Sometimes people say that water is removed from c-eeq2yf;svuhf kzo x7 9l5))elothes in a spin dryer by centrifugal force throwing the water outward. What e2k -qxfzvfle o9h5 ) yus7e;)is wrong with this statement?

Will the acceleration of a car be tru,c,z(kz 3q zhe same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve 3zrkuc z(q,z,at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whereezof9jg+- ,h s 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 stretch near the bottom of ,+e9zjofhgs-a hill?

Describe all the forces acting on a child riding a horse on a merry-gogm2fm h:(. d11tykqxs-round. Which of these forces pr 1k (qht21:syfmgdm.x ovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillin*amt6a, cf .ea mmb*,cg out, even at the top of the circle wh,ebc. a,mfam*t*ma6c en the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three hp-4*oi1: atybmn wyy 39kp:bcontrols in the car which can be used to cause the c4mn3w- :p b a:yky19o*hpbtiyar to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, ack 33o.adc*s)vr/( vk iu+h zas shown in Fig. 5–31. His sled does not leave the gd+vakrcz ova* /si)3 .3 chuk(round (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 high spe)d+ 5 u:qgqgfot9b) naed?

Why do airplanes bank when they turn? How would you compute the banking p- .azp 6tpho89u)cwfrpo9o/ angle given its speed and rad /z)8p9.a6pouow -o9tphf c rpius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.:x(y6bzh dat ( She wants to let go at precisely the right time so that the ball wi 6bza((txd:h yll hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitatioeubi1 , vxr7/bnal force on the Earth? If so, how large a force? ,biveb 7u/x1 rConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moo3yl 61fh .mbrmn’s orbit b1hr. fbl3ymm6 e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on thmg;, 62vgy6m(hzy7xmicf i v3 qtm:(w e Earth? Whic6(i mmiyxv,(3q6h ;mtwmvgf z2:7g cyh accelerates more?

The Sun's gravitational pull on tqn rsl2p0db, 0he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consl0n dsr2q 0,bpider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatad;n.ggm 6 ,ytor or at the poles? What two effects are at work? Do they oppose each oth.d,may 6n;gt ger?

The gravitational force on the Moon due tc soz3y;myf 0+o rm2k8o the Earth is only about half the force on the Moon due to the Sun. Why ior0yf mo8 skzy+ ;32mcsn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mj+;a5vm ;quod ars in its orbit around the Sun larger or smaller than the 5uj;+ dvaqm ;ocentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (blx3k4v/ lw u;)fs3j tvz:5jcq) toward the west? Consider the Earthk) c:qv j/l5 ;sjf3tvlzx43 wu’s rotation direction.

When will your apparent weight be the greatest, as meassa6ka7hx + ogje2f1p4ured 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 leastof ax6p1sk g4h2a7+je ? 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 ou mef7a.8 0/xrwa: hoxexw3nrz4 9fjr;ter 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 ir rh7w3joxwxz4m8x9ar.nea 0 f:; f/e nside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weig.8tc3 vh:deyfhtlessness” betwee:c3e8fvh tyd.n steps.

The Earth moves faster inav; q5.mhmk+ e its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.+ kqahe;v5 mm.]

The mass of Pluto was not knowno .781h gu q1hw4na56adiljrl until it was discovered to have a moon. Explain how this discovery enabled an estimate of P71 ulan.q h l8w 51hjg4oai6drluto’s mass.

