Sometimes people say tfxeygu5w1w953fuw l- hat water is removed from clothes in a spin dryer by centrifugal force throwing the water outlwg3y5 -wew xu519ffuward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a shb )p2sil9q g3osgt0n0arp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expl03ogltss20ipb g n) q9ain.

Suppose a car moves at constant speed along a hilly road. Where lb p/1oq zsq/9does 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 nezs/b9l1q po/ qar the bottom of a hill?

Describe all the forces acting on a child riding a)km, nyt4mtclt7z;. hrcs, t; m34caa horse on a merry-go-round. Which of these forces provides the centripetal acceler;ctcamt.4 ns4 ,r3hy;m)l,ta tzkcm 7 ation of the child?

A bucket of water can be whirled in-tvukm dr 5e18byf*)5 n,k rmg a vertical circle without the water spilling out, even at t d)kurrn55 m - ebyt8v1*,kfmghe top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There mh/ar y.:0 udware at least three controls in the car which can be used to cause the car to accelerate. What are:/0ham rdw y.u they? What accelerations do they produce?

A child on a sled comes flbcy b,y*5nl.7m dk6pw ying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feelsl*,5c wp.bybmyn6dk 7 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 leapl3ocjt5r:2zf (dngo b1*t q*n inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you civ9u uh/ypa;v 2 vs7f2ompute the banking angle givfvupv 2sv;2y ua/i 79hen its speed and radius of the turn?

A girl is whirling a bals1r 6;+jtenvhre: -oh l on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let;+t h1r-eson 6hjrev: go of the string?

Does an apple exert a ewn7-s0830c1d:suc4gr 9vvc caq khf gravitational force on the Earth? If so, how large a force? Conside :gsrcuv ck78 wsh9q34 d1f0-0nce cavr 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 orbit k,s+kf fewe7 .3d i)jwbe differe.dse)ww,kffi3+kj 7 ent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mooh*2 0 ynazwcb0n on the Earth? Which accelerates more? yzhw b2n00*ca

The Sun's gravitational pull on the Earth iy) n n(r5 wnqpuz-:cb1s much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull:n1u-r ( n bz5pqn)cwy from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wh gx2lzn2 klylvl ) gc66(t7ft )y/+vxwat two effects are at work? Do they oppose each 76 kxlv ltt62f)/(ly ywzg 2c)gnx+lvother?

The gravitational force on the Mn3e*vo,kl t0 qoon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moo3lkn,e *0q vton pulled away from the Earth?

Is the centripetal acceleration of Mars in i9caht.z - eb2bdl mg ,(dexm59ts orbit around the Sun larger or smaller than theexa5t,zd e2 b glh cm(bd-99.m centripetal acceleration of the Earth?

Would it require less speed to laun8zcd6bhg8o*jv*vdevx- 3qx+ ch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s ro -oedb dh gx8jv+vzqx* c6v*38tation direction.

When will your apparent weight be the greatest, as measured by a scale inf.e nz x-a,-m ec)nm6y 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 f.e z6n)men-m-,ycxa the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coulw4*8 ivhk-1oeb/ ,zn/dt fack d be adversely affected by weit81 oc/4,zafi/wnhkbv* dk- eghtlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” orii. ijnlkk/e rc gg)x6h48o(w nh9k 4* “apparent weightlessness” between slr)xgii / i( 4h4kne.kh6wngk9coj* 8teps.

The Earth moves faster in its orbit around the Sun in January than in J bk u7k*nss7*nuly. 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 factoss7* n kn*7kubr 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 zdcq .qfpnbgg+:hqbd j:6 )):j/ru, imoon. Explain how this discovery ena+gjuhd 6 ) izj dg/:cq.b:rq,bp):nfqbled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth isku hhh) 7rf.) pv(d.hr 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 with a speed of 1.25dk hp)uh(h7fh r.r. )v $\mathrm{~m} / \mathrm{s}$ . 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 c 7fb7eghzqoyl- m 5:.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 its orbit around qps(3gi-vsy,+ vxk a 9nl82mo the Sun, and the net force exerted on the Earth. What exerts this force on the E8nl9vixk(3gs,ayqpv +2 -somarth? 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 2104xv9l0heleo2gzd;q . N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the sp;lhzd.q29l o4ve eg x0eed of the discus.   

