Sometimes people say that water is removed from clothes in a spin:f.r25i4j8sq z m awkr dryer by centrifugal force throwing the water outward.m:4 zfa.sjwi2r5rkq8 What is wrong with this statement?

Will the acceleration oppv, 4po+k4sd8fc2 5 4dn0 ehybxi1q vf a car be the same when the car travels around a sharp curve at a constanvxisv pdk4p5odq p0yf b1e4cnh ,28+4t 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speedd t8 -smiz00lme ,:3 mb3kumas along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch30t-e8:m 0zmakd sius mm,b 3l near the bottom of a hill?

Describe all the forces acting on a chi2y *wj- 8 lp-8xtkh9hpw0*txd goihq4ld riding a horse on a merry-go-round. Which of these forces-hjq9gti hoxp 2*8lwky - d*w48x 0hpt provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wn9dq,/2lo)pc3 uyt w rater spilling out, even at the top of the circle when the bucket 9yr od)putl, cnwq3 2/is upside down. Explain.

How many “accelerators” do you 5myi, 0k9o 9iq*fktcm have in your car? There are at least three controls in the ci0 qtm9 *k kmyocf95,iar 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 crest of a small hill, as shown in r z(s1wxhi(8y s2 cr,tFig. 5–31. His sled doe1h(y8itr 2sx(rsw z,cs not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hh ,aa2c7(8 a:no dygxpjc5o k+)s,yaaigh speed?

Why do airplanes bank when they turn? How would you compute the b2.ev;pnuldrg0wh7u)yus 6y r+p jg8 2o4ob +aanking angle given itnpuy8.o gb ulwh 762s4u0rdr gve2;ya)p o++j s speed and radius of the turn?

A girl is whirling a ball on a string around her hm2af,er1g8 06; zx0 3vtleysos pkjn)ead in a horizontal plane. She wants to let go at pre08;sse3e6f0zxkomtv jn, yar1 g p)l2cisely 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 forcepcmj q4 odv:ra, -4yi*a+sg- x on the Earth? If so, how large a force? Consider an approx ,a+p*-d:4i- gyv s4m qajcle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would mcfcp:jlq6 2 l/(+ ;zlq(xtss the Moon’s orbit :((6/s + c; lqsfpl ljz2xqmctbe different?

Which pulls harder g; it: m(e5m tqw-nict//nghs mt3 bg94ravitationally, the Earth on the Moon, or the Moon on the Earth? Which acce mt5htmi/q ;-(gmg c 93/tnetsw:4bnilerates more?

The Sun's gravitational pull on the Earth is m1vq)i8oy08cgl *uw p( pox-oxuch larger than the Moon'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 *pqov0woyiop-() x 8u8 1glcxother.]

Will an object weigh more at the equator x+ q;:wowb)ckrekr o;i57xm8or at the poles? What two effects are at work biork;+7eqw rx xk)8; mo5:cw? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about bu2x*-(ysp /rrnf2lnj xgt /4 half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from then2bpl2u-/ *rgrxtf(jx4/n sy Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger 5xa o1yq.g ,ofor smallgo15 y.fx a,qoer than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towbf 1oh-t-uyw 7u40vghardbuyf074t1hwv og -- uh the west? Consider the Earth’s rotation direction.

When will your apparent weight be thp4ks0q2:1az yklvfm 3qj v.d9e 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 ua 4.qp 21lv3jdfk:qzy0k9vm spward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely aff9 j ,,j xa)c,fmw(mjwnl*t 5;xm i.rfrected by weightlessness. One way to simulate gravj 5,xfijrt*lmj ), (wf cwmm9n rx;.a,ity 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)yo eteqxwif s;- 1/wkzka84p543i et experiences “free fall” or “apparent weightlessness” between steptwze oewti8fq-/p;)3 4y kkxe4sa15 is.

