a 2.0-kg discus as it rotate;fwi-:7wk b i2bui(smi mm; g,s uniformly in a horisiim -bmum2wf(7i:kg ;w;ib, zontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4q 3+u,t b4f gnls04jfu00 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its,bfg3u0 ts44+nlqf uj 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 ojvfk;n. f8vz.)jhg:ah.mm z6f clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?gz m6vh8.j jfvk.mf.)a :nz;h   

  A ball on the end of a string is revolved at a u4 geimh0v lr93r86 kbqp wh; p;y+eb3vniform rate in a vertical circle of radius 72.0 q3lvb9+ phhk0pgme3r by;8 ri6v4e; w cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a 5s i n06*xaidbturn of radius 77 m on a flat road if the coefficient of static friction between tires and road is i*x 0s5 b6ndai0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of stat* clno s/,:wc,+sq)go/vacjh u nt- -tic friction be between the tires and the road if a car is to round a level curve of radius 85 m at acvcla: to nj /t+o/s-, uh)cs*nqg- ,w speed of 95km/h ?   

  A device for trainingvgrw0,2 sx9ub astronauts and jet fighter 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 timeu9 rgsbx2w v,0s 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 4ttuln9uk, g2 a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remain92nutt k4l g,us 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 tbu9h5st hm e:)he top ofbe5:thum9) hs 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 mass 950 kgb :,cqj3fzd9t (including the driver) crosses the rounded top of a hill (radiubc3 ztj9fq:, ds =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 whllo w 5tkri35i 0jqv:d, 2wd/zeel need to make for the passengers to feel “weightless” at qwo ji v 5 k20d/tl5zlir,dw:3the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius t,(myek i(:4hpz 9dj f1.10 m. At the lowest point of its motion the tension in the rope supporting them(fyph,je:idtkz 94( 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 parti uc5o-dk0ti( qcle 9.00 cm from the axis of rotation is to experience an acceleratiqot(kdu0 5-i con of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot.rso5 z2k** drnkjd 1yated in a cylindrically walled "room." (See Fig. 5-3j krny dos52rdz.*1* k5.)
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 tabla)/-)6 c;igt wvev:cm1vf k dqetop, and is held in this orbit by a light cord connected t1fv)t-vwq g icev;m:k )c6/ado 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, bm; lrt7l (u)ndy not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude ldl)r;mn t7 (uof $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 cy s+j0v: r.xgm is perfectly 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 massesq0glz03 9ahl t $ 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 manc33.h kc r tnl ly2-qjnft1e(-euver 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 the net cgne3 dm x4f;vcv8f4*force exerted on the car (by the ground) in Examplem vv4dfc4fnc8; 3xge* 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 Indianapolij(66ndbt jzok,-fkuko 58yq 8s 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acy 6 tdoqo8k,kz(u6n5jjf 8k-bceleration 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 ho0gg nyoaq2 m++e 31so)r1kw nvrizontal circle of radius 2.90 m . At a particular instant, its acceleran1a+q 1ogr)snywgeovk2 m3+0tion 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 m ogd7 g)r8licnu**e :Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above t:n*mru* i8 )o7dgglce he Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mls -qox5+uw6/( m*ha3+umu( b3nvxkixfse9iagnitude of 12h3ssn9+( iu 5oxk*ivm6qlw a /bxf+u- m(3uex 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 d35e nlkr-p-upi +g0 ooue to gravity on the Moon. The Moon's radius is 1.74 +ou-kp5pn0e or g-l3i $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 xhv ric f5dn:+ rjy0p9,3sf.ptimes that of Earth, but has the same mass. What is the acceleration due to gravity nei5df,ph.xrr9n 0+ fpcjsyv 3:ar its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius.s:.-vjp a mps .( v0np1htqvk8 What is g near itsapp1vvqk s .p tv.jm-s0n8:(h surface?   

