Sometimes people say that water is removed fpxnl 0/du*9qa79qzqi)6 3oh; crfwi kd8k su1 rom clothes in a spin dryer by centrifugal force throwing the wa8wp;l9qfzoh sr0di36 *qu kkid 7x1/nu9)c aqter outward. What is wrong with this statement?

Will the acceleration of a p:7z;hv7liy m car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle c:z m7li7;vpyh urve at the same speed? Explain.

Suppose a car moves at : d9zwp9lta(m.8bb pfconstant speed 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 stretc(z.dmw b:9 9bpaf8plth near the bottom of a hill?

Describe all the forces acting on a chiltoehbriwn 38.o aa1,-d riding a horse on a merry-go-round. Which of e31thwnai b,- o ao8.rthese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a verticf e))gb 2 8u4dl-jvogb+n3sdcal circle without the water spilling out, even at the top of the circle when tcg d)u n8ovbd3lf )s b42ej+g-he bucket is upside down. Explain.

How many “accelerators” do ys*-*- k yflqg8qeav s10x4khsou have in your car? There are at least three controls in -fye v q kk qglhxss-s1*4a*80the car 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 sma(i q*esaflin .b 1fvidlzs o+7d*4 )m5ll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal fo)*elio(sa+ 7s5 df flbdi qvm zni*.14rce 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 vw pqlh22/+dxwhen rounding a curve at high speed?

Why do airplanes bank f *gbp:y26rz h4rlk5i when they turn? How would you compute the banking angle given its speed and radii64kl2b*5f r ghzpy: rus of the turn?

A girl is whirling a ball 5iwwq sp+3g ,-lkoqx9/vm h g/ ,6q3hdaq, oqhon 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 gqawdh,/ wsv,l 9q63hom+hqoq /53qgx ,k-p ishould she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, ho)no-ilvt434(ol ub1yec 5a d*uwteq2 w large a force? Consider ano4wo) c 5lyi3ql(bv* 4ue nt-1utde 2a apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbinfr v.4-mdrp.)(otln t be different?)f4nn tdv-.op rr.(ml

Which pulls harder graviw- zkzem+sx2 (tationally, the Earth on the Moon, or the Moon on the Earth? Whicx2zs-ekm+ z w(h accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th8ysok)(51y * 7rs.tk xyo w7obkr6cywt 7r7wykxokoy(ows 8k*s)6y.r cb51 ye 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.]

Will an object weigh more at the equator or at the poles? What two02synavim8 +7 cw n:jh*d onk/cacf:- sr(tg: effects are at work? Do they o/g :nrsc nn:w7sk2* 0at cho8md(yajf+- icv: ppose each other?

The gravitational force on the Moon hw(p6di ez 8b(due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled aw( ib(pedh8z6way from the Earth?

Is the centripetal acceleration of,b gj4p7n is nt nqdv3;n)-pb(fc9 lw+ Mars in its orbit around the Sun larger or smaller than the centripetal acceleratiotl ,pgi(wd4c7)vnb;n +ns jf-n9bqp3 n of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (3q4;z +s+kdld:4zhsipxv *z oc.9 nsc b) toward the west? Consider the Earth’s rotatisdv;p c* n9+qdz+k lzi3 :4hszxcso4 .on direction.

When will your apparent weight be the greatest, as measured by a scale in a d1asabq2y7kky (n,; j-n3ewcln,1z d moving elevator: when the elevator (a) acceler3; ,j17q1ea(lsyd-,n kdwnya n2c bzkates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodsg yw7mtcd)::l in 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 wel: wtc: md)7yg feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apzwme*u.; b qg;ce/an:parent weightlessness” between s:zq /*gebacune w.;;mteps.

