Sometimes people say that water is removed from clf i9):gd1ea2 iqlut ;wm*pbw ,othes in a spin dryer by centrifugal force throwing the water outward. What is wronb*ied 2q l: wwia ;p1)g,muf9tg with this statement?

Will the acceleration of a ca 1:xv b(y2p1iwbs. +m fj/xdojr be the same when the car travels around a sharp curve at a constanyd:i /.b+wjbs12x voj 1 px(fmt 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where( hqex.up (iw/ does the car exert the greatest and least forces on the road: (hqwp.x u/((e ia) 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 acti3dgsnwa,kct-bzb- , e :hz4e dr8 nuetj4-v8(ng on a child riding a horse on a merry-go-round. Which of these fo:8rd,d3b ( , vucg4akt-njew -ezzhes- 4b8t nrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withou*y x evzyw-jr-;t 1e1-l3pr;mywa:wdt the water spilling out, even at the top of the circle when the bucket is upsp:;day 3-l-zwwej;w ryex-1rvt1m*yide down. Explain.

How many “accelerators” do you have in your car? There are at least three contro s v-lo*v.j u(l:od2enls in the caru .e(*sv-l :dnlo2v oj which can 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 cre.fi- cjy r0 ,mzt j+3cju,)yyost of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. ,r 0,imyuzy cj-jjf .)o+cy 3tExplain this decrease using Newton’s second law.

Why do bicycle riderc s vsa-+2s.ews lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn?m9. )+pahx:kba6haj4 t wuv, s5jx(ia How would you compute the banking angle given its speed and radius ofa vm ,( upbxt9x6hj+)kj5s ah4:aw.ia the turn?

A girl is whirling a ball /mzlx9cp)t-hy5 h: qs on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the mchtz yx)l9:p-q5h/s string?

Does an apple exert a gravitational force on the Earth? If so, how lar( unk kob;g:8cge a force? bn:8gc;(kouk Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in w5)um,nc3fvs3/m o v6cftqo +s)ngfp 0hat ways would the Moon’s orbit be different? )u,v3cvf)ss tgp 05mc qn+oo6mf3f /n

Which pulls harder gravitationally, the Earth on the Moon, or the Moonx/6ejaq 2pi9u on the Earth? W/qui6 j2e9pax hich accelerates more?

The Sun's gravitational pull on the Earth is mu4av2ekz5 85u l)kn ywjch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational45)vwe2u najl5zk 8yk pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at m scp;2/wj7qbsj 3y2k*q e7fi the poles? What two effects are at work? Do they oppose each ot7m73s2 psb wjj*y2q/qecik ;f her?

The gravitational force on the Moon due to the Earth is o1ki(l/ 53xzll6vgqlvnly about half the force on thlv 6g lq13 (l/k5lvxize Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration ofu chqa-6umw+d: 2l j za;ik(d5 Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Ear-iqaduca6z(hm+2k5l d :w u;j th?

Would it require less speed to launch a sq ytb*l1vw: u/atellite (a) toward the east or (b) toward the west? Consid1 bu vlyq:tw*/er the Earth’s rotation direction.

When will your apparent weight be tox2 h.vx ;7e, o0e3dsyjs1uuzhe greatest, 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 least? When wouldzuh;,ed.3xo7o 10 sxyv sju2e 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 77 -mc cgo 5q*fvuz9osin outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the 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 yo zg* sucq 7o-c7m9vf5ou can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwee3vypg/iv81 wln sl/g vpw 18ivy3teps.

The Earth moves faster in its orbit around the Sun in January than 8.63gs abkrmyjk m1w-fma fw6.gb:+lin July. Is the E jw+1rm:f8k6bfws. bk-6 3 magyalmg.arth 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 orbit.]

The mass of Pluto was not known until it was discovered to have a mkv8xqrbu 1,)b oon. Explain how this discovery enabled an estimate of Pluto)1xquvb , rb8k’s mass.

  The Sun's gravitational pull on the Earth is much larger3wac/i4 h(q5g;ak ktz than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider thew;(hkza/4aqi t5kg3 c difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19toa84nh (5q zm 2t5b :eyvvbr980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 o qb( vke04j-wuf the Earth in its orbit around the Sun, and teq( bk0uw-4vj he net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotatn ,g5h/r/ quxdes uniformly in a horizontal circle (at arm// qhrud,x ng5’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cibf smtg7 ;;0ktrcles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of0;s;tkt7mbfg g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accele)u e bj l+1lo 1awu4t:m3njym7ration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamete4ul:131wmeo juy lmn)bta j+7r is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verujaw.xds5 :w -mdx: d: q,cs(itical circle of radius 72.0 cm , as shown in Fig. 5-3 axcw.wsmj:udqd d 5i,-x:s(: 3. 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 whqz h3x2:wwiewxk// (ihop 75 qich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is5oe7khiwz/p xx q23i:/ hq(ww this result independent of the mass of the car?   