The Earth moves faster in its orbit around ht,mxd*smikj+:7hb p((stk ( the Sun in January than in July. Is the Earth closer to the Sx(bs*mdt7s +j: (h(kp,mthk iun 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 moon. Expjovztvnu/ v8)cs ) 1q,lain how this discovery ,vq1z tu) v/sjocv)8 nenabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the bbgjfrcssrv -z()9/. Moon'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 sitting 1.10 m from the center of a merry-go-round moves with a speed of 1jb cs rb9zvs.rgf/ ()-.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 x7fqw2h*muo s:+e8fq 6 8yu7x mwryv-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 inslt i*5xgoy6; 5u won0 its orbit around the Sun, and the net force elo;yuixn o*wts6 g055xerted 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 j6wwm7aoh u9; on a 2.0-kg discus as it rotates uniformly ;wmoauhj6 97w in a horizontal circle (at arm’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 lzy)(llr +o b1circles 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 gravitational acceleration a 1ll(b)ol rzy+t the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a3o; bdn cgtq m+;h+68f3kevkn speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minb+eof3vd+hc 3n ;k ;n6q8 ktmgute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a striywby hj+kn:r swg(105ugt k,1hvp, t+ng is revolved at a uniform rate in a vertical circle of radius,1:wgk5nh(0 kvt1 +gb+sjyup ,ht wy r 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can roua 0; ruvczt 7-m za6:m*zv0amrnd a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is tm6aravcu r v0tz0z7az m*: ;-mhis result independent of the mass of the car?   

  How large must the coefficient of static friction be between wk 2u erk:a(bp*b2u8m the tires and the road if a car is to round a levb8:a2m* we(uprk2kbu el curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts anh74,4ar5zbvhj6uu a ,)wngtg d jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own wn7 ah5jtg, b4hu,grwv 6u) z4aeight, 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 ofety65ub/p 33u36a wxsz.a0nz 9aevh b a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the tuz.b yuh6ebwus3 6 t/9a3envap0a53x zrntable 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 9qi:z-s+ren qwhen upside down at the top of a circler qnqe- iz:9s+
(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 rounded top ttq es341+yitxnvfry8 4) 4q jof a xtqyi j4tr+344fte ) n1 sq8vyhill (radius =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-dimux7uvb- z.pfj,o- 4vi;l7wkameter Ferris wheel need to make for the passengers to feel “weightless” at uupi kv-b, -7x;vjz4o. 7mwlf the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circl3a/8)qsu2y 6tkg,/zu b ppd lle of radius 1.10 m. At the lowest point of its motion the tension in,6qsa)/lp/8tukg bp2 d ul3yz 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 particn+rwo 6(us mcu ,p);/ d ffe,9c-gdmwule 9.00 cm from the axis of rotation is to 6)wcgcu f9dmm ufw,dr/e; s- +n(p,uoexperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivatm+rrm(pi: j6l, people are rotated in a cylindrically walled "room." (Set:+p m jirmr(6e 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 cmg h97iru al;y9 ct4b/ircle 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 cen/7 9 b 9m;tglrci4hyautral 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 , pre;z7wj y lcu.f8,f fl.fcisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, f llzf.fw7. ;8fuy,j cfind 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 ihttpsa -fkquvq1ru22 )0e 7m(s 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 masse1+hhppj0n6)z*csd)-k t k wlfs $ 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 maneq; /81xjalz cnuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centri pfs.l1lk0,v kpetal components of the net force exerted on the car (by the ground) in Exampl 1vkf0 ,lk.sple 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 .sh iswys*1ams5 x *z0zoy:(xaccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficieyz*:zi *yx(m0 xs1s.o ws a5shnt 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 ofr-/ qpcokb s4, radius 2.90 m . At a particular instant, its accelerationqkbps r,o4 c-/ 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 gravity on a s+gee98uzqbb ztz458vse8 m t 9pacecraft 12,800 km (2 Earth radii) above the Earth’s sue49v9z8s mqg+u5z88tezbe tb rface if its mass is 1350 kg.   

  At the surface of a certain plaq): -*w cknkxrnet, the gravitational acceleration g has a magni ) nqx-kw:kc*rtude 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 grxyq. (,dj :hbmavity on the Moon. The Moon's radius is 1.74 bq, djh .(y:mx$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius nolrg w3gmjkq*h31)72 / r ulx1.5 times that of Earth, but has the same mass. What is the acceleration due qr/) g*hmu7jxlng 1l3 2 work3to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bq4)yprb:ozh u +3ja +0pxsp )iut the same radius. What iqoa:py i3r+hu)z)sjp x+ 04p bs g near its surface?   

