Sometimes people say that water is removed from clothes in a spin dryer by centr.( vek6gv n7dpifn.e6 (vk7 vpdgugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be v.jlx+itj,9qa6fyd9- ce q0 rthe same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explc9aid.x09 jj6-l e +rqftqv,yain.

Suppose a car moves at constant speed along a hilly ro,5 z*tu4dc4 7 w,khma*nesq elf+(fwead. 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 stretch neauw m ,ls4+c ff,te 4wkad nhz(**qe57er the bottom of a hill?

Describe all the forces acting on a child riding a horsq*s ep5cfmrv avbdf(: 5p(y*4e on a merry-go-round. Which of these forces provid r(b vp:5m*e(vpd5q yffcs4a *es the centripetal acceleration of the child?

A bucket of water calv9x7vzd .0sx umlu. :in;nm+n be whirled in a vertical circle without the water spilling out, even at the topxzmdu+..: vs; um70 nin9llxv of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your *)6almn/ei+dqtd y pv8;q 7fi ed,0jwcar? There are at least three controls in the car which can be used to cause the car to accelerate. What are theyian * d0jf/;7+e qdmylte,86v)p dwqi? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fi/f9x di2pesx,bg g 1l;g. 5–31. His sled does notdggbfx p2lexi/ s91;, 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 rider1e+qd2 n h tgp4p jb;f3.durw:s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turhajhl-pv847. ,l i 5mej:rv(n sj6afmn? How would you compute the banking angle given its ai r-lmfp(eh4sjv8 mnvj5ljha7 :6 ., speed and radius of the turn?

A girl is whirling a bal d5.zwuxwv4:4jk *v hjl on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the b4kz vjjxw 5*4hd. :uvwall 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 force on the Ea i a4m,ab1tl315 fzj lzqjpm,6rth? If so, how large a force1, laj,fz5qb1m l 34pmai6t zj? Consider 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 Moon’s orb *pu4 sv* uwfou3g79(z jig:ogit be diffwgvu:ji* (zo o97ugu4p* f3g serent?

Which pulls harder gravitationally, the Earth on the Moon-d5lz4o e t1xb, or the Moon on the Earth? Which accelerates mor5lt4- dxzeb o1e?

The Sun's gravitationa hfc32t9rcgw 5kb6ph )l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatir5htgp36 2w c)khbf 9conal pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the t8i.yspp.sq657zs mzpoles? What two effects are at wors z 5is 8pz.qy.sp6mt7k? Do they oppose each other?

The gravitational force on the Moon due to the Earth is igdoup 5 zx7cr 8b-k56only about half the force on the Moon due to the Sun. Why isn’t the Moon pulle55c 8 6drk7ib-oxupzg d away from the Earth?

Is the centripetal acceleration of Mars in its orbit around q;75hrm s 7mvf / mawn6kvra;5the Sun larger or smaller than thevr;7swq6 7ankmfhm;/ra5m 5v centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the es00z2t gefsjp/n;kv do.x p(.ast or (b) toward the west? Consider the Eart0/p.nekx2 0p;sfvtj(s od.zgh’s rotation direction.

When will your apparent weight al f8z bzr, h)-2dx-vybe the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? hl y dza8,)fr2vx z-b-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 affected b2;elu +xhoxt2 y weightlessness. One way to simulate gravity is to shape the spaceship likhx2;utl e 2o+xe a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betdmr4 hn0+6fjo weenhf mdr o6+j4n0 steps.

The Earth moves faster in its orbit around the Sun in Janua-obz9d f 9o prr zd-g3j e)29tu:l4qbyry than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not mr3oed:bu ljrpy4 z9 2bdzof )- 9-qgt9uch 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 i7w* bwelt2*m- yr n3wl*5svb not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s lv* w e*57mri n bwlts2w3*-bymass.

