Sometimes people say that water is removed from clotz+in4/re/g7pu)kh( qispb l,c j7g6 bhes in a spin dryer by centrifugal force throwing the water ou ,4 gsezhc7qpp6)7(ir/ju bklin+/g b tward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tr-s.rb c7zv f9gnn;+fn 6sxln;avels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same c.szf 6n-;b lvnn9 ;n+rsgf7x speed? Explain.

Suppose a car moves at constant speed alo9y h;gopr.-vms2jh)ey;s , bbng a hilly road. Where does the car exert the greatest and least forces on the road: (a)svm 2hgsb.eb yh-;)p9y ,orj; 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 actingl. gdf8)o h k+b0pwh2qg,p6 qq on a child riding a horse on a merry-go-round. Which of these forces provides the centr g 6)wpl2q. ob+,0dgfqh hkq8pipetal acceleration of the child?

A bucket of water can be whirled in a vz9t3hsp n0 ayh8eu5o -y ,mmm;7u2waxertical circle without the water spilling out, even at the top of the circle when the bucket is u7pymmh 9znohmw3u85 y;u0st axae2 ,-pside down. Explain.

How many “accelerators” do you hav u+wh,v n;ju2ve in your car? There are at least three controls in the car which ch ,unvvu2+jw;an be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small :a x,xcb* g/-v apz4 lluqse;/(ecqh-q) 8ithhill, 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 decreaseg)zla e, / ( h*48itcapbvc qh-e-xq q/lxu:;s as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwyh2*:n2xarlm ni .cj -h:)n p qk3f;yx6.mxkmard when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angla,4 ctclhroz *j ++;gwge,+mreqa48 q e given its speed and rle 4rgg *aeh8cm,+zrqjaq,+ +;ot wc4adius of the turn?

A girl is whirling a ball on dc7sv 85lju4z4t5.u sjm erj+a string around her head in a horizontal plane. She wants s7j844lcu jm d+vj 5rzu5 .setto let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational fo) :pj;a7q namltx,x:rrce on the Earth? If so, how large a force?ntax , pm;r::qj) a7lx Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouldii( oqi* 0n4(tlgf9gh6 q3d xn the Moon’s orbit be gitdin6 4ohf0(qqi* 3g (l9 nxdifferent?

Which pulls harder gra)go (9v bycv.rvitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?gc .oyv)(bv9r

The Sun's gravitational pull on the Earth is much larger /in.wcx+ pcm nio47 ;n-laf7k than the Moon's. Yet the Moon's is mainlypiwf.l+;na/ck- n4 i7onxc7m responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more a+ z:e;1o sn )smafiss2t the equator or at the poles? What two effects are at work? Do they oppose each other?ss;noz12ia :ses+ fm)

The gravitational force on the Moon duer76re bfah,/ppb/fx ) to the Earth is only about half the force on the Moon due to the Sun. Why isn’rbxpf, p7)a6bre/f/ht the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arofrv 7h5yq6ved0 5dn r/und the Sun larger or smaller than the centripetal acceleration ovrer57qdh5 f n vd/0y6f the Earth?

Would it require less speed to launch a satellite (a) towac tuax sy .-3h*f kqrx q4u)da(i7ii5dq05v8erd the east or (b) toward the west? Consider the Earth’s rotation divei d sda57qu)f85ax c x4qqh-*ry.(t0 iiu3krection.

When will your apparent weight be the greatest, as xt5h/ +t7njl1w9 qhrjmeasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the leasl7n r/+ hw9j tt1x5hqjt? 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 cous8:e uev+p vv;o/b* qhld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astr :qbvh/v p8se+ev; ou*onauts 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 f q3gm;6ylvc+ iall” or “apparent weightlessness” between sc6;3+gqv ymi lteps.

The Earth moves faster in jv3kq qq1:n 8hits 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 of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of it: khv1n83qjqqs orbit.]