  Two objects attract each other gravitationally ds: 6 kwxl, 7 xwiomkn3xjh9,a.n+o6twith 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 value of g , the acce-*j1h sw amw)rleration of gravity, at (a) 3200 mw )sh*ar -w1jm    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from tncm8i8( scdo tas((t *he Earth’s center to a point outside the Earth where thegravitational acceleration due mtsotnc 8(c8i( (d*as to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mas9zv )hmqp96v cs of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monste 99z vmqhp)v6cr.    $\times10^12$

  A typical white-dwarf star, which once was an average s ,6yeyloqr9afik)x/8tar like our Sun but is now in the lasty 8)fi aq l9e/xyo,rk6 stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spacedrqtvsz7)l jng6+, 2o )(r kqf shuttle. Youz)vqt ,+ gnr j(lfk)q6r 72osdr friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located ak /o1gc jms34lt the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exertm1s4/jc lo gk3ed on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mo duyl ./ y63*f*xm5js +coucvqst of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The massefx /*ojs.vq c yl63y md5c*u+us 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 surfacezw )t r8g7fugnq*9(xl60 qa iz of Mars is 0.38 of what it i u 0*zf7n6(lx9ig8agtq zqw )rs on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valurh;wq) cn4.e4 ;ze(i uwg o/ghe for the period of the Earth and its distance from the Sun. [Note: Comq;g) e 4uwin.og;cezwr(h4h/pare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the 1yuqa vun7s /wrv .-;cEarth1wuvn. ;yqs vcu7r/a- at a height of 3600 km.    $\times 10^3$

  The space shuttle releawktqo0 yx1js.(:as:q ses a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release oc:. xsyaq1( qj0s:wotkcurs?    $\times 10^3$

  At what rate must a cylindri8eogy1qz(-cz l5.gi/ dfbx jvi .t g8+cal spaceship rotate if occupants are to experience simzifb.cvlgj(dg e8+y8qgtz.x 1- o5 / iulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for qbz72blgoa*i 6nur8 2a 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 compared to the radius of the Earth. Does your result depend on the mass of the satellite8qr6u7bn 2 ao2b*gizl ?    s ~    min

  At what horizontal velocity would a sat-hsqnzg+bhwfig ,8)-q ,kep - 4jvl.9y ic3qb ellite have to be launched from the top of Mt. Everest to be placed in a circular orbit arol9 nib g,-hweqh+yg,jqq zc i .f3s4v8--bk)p und the Earth?   

  During an Apollo lunar la )s4elxa(0bgo nding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go aroun)aeg 4l0x (bsod the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. szwso,(;()jbnugxq1ni h83r. dg3 drThe innernrodbj3gi s(3(n ,uw)hx1q .;r sgdz8 radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whatp405hwo.p;nr r yuk 09rhv+qv is the ratio of a person’s app w 0h. rv0u;9rqnyop5p4hk+rv arent 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 the7xcolo)c+mo( Earth's Moon in a space vehicle (a) moving at constant velocity, c7m( lxo coo+)    ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Thez49 cuq2)ek9qrgt.ts)q kz q3: /ynmr y are observed to be separated by 360 million km and take 5.7 Earth years to orbiqzk.ent)u9 my 2grqtz qrc3 q /ks9:4)t about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an e qr( ccu(70qvxlevator that moves 0u vqr7( (xccq
(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 susp* rbd2d.iq z(mended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerdzdm i*2 b.rq(ates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a plane 8bkt -b;+zb, -stsflat with period T , the density (mass/volume) of t, azs-; b-blbkft+ts8 he 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-jivo7gr) 3t9.(+p s vnytva j of the Moon (27.4 d) to determine the period of an artificial satelliytgi+vp )a .- j nsovt9rjv3(7te orbiting very near the Earth’s surface.    s