  The Sun's gravitational pull on the Earth is muv.mat 4fwm 9o8ch 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.]A8m t.ovw4am 9f 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 travelin iz2ig 98cmgw.hyr)q4g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in iptm/2 6vo 1vsrah3o p)ts orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assumev oaos2 rphmtv)1 36p/ 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 exerts.dklbxm;rx.v0.c (y ed on a 2.0-kg discus as it rotates uniformly m b; x.s kr.x(0dlycv.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's8g5 nr-y*c8ef0oqnj b surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shq-8cr 0jg b 5nfen8yo*uttle 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 sp ta q pi3s3pb.z(l54nsb0agq, eck of clay on the edge of a potter’s wheel turna p ls3igz.p5n4(bsb0q q,ta 3ing at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate *7,*lk;1cg ax5-o mdaz hf uplin a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0axp;7a1kch 5 om *gd-*f,l uzl0 $\mathrm{~m} / \mathrm{s}$ 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 tus ;fc 3or9*iimrn of radius 77 m on a flat road if the coe*i s ;r3mof9icfficient 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 stati h*( siuvuz3mr gw7rbh6 m5 jlw*mz08:c friction be between the tires and the road if a car is to round a level curv6r m g 7*hwhw*zv i(:z0 ums8ub3rjl5me of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rota x5bojg,bdq2( te a trainee i,bbgoqd x5 (2jn 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 t29 8s nzb;uo4tjafkof8d)p+the axis of a rotating turntable of variable speed. When 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 z 8t no+9ak4d8ffo;)tj s2bpucoin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rol0u eup(i8q. z9/ i bkeg0s(bjbler coaster be traveling when upside down at the top of psb09(u u0(8igqi e/j bbz .eka 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 theuy fg96w qexe*k5f;sch5+t7x driver) crosses the rounded top 5eft7sy9u gxf kq5 exwh+c; *6of a hill (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-diameter8 i;vl+mk xg)a Ferris wheel need to make for the passengers to feel “weightless” at the topmost point? m;k8)vgi al+x    rpm

  A bucket of mass 2.00 kg is whirvpsa u o(2*xoywypcpxhs),6wm z7 l1(l;6p n 9led in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 zcw p, h6(p xsavso9py mly*ou )72l6 nw(x1;pN.
(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 fro0zpn b x/r9(ylm the axis of rotation is to e0p9y(xnl/ zr bxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in :c8pda2sha e:u o/b6v a cylindrically walled "room." (Seb s: eah2 po:6c/avu8de 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 y xep8cx2ko.o eubax/ v- ;g70frictionless air-hockey tabletop, aogvb28oxex/;u ckx 7e0-.ypand is held in this orbit by a light cord connected 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, by not ignoring the weight of io/ :nyk,h/4zwsb+a mthe ball which revolves on ayk//:sz+mo nh ,4iwab 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 mo thplr;s +*)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 massesggf/bk)l+51i zmih a - $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at j u9o)f glrr)u5lzo 4; 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted on prqg8uopf xq+ 5c v(*8the car (by the ground) in Example 5-8 when its speed is 1v8oq +cppq 5*x8 grfu(5$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelero,; yslm ykb4oej tjvt 612h.5ates 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 halfwt 2o.e1 5kvsmt4 oj6 jbh;y,lyay through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizon +qhy b* 0p)jhzc/p5sntal circle of radius 2.90 m . At a particular instant, its acce )b /0*hcspyn5 jhzq+pleration 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 spacecraft rk83 gt13ybcx 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg g8cr1kbxt3y3 .   

  At the surface of a certain planet2 6fpeimrxtx )+h qugo;sf86p4b b(n, , the gravitational acceleration g has a magnitud(fs6pbn2q;b f4hiep u8 6,xxrm ogt)+e 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 gyoydgx8):oi4y. u vq)7m 3hxhravity on the Moon. The Moon's radius is 1.74 uviyo4)hmq87 dygy ): 3x x.ho$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that ofng- 8a k3z9)i-x c76rcnflt 1nlwe4gx Earth, but has the same mass. What is th6ln4 -inz1er t)cxc 7xw f-gkgl93 na8e acceleration due to gravity near its surface?   

  A hypothetical planet ha rg1mk r/,i, 8qapez pa8k4c0us a mass 1.66 times that of Earth, but the same radius. What is g near its surface acg8u41kr 80a kpqp/em,,riz ?   