  How large must the ctoi3k /ifps1 .k-9y kgoefficient of static friction be between the tires and the road if a car is to round a level c9 kogi t3/ksipy.-k1 furve of radius 85 m at a speed of 95km/h ?   

  A device for training astron7.dojb/c ( 4ddi 2obvro5vm4gxj .va5auts and jet fighter pilots is designed to rotate a trainee in o4i.2(m.4 oob/dcagvrvx dj55 j v7 dba horizontal 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 rotating turntable of variable speedi hdslu1km dp3h:r /44sweu. 4. When the speed of the turntable is slowly increased, the coin remains fixed1mkuh 4u4led ./p4ihwr:s 3 sd 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 dowdi+: vi)ard go4/.xqtn at the top of a cit)vda 4 x/q.o:iid+ rgrcle
(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 th 3r(2zx8.pcok2dsjxhe rounded top of a hill (rad8 32zx.pkhxorj ( s2dcius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to0jylwv a.,h4zh n2 m63g-c( e ;qxatjt make for theqy 0j-ta, 2avgl3(n.thch6ez x4 jmw ; passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiug3o7 odvq5-jl,jz8/*lqw t f j1gql -as 1.10 m. At the lowest point of its motion the q*7 l1l wavojj/ltq,oz-8jq-3gfg d5 tension in the rope supporting the 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 partkb*tg+td b :*jicle 9.00 cm from the axis of rotation db *gt:b+k*tjis to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylingbwj2,+6fhbp qz6bl-61fhxnb ;/z e gdrically walled "room."e6 h6gw l+qgh1fxf bpbb;,-2/6 jnb zz (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 rot+74nyocwp bq+zbu7 + xated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central bun7ybo+ q w+cp xz+47hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by m 53h8vdtt; 8nfngf i6d2q 3gunot ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, 36;mig85 nftfdvu8nqtg hd23 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 8hh xzegj*-g818 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 masse 1;t7kxz ssatjq0 )kiaz.*y n3s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically aty3p(y8 qvzdz ; 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 force exerted on :*p dlepp6nb3 the car (by the ground) in Example 5-8 when its speed :e* 3bdppn lp6is 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 area4+) 5bgnhl0:ex+puj u-dxvv n, going 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 coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping o4+ug+5ehp bvu :0xnn djlx) -vr skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular ii l7hnk;klis,ql5 2yt qx am*) +fvlt3u5to9(nstant,l x5+i k) lq7t5kf9y3(ts; thu,q*i 2lvmolna its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravit8fl3/8 ud x6ac u )hxexkk0k;ry on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is x/cx6ad)ke k8lufhur3x; 0k8 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magn wnw5c5o2pvi u0s nz5x(l)x,+knyn +hi ln+h2k)+5(5,iopn0 5nwzsvwynu xxc tude 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 Mo1 10mpm8 ;7lwr anwfu8l 6orlbon. The Moon's radius is 1.74 01;nlplmw6 8w1rfbom u8 rl7a $\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 Easn1pv7f ew1 ;hwfm *p,rth, but has the same mass. What is the acceleration due to gravity near its surfacpwwphne,*1m;f 7 f1 vse?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. hx*b 17))gz + phevnqmh e5u-sWhat is g near its surface? x)5 eb*ezh q7 unm1)hv-g+sp h  