  Suppose the space shuto hs/ z61gjrg+ (ouip,,1cna ntle is in orbit 400 km from the Earth'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,apgs+h igo orjz u/,( nn116c terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck.jbra83bc9 ro of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minub oar. bc8r9j3te) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvedu0ue r.2kd 8lp at a uniform rate in a vertical circle of radius 72.0 cru.dl2 uke8p0 m , 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 oynk)ty ; n4/(gmhpc1kf radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Iskp4 gh/cym1) ynt( kn; this result independent of the mass of the car?   

  How large must the coefficiec1lmv(/v,9unkb mt 3 v k9vln:nt of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a spee 3 (u /kcl1mlbm vt:,nvkn99vvd of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate an*urv:3qk1z6ltsn 6h trainee in a horizontal circle of radius 12.0 m . If the force felt by the traines:6*v u 3trnq6khl1 zne 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 tc ds gv0dl *u:byiclhd w+.6e39 pap:6he 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 coin ivw g6c :yphdusd :. bp09a+ll6d3 ce*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 downax 6x4y01zv tvbxi e3;e*; egl at the top of tl eex0*zxavgv6b ;i e;1 x4y3a 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 6ti g4mg(v:bs kg (including the driver) crosses the rounded top of a hill (radius g v4it(mb6s g: =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-di : dfb,+1dsu xef8/p8milzx9 lzp:w :mameter Ferris wheel need to make for the passengers to feel “wei9,8:1ddp +zlfz xlm:i8sw/bmux p ef:ghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of +hg8 agvhzd4 -pva+*dradius 1.10 m. At the lowest point of its motion the tension in the rope supporting gdg+-h+a pvhd 8a*v z4the 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 particle4c7 st8dhe6 x- ojgo*e 9.00 cm from the axis of rotation is to experience an acd7ox8* 6c4t-e jg hoesceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotate d1;jzm8r i6hld in a cylindrically walled "room." (See Fig.ml jr6;18zdi h 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 circlx9 zwy/yu2 cftntg(6/e on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dx2 t/tugf6n/yw9 y( zcangling 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 ak l ;hui4jj n0/mh 8/ytnzn(h3 2f9alweight of the ball which revolves on a string 0.600 m long. In particular, find the magnitun mfh( ;0//a3uz24l8jiykjh9 hnln tade 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 perfekg-w3+9;w qeb jmfr )dctly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses c3+9cc 6g +qbn r7zgwso,.9cfeul6ge $ 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 qor .+uhg l9;qat 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 tangentialpkdp3i.3p :q(n10ru(cpe y(efa ivn7uh*4 do and centripetal components of the net force exerted on 1i(.(rd yne4pvp fnquku*i:(p ophd3 c7a3 0ethe car (by the ground) 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 pit area, ghbj,pzl2s dgi i18l 03zn p0u2oing 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 acce sp3b djpil,2z1 hgil0n 0u8z2leration. 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 horizontal circle of radius 2.90 m . At a pa632x0 t 1vl37rfaifoen pjff,rticular instant, its acceltj nlv 1x7fp2r 0iaoff3f, 63eeration 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 12,800 km (2 :m ) ;priiw 1edixw1d01rjoq 3Earth radii) above the Earth’s surface if its mass is ) i1w jdxqmr1;0:e1riid3po w 1350 kg.   

  At the surface of a certain planet, the gravitational ac ve;.izi*m)/)fkyqs + rp1bnlceleration g has a magnitud 1s*/eiqf.nb ; klz+vry)ipm) 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 gravity o op1n :4jx88dz5iacm9umk)v on the Moon. The Moon's radius is 1.74jo9)oi81ka nxp4mm zvu: 8d5c $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same ma; l s8n4p,d7l koy4nr wgly03vss. What is the acc03vo;rdl4k4wlyg 7 s 8n,lypneleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same ;k h*7rq3 qeo vd03ofqradius. What isqeqr7o odv*0q3; kh3f g near its surface?   