The Earth moves faster in its orbiv gzf2ybc14q: t around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in y1f:q2 vgcbz4producing 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. Explad6yte(ouk b.al+ helur7vk3epb1*74in hb b(d kveteuhp*ra6u4lkeo .+7yl71 3 ow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth isd2xj l(col (c9xxc :r ):4ykju much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference io 4jy ckd9 lr:2xjlxc((xuc:)n 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 4i6 smuh:8ca h 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 n6jcz1; 5g wjmthe Earth in its orbit around the Sun, and the net force exerted on the Earth. Wh1zjn56w;g c mjat 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 dil8n7 fjta58dsscus as it rotates uniformly in a horizontal circle (at arm’s let aljdn87f85s ngth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the 3z1emc 0xlv);n hg m(drdht 1(Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space )xlgmh ((czn reth1v3dm 0;d1 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 acceleration of a speck of clay on the edge of a poii30r1 zf d7.skr16c l)ezov ow2ta +dtter’s wheel tur fzoi) ds od11ri6 07tlr2vwkce.za3+ning 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 uni3 h+ jh;rps-ieform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed sp+3 rhi-;hj eis 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 o7kfe4zn- q3mj* o*ddo f radius 77 m on a flat road if the coeffzdme*ofnq- d 74j3*k oicient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fr1/zqcx/k+ thq iction be between the tires and the road if a car is to round a l/kt/qh+1 q cxzevel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed suuwcgen2lin1b+142 s 8f:c pto rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the train8:n1 4cn bis1ulcge2upfs2+w ee 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 s p3 npxgiljb42u .k5(npeed. When the speed of j5lx4p.g2(knpbn i 3uthe 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 roller coaster be traveling when upside r9gr ws e9scqs )z9k,:9er,u gdown at the top of a w :k 99cg sr re)9gqu9es,srz,circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundjsb*e + t6ipx9ed top of a hill (radius =95xb *t9+jpei6s$ \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-j dzh 0,3wdczxcpz/l, zrv,** diameter Ferris wheel need to make for thehj vd*lwx,,* d30/zzc p zz,cr passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circdj)h wbv* v.-iv8:gku le of radius 1.10 m. At the lowest point of its motion the tension in the rope supporti gvjhbv *-i:d.uw)8kvng 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 particle 9.00 cm from the axis;+ by,c*0r/ quhjtzxg o*yng : of jy *c+qzrg0 g:n b;,u/*yto hxrotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa:xxuip 6 0d;dllled "room." (See Fig. 5-35l0i ;x6dxupd :.)
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 ia9h:wns+g+ox n a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blxnhs +:w+ oa9gock (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely t+;(r) 6j 0fj0ko o/faoxoz btyhis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, fin+ ky)0;aj x ro6oot(ofz/bjf0d 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 is perfectly banked for a car traveling 75 )* ay*drd vdf8$\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses-zo6jbkb2thvl8w+ y3,nn8;t mmyv 3y hq2qr: $ 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 vert1 h85wgq5 efhnom9d 2.uvri3) umvbt ;ically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force ux 4nl 99g7wr1pulmj0dnh-h+ exerted on the car (by the ground) in E lu+p w0 1jx9n 7hmugr9dnh-4lxample 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 unp y pm+/rnxdy, dha o7m0r*:-giformly 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 coefficient of static friction have to be between the tires and the road to provide this acceleration witmgr y xd +pa, d-no*rh:0m7yp/h no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.9 knlxy3mk .3*j9 m u9lgv3di2z0 m . At a particular instant, its acm jykn3l9* mgd3 kuixvlz9 32.celeration 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 gravityz (m tfd:.ou +sfbue 5-ab.+ fn6nwm;r on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfat5+bn r-f+u.6znf wb. df( s aoem:mu;ce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acce/ urf)j 1xeoepbd1 x65y: mh/xleration g has a magnitude of pxybx1rh o 5ee mfj:)/1dx6u/ 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 gravitl 4cf -93qobd;p enz:ty on the Moon. The Moon's radius is 1.7oc3 eq9 tf dnpz:-;l4b4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a rad.s.qf8m7x.co x b;(ep nx3q npius 1.5 times that of Earth, but has the same mass. What c8no n;7bs.x.f e(3pqpx xq.mis the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the6q1,o8 ;-ta0tz rnlbnwpzj /z same radius. W8t n0r6z -/nbatl pzo,w1 zq;jhat is g near its surface?   