The mass of Pluto was not known until it was discoverede7u6-0 9nwd d:ckmh ql to have a moon. Explain hnw76c u: -hq 0lmd9edkow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Ye eswu43u adr/s h/pr1(t the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from /s(p sh1/4rduwure3aone 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 e 3t8* sfq3yfu 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 xjy* 8;qgc wo/0o r5;s)jrbksthe Earth in its orbit around the Sun, and the net jj)0b;5rc owyk8 rg ;s*/oxsqforce 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 exerted on a 2.0-kg diseg 0g6 *:9bwg:wdzgv dcus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the spdwdbz e*gg:gw: v09 g6eed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfac( 8r h5: qkdbhnp1,3m49lsy lorre (cse, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitar(l (so8l5qh cbm nhresyrk:3p94,d1 tional acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a y/xp,f 5u sdh91c nd/mspeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per 5psx f/my,hc9dn u d/1minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is rn0vdnp7r ) x520u kuvnevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed i 0pk5vnn7 )ud0rx v2nus 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 z8p5f;wq a,ox of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent x, 5 aqzof8p;wof the mass of the car?   

  How large must the coefficient of static friction be between the tires and thek- p /2nes-u ak/irsb1 road if a car is to round a level curve o/ub- psikn reas21/k -f radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is depo44ksc;g6h8.tslxlk ch f .(vdrf 16signed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her bsrlpg.k t1co4xf ch;l.k4svd 6f6 8h (ack 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 rotw e:nfx/zkgr dw7mf 8.c635ft ating turntable of 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 statideww 8 r f3xzmkgn6 7.:tff/c5c friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down ap5d47qf.2qlf,:hu*zr re l2 v fob7gr t the q577p2heg,*4b r do qfl rzvurffl2 :.top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of muloovd- .fb6 ;ass 950 kg (including the driver) crosses the rounded top of a hill (ra- .fb vo;olu6ddius =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 whee*pu2fy**rql lm)( p)ba)zpara uu9 f(l need to make for the passengers to feel “weightless”f(rufpra))*lum*2lp )qya a*p (ubz9 at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of r7 9r0:cp9 apcx e x7(z-ycgpicadius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buc(pz- e7g 0:cp97rcxaxp9yc icket 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 centrifugera)m 6h1fifq 7 rotate if a particle 9.00 cm from the axis of rotation is to experience an acceler6qi fh71am)fration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are row7-ow;tp9,7f d q;datmeo3 edtated in a cylindrically walled "room." (See 3-eea7qfd; d m 9w7t,od p;owtFig. 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 rotatego 7vvlhq3pm/ rh)*q6d in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a da )gmp rhlvvo67q*/ hq3ngling 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, b l mccc;0ry,g82npx(qy not ignoring the weight of the ball which revol2nlgm rc0 y ,x(8q;pccves 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 radrhi4sw 0alk4k:oq,1u j f/u: dius of 88 m 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 masses uqj9di)a: k0 d s2i);n:e mxeg$ 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 migj 2gw,/,yf saneuver 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 tangentih//cn h/-ihoeal and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 wc//oh-i h/ nhehen its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goiqf( c antfx),/ng from rest to 320km/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/xt) f(cnq,fa 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 horiz1.jz5g ,b x zrg -m9lvpq/m3q e4ayj.sontal circle of radius 2.90 m . At a particular instant,amj.q re5.qxz1yp b,4lszg j3vg -m9/ 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 Earn,iwi6ln u p7b.2f 5qdth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s sq2 lnp n,6ui75iw. fbdurface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationa46coao w o,6 r7*bh;sjrh:kakl acceleration g has a magnitude of 12 m/s6wro6o4 r :osjc7;ahkh*ba, k $^2$ 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 is 1 (( /2bv2m:djxxj+ ui cj4jldl.7d(j(jjd 4x j +x22ibl:lcuv m/4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Ear+rbtcha) bj(qgw;cl+ec 3i-tem;i,0 th, but has the same mass. What is the acceleration due to gravity near; i+ q,b b;aj+-cm tw)h(e3 itercglc0 its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bet* hoh55 vvy0zcj07(-gka5i i tsi q:p/wi g/ut the same radius. What is g near its 7y5t zp5g i*a0ik(e j/gt:i 5wohhvsi/c v0q-surface?   