  Two objects attract eachs/bim(s cx5n;xa-awvsj.(/)zdv )pk 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 value of g , the acceleration of gravity, at (a) 3200 03wmv fkif; 1dm;0m k vwif31df    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ;gtnj-r avogw g8.2f 75tp; byoutside the Earth where thegravirt .w 7g2f v8;tga onybpg-5j;tational 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 3qadb c6r2 7zm ip p;zxsaj:54packed into a sphere about 10 km in mzp 4ipardbxa6 :7qc;2jz5 s3 radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avev,s7ilf0y*q grage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is0v7ql ygfis *, the surface gravity on this star?    $\times 10^7$

  You are explaining why astronaut- wa *5+t ek5vdmg zrs(yf*y)0asvyt)s feel weightless while orbiting in the space shuttle. Your friends respo*yrmz fyw5(vs)ksge0t yd5-* aa vt) +nd 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 at the corners of a square of side 0.60 m. Calnlx n5igt9 4;vculate the magnitudn tv 4g5;nlx9ie 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 most of the planets line up on the same qox7v2o8 (es xside of the Sun. Calculate the tooxo2(sqv7 ex8tal force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at temiy7crq h0-)-kd+ hri1 uz+:;b yg cthe surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass ofehz 70:-kr d yri+u+by1cchqtg;- i)m Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for l8grtiv am)w.mw.(5wthe period of the Earth and its distance from the Sun. .lww.am)8rwt vi5m( g[Note: Compare 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 b m/ou,;6xjlmz75rfpthe Earth at a hei6mu/ xlmob fjp,7z 5;rght of 3600 km.    $\times 10^3$

  The space shuttle releases a3-m*fxetnkyk p+p d61x+ n6hq satellite into a circular orbit 650 km above the Earth. How fast m y16-tdxx3n qh+ +en6f*kkppmust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to erk7/9v lh zozbl.*0 exxperience simulated gravity of 0.6x/ 0h 7 9lblkz*vzoer.0 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 takez+s7tg g5x,zds for a satellite to orbit the Earth in a circular “near-Earth” orb gs,+5gt7d zzxit. 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 satellite?    s ~    min

  At what horizontal vel iwjj3/rqym5( ocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around thejjw3q5yir m/( Earth?   

  During an Apollo lunar landing mission, the command module continued to.(h: kpbeiszc 5p,cb o),ee p- orbit the Moon at an altitude of about 100 km. How long did it takepkp- oc:, cebeb, )(hezp.s5i to go around the Moon once?    s

  The rings of Saturn are composed of chunuck:l941 j 2w,bk hgqaks of ice that orbit the planet. The inner 9q4jb2h1lc u:gka, wk 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 e3s /1b chdaoj *r0qnb1u2-cs in diameter rotates once every 15.5 s (see Fig. 5–9). What is 3-1bcqd ha s1/c*ruej 2onb0sthe ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the ce17ay - i7qpsi1dhh(6z6w q )dq fx;iwqnter of the Earth's Moon in a space vehicle (;7dq wwy1ih (q7-1)6 shqa6xifpq zid a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They arhp2 x. q.x.sd3nd;rc9b *ze tfqa, k0we observed to bh0fw2,.kzsc*; x9. etnpqrd d3 x.bqae separated by 360 million 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 scb/83ty 9sgb)ra/jqd9c. azdpale read for the weight of a 55-kg woman in an elevator that83 s d)pgqj /abrb y9/9ztc.da 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 suspended from thlxv68+ u)kicgn a*qr3t b 0d6le ceiling of an elevator. The cord can withstand a gcnr0l u36)t6biqla8 *k+dvxtension 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 orbit9uh70ga+br k9 zu txh)cpp-p*s very near the surface of a planet with period T , the density (mp zup r7c*)9 k-gx+9tuahh0pbass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) tossq(y )6 r50o gt1un7d5t-k aedco4; tkfc m;q determine the period ofgtm(;cq 05 se5 rudo6a1;)kk7qt fs- n4ctdyo an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the i,q4tw;2+.o zoql a rzSun like the planets. Its period is 410 d. What is its mean distozz;o qartqw, +l2i. 4ance from the Sun?    $\times 10^{11}$