  The Sun's gravitational pull on the Eawhauy/c*0 r2 yrth is much 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 other.]A child sitting 1.10 m from the center of a merry-go-round moves wi/ cryw y*20uahth 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 19806vlq-ftua4m -n +,tn t $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in it5qsl, )c wv7lls orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? As )ql,slv7c5lw sume 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 discumzq-9 nn2f fax2fco 99s as it rotates uniformlfzcman99o-2f2nf9 xqy 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 m+vo.ig nsij1 : ad+ge03hz4uEarth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in termgoahin4 z+ jd+is g:e1m.u 0v3s of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of t-3 umkpp;1lr5oia(vrk cr* 4ehe acceleration of a speck of clay on the edge of a potter’s 5i3m 4re uc;okrppa1-l*(r kv wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a q+ 0il 8 jcs6nn.uxxy*string is revolved at a uniform rate in a vertical circle of radius y6j*n+sciqulxnx 0.8 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 round a turn :z 5ev3nzo8hizu*z t4msv/l5 of radius 77 m on a flat road if the coefficient of stozezsv8zh4*t z:5vi5 unm/3latic 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 friction be between the tires an8 rju*,rzhd6 wd the road if a car is to round a level curve of radius 85jr z*w,hudr86 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighsg;w.gx + fr6q.k x96gp3e ufmter pilots is designed to rotate a g+wrfem q;pg9.x6 u.gk36xfstrainee 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 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 adbwu5-hypml+r7e pr/ -h -r8onvj a c2id2q9* xis of a rotating turntable of variable speed. Whbilocvu-r9 jd -n/*52q2phy-+8 d7me rwhpr a en the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsi +u(;/xptpp:g i)xr e:; eg3a6qzi1jwyo *esfde down at the top of a cirj/3*gyx6+ppwxiaio(tf q z;:;ur ep 1s :e)egcle
(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 mass1x hu(3n uep7u 950 kg (including the driver) crosses the rounded top of a hille3hux 7uup1n( (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-mipfcphzm/ w (vzrz,r8 py,;wp,r bdf )4 ;ek*3-diameter Ferris wheel need to make for the passengers to feel “weightlei3y f ;) zzpwp*zrf;b 8hm4/ cwkpdpr,,r(ev ,ss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical 0jb- /fxzrfo,9joitgsl x iudq jnet; 086976 circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket6b6/r0,0 lq fxoj sitjgf 9ztx8;unde o-ji79 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 par08/ khs9f )t1auihnrhticle 9.00 cm from the axis of rotation is h9)hihtna r/8uk s1 0fto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa*5*2rkcxqqg 2 ft 7:urrtr /0er8ol gylled "room.rtu y2efo/r: 7rclr* 2xgq8 ktq0*r5g" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tae+wpt; dw5g ori1g5l *bletop, and is held in this orbit by a light cord cor5g +i1 ld;wtoew5 pg*nnected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, /ap , w:yy + fputsp/crm+ft3(by not ignoring the weight of the ball which rut rcf fp(p ,a +smtwpy3y+://evolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a ci8,eu tl);c(fwk mkv:/ ry+pxar traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses m ,,eq ;nox,o lqvl*0 myn)hb6$ 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 divin4rydv cdxa:)d ;ib5srd+d9 p2g vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerte ( ychl.gm/xl9d on the car (by the groundg/cy.mhl9 x l() in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the v5f19 lijr 9cugc5o g+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. 59 cr oi5lucj1 v9+ggfIf the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular 1a-yvi5t0sr z5(l,xgnlkg g, instant, its ags rv5(5 -txgay,1g l kli0,zncceleration 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 E,/ipj1o 4p vl7lztsv+arth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass ij,lps z7t4ov lip/1+vs 1350 kg.   

  At the surface of a caz.s ++0 jsbi 9f5gqjo5u; nnxertain planet, the gravitational acceleration g has a magnitude ogbf+on+ 5z .s0jjnuxas9 5i ;qf 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 Mo hc;-kr k92w8ibkg *ryon. The Moon's radius is 1.74 -rg*i k2ry;8 k9kbwhc $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1. 3st+-a2i/nsgt mtrf:5 times that of Earth, but has the same mass. What istgi+/f m:3stan t-r 2s the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but yb*cl)r2oo :2 pgk g jurgn3-/the same radius. What is g near its surfg-g * lg3rr2y):2buoc npo/kjace?   

  Two objects attract eac/v: z*o 76uieqleul *uh other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valuem5n,mv,3hxqki 6c+ a5mcsky ) of g , the acceleration of gravity, at (a) 3200 mh5a,v,my6s c)nxk+mq3cm ik5    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wo rv*p)ib lo rzh(6nty*:t7j7here thegravitational accele o 7zvht :*ilytrboj7p6r*)n (ration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha lt9* .;nbw+jdonoedt.;l mv. s five times the mass of our Sun packed into a sphere about 10 km in radius. Estimato dj+m.l nl;dt.o; . 9bvw*ntee the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which onr::wlkjb nl gbk3d50x 3-xj9 zce was an average star like our Sun but is now in td35g0wbk r -knxzl bjl::9x3jhe last 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 asb./ylka qfu(e ,7c mp7tronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surfa(u7qlfba ,y/7kcm ep.ce in terms of g.   