  Two objects attract each other gravitationallyf7z 2+7nyzuu g with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valueuno xui:i2 + gpq7b+ j2lja*l5 of g , the acceleration of gravity, at (a) 3200 m 2iu+n:ua l*2xoq + jb7jpli5g   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth q)jkzc e:2chz1ucgoub2 41 : wwhere theg: wcu:c1cj2oq 1gubh)2e kz4zravitational 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 the mass of onk 0sw l:/j.u -yzs-brur Sun packed into a sphere about 10 km in radius. Estimate 0-swuy. kl:rn -b/zsjthe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was aja:w koi kk 174q(-ywsn average star like our Sun but is now in the last stage of its evolution, is the size of ou y 4isq7a owwk-k:k(j1r 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 weightles uifphu+j0: .ps while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the accifph+j. p:0 uueleration 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 sqwx :b9.4 w(kjuibitg,uare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerjbx (9k :iiguwb4,.w tted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of th +*z1bprs/l ure 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). Thu p*/rs1 lzbr+e masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 ohq(rn;8+h4x v:vvozh cgh6 s5f what it is o( n vg hso;z6hh8: 5qvh+xvcr4n Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using t) rv(5yv hia9che known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepleryr9a v5ci)h (v’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboub *6bj r3uxwp (v2qi.nt the Earw 3(qpuv 6 b*nj.ib2xrth at a height of 3600 km.    $\times 10^3$

  The space shuttle rel*jo j(9 ovxfe3eases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the refxoe j9o *3(vjlease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotanh0lk q2-il0ate 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 t0n2lh liq-ak0 ime needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it ck.,sbuk3w; 4ibblu b:z-3 +fje0x hwtakes for a satellite to 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 comparwc.s 3 k bz-0ei fwxju:,3lb4b bkuh;+ed to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velo;vd-42wziu /t 1gjfsncity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit arv fsgu 4-iwtj/d1nz2;ound the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbi wcf0+**l, a korj;ac02 c4uredvpz l7t the Moon at an altitude of about 100 km. How long did it *0fd 0v7*kc2lu+ wjalazc ;eorcpr 4,take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Th aw4 gvm/tmg.lght+:0e4m e9he inner radius of the rings i0/ hwgv4:gem am9 mh4gt +l.tes 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).lsa2 (mg f3frhdk5 c9*o f1jr. What is the ratio of a person’s apprs(cj 3gf*h5fadl2 .9k rfo1 marent 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 5y w,2xfk5i . hedpdg/the Earth's Moon in a space v5h. dp k2w/fdy5 ,exigehicle (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 eq5gj l.pc )yqzry 1e*t*ual mass. They are observed to be separated by 360qzj.5 g *y1)tcpel r*y million 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 cv ia)e95yli ,read for the weight of a 55-kg woman in an elevator that m)ly9 ,e5ivciaoves
(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 ceisnhq*z h :pp gg-8zf)1ling of an elevator. The cord can hzpzfp)*:n 8 hsg-gq1withstand 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 orbits very near the surface of a plmgoz ( h 12 1ajtzx/hf4k9fzl3.:zzza anet with period T , the density (mass tz13 zl9zka1j :xzo hhfa42mzgz(/. f/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to det9 f93 q)edekt-f ue8eefi:/y xvh,;pjermine the period of an artificial satellite )xkufhfi:t;ej/-qd yefe 93 v,e8ep9orbiting very near the Earth’s surface.    s

  The asteroid Icarus, -lsbu3 makf5xh(c a;*though only a few hundred meters across, orbits the Sun like the planets. Ih-u3 kxc;aml* fs(5 abts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag(zhafo, m+jh.r0 j:l8x(xbq tb2wlm1e 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 th jc2e5b sk63s qabw:)ke Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What pl)2swj6 3q kb5aeb c:ksanet’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 Galaxyp:mo p y9j.c)r $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 lar6e9*amjap eg (6h3mcs m 43vzlgest moons of Jupvm*39e4eg cmsaj ma3 (l6zp6hiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distancerdq d o(+4g+gb,d i:7gs ioi(i of the Moon. b4giird idq g7( ogo+,:(+sd i   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using u us v,;xht.7mKepler’s third law. Use the disx .7,sumvh;tu tance 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 Jupitepc/m f wk7m,o*8whf+hr consists of many fragments (which some space scientists think came from+m8, m cpf7k who/*hfw 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 artific n: r+k7vc: q ksoq75,mfpun8eial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly veq,+ 5s8o:7fm q7kn nu:k rcpenough 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 arvoo ah2w5mk.: c 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 tolerate at the lowest point of his swing? His mass is 80 kg, and the vin:okvwmh.a5o2 e is 5.5 m long.   

