Sometimes people say that wat 3v i q8vym,i7bse*;o)zgwc; per is removed from clothes in a spin dryer by centrifugal force throwing the watervw;;o)ezcq* mb7vg8 3si,y pi outward. What is wrong with this statement?

Will the acceleration of a car be the same when the c937sv rd c0kwyar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sp 0dcys 739vkrweed? Explain.

Suppose a car moves at constant speed a,/) ,7 i+n0wqrajc r q*wccfxwlong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) af,r c )w,iq+rwwnaqc0/*j xc7t a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-roun)1z jjo+y-c cid. Which of these forces provides the centripjcyozj- )i+1 cetal acceleration of the child?

A bucket of water can be whirled in 6uqebi4t p; (pa vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explainqe u46it;bp p(.

How many “accelerators” do you have in your c+6 6bev,f n (6xpumlae.d h(ugar? There are at least three controls in the car whhanbp6 (muu,v ge.6fxe(6 + ldich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smallkc iy)ze+81g h hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he kz 8ygi+e1hc)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 inwkeoi*+t+swilgh 2 oqe a;:0s me//a k4ard when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bn7c asdf2 ae45d *nqp.anking angle given its speed and radius of the s nnafad.c5e72q4d*pturn?

A girl is whirling a ball on a string arouk2my8 tj6,(az(qi0 zng9w wtm nd her head in a horizontal plane. She wants to let go at precigin(wz2t wmz6y 0 jqt9, mk(8asely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational f 75 ;48nszn soljl/9xfnv//h8u2ugq h zszfg /orce on the Earth? If so, how large a force? Consider an an zxuo/ luh/5 7 8ls4zg/nf2s fnj8;qv9z hg/spple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what g/t(c58kvn3e krp*-rk ti j4o it is, in what ways would the Moon’s orbit b3/eri n-kjt5pok*t 4g k8 vcr(e different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moonmkx78y:fj y1 3qn bt+x on the Earty7f : b8yjtk3qxn1xm+h? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'sbg)i.9p(;+5 aaerasftlkc g *. Yet the Mo)kaepb* 9 is lr+c5ag;aft. g(on's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles?ylar:; +ph;x2jc*gvt w6j9n6 k7 vt rb What two effects are at work? 9avcl r*n rvxty7 2 gthkj; jp+;bw66:Do they oppose each other?

The gravitational force on the Moon due to theev u6s2u:ncp- Earth is only about half the force on the 2pvuu-s:c n e6Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroundilh o4xr 7b7s4 the Sun larger or smaller than the centripetal acceleratio bhlxs4oir4 77n of the Earth?

Would it require less spelkz 5sw,4z6 ched to launch a satellite (a) toward the east or (b) toward t,slz w4c kz6h5he west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as m0d59 zwsj ;mmoeasured 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? When would i 5;9sjdmwom z0t 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 s -8up1maf p8x.6g9p fq9usqiby weightlessness. One way to simu 1x uf-ppss9aq6gi.8 9p8qfmulate 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” or “appar2zcdzc tl6awdl8 v);ci5 3o0fent weightlessness” between ste30c;zz) afdtl2do l5cci 8w 6vps.

The Earth moves faster in its orbit around the Sun in ,(a9q6w rv5a/s zo; z0hhw cqaJanuary than in July. Is the Earth closer to t(ahv6zw 9r hsc;ow, z/a0qa q5he 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.]

The mass of Pluto was not known until it was discovyt,y0fajqi7o :2. lvlered to have a moon. Explain how thi ol:2iqv ,.t7fa 0ljyys discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Ye 30j j(v2cmgra6y3ce,b3w hwct the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationalb2 v wjm 03hwa6gj(ycc 3,3ecr pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 j 998u6yewvyt$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceler0 ucfhwx7apajy/lgd;ouki( /+j/ 7d 5ation of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Eart x(uiahgudfc+loa; 7kw/ 0p7jy /5d j/h? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is efpcewd9nd1e6638ioj8 zl- jlxerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculanjwp 9fi 6z cl8lejdd o8163e-te the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth1v 39lehxt 9kt2 k*ift's surface, and circles the Earth about once every 90 k3te2*v t9 k 1itlxhf9minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudeqbe y58aq mf0+ of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (rev+05mb qa 8efqyolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertil(rtcqb 3eo::2d(p)r v x9o e ws4l(krcal circle of r:r9xl:2s bvoc dk3qro(p)(elre4 (w tadius 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 of radi5g c) erbbw:8rlmt l1j-oz p25us 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the carll15r:pme2jb5 z8cb) wg- o tr?   