  Two objects attract each other gravitationally with a forceux(a3s7jd,z g k:jsb6ssbgaht x79rg ,z)0 a) 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, b310t w ; cnug5qvs. veozz7h0at (a) 3200 m wctn;e gh500vzz. su17 3qov b   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsiphtz8pl:i-y ,4ze ii) 6 xv:dude the Earth where thegravitationaly vip48 z,pdt- h: l)6zei:ixu 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 thej02 qogs(zpxzt;nf ). mass of our Sun packed into a sphere about 10 km in radius. Estimate qz(2 gtn.f0;)xzpj osthe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averagnb+o ;)nut l(ie 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 is the ltonb+ ()uin; surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts1:a 2nfhaczim6 -d2yj feel weightless while orbiting in the space shuttle. Your friends res2ch6yjzam2d : -n f1iapond 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 si(ye/oh nz1s w2ia+e;ude 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one weoaih sz 2un(e/ 1;y+sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up oqn (sba-1j uy 5q 8yw.ack74mun the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all y7quy(4wk. 8aj n5ba1-ucq ms four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of w4g,pz(cmmwxvm5 / j/ dhat it is on Earth, and v( wpmzxc/4/5,dm g jmthat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usi3 anmfqe;q; ,3ycw k7jng the known value for the period of the Earth and its dist q3e7jknm;;ya 3 cw,qfance from the Sun. [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 st* /13apovsz h+hgf;3j k,vhkk :okx 9vable circular orbit about the Earth at a height of 360f 3kzjsp93v ak + /v:;koog1hhhx*,vk 0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular qve0blcq ,-cno n2 +ct;7i ps rz30;dforbit 650 km above the Earth. How fanq ctvs,nd7q-+p;e2crb0clfzo3i ; 0st must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantscli.c1 5q, j+mot+ufx are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Quc5jq,. f+i xmo t+l1cuestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit a(jzl,yo96 y/ 09 jq ,vav4phx5ksm,gnkc z t8the 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 t ,8 z,y(9g,hp6v tvko5aknmq c 0zjyxa9ls /j4he Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched tx4 d 4-h;(ft(xjyvbtfrom the top of Mt. Everest to b xvtyf4hx4t td-((jb; e placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modula v :yfo5+ -+r6eszcwcs ,cwv ymj.ll2(kn :k)e continued to orbit the Moon at an altitude of aboutc(:y-6o+ f mel vl ysa:.kc5c,sjwrn)zwv+2k 100 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,q ),cm: usnozk)mas9 the planet. The inner sa):u,m nsq9ko) cm ,zradius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (s6.pjg zf0i5d gee Fig. 5–9). What is the ratio of a person’s apparent weight to he 0f g.igpdzj56r 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-8xgzhujh. , g from the center of the Earth's Moon in . xg-8gzh,j hua 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 system consists of two s3 bc opd7ev8 +b4uznw/tars 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 z78p+u3 vobn4ew/cdb is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevat966wxnoa im+bor that mw9bo6i mx+ 6anoves
(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 kmcoz592k ys )39zkl zthe ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s mikyk 99k2omzl)z3 5 csznimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very n2ok/ mmt ;+vbnear the surface of a planet with period T , the density (;+t2 mm vkbno/mass/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) to determine the period oi/y* 1s8jn 6simwl0 cw:l4plo f an artificial satellite orbiting very near the Earthliolww0 plm1*jsi4yc/s: 6 n8’s surface.    s

  The asteroid Icarus, though only a few hundredj*l3vthn,w*6i 3/+mth vy/ jn) xoicc meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from th vtcw+, o/n*)i*6c jthijh m/n x33ylve Sun?    $\times 10^{11}$

  Neptune is an average distance of gc p2h5,.stwxp ke 5f, 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close ver)m1w,: ) p- o ry3zqg5txbrt ym2)kto 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 whenbpmo2qt5t1z:y v3y g,)r k)w-r rmxe) 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 cen6oxba l 1t r9fnd , nkm6,cx8dja1xs:+ter 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 dista mq: 0.5eqslsjnce for the four largest moons of Jupiter (those discovered by Galil. ljmqqss0e5 :eo 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 Ea+b9xvryi7h 6q./o ) *vggxxxu rth from the known period and distance of the Moon. 7q )gv.h+9vi*6 gbxurxxy /xo   $\times 10^{24}$

  Determine the mean distance from Jupiter for eac(au*j. scr:z+; p3c7 opislkhp (q 7nyh of Jupiter’s moons, using Kepler’s third law. Use the distance of Io(nz7;ui*ha3j7c+ps ( y o:ksp.ql pr c 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 Jco*mx rj e(;b:xzxw80n pz0mri)p udh(0t 08 iupiter consists of many fragments (which some space s;80 x0dnxihm txzw(( 0 8oiucrrpe)mbp:0 *jzcientists 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 describes an artificial "planet" in the. 4h(jhuayuwy2 53jjtp3bzu* form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to 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 ofb5(juyj 3z34au j *w.tyhpu2h revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanginrmsjb+iq7y7ngs 2k*(k 9 v oy+g vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum spe7+b9gry qo vksysnmi7kj*(+ 2 ed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be +;rf+zzs/s 4-bfjvp m s+ zvx4hz1ze3 half what it;s4zb+s zp3 1 fz +/h4zmesvvjzx+f-r is on the surface?    $\times 10^6$

