Sometimes people say that water is removed from clothes in a spin d +vr1 c atqe8hl;wf-ys )pu*z2ryer by centrifugal force throwing the water outward. Wha 2pz+cy-* f1tq wuaev )s8rlh;t is wrong with this statement?

Will the acceleration of a car be the same when the car travelsawnf8.o 4eop - around a sharp curve at a constant 60 km/h as when it travefwp48 ne oao.-ls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly r.srcl)t7k t v,j ;xyh+oad. Where does the car exert the greatest and least forces on the road: (a) at the top of jc +l.x, 7ytt )rvh;ksa hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on zp px2-(cdsl 2a merry-go-round. Which of these forces provides the centripetal lp2x(czs2d-p acceleration of the child?

A bucket of water can be whirled in a vertical circle witho91o/vitidc 4q(k. vw qz lg*8wut the water spilling out, even at the top of the circle whenq4kc*/ v8(q9i.wzvt 1ldg owi the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Therzvalif;/ p78 -h3+ yq/ygzg koe are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?yq zf83 ah zyl7kg/v-o ig/;+p

A child on a sled comes flying over the crest of a smm/spuhr92 . 4 sv4dmozcnz :5pall hill, as shown in Fig. 5–31. His sled does not leave thsp9zh4 4zpo5sndm/2.v cmr:u e 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 second law.

Why do bicycle riders lean inward when rounding wi)8mbos9rt:l1y)hcx ib7 6d sy4*w(0apsm sa curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking an +ntqw.axmbx1 x5,p5 agle given it nm5xbt+aq5x w.a,p 1xs speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontalhi7 m cdiwk d6/cdojm/.o--g. plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. m-.j o7k cm/6/odi.gid dw-hcWhen should she let go of the string?

Does an apple exert a jn)edqzto+6f(c2gep q5w (.egravitational force on the Earth? If so, how large a force? Consider an apple we 6j5) n(cqeetogpf( 2+qd.z
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the + o(,em2h acbdMoon’s orbit be differem,ea(c+ bdho 2nt?

Which pulls harder gravit(g3;w5f fohfx*,dzag1zh -nqationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates-hdf,f;haxz(wqng3fg *51 o z more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yh;e;gd9upto1o4p w ev 7 (og*qet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull frgop (eotgepu9w;1q*4d7hov;om one side of the Earth to the other.]

Will an object weigh vf re2*fe c3nf;q9u:fmore at the equator or at the poles? What two effects are at work? Do they opp9vuer2:fenff;c3 f *q ose each other?

The gravitational force on the Mo,5dk(d 91yo4ul(z aye6 xxdkkon due to the Earth is only about half the force on td(o5u, a l94d xd xkeykz(61kyhe Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arouncf 7eo7fw/ 3b30oikk u,whrdkv8 d;v6 d the Sun larger or smaller thaov3rdb 78;kvfef u/,c o0h63 wk kidw7n the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite n ;twn:a r1)7gt ( gez2f+sbcngo-jx0(a) toward the east or (b) toward the west? Consgt) s0naxgte(f r-jng2 bzwc+:o n71;ider the Earth’s rotation direction.

When will your apparent weight be the greatest, f( s*teodt+n ..y vdk*as measured 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 leakn s(d.fd vto* e*+yt.st? 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 beq3n c igr*s j2pj1mobi873u1a adversely affected by weightlessness. One way33imj7a1q i n8 uogcjp1*rbs2 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 weightlessne7 g.)qirot+g yss” between steps.r+t) 7q.iogyg

The Earth moves faster in its orbit around*jbxmp*yk4choa v- ;9 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 its orb jvapb-yck9omh4* ; *xit.]

The mass of Pluto was not known until it was discovered to ha 1)+b*gzlt)qhp kgf+xve a moon. Explain how this discovery englfk)gh b p1t+)xqz +*abled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moo+m /2 b:e pus0esqd:-s 1wjyron's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child -eqospu1d r / 20ss:wbjey+m: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 travelin)7iev1 idh oa0vlo g1/m 4q6cig 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 the Earth in its b- c(7zb +jhd o0ut2o a53klbgn:6tieorbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's or ecottnugb6( 2io-j:dk3z+ah5 7lb0 bbit 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 apk h5u spmt)c -;n9j: 4eh,sxn 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the4 ,hk sh)-;nxmsn :tpc e9ju5p discus.   