  Two objects attract each other gravitationally with a 0ml1m9mqkuph-j mb2 c3yj)4j 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 /+slf4jfa8umof g , the acceleration of gravity, at (a) 3200 m +jsl8amu4/ff    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside dob9tuq ,2m 3mthe Earth where thegravitatb,m9m2otd q3uional 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 our Sun pacs* /p:prk*x jxked into a sphere about 10 km in radius. Estimatr x: *xspk*/jpe the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf stard2vetr88 yo98k8et o0 7vpzxi, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of oixv8 zke8d7eyt8 8oo20tpr 9 vur 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 the space shq .s;i(f .xwt,st )eiguttle. Your friends respond that they thought gr ) (iqiget,fss wtx;..avity was just 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 4)p+wgu, mqn glocated at the corners of a square of side 0.60 m. Calculate the magnitude and directignm4) pqw,+ug on of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yekgngu9fo)/h+*t: e9;bqf b qears most of the planets line up on the same side of the Sun. Calculate the total force on the Earth dun*9 q;ufft:gbeogehk/ q+) 9 be to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whazhk .hqv1 .7ocw +*ngrt it is on Earth, and that Mars’ radius is 3400 km, determine the mass ofwv.o+z gh7n 1qrkh.c* Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value 8s:ftnaju d(3q12x neiiy )t: for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained j(2ui83:xd qt itsn1a: nfy) eusing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orb2ryv-e9 w vimrtq;z5p c6u6v3it about the Earth at a height of 3er6; 9-zpvyqtw63 v v5micu2r600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km j4bx12 mwxwpfiq . 0)2jbjp 2+doglo5above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occu1 mxfp2j 2id+4) wqgjobp.2 owj x5l0brs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatq64+ts1i mpn*qmp q1*kp -5bj f 4gg,7wb dixre if occupants are to experience simulated gravity of 0.60 g? Assups5tpqrqx-fk1ig1dpin+bm4q6bgw, j * 4 *7m me the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbios1 8hsjp5a knk/rs6w k6t y;;t 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 your result depend on the mass of the satel;a1 rty sns;o5jkk k86/pws 6hlite?    s ~    min

  At what horizontal velocity would a satellit.p)(raj v ccl4e have to be launched from the top of Mt. Everest to be placed in a circular orbit )rp(la. jc4vc around the Earth?   

  During an Apollo lunar landing mission, the comc aod i8b3um2584 b/*ov iqvuvmand module continued to orbit the Moon at an altitude of about 100 km. How long did it takeca3ov4*5q /bdu vm 8u8ii2ovb to go around the Moon once?    s

  The rings of Saturn are composed of chunks og,oopsc acz(t;:4r46zff g7bf ice that orbit the planet. The inner radius of the rings is 73,0bf oc4p ;( o 4g:6,7rzsgtczaf00 $\mathrm{~km}$ , 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 diameteva8 0z; u6 :.a7wvpesmg0+ptql eme3ir rotates once every 15.5 s (see Fig. 5–9). What is the ratio of ae.et 8sv+zm0p:i6m uvlw;3 pg0 aq7 ea 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-kgva 2aso3ro*-qhp7 l (f astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constao o2raqfh3 vp 7-*la(snt 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 twor+vw to3bs;;-k *xixfy ev1/b stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What iosxv+ ;1bb-k e;r*3vwxif y/ts the mass of each?    $\times 10^{29}$

  What will a spring scale read for q;.;z4 0t aefocv0;ph)p 0ta5xerejo the weight of a 55-kg woman in an elevator that t;rxpojah.ep;0 )qoa e54v c 0;fez0tmoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatoruydo5:2osu :l47g6jdg nej+y . The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude +d6go uoejgsyj 7y2ul4n :5 :dand direction)? a =   

Show that if a satellit/m-fv ,i yrezxy :gw5w7lxi;-e orbits very near the surface of a planet with period T , the density (mass/volume) of the plf m/z wxygiiel:--,75wy vrx ;anet 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 thec7;y1fvruqx *1* n0 :db(zfp9kjl drs Moon (27.4 d) to determine the period of an artificial satellit0s vqxdzkr 9fb1f 7* pdc nul*:(jyr1;e orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a fefg/c h .a9up1bw hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance f .fb/gpu1hca9 rom the Sun?    $\times 10^{11}$

  Neptune is an average dixunqzx,f)p 5w ui*:zdy.:1 3aqhf 5eb stance 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 co8no 6ozwoati1)m l*y6 mes 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: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sunoomn w6liyo*1 z86)t a.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy eh.( +kqrg-q z$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, el nlpn51pwemvyft l*j9g9)cwc0,u1n ++ x0 hperiod, and mean distance for the four largest moons of Jupiter (those discovered b0c +cu,pmn ) 1ge9 yx1l*e0nl+ljwtw5vhn9f py Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance;;3pxr* fx ;yregcf0n of the Moon. xypgr3;ncf;r ;*0fx e   $\times 10^{24}$

  Determine the mean distance from Jupiter for e)9/ a7 ;81z lst/fz myitnffizach of Jupiter’s moons, using Kepler’s third law. Use th s /n8/zt 7fifzml;z1i a)9tfye distance 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 m erhd7k ;nx(,and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but waem7hnk;x(,d rs 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-)+t5u9 p9v; ao6a6ei exv ipxzpd*ru artificial "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 the9 pdv; upvu656+xpoxe aez9)ai-*r t i same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc 0qfk 1r44tj8ps(zt hn *k( sp6wbzu,bfrom 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 vine is 5.5 mn4kq*4(1bszsktb (0rwj8f p6 p ,tzhu long.   