  Two objects attract each other gravitationally withtaoq9 hl kfyn8.(b;4 y 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 acceleration of gravity, at (a) 3200 mn8ozjnx,ru 4 5 rzunj4n 8x,o5   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside8fe : b3 z0mdhjq*znz1 the Earth where thegravitatijbe:hf*z3 z8 m0d1 znqonal 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 packed into a sphere ags ,dg4hgah 9s(-lxy *bout 10 km in radius. Estimate the surface gravity on this monster sg* ,a-h4dsly9gh(x g.    $\times10^12$

  A typical white-dwarf star, which n5y:;no l.sw y1s+cjponce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but ha+s.j:nl no1ywc;yp 5 ss 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 th/ dn25xtv orzo+ 6.npke space shuttle. Your friends respond that they thought gravitn5k vt oor2 6/+n.xzdpy 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 at the corners of a square of side 0.60 m h/vs9/pg go0j. Calculate the m9ghovs j/g/ 0pagnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostdgw)w( g .0ojtq8 het8 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 pl .dh8ge j8(0gwqotw t)anets 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 a:vn, :4nu um4:stnfwlon 1 lm4t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the n4v ,:4wu:unmf:nsll4 no 1 tmmass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known vjcfd 7(*knh+ralue for the period of the Earth and its distance from the Sun. [Note: Compare your 7df+nhc(j* rkanswer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed v.7.xhg u9gzn-sc*q n4xsl1 a of a satellite moving in a stable circular orbit about the Earth at a height of 3600gnq nv czh.x-*sal.u17 x4 gs9 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbibbq26 .gxo( zs 9ekh9lt 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs( z9es6kgoq . 2bbx9lh?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experien. .txmzq* .afdce simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give yo xam*z.qt.fd. ur answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a ;ms1 jgxsp:u7b /gf9 xsatellite 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 depen;p gs/x97f jsm1u bx:gd on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitq kitcq :leis+)8no (2e have to be launched from the top of Mt. Everest to be placed in a circular orb c: k+(2q) ieos8iltnqit around the Earth?   

  During an Apollo lunar landing mission, the command module continb5/;wh utomr9 1mkuc7 ued to orbit the Moon at an altitude of about 1umw7o5c;9b rum/htk1 00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit tho j1nhpx8u 7z/-ek 0ksk6usm8e planet. The inner rapo1ukz s6 e u0k-/njxs h78m8kdius 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 11+9 o 5:/jc k+xlzi+oflagkwu6km0np5.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at thox0iz/uflg+ 9kk kojp 6ac1w+5 m:nl+e bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astr3 q1hlz;voh v)onaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veloci3vv zo1l)qhh;ty,     ----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 systyd fh)r82cf0lem consists of two stars of equal mass. They are observed to be separated by 360 m rf08c dyf)2hlillion km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weigh2guf,eet+4/rfo qrx. t of a 55-kg woman in an elevator that moves 2f+.,texgqe4/ u rorf
(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 susp6g /rozt(4r b e(stum.ez0sa-wsw;8nended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimusw(m0- eu8 ;tbw /4.zr oe6tns(zras gm acceleration (magnitude and direction)? a =   

Show that if a satellite orbits vo 5 dz6wg-evb/ery near the surface of a planet with period T , the density (mass/volume) of the pla g/z e-w6dv5bonet 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 t 9fcdyd mbp+*i;-d (juhe period of the Moon (27.4 d) to determine the period of an artificfdu+ yd9dj*;c-ibp (m ial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though 0k 1br92lpd r3+bnt caonly a few hundred meters across, orbits the Sun like the planets. Its pr1kb3b9rpc 2 tl 0an+deriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance8srdpgsve3 4ihq4nf+82sv ck5awh b g (0); pe 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 roughl 4t 2hi engq:7)wblj*4malal1y 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 1e mwj)ltb4aaill4*:2gnh 7 qthe 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 Sun.]    $\times 10^6$