  Two objects attract each other gravitationally with a for)1n wiu g:yl)l;5pyoykz7 wd .ce 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 (a) 32n+8 p:kiks( fh00 m k+ipns:h 8kf(    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frt 5(t)o/ yfhs 5hho5i6. mqulrom the Earth’s center to a point outside the Earth where thegravitationaq5/5oh oftrhmsi6.h l)ty( u5l acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times th2gvzr)4m/ kf je mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity jfg4kzm)vr 2 /on this monster.    $\times10^12$

  A typical white-dwarf star, w;;*i /f-hs ar xpj2fb an*ds)ghich once was an average star like our Sun but is now in the last stage of its evolution, ijga 2f pb/if;sa;x)d -n *r*shs 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 orbiting in thcg3,e5d is61e p m4ycrag8ac .e space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration e6a ygm 1cr5p 3s igeac.c4,8dof gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lofh2fve/g)2 nb0i.: ayyhl)-qe d5ilq cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thnqhy2:)ey /bdf0e-ii lv.2g aq)fl5hree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mos xi)a))9 rhevst of 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 masa9)sr ixh) ev)ses 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 ofy z umr(/tl*ggtp pdp9wpz2)s0c5(+t Mars is 0.38 of what it is on Earth, and that Mars’ radius iswpcm+g y t(zpt)p sgu*z /2r0pt9l (d5 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuesxcph q:s p*n9hgg.(: for the period of the Earth and its distance from the gn:psxh q c(h *9:ps.gSun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed nc/qa; ft .2 -yeudc:pof a satellite moving in a stable circular orbit about the Earth at a height :e-c/q .tcdfyn2up; a of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite w3u4 23.fevv*qo6ws72 lwvelueb h1e into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rela fveu e6vo w4 e vbl23h7wl2u3ws1q*.etive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyliz*x6xg02od.xv+dxc0e 3-hx sfm /6zy;zlp n mndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Ques/06;fo 6e* vzy3 -xx xzxdg+lpmc2 s.xmzn h0dtion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to0q/pr 5i 9ntp *rdjb:/qost/c/qm9qzbcb9 b0 orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does y0 i5/brqrq b/tqq:0bj oz/*/ 9c mpsdtb99npcour result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launch 0p8m 9utyz;jned from the top of Mt. Everest9tun mj8p;yz 0 to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit / ci (p-eg 0m. v/ce87ldilmgcthe Moon at an altitude omgi(gceld/i8.lp 0cvc -/7 em f about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of*h+mdufzo vh)jud /:8 chunks of ice that orbit the planet. The inner radius of the rings is 73,000m jf+oh)/u* h zv8:udd $\mathrm{~km}$ , 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,y 05j ioyx*js47 5mfknwv xq83pd5go.5 s (see Fig. 5–9). What is the rat8dy3np0jqgi oj f* vo45wy75,m k xxs5io 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 thenrk .;/fkc5rb Earth's Moon in a space vehkkb/;.fr c5 nricle (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 two stars of equal mass. They ovkd8f 4(c6lbare observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway l 48db6vf (okcbetween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an e do-rssa0h2pc76bsma 4sv 5 v3levator that mo 2v7scb4psmvo-rads5 6as30h ves
(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 of0*,ek :lv xfltk 9,hzlnjqwh. ;s6nc; an elevator. The cord can withstand a tension of 220 N and breaks as the elevator cxe q,6 j; lth*ll:kh vf.9;, wn0nkszaccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits6c 5nles fz5 2klh/ep; very near the surface of a planet with period T , the density (mass/volume) of the planet isl/nf;cs 56hz52pl ek e $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine t bsbf( 2yumzbf4wai6 t7 u3o*n5/;hy rhe period of an artificial satellite or uytf 6bza 2yuo/wh( f3;b7*4mbsni5 rbiting very near the Earth’s surface.    s

  The asteroid Icarus, though on,( 84knt-imby-svpg zly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d.mik znb,(t8p 4-s g-yv What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagi4wdnv).2)p8zu j ge ge distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very cl++kpq25; z tcdbgka6pose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Suza +;cpb2 5ktqd p+kg6n. 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 cg,x6 io lfa4wjb0 w3x5enter 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 distancemdvz+c+sd dd n:t-1 l. for the four largest moons of Jupiter (those dislztdv+1d +- ddcn.sm:covered 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 Ea4ptm zuin(3- nt qcek::4oq)grth from the known period and distance of the Moon. e:k-tcpg 4m zn:qo t)inu3 (q4   $\times 10^{24}$