  Four 9.5-kg spheres are locateh/6 y ;31mhjs)0i iv12hey vw kjgys;id at the corners of a square of side 0.60 m. Calculate the magnitude and direction /hsiys; hg102wh iiy3;emkv) jv 6jy1of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on8.u-jfh6xca fyf ma2 , 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-.f8, am-ujhxyfa26cf 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 lolvf,qu64ga j -a5.iat the surface of Mars is 0.38 of what it is ig6-,a.laq4fu jo5lv on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of xnasc3 0kx94/6qi vcbn7bx v 8the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampqxxacki4bx79n3 /svbv n 0c 86le 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a l3yff jhn24*g stable circular orbit about the Eah*lf34ngf y 2jrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releasxkjxd j7)ol*vsy27 f.es a satellite into a circular orbit 650 km above the Earth. How fasvkoxl. sdx)7yj 2*f 7jt must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate ifmfor;k/d .aubw6 w4k43o5etfrkaaxv ,g9:f ( occupants are to experience simulated gravity of 0.60 g? Assume the spaaft6fka9 5:reo xw3k o/kg.4 umwb;frv a,(d 4ceship’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 orbit the Earth s:z -rfp h4kn,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 :hs 4 prf,-kznof the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wouldu-(a dlvuds(dl(( y+plq 8s.p a satellite have to be launched from the top of Mt. Everest to be placed in a circular add(+spu(sl p d(vy8-l u ql(.orbit around the Earth?   

  During an Apollo lunar landing mission, the co2nlds:de ; ig ;tv5w(ommand module continued to orbit the Moon at an altitude of about 1002g:tinv odlw(es5;; d km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that or vme4n o ip9sy ;:cdv(fowy;.1bit the planet. The inner radius of the rings is m9;cy wvo:4 fv;.sn ip1 o(yde 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 is (:tq/qpe8q4ig m;xs (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight4gq(i pqe8q:m xsi; /t (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from thwxum7u5nig (ggfs e ;d(.a.w(w(j3bre center of the Eawes5( xugd7(g(( fb j3na. i.mu; gwrwrth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star sydk*6(wiss,i)3 ob j(z :dce*zxng 4bgstem consists of two 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 is the ma*d xijkb* i zcb),(: snw6g4se dzo(g3ss of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in wjddm6eql2 *rj p9jjm;7d u;i * .n*ezan elevator thate67.n j9wjp2;j;jdr*m*u d d qiz*el m moves
(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 suspea0f f:3wi1 kg *wc6jytnded from the ceiling of an elevator. The cord can withstand a tensigcwtj:fkf0* i61 w3yaon of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of y6o1 q7e :awraa60 scla planet with period T , the density (mass/volume) of the planet is yceor a0:a6 lwsa1q67$\rho=m / V=3 \pi / G T^{2}$ .
(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 1myel6 la-f -qthe period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Ea l-m6eq- aylf1rth’s surface.    s

  The asteroid Icarus, though 7spm mppo pt7km9172 sonly a few hundred meters across, orbits the Sun like the planets. Its period is 410 dmks p2m mpp 17p7st7o9. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4. -s:topzbcdk2nd 78z7 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 co( ew tk.tlj1x1mes 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: Thejtk w 1.(e1tlx 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 centeri6drp2t b/v 1j 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, anrnydtk:6x zc0 *y s:(o w-+vlqd mean distance for the four largest moons of Jupiter (those discovered by Galileo +d ownrlyvzt(y0xc-sq 6: *k: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 Eztxitdrt ; :.3arth from the known period and distance of the Moon. ;tr.dixtt: 3z    $\times 10^{24}$

  Determine the mean distance from Jupgv,r.vq i1en8 5 xk7 1)mwfogqiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods q,i11 e.x)7fvokm5 qgn vrg w8given 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 Jupiter consists of gydruh tn292.) qcdcg1/y t5vmany fragments (which some space scientists think came fromg1g.vqut) /chrd25 n t9 2dcyy a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form g3n 4jc 0m84rxm uui6cof a band completely encircling a sun r xc6m8jigu 4u0mc4n3 (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from e0; )p1lgm gfhnj4yyd0+t y)m *y+ x(qui/ uhwa 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, an xp ;4 jug1hhi 0g)t+q fwd*(0u yl+/y)myyemnd the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerll/*4 i;1c tdqz(awtration of gravity be half what it is on 4lrqlwadt1t ; i(/z*cthe surface?    $\times 10^6$