  Suppose the space shuttle is in orbit3q b )jw59pot kpns:v1 400 km from the Earth's surface, and circles the Earth about once evqk w n :po51v3jst)bp9ery 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the ak zn0 4:wadl8nvke y 8,3tr;clcceleration of a speck of clay on the edge of a potter’s whe:k0vwk 8e;lcy nar, z8l3 n4tdel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verti0 1.3nem( 6h gtutbnhpb9uv q76xes1vcal circle of radius 72.0 cm , as shown in Fig.6 tugbm71pn 6nxhuehb.vq se30(v9t 1 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 turn of radius1 al.icbj/q.19kzm zv 77 m on a flat road if thez lvz9q b.1m i/.ka1cj coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffic6p f),jik)jx +8hd/zbn two-o lhhm6.ient of static friction be between the tires and the road if a car is to round a level cur-)fh dohjo)w/mtp,.hz6 x kijnlb68+ ve of radius 85 m at a speed of 95km/h ?   

  A device for training astronautj+o 2biu6lrbf2z /- ; ham2tids and jet fighter pilots is designed to rotate a trainee in a horizo- l2h2biaru m/zijo6 fd2+b t;ntal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    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 rgsf6 wcz8g2j)otating turntable of variable speed. When the) 8s2gwgjcz6f 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 turntable?   

  At what minimum speed must a rollerx/dm6an+d+f xd8 cs5f nrrp5; coaster be traveling when upside down at the top of a circlf ;m xd5d sx5rcdnf r/+na6+p8e
(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) crosses the rou :+ir bd9 c zvfx8jq:u j-pry6z+q8y2fnded top of a hill (radius =959yq: z qp8+fi burf8-6xjd+v2 cy:rzj $ \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 minutqu(k6w.ri8v s e would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost 8w6s( u.rvqi kpoint?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.1i3lg p;7c(kwp0 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2 3cwg7ippkl; (5.0 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 centrifiv y8(8ikkwpw/,(h oquge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,0 (vkwi w8 p,/y8(iqkho00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricxsms,kjl e* 22ally walled "room." (m ,sxl2*2esjk See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hordnmfk )* v.h3.)wzmpz( 3o mex7y)i ockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cente 3zo))( f.x mywimorpmvnk3dz7 h.) *ral 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 t4q +lzf+bo8ct ime, by not ignoring the weight of the ball which revolves on 8ol+z qb4c+tfa 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 isyxsy5:p a 3bd 9ugewj0wp5ev-*1w2w g 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 masselvv, w99 8wnvvs $ 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 div)j :td hoyvm;0ing 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 compos;..kdohg (qa.hwfrd/yd33 dnents of the net force exerted on the car (by the ground) in Example w..a.o(r d3s fd;/ddgqh3 ykh 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 accelerates uniformly from the pitn3tcwy1w/4vm6pk tk * area, going from rest to 320km/h w6m/ 3w ck*pnt1ytkv4 in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radiqq t,eamq*nov is+82+u6m3r thd09 zlus 2.90 m . At a particular instant, its asm *9hl0+ntv8 ,zeqt6ord quq3im+ 2acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravit2 /u+rut, zonol7+8s fhc8sb jy on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface su 28+/jln7h o,f8 ozrc+utbs if its mass is 1350 kg.   

  At the surface of a certain pla.9 njtw*hft/ *b8m 4l gcos2z-e6ri ydnet, the gravitational acceleration g has a magnitude idg9 c*-* rnt2l fs6t4wbzeo8/jymh.of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1hdnnzwu1 y* e;33/vx+ + egcgh.743 g 31/hnve*guhec+ dxz;y+w n $\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 ,hy:hty ,yw6n:m*z h0eqtst /of Earth, but has the same mass. What is the acceleration due to gravi/*: ,yw,mtntyhsqtyh z:e6 h0ty near its surface?   

  A hypothetical planet has a mass 1.66 tim f (wxv1;plm0kes that of Earth, but the same radius. What is g n(;lpk1 fxvwm0ear its surface?   