  How far above the Earth’s surface will the acceleration ou lgte c13.uh:v6 z/t5 ggwq3yf gravity be half what it35h lg3t ywu 61e.c/vuz:gtgq is on the surface?    $\times 10^6$

  On an ice rink, two skateqdf9 ( itakda51v0 -bars of equal 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 60.0 kg, how hard are they pulling on one ant(abd5a9qi1kd-avf0 other?    $\times 10^2$

  Because the Earth rotates once per day, the aw,wgz 36i (t z;qdy;rupparent acceleration of gravity at the equator is slightly less than d ;,w r(iz6tyzq;ugw3it 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 dpmph,g: j3 3w1i v;aqqbas08 will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon 33: d g q;ahsvpi1ma80jq, bwppull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an eleo) os9y+we a,pvator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direcpo+,9 ywsao)e tion?     ----待选择----upwartddown 

  A projected space station consists kk/vy *ykjp,9of a circular tube that will rotate 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 ,v*/ kkkyj 9yp(1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertickc9k2s rf agz-yt,z; ogt)0 e2al loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radbx l2b0zvsb v,cs;)r9 ius r, the acceleration due to gravity at its surface and the gravit,z;v20sb9r s bx)bv lcational constant G.

A plumb bob (a mass m 9ckf2 3ufy.yk hanging on a string) is deflected from the vertical by an anglf9fu3 ykck2.ye $\theta$ 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 bankp aa4)t ye,b ;ra4 v:.2r/ 5vjhyafchzed for a design speed of If the coefficient of static friction is 0.30 (24j.;ha har abr)t:cy 5v /4ef y,zpavwet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating sohe)wkd/ ysj7.i p m45qowl,+pnx8on ) fast that objects at the equatoopohesm .j n ipl48+q xdw/n wk,y)75)r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maekk 6 )bxggewjufn28. -kua++intain 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 cucdm(vs,ebfp u,s3junra8) 0 9/yk ve3 rve of radius 235 m. A lamp suspendeekmusu v3j pv/d 0s,(a9n b3,c)erfy 8d 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 maxe4*;c8:mt7: bdxztn f:wksow 4af 8n;u7ayd 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 experience at the equator of such a planet. Use the following dat k*;t47xn o u8mwn8sy zaxewfd f:btd74:c;: aa 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 S7k3coe/ep-x on bn/zvmn:7x,pace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this xm7vx/n eo3en -, ok:n/cb 7zpby 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 5npt ,miu;mi vn2igzf6aagia/k -)1 9it 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? Expl n9,ii6;2ii1ak)g5-tg mpazu vfm/ anain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Spx:am a 4* qsxpb/23+ic*;xn 0 yoqfvqystem (GPS) utilizes a group of 24 satellites 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, allopo4+ m*qq abv:p icyafns;32q/0*xx xwing 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 biwi)foc j.f(k.f*ke3 allion km, is meant to orbit the asteroid Eros at a height of abo.3f.fk)jwk co(*ae fi ut 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*eag/uh 5dpiii+gw2 8 in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same rg2i gdp85ie+aw /*hiuadius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000h5, ; :dcngdzr years. (a) What is its mean distance from then ,;g5dc: dhzr 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 be if yoq8(qn 1mx*;2nx6 qhc jb9pdmyu could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions,9q1 xp8hnb mmcq;j dnq2*(6xy like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around th0xinpimx,o+ypu h9zw 4 lr-) ;e center of the Milky Way Galaxy (Fig. 5-46) at a distanc n4o+,z9lwr mi-ix);hy0 ppuxe of about 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 b5y c /xn3:dgf0.50 m on each side. Find the magnit/3d xn 5bf:cgyude and direction of the gravitational force on a fifth 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 E0:spmlrowjhp8 yceespu ed; (u63*6 )arth $ \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 t;* nhwv+n y,bbhe tip of the 1.5-cm-long sweep second hand on your n,vhbyb w *;n+wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and btluzv 2t c/0 bk9n mga5y1bz( s*c3l,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 anglt 0bguc/3 ,5mavz bntblk19z (lcy*2se 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 designedb1cv sxjmg*dbr1lr/ t72keo ,at lfa(6f /-q2 so that a car traveling akob1f- xs l7 ,/je6q/2*tmarr2ct v(1fbdglat 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, u1*hs gcsn) x6ntilizes 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, 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 neede*g hns6)cns1xd 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.$\approx$    $\times 10^2$