  How far above the Earth’s surface will the acceleratzrf 2oo9 p:t+zgpf-57e ryov; ion of gravity be half what it is on o-79f fo yv:5 +pr2ztzrg;eopthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a muba1el*o ;)+p9 xpzhgu,7khf; si kko2tual 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 o1ikzfug2obkhl;x9 a7 os*p,p+)eh k; ne another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accele/jjpca20g wk5l3;t f oration of gravity at the equator is slightly less than it would be if th2a0j t /lowkf5pc3 j;ge 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 travel 21cbfohx l3p1ing directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and o2fc1x o1 bp3hlpposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whe kf t0c, l8*piam1gr ey quc(ta4j*.1nn you stand on a bathroom scale in an elevator, nmjryfe,cu t pi**a g 018 4q.at1clk(it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube td4uqwl6e+z +uki)1v m hat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). 4ei)lzu d1u+6kq v +mwThe 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 be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vert azpoczu* bfg.36 6am:ical 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- k/hoc)hvgb gpy7d.m ya/( 7z terms of its radius r, the acceleration d bg k( g-d)yo/m7 /7zhhyvcpa.ue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) 62*jz0vvvbwq1 f*fhfmca3 t:is deflected from the vertical by an an:fvvha vqb1cjf *0f *2m6zw3tgle $\theta$ 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 theximsh/tc0 u(811qoqz coefficient of static friction is 0.30 (wet pavement), at what range o8 i 1qo qutm(c1xhs/z0f speeds can a car safely handle the curve?

  How long would a day b8sxx f/-chrn+;3v2yks:xqp( aaj ly) e if the Earth were rotating so fast that objects at the equator -sn3aa+k:v p xc2/xhq lj 8s()rfx;yywere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constdo7n0gc h:t, kant 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. A cd:+e kwb j hgt,r30/wssz3+tlamp suspended from the ceiling swings rks0w bg3zs/d3jw+hte c +t:,out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 ts7axm,k xi43aa:m 1c ximes as massive 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 experience at the equator of such a planet. Use the following data for Jupiter: mass =c x ka,s1:xmi 73aax4m1.9 $\times 10^{27} \mathrm{~kg}$ , 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 Spackqub.how73/urkpb ,(/ c*nmve Telescope deduced the presence of an extremely massive core ih(bp* //nuu3v 7c,komk.wrq bn the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill a 7fag0h bu45qond 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 the car at A, B, and C compare? (Whichqgo750uh4 baf 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 sate k99rcusmf cu/eyrn6 )/;( tegllites 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 approxi9c/n;/ucf s6 m ge re9ykr)(tumately 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), 7l) s(xx:js)h,m jyocx+(hjm after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a heightj7l s+j,()xhox()mxchym j :s 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 scwc/gj l5wcua g; l+q6wa70 *whuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sa0 w/g6awljqa w5+cu w7cg;l c*tellite (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 mean dist6 z7xj*k 1mjuoixr8ov3)ok/u ance from th k7juz xuvjirxo 1638*mko)o /e 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 need to k+v:ll+nf ifgxn1 ab(7nn4.w be if you could actually "feel" yourself gravitationally attracted to someone ne fgb1nlnlnf w+ + :7iv4x.ank(ar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around mi4s1n7x,e o sthe center of the Milky Way Galaxy (Fig. 5-46) at a distance of abouts 7 mi1ons4e,x 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 l6 wdqj9 oo1i2square 0.50 m on each side. 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 square. 2djooi 6 91lwq   $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartojqwv* 6, y(r/yx /nfpbyuz+0zf1gs 0 h $ \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 *mksu)evm 2zo2; 9lcz second hand on your wrist watch2 s* el9;zk)mzcom v2u?    $\times 10^{-4}$

  While fishing, you g//fsx a::3vkf n wj+uget 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 is the angle that the fishing line ma fj:s/nu/afgx:w kv+3 kes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desig z8dyo )1 mukeg):nmn1ned so that a car travelu k8myng)):n e1do1mz ing at 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 trv;u50:db dik5k483 h 4)vrsrywanx-hz(p y ahain, the Acela, utilizes tilt of the cars when negotiating curves. The angle oy);dsw v 855vub4kh yp0kn3h hxr za(r-da4i :f 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 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.$\approx$    $\times 10^2$