  Neptune is an average disfl0ge b o/53hutance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It8cij1 (o k)5owlq/8bntp t5brjl7no - 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)-w/nbtcpoin15okr78 o5 (jqllj8 t b” 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 c txv3 )o s;xszb2bm-l6enter 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 do0/*2,i1k d:,kbnh jt oiiqd mistance for the four largest moons ofo*jmoi,/i ,di12 qkk0 n d:htb Jupiter (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 thr9(pkz sv0vub a0 4pr4e known period and distance of the Moon. r0kv0sprb u4(p 4zva9   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter jxvp41lg y14qkh 0p- tbnj*k)’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table. q0yhnkjt 4 k* 1gb-1)px p4ljv
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter co3: hsbg.p3 h m3oaqh-gis(j x8nsists of many fragments (which some space scienti:g3pa -8so h3m (.sxjihhg3bqsts think came from 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;6a yl b1qw8d,(nuu1n 9pakcx describes 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 diydn qu 69pakulna;w x( c11b,8stance 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 hangivuf ij xm/n9p:5d vv045hy :ltng 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 swinvlu:5fxjvvm/p:0i4dty n 9 h5g? 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 vi(+th25 vzcdwhat it tdh+v (c5iv2zis on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab bg bp/ir.w8*l hands and spin in a mutual circle once every 2.5 s.*l gwir /bb8p. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity at .nyk+ihpnl54pmfeust cp +j.2ys -2: the equator is slightly less than it would be if the Earth didn’t ropk ys..pnsm5 yjfl +p +:-henc4t2iu2tate. 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 directly,g.od 5jbn7ip from the Earthpgd.b 7jo5 i,n 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 (j*jwmnhd1u - stand on a bathroom scale in an elevator, it says youjm1*hw-dn(uj r mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotvtk2 ppquz obce47)b*4np15y ate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per *nk)5744 p 2ye zbot qvb1upcpday) 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. 5–43). aq(kee12tdv :
(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 ofoula)+(d tx9 nkbv1-yn/lob / its radius r, the acceleration due to gravity at its surface and the gravitational co-oon91t/ l)+vnykbabl d(u x/ nstant G.

A plumb bob (a mass m hangin 6t ah4qn w6u)uyt2c+mg on a string) is deflected from the vertical by an a u 26qty6tn +hwcu4m)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 for a design speed of If the co7oshkce 157 ufefficient of st hfu oce775ks1atic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast tpy :ja5(o:0ugnmt :s7zhxx6 phat objects at the equator were apparently weightles 0:zpy:657uhnx:at(gj os px ms?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o xt3,w r4qr;s4lusju8im1vl 6f 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radiusdjo/v gu0r7284ya zuy 235 m. A lamp suspended from the ceia8ydu04o27gzu j/ r yvling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has b-b2 ivw*di6 ge-qkx:0dm ue)zeen claimed that a person woulkdz)idwxe*-0gu-v 26 :b e mqid be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremelk99gug s3f .;dqm gopt-f;cpft i6h14c4 i*uhy massive64hs9fouiqkf ;hu ti ft -1;gmgpp 4d.3cgc9* 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 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 th idzc8 0/zh0aaaof-q 6e 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) zzi ahq8 oaf/d-06c a0Where 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 Systempq4qqhbeyu13l- 1ht , (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, all3ybhtq1eql u,hp-4 1q owing 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), afbqz-)wjm t)dz,n/b.xter traveling 2.1 billion km, is meant to orbit tjbwdz)-/m t, )zn.x bqhe asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursui ui4ub fdr5,+gng a satellite in need of repair. You a54rg fudib, +ure in a circular orbit 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 period of 3000 years. (a) What is its mean dihm,rlxnr;n :o4p0ff1*g v phs:u(k5p stance from the Sun?psxfro*(4 5h nm:;gk,p uhf:p0nvr1l   
(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 l jp(tgx-0zn7 "feel" yourself gravitationally attractexjltn7 (pgz-0 d to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky W .9x:ruqcb*:it*v asgay Galaxy (Fig. 5-46) at a distance of about 30tra.gb9vi* c:sx *:q u,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the4g w )kgkk9:wfsua,/ s19w oo dmv.*ia 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 *:9wwi kwauaoovf) ,9 .mk g/k4sgsd1 placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbit(gkfeg (tq 77,cei3z bs 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-long swebwh.)f7i7 )mu d-nyraxuo o 55ep second han idy).7bn7 ah55orwouxmuf-)d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing * apo0po+g kn,a sinker weight around in a circle below you on a 0.25-m piece of fishion aop*kg 0,+png line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so1tt e)fmkc*+w that a car traveling 1*+wm )cttek fat speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whj0cv(0zdxp ap .q)mc:en 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 of mass 75 kg if the track is not banked and the train does not)jc p0cx.(z0 qmv d:pa 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.$\approx$    $\times 10^2$