  On an ice rink, two ssa8hux f5 cx /zvrfngft z))0n,1/fe0katers of equal mass grab hands and spin in a mutual circle once every 2.5/rxf u5zfn xs)vf0/z t a,gnefc)h810 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates oncejk;b:h) 2bx9m z)mjsj fc5i.t per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t robmmc;kixh s:bt2)5jf 9)jj z.tate. 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 directlc14 t,+rj90tron xrnmlz9e 3py from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppospnrjt l, n03 mr9tc1 x+e4orz9ite forces?    $\times 10^8$

  You know your mass is 65 kkdfk(4lr3c:s, 34fwz 3mwpt ag, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wh(drfw:wkc4fmps 3 ,la4k3z3tich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate 9pu/ez7y zhfw(+ lc mtnl1a7:about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be fe1z/f wnm cz:7(u9a7e+ hypll tlt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4uti;(jlu 7 ew )jf5z 8gye53is3).
(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 a9bupi j 12 .lq,fw+yen planet in terms of its radius r, the acceleration due to gravity at its surface andnjei2pflu,yqb+ w1 .9 the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected frzs)qy /myl) f9 7)f;1asbzeumom the vertical by an angle m)yz1msye lz)sa7uq9;fb ) f/ $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of*yqv w0d tp.s6 static friction is 0wpqd* v .6st0y.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 f*dc5n h-t2torotating so fast that objects at the equator were apparentlt2f*d ch-5noty weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dis)i1z4er bwys ,tance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a c4lz0mm b-eawyu- dmgz+z:9 b 6urve of radius 235 m. A lamp suspended from the c9ugza- zm+m- d64zlbwm yeb:0eiling 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 ml0ldr ggvkjok 2s(d/ 6 8+a.rpassive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a p l gsd80advrjo6gr /kp2+.lk(erson 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 deduce -u(h7vu mcyi.d 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 spe-y uc(.viuh m7ed 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 an g(m ,bshcy78 eizub(vsa47z ai*tri (2jzj/*d valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without ,jgys2b bjiv(ics(iz77e/a*z (ht*rm8 a4u zlosing contact with the road at A?

  The Navstar Global Positioning Systi vnp,3chsne2an 5 +h0em (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing +h,vna s0 n2np3heci5 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 thgb a7fr, 1wl4raveling 2.1 billion km, is meant to orbit thew7g4ha 1lb,fr 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 pursuing a satellite in need of re-l ji;re73 s obdwy*l1pair. You are in a circular orbit of the same radius as the satellite (400 km abe1bj3- y* lswdo;7 lirove 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 periodr jlae+zo -dei+c mo0:q0-mj* of 3000 years. (a) What is its mean distance fr qloej o0z+ im*d0am-j-:+ ecrom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value ofsx;:o ydxo x7+ G would need to be if you could actually "feel" yoursel:doxxoy7 s +x;f gravitationally attracted 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 Wazrjz dgg.7p;3 y Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from 7dzg p.;grzj 3the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a +p:sv2fdje; 4c uu-zof7 kkf5square 0.50 m on each side. Find the magnitude and direction of the gravitational forcufu vd5e;f27fj-oc s4+ pkk:ze on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 ky p7zoy9u6pw8b: qz 1sg 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-l)2fj+qmus)gm/c3 fejsvu64 uong sweep second 6j+vqs24 usm cf guumf/e))3jhand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker w-l hamtft(h9(v- +opj eight around in a circle below you on a 0.25-m piece of fishing ll mfp9tj ah-t+(-o(hvine. 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 so that a car tra tz,e 9l/cz6c1)az,itzetl v 5bm ht,733yhdm veling at sp /zv3h ae ,tyz,17i6mc53httlmtd)zbz,c 9 eleed $ 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, util 3t;f 7ncipidn +nrexxw +0b05izes 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 tra;+riednn+3b5xi x 70nwf tc0pin 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.$\approx$    $\times 10^2$