  Determine the mean distanceu3, c1ia dikh, from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance a,,c hdu31iik 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 Jupitr, 07;x jlbgd ub3f9iyer consists of many fragments (which some spaceby;3 ,rgf9ld u07ixjb scientists 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 artifici 3p )sxhkuyq1y -q9gr6al "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 myrg9qy36s-p)h k u 1xqake the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging v+bn:(et5-saw : t wk5bqo u0roine (Fig. 5–41). If his armq -5e a::trskbn woo+wbu(t 50s are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravx -j c bkr zq3t7i(md2u3z0gy8y g*d5lity be half what it is on the surc27m3t-(g rqlz 0xk5 jy8i*3ud yzdgb face?    $\times 10^6$

  On an ice rink, two skaters of equal mass gc7j1 9 ol6swosw0c u,orab hands and spin in a mutual circlec o ow170wu9j cos,ls6 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?    $\times 10^2$

  Because the Earth ro *yots7vzy 96atates once per day, the apparent acceleration of gravity at the eq9a* 6yzo 7sytvuator is 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 Earthic-fv +)l/oiith8c c 1 will a spacecraft traveling directly from the Earth to the Moon e -1thif )i oc8vcli+/cxperience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whql6coe)nb f )9en you stand on a bathroom scale in an elevator, it says your mass ifc9el)q )o b6ns 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatp6n0xpw60.+ 6cw6wg oizxvx pe 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 the Earth (1.0 g) is to bp6. 6zw6gc 0i+p 0oxp wxnxw6ve felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a v4,6phwh7uu -s3 whek qertical 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 pa ny84;a+ wd:qfz9uw8t al.krlanet in terms of its radius r, the acceleration dwfak+nytl a8 w4r:zqa.8 u d;9ue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertihjha,h 5c9e2x ph,cx,cal by an hhxx ,,c95ejh p,cha2 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 -y hmv9jbr+cwuw 6 0:lm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can6wj9v +mc :wyr-b hul0 a car safely handle the curve?

  How long would a day be if the Earth were rotating so 0snlh) cm-uanqmy5p /* a:k8 zfast that objects at the equator were apparentl5 -a:u/nh8la)0mqpzc*nm s yk y weightless?    $\times 10^3$s

  Two equal-mass stars m;sdn lbnpts4ymkp18 :3gr56 daintain 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 speed rounds a curve of radius 235 m srz .0i490dl,caoo se. A lamp sus ,0 r9sso.a4docle zi0pended 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 mawpffts;rm,2tnm6g; 3 ssive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experfmtg2 tmwrns; f36; p,ience 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 Telesc1yj-gzkx2z- ph- (f ndope deduced the presence of an extremely massive core in the dist2k(xfph-j dgyzzn 1--ant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and vallehi+8z ddn +f,sy shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, 8d zfsi dh+n,+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)t5spk( t7af9 wx)wu t1 utilizes a group of 24 satellites orbiting the Earth. Using “t591 )p x (utsawtkwf7triangulation” 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 each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bil c d8lyivss:ogpv2mhjtj9:.un/fg n,.f -c4 ;lion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40ptgg;-m. yjnf/ is of vv :n2h8sd: l.9j,c4uc $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 repaidft schmp/r ,r vxl f4/:7i+b*r. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25f4+flr7m dc: bhpxi r/,t vs*/ 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 .ts8 gjd4et*k xvnp:.) What is its mean distance from the Sun?s en 8v*gj4 tdpt..k:x   
(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 vaguo2q6qhx9ir,v12g k lue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like g2qxok u2,1rh gi q96vF $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) a diyo884xaegpm6s 6 0tj lu.k8t a distance of aa6g 8kp8oymx0.e64l j tuis8d bout 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 aig- y f8zqg 4card9(/dt the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth/y c9dgz8(di-rqf4g a 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-g igi4o(qxs/9t lmu 5 Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep secondnvf9fl a4gz04nxxo --:lxxik2 :u9rg hand on g42axx 9kn 9lfof :0 i-4rlzg-vu:xnxyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ar 6uo3ci:tv)bround in a circle below you on a 0.25-m piece c6o r:vt) bui3of 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 that a car trave3 fk/mj,zv cmdxb 47a)ling cdvz)b/, a 37mxkmjf4at 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 the cars when nego.ba7ysil8t , ztiating 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 com ay. 7s,til8zbfortable. 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.$\approx$    $\times 10^2$