  The asteroid Icarus,ktd;azvo+4 b u; lv9qz51;yt i though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is ittdlyt+k zuq9;o z4vv;1a b5i ;s mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of fiq(t6 ;-xn0 m4bw wh35euvxn4.5 $\times 10^{9} \mathrm{~km}$ 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 Sk1 2ibripal;k*63) o7c pgnz dun 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: The mean distance s in Kepler’s third law is half the sum of the2)7 bk1p*izrkcad6o g p;inl 3 nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of 0t9j4 p92 mq ao0vi8lpuhchl/ 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 m:sbp44sdfqqc2yf2ye bxn:82 0ybk7 h ean distance for the four largest moons of Jupibp8x y24 7 fqchy n2f0ks::yb4eqbd2ster (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 peri- v3pb1u0) )3 lzpwwa8viztlo (wj dd2od and distance of the Moon. ju zl)z-l0)v dww 3( pi21tpab38dovw   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupite/0 cyuvrrf6:v,cx t 3dr’s moons, using Kepler’s third law. Use the distance of Io and thef v6:yxrt/30v rdc,cu 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 Jup p3 /)iqudht8p,iv +bw:f ghq.iter consists of many fragments (which some space scientists think came from a planetqfi,3ugph+p:iqth/) w. bv8 d 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 descrmh-vi; d*5v+s+a: hwx cw4lsuibes an 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 the same as the Earth-Sun distance (to mad5; uhm scai vxw+v-*lw:4h+ske the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. u 2.f vo yy8r6wh(os5a5–41). If his arms are capabl5ow 8h.avu62yo ( syfre of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what a5gk 5h;b0 pw2,zpv ybit is on the surfaca5 y2vp,zw bbk p;5g0he?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and c8ysj:ogriy*e6 +jn )u *7ez bspin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their i6e jcigoj e* )r*zuy8 b+7s:nyndividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratiafl j x)pa196gon of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the maglpga jx9 f6)1anitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecram wbxriozp9l.;/ s-,sft traveling directly from the Earth to the Moon experience zero net force , o;s m.9rxzwil/ s-pbbecause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you98i6qjvvo .g avwl2 j -qr)b6s stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelerationovjiv9.rvab6)qg -w l s86jq2 of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about ia*b4 pscu l6ms*jwx+ ge 4-luwy5cr8*ts 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 da*e-ubgx jm 8ssr +l*4yccwuawl 6* 45py) 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 vertiljllf06z+fq : qco /ms8-hwy7 cal 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 off em.z/zh( m2+c81t8wpt m nvp its radius r, the acceleration due to gravity at itsv1t2nmezmp8/ ( c.z m8 wtfp+h surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fr sle/h11f l :hr)w+pdf .b:bpoom the vertical by an angle f d el:fp 1.:plh+/owr1sbhb) $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient -s,2szbu l /qfi biq19of sti bz/li9bfu -qsqs21 ,atic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day ( vcpnpn( knb ic408q8be if the Earth were rotating so fast that objects at the equator were apparently weightless?cbnk8npv40 c8(np q (i    $\times 10^3$s

  Two equal-mass stars maintain a constantd/q; tp4 +r o0f3a csr79pjbpz;nugk9 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 ;pv,dbv qj48 pxgj4-fconstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 1xjp 4; -4fqvv8p,jgd b7.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth*v co)9/ptmb h0s-gh s7sap7h. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since peopvs po7c0 9*sg-bhh)tm7s/haple can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the a mhvy2a e2t((Hubble Space 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 by measuring the speed of gas clouds orbiting the core hmt(v(ey2a a2to 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 am+,sarx2 gm9gj8 up*z-,2kh b0ej: 2mc xskwms 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 he+,2smmk9brju2,a0 p :gksgzmw8- x*hc2e jx maviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (3ekdbv30 +z) 2pw-icbxl1bev 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, allowing continuous navigational “fixes.” The satellites orbit at an alp + w2lbb3k-eexzi3dvbv) c 01titude 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 Rendezb07d /- e15pzg:ox;q jeem lzbvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rgp7:b-x/5d1;q z0e e jembolzoughly 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)fx fzc0gpawax 4g6: 7 space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400f a) cgwza0g46p:f7xx 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 y 6 0bgsp(jhg,*rbzc-i ears. (a) What is its mean distance fro -*gsh z,bbc6jg (0pirm the 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 you cotho.k1xwx m5 +uld actually "feel" yourself gravitationally attracted to someone near yo+5mt xw1okhx.u. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky f. q* ged)l2c0 n.mb)rg8el axWay Galaxy (Fig. 5-46) at a distance of about 30,000 lightd.. n mg clq28*g0axr e)lfe)b-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 squ0raqna crc6mnhk 1. ,z0xs* x,are 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed k0rza*sq x0,xa,mh nc.n c6r1at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orc/*uaopkwul96 sb *e4 bits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration lmiyl**6*w wg92o s*udx ;pdj experienced by the tip of the 1.5-cm-long sweep second hand on your wrist watcs2owxl* l9wpu6i*ym;ddjg * *h?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a mmk7 /t3i4bm4if j1k/5dhlg m 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. it 7hdk3m54m4bgk1 lfmi jm//What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R 4 /gthm,9 olhdin a new highway is designed so that a car traveling at stoldhmh49/, g peed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negoti4:cgwz 2z 5*plkljte 7y 0(frddvtf89ating 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 *e df:d k9fpllwgt(57tr8c0j2zv yz4). (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.$\approx$    $\times 10^2$