  Our Sun rotates about the centerkvqg+l 8dq*pa:js.x- n1qv-u of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four larg : zg7aki n*)o2 hww.exq:j/erest moons of Jupiter xz 2ow :k)iag wjh neeq/7:r.*(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 ofo-jwr.qu 3heahfsx,e +( )n-l the Earth from the known period and distance of the Moon. 3.le,qf(h n) e+xwsjh or-u-a   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin4p)::lm hjz otg Kepler’s third law. Use the distance of Io)otjp:m: h4 zl and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiteftfn0(s;yr; h :gi9cfsf :pw g p27q3rr consists of many fragments (which some space scientists think came from a planet tha ;(twp qyf2n3rf9ifsc0;gp :7:fr shgt once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bavroj5w(ja-s c1,: pycn4k-m/g ldes 9nd completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine tr sk-e wcl/vgna4yj s5cd,j:(1 m9 p-ohat 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 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 (Fia51azzs ofd+ 6g. 5–41). If his arms are capable of exerting a force 6z1asf 5oza+d 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 om7 0yxxfe278v fe wyl6f gravity be half what it is on the surfexly2 8y6f07 evfm7x wace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and fo (mli1fuy cy. 6mrrl 47l22qspin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual mass 67llmify yl1c4m2 r (oq2urf.es are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelera7cg wf -15wrh4ata:bv tion of gravity at the equa tvbg1 c 4hrfw:aa5w7-tor is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dire8lxbg2r+ m+mpctly from the Earth to the Moon experiencr++8lx 2m gmbpe 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 scale-o)(5 irdl -v.8ihz7lki bysd in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wh.-h -y7i koilr )idv5l(d8szbich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wil)cr g; 4 pb4pmih/ 0wk9g2gg(v1 itslul 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 v sgk)4g umh1gw0c9 itbg/2i4;r(lppthe rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4c6u 3kugf 8xs25e 1ahl3).
(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 o3cll2wa 46rzvz .f5 gsf a planet in terms of its radius r, the acceleration due to gravity at its surface and the graslz4av2l. rfg5cz3w6vitational constant G.

A plumb bob (a mass m ha6ci 7yg n ln53+e+x;kpi2fu ebnging on a string) is deflected from the vertical by anyp5fl n6ie ikbun2ex+;g 73c+ angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is ban h9zziq,o3z9-u*z z ofked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spz-u z3zo,h 9zfqz i9o*eeds can a car safely handle the curve?

  How long would a day be if the Earth4 mwwykf b o*::.ab7n)px 0yqd were rotating so fast that objects at the equayb m*qxf4d b7yp:n:)okww a 0.tor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a const8ont,db2 op + pqnk6)jr 8,rfpant 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 rogani7m 3 xnwof2.) ws8unds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17i8 7n.ogf mwnxs) a23w.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as tdkx4owqfa :k/j) x+pk.70 mvu he 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:vmqj kk . a)xo7/wpk4u +0xfd 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 Hubble S:tp- 82apnwwvs7)g 5wdd *aospace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, s *ssapp 87dw)nv5d-g :2tawo wo dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and vallnam+m1h2bfr ; +i4fy:6r avkoey shown in Fig. 5–45. Both to v6kr++y frn1mm2afb ;:4aihhe 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 car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliteun4b: -ix3 akk3bxyg 7s 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 satellites4ib: n- xbu k73ky3axg 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 Renddl k-l(qsv5tu8x04 spezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly k 8v tls40uxl sqp(-d540 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttv3du7 z -h fmrkvfg+ /9s)koe.le pursuing a satellite in need of repair. You are in a circular or hmf/ v.u7k)d-93orz+gs vkefbit of the same radius 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 pd.tq2bq dqn-f al-+y 9zpy0a6eriod of 3000 years. (a) What is its mean distance from the Su+2 d.n t6 9qabq0zyld-fpya- qn?   
(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 0xvlyc.9hsn .4mb:c u(s-zf *u. epye G would need to be if you could actually "feel" yourself gravitationally att9 ec :bfu*leync .zs. 0v4-s.(h pyxmuracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of tnljioj+0 m,s:4c(k zu he Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 mjin c40(uzs:k o,l+jlight-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 loc fhhwao aaw/-c zc(qy h+f,/ ,i*vs.u0ated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square. .qaf*ua (hcz0-w/hiyoh v/+ c,,afsw    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kr9z6 j9yq fp,f)fsll 6g 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 experienced by the tip of the 1.5-cm-longz9;lk e, 2oafy sweep second hand alo2yz9 k;e, fon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and 4w;zo*2r2ex*c hzxjy start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: wxzx 2ocr ze;* h4yj*2See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed dkmdty f+6i hr-aj2m9m2- sd*so that a car traveling at sky mj2idfam *r--d +62th9smdpeed $ 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 o gg(itq0mn+ak 93cm*gej 0j l.f the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the pas(kn0q imeljgg.0 *+ mca9tg3jsengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$