  On an ice rink, two skpz z+taddx)*(aters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.)x a(dd*pztz+80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dgzwjtgi3 k 0 .zu;:x/dn) /hgoay, the apparent acceleration of gravity at the equator is slightly less thhgn/j)w/ x; .g3 t:iudgoz k0zan 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 t0i4 upm. q5w3ig(zvd6dd bgu /he Earth will a spacecraft traveling directly from the Ea 3v z.4uw d(iduip0d g6gq/bm5rth to the Moon experience 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 scef(q,kx*q.5j9 qrx2cljg+z tale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, aq,. (f+2ltcej*xz9 qkxqjg 5 rnd in which direction?     ----待选择----upwartddown 

  A projected space staticge 4nq. -vl238npgw ht(vxj rkd3n:9on consists of 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 speeglncdk-n3q nhj4(.g3p :xvt 8we2vr9d (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 loo th7sn7-o v,b vyx js-5aa66ypp (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 th20-u y.shrwl/azbcq b2-r 1xqe mass of a planet in terms of its radius r, the acceleration due to grarrasb0b1wxh-z q .c2/u l-q y2vity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a stringpz tg j,43r,chd/i3xf:3kqg a) is deflected from the vertical by anz4:,/p3x ftdr 3,ckjaigh qg3 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 banked fg667h 2;hrry-+y pl wqnql; as); cigmor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what ran2ynchl6 qm)s +; lr-pgr;gw6hya;7 qige of speeds can a car safely handle the curve?

  How long would a day be ih 3:pp1sv t9itf the Earth were rotating so fast that objects at the equai19 tv:psth3p tor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0xz n4ch:im zef7y-8+l $\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 constani lr/dw; hp c*-o/ph88ptq i/pt speed rounds a curve of radius 235 m. A lamp suspended from the ce*wrpp d ;qh/ tch8lop-/ 8iip/iling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eartpqmkfr9 fr3ko 4i7u.7h. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupitep.97fk rmkou7q rfi43 r since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =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 Spaqkaw rk m,-9(oce 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 cl rkwaq-o9 km,(ouds 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 - :fznzk-5cvs it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley hakv z-:fcs-n z5ve 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 sat tl/qp g6+2xn8brde7.: a ngztellites orbiting the Earth. Using “triangulation” and signals transmitted by tge 6z8g a:t./7nqp2 dr+bltnxhese satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of 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 billion km, is me(8b (55v qckl0 aworaeant to orbit the asteroid Eros at a height of about 15 km . Eros ca b0a85lo wrq(k(e5vis roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a e)4uw.jaep) 7agx5xnndej 8;ww9 j6 wsatellite in need of repair. You are in a circular orbit of the saj;jw 9ww.nj6e78w egx axauedp45n ))me 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 period of 3000 years. (a) What is its mean distancql xej a228vf;e from th8fqx lea2j2;ve 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 could actually "feelnigv7*)l 56gzawuc 1v " yourself gravitationally attracted to someone near you. Make reasonable asl *wun5gi z 6vgvca71)sumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) jy4 fin vhqs5(5x .ik5at a distance of about 30,.jn k55i(sxhqi5f4 y v000 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 locou )tz 9f1ga(ou 59vl4sr0 uuqated 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 o9t4 luuu1(ogqr )fsv 9a u0o5zf the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kc9w8ncc8 rgfm b:b395b8zhlmg 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/8bawnv.aqvep,* . yy experienced by the tip of the 1.5-cm-long sweep second hand on your wv* wa yq,ye..8pna/v brist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing 2 ne)z/ g kir+0achfb8a 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. Wha iz0kb2hcrg e8) /fna+t is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a.3w+wf y)h dhgb bv,o*xo*r8d0o/jpj new highway is designed so that a car traveling at speed dr+woj*h3 h jwo0d* gxo,)py.b/fbv8$ 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, util2u6z z599cvutp 8yighizes 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 needed on a train passenger of85z ctzvu2hy 9g96pui 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.$\approx$    $\times 10^2$