  Two objects attract each other gravitationally with ay 5 lab0j13g:li:lvsk force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the 7v ye7,czhpy) acceleration of gravity, at (a) 3200 me,7p7hy ycz)v    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wherejthrcab60 -6r88k vv5uq omp * thegravitational acceleration due to the Earth tqjv6h50pu68 -c8rma rb*o vkis $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has h*k/v 7q0xn3q9gfzkn five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monstenqgkz/f7hkvn9x30 q*r.    $\times10^12$

  A typical white-dwarf star, wt 5f7o-z2ny2wxi7h o ohich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of ouwfno 772 ohoxt 2-y5zir Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbihua attl-/3h441q n zzting in the space shuttle. Your friends respond that they thought gravity was ju h z431tal a/hnqu4z-tst a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calc9dq.aww8a/z187ay:x kmd i epulate the magnitude and direction of the total gravitational force exerted on one sphere by the other three9dmzw8qw./1 8ix:dye a ka 7ap.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.w.x mclcu( h)0 Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). Th xmuw)0lh.( cce 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 +owmk62o1q dq eba ,gziu-n8v b20xl 7surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius isunbx,8 02 6qoz+ vlim2aq 7wob1g-dke 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthjpla(t+44 faw0qh s )z-2htc h and its distance from the Sun. [Note: Compare your answer to that obtained using z cahw4 tfq(a+h )42 l0jp-tshKepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cicaj 5:qzs(s9; xbz4irrcular orbit about the Earth at a height of 36q azr5bsx4:9(z csji; 00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above t .nr7/.qqaa0nhez-bd e g*pb/he Earth. How fast must the shuttle be moving (relative to Earth) when the release occur h bapqq*-0ne7gd e na.zrb.//s?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants +aiw-ufwa+gv6;m h*)kg+vn g are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the ta) 6ai-ghv;w+ u m +wk+nfgg*vime needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelliteam gbqgkzl6tqxx8)f( +, w ).f to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Eart+ gmf.qaxf qk 6(w)zxl,tb8)g h 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 bez jkyb4uh/dv1 y 0)fr;7plvl. launched from the top of Mt. Everest to be placed inlh vyl0vyf)jz1r /.4;pk7 bud a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to -ml1egjr*. ccorbit the Moon at an altitude of about 100 km. How long r-l mg1*.ejcc did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of iztrer,,b( fc*ce that orbit the planet. The inner ra ,cefrt ,(b*rzdius 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 f.pwbil) s m-g, 5 pv/2dogzbh4p/ 0ysm in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent wzlp5w2 pdp0 gvo/hsy,bfib/4-) s .g meight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-,lvz.y. vfj z5(1u3s*6wke. eztexs wkg astronaut 4200 km from the center of the Earth's Moon in a sp,zv.l.zfs5 we.wxestj vu z*y(e3k6 1ace vehicle (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 db0-h98ey:j gcm 9httof equal mass. They are observed to be separated by 360 million km and taj9b:m0yg9htd tc-e8 hke 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 scaclwp+ g2mb/b0 uf73usle read for the weight of a 55-kg woman in an elevator that movebcl0/gs bu7+3mw fp 2us
(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 ceilizwsd9-azo6 .jvia (f 0ng of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elez.0 zw6dos-(ai faj 9vvator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very on2dkgeac x6/gb14b (n1t -x inear the surface of a planet with period T , the density (ma enoic2-b/xgba 4k1g n6 t(1dxss/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 thxrin l6au 5vzf*05l+v e Moon (27.4 d) to determine the period of an artificial satellite orbiting very near therf+ 56avx0u vz ln*i5l Earth’s surface.    s

  The asteroid Icarus,g u34b;z t8./vweusy.7xfzgg though only a few hundred meters across, orbits the Sun lik4s7z;3 yte /xwgugf .8v.gbuz e the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancm uo6/8qnbi m6e 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 Suno11y zizz7:d csa 4gc8p 2 c6t+g4bvhu 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 planet’s orbit is nearest when it is out there? [Hint:+yuzc a7z8 zt:421o p g1hcscdibvg 64 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 of2 atttcl5qu7k81rd)m,e tym 2 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 distac4 i7q;ieccg 4nce for the four largest moons of Jupiter (those di474 gc;eiccqiscovered 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 theif*su/;y13d iw-(awwp, x7yb4 ak:iimghc 8e Earth from the known period and distance of the Moon. p-4im3wyau (b7af;i1 dx: i *cgs/wkiyw, e 8h   $\times 10^{24}$