  How large must the coefficient of static friction be between the tiremvf s-55aln dqued,+9y9tuj (s and the road if a car is to round a level curve of radius 85 a sd5d5ltjy 9ne-uu qv9,f+m( m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots isu1p.z vzc*5 pw 7eotnv0pck,h 1 l*/qe designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fasq5h v*1cz,lp0zn 7 putv*1pe.ce/kw ot is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable ofqceixl. m+ybfcax/.qxze/1qqt43/ 8 variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable un8+xmfz4/q elqebyxi3/. /1taxq c.qctil 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 upsid70 ca2ob;tltge down at the ta7lg0t; obc2top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosse)su y k; s3,bm3q u1pbrg4ecx-s the rounded top of a hill (rad s e);mq3s 4 1x,y3g-bkuupcbrius =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-diameter Ferris wheel need to ma zl4 )0lvf4krake for the passeng40)vrlk afz4l ers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertic ut /ju+c+c*ceal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.* ue+ctuc /cj+
(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 par 9 r:uoc:pkc6pticle 9.00 cm from the axis of rotation is to experience an acceleratio :u6pocp:r9c kn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cadswz77zqv z :r9afs p5x4 it(dw27s.4n yy:mprnival, people are rotated in a cylindrically walled "room." (See Fig. 5t2dra:5(nz vsx7zfipzp m7sw4w qsdy.y:974-35.)
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-hockeyrh kk8w*v d,b),pgy/ m tabletop, and 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- *wkpmy,h krv)8 b/g,d
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 wbu3 :qjbou3 +leight of the ball which revolves on a string 0.600 m l+bu3ou3 blq j:ong. 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 radiusb)qltz c(q- e e geil.ld2,a,7 of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massep dz5+ +uh3b5v d v;hth 918pd*(nos0ootta fis $ 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 maneex a :819pcvlruver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential aforf0u:8o 0rond centripetal components of the net force exerted on the f0:0rufo o or8car (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, g1tg880cyr1azs u8hmloing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with z1hlay1t 8cs ur08gm8 no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m vh qh83wkzj8z ;n ir s/mdlp**4 q1p9c. At a particular instant, its ark3lq4d*18jmczws;pi /h* 8pvn q9z hcceleration 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 (26ea;p 9 /4rrlocfhr f- Earth radii) above the Earth’s surface if ifhro ef 4lcrp-/9r;6ats mass is 1350 kg.   

  At the surface of a certain planet, the gra/a6426;po iq*awpr j+ogww mavitational acceleration g has a magnitudm*q/aoaaop 4jw+2 p6;rwg6 wie 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 on the Moon. The py 2)ppkan-fqu7-s lmt *.pyync+: 9 lMoon's radius is 1.74 p )unn2l*-clt+.p9 :mp7yas q-ypyfk $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 to(wwxqc*. 3cf ,rrsuvji9 4 ;pimes that of Earth, but has the same mass. What is qvwuc(9rxs3fiwp ;.4cr,oj* the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eq *8: hoaw2oxxarth, but the same radius. What is g near its surfaa :owhox8x q2*ce?   