  Determine the mean distance from Jupiter for e /a9iq.4qgmqi* vi7ceach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Comp9*qq /miq7i. 4 aeigvcare 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 of many fragments (whib 6 bfsm;5m l*,uyxro;jhfy 4pu+yk 24ch some space scientists think came from a planet that once orbited the Sun buy6x ,ybr *ufsmof ybk+h45;m p2;lu4jt 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 k1m /wzf,vn z x/5ct6dartificial "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 enough to produce an apparent gravity of g as on Earth. What will be tvmf5t ,kzdwn z 1/x/6che period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge3,e9n a/+,k maiisjl r by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum sp,9 ai3s+rn/kij ml, eaeed 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 gravity be half wha+f 9ts3xo1ke mx*oq(t+-icdlt it is on the sxt(-s qx*+tk d+3oo e1fm 9licurface?    $\times 10^6$

  On an ice rink, two skaters of ea s/7x4v qua7tx(-trl qual mass grab hands 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 6tu qrxxs7t-/va(l 7a 40.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dcrb ak,/ 2u:tlz/d3 xuay, the apparent acceleration of gravity at the equator is slightly t u/lcrz3u,xbkd/:a 2less 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 travelin4 m(wy ouie9ock3:8srg directly from the Earth to the Moon experc3i9s ( w 48okrey:mouience 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 when you stand on a bathroom scah 5cxy0;q b:kmle in an elevator, it says your mass is 82 kg. Wym 5qc;hbx0: khat 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 rotate gqvtwb.yjd0f20cm)5 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 Eg0vmdqb )jtw025fcy .arth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verticax mi -0 ;vp3)jccten/:5mpx*lshqv7 ;j8w jj cl 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 ir0ww /p-ds+1ep +s03dj jzgrh ts radius r, the acceleration due to gravity at its surf h0rjz gpd +e0jps+s-wwr3 /d1ace and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from(o 4 nzbesv o;7,q0vke wayj/qbl :*;c the vertical by an angl,j v 4ynwlocvee: (soq7/0k;b b q*;zae $\theta$ 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 des pec q65q8wm3bk9puk-ign speed of If the coefficient of static friction is 0.30 (wet mk5p9- eu wc3 kb8pq6qpavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if thebyw/ivij-/o1 -n* ebw*qv.n u Earth were rotating so fast that objects at the equator were apparently i*v/- u*enow.-qnbw iv/y bj1 weightless?    $\times 10^3$s

  Two equal-mass stars maintz1az3 -:h kjrtain 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 dl(-,-lwwne za constant speed rounds a curve of radius 235 m. A lamp suspended - ww-,leld(zn 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 massive as the Earth. Thus, it hak /qhotvcc( 73s 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 7t cc(/ovkq h3 '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 an4rsbo /.8,fh7sdtw e m extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which ,4dwstbo8 s. fm7e /rhno 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 6-v irk3bbv,qspeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on 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 carvbqir, 6b3v-k go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliteh2,xg ie0x k/cs orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be xc0h,gi2ke/x 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 Rendecr s)n *tfs 6qq9o1 cv *x;o,kz0h6qd*bq0 objzvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km .xzbh cot;)6*r0sqq odn 9cjoqkq*v,*6 0s 1fb 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 3e;l xqkp51zax0 d2fjl 3nt-cin the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abovqn fj- 5e2za 0kll1;33xxpcdte 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 perisy7(9 ifj9:ar2srtar od of 3000 years. (a) What is its mean distance from the Sun?sj7 f( 92i 9:arstyrar   
(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 l86kb25fseyf would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, k25fsbl8e6f ylike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-4v/m mpm* ou2mr1-bd)k 0bglq66) at a distance of 0mmbbmk /o2l d-1prg) mu 6v*qabout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0j6xx y sbg+n+g7u2b h9.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placeg +x+ 96hsy2bgu7 nbxjd at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 1cxx)f x,9:d cwz rog/kg orbits 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 acceleration experienc drrm e7wklic.v s;901ed by the tip of the 1.5-cm-long sweep second hand on your wrist watc0.wdrc97e isv km ;rl1h?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around id66bdzn 5us /an 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 makes with the vertical? [Hint: See Fig.6adun/z5 b6s d 5–10.]    $^{\circ}$

A circular curve of radius R in avh,9. 2zq:keg9k c rxwz-4gzt new highway is designed so that a car travelik4g2gkz :hr,wv zq-.9cet z9 xng 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 train, ru8v0 zqm0rsp7huh 4 /the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, tr7m 8uh0v4q /sr0hpzuhus 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.$\approx$    $\times 10^2$