  Two objects attract edn1h0rp:l y3hz:7e ny ach 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 acceleratiwnb uk 0;: vz;hkff2jf/8y-rton of gravity, at (a) 3200 m wz:;j ftnhfr2k b/y0uf v-k;8   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside nhdr.f 8r*d+c+g9 mbm the Earth where thegravitational +nr 8m.rdb9dh+g*c fmacceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a st2(ap 4 ztjfa()edg6 zh 8(rbkphere about 10 km in azpkt6 d4(b2 r(t(a)ezh8g fjradius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf stamy -ko--g/ g hu+z(1oh9e: ;yofmoc cvr, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mao/1vfg:9h - o-zc;mm ykygoe+ co- (uhss of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why a7s b*)jxp hqb0stronauts 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 surface in termbx0bqjhps )7*s of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcuyknk3fc,57dpt u4yd er dl 69)late the magnitude and direction of the total gravitational force exerted kdk7y fd6 r)ytdu9 le,c3n5p4on 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 4,4ty- cwodsbxv 5)a/zv) dms same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four ps4o v5txv)dam-c/ z, s)bd w4ylanets 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 ni+z4 pmz4igp 64i*n db 1-iswj7n4zx at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mbxsnz6 zimiz1pj4i4n*ngi7 w +p4 d- 4ass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for c03 uj+x6rrfew06jrfwe 6y p4 the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s l6pjuryf0xr 6rwc043 fe +6we jaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed sc;gglql:y+hnge: 50 of a satellite moving in a stable circular orbit about the Earth at a height of 360gegn+s;g0 l5c y::lhq0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th,4azecv(sz2 gsww 3y/hhtr-4e Earth. How fast must the shut 4twg2e4(3yas-zhhs/ zcr v,wtle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshi/ - pkn8gcod4ep rotate if occupants 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 Quest g4dnpoke/-c8ion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “neyd9 ( wo:s ++men;lfjnar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very smal+9n:d jfym owns +l(;el compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launcyb)jd t 90lt-4q85ty2 u besndhed from the top of Mt. Everest to be placed in a8bn42 tt sl y)uyqd-ejd9t50b circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuedlik vob 9:8 p8bk(1h ipyx (m1 xrxpzfh.7:w)d to orbit the Moon yf k8xo.h91(p ph d)xzlirm8k:x: b(wb71vpiat an altitude of about 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 th1 e lre03gzt3oe planet. The inner radius of the rings is 73,elt0 go 1re3z3000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig.b-yssz, c,t ou:; ngq)fx t sj.z075zg)hshi+ 5–9). What is the ratio of a person’s apparef-jb qgzsi 0tn )s+co)sgy tx s;zz,hh,5 :.7unt 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 centereo*yv:t93l7)x qt ac1 4ogjvr of the Earth's Moon in a space vehicle (a) moving at constant velocity,*yj xlq7tv )t:49e1or go3a cv     ----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 cnl2 ly ju,6+ttonsists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to or+nj 2l6lt,ytu bit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the wecw t:gq,p9uv. ight of a 55-kg woman in an elevator that moves9.u gtw,c vp:q
(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 con kwa3f,c7-kcrd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acceleratwaf ck,nkc3-7es. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surzjv9sqnt(v9 b0d0r f. face of a planet with period T ,f( tqvdnj0 r909 .bvsz the density (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) 9mesq13tq4j: grek+u*ml35xw ;q wlzto determine the period of an artificial satellite orbiting very near the Earth’sxj3;e1qqq*u:93 5kt ez +g rswmwl4ml surface.    s

  The asteroid Icarus, though on):oy tov4vzj)lb (q;hly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun(v4o q):o;)tbljhzyv?    $\times 10^{11}$

  Neptune is an average di,:m )2q/g6/d bkzcjv8iuxx f qstance 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 orbit g/ b,)fq7kc wj;+wnnms the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). /j;)7nb ncq f+w wk,mgEstimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxyzu*rxqq 2 )a7bx 3mqo, $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the foso7 gj or-ywrk)qu-s+q2q 1:pur largest moons of Jupujp:g1s )-q orr+y2 qq-s7o kwiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period andl-.5iupj+vd 4 0qya:w 8ezj mk distance of the Moon. lde5j0m pwauz-k.:4+jyi8vq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each sw*ef xz7k vvhyz 1121of Jupiter’s moons, using Kepler’s third law. Use the 7s*2wx11vhvzz 1 efkydistance of Io 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 Jxczh0a msi)ef+4q7+q vle 0, jupiter consists of many fragments (which some space scientise),e0+ z0 h mqcs 74jv+aiqxflts 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 "planetqzth*+i)8 o49b-zsn h kt/ rltn w5(ca" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be t5sc*onk r+z-t9q t4/h 8l )zbt wnh(iahe period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanginb6kekl-6o2xqtx d p9)g vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is tx69)ltd e bkq6pxk-o 2he maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surfjxihby:.ol;jt32( y aace will the acceleration of gravity be half what it isj2jy:iha3 ;y.ltb xo( on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gmv5xj n)5cgxnkqobz w82i)80 rab hands and spin in a mutual circle )omn2wivkbg0x8 nzc8 )jx q5 5once every 2.5 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 once per day, the apparent acceleratl ew .otb:/a.wion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effet.:wwb l. oae/ct. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will d emp6rlj(-)q a spacecraft traveling directly from the Earth to the Moon ex-)(qdm jp6 lerperience 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 sca/pzzj+5 1v b+xi/hnjtle in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which diz5 z/1thn+i jbpxvj/+rection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itv0d1e5ql0wj t s center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube haw51t0qdj l 0ves 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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft i gn 5+6xhhxz 1yv1ow:en a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mas/u u xwh:fr2co8;nt- ds of a planet in terms of its radius r, the acceleration due to gravity at its surface and the g h -x;n8to2rfdc:/uwu ravitational constant G.

A plumb bob (a mass m hanginwav90 i.tcvqmfpd-4)ylq:6 wg on a string) is deflected from the vertical by an an9wa6pyl:qwv v)-t .c qdmi f04gle $\theta$ 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 bana26,2ur uhm9gx un:)irsi7in ked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at gur7i) anmuhni xu2r 2is96,:what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the 9r md8cxa3x e)equator were apparently weightexra 98d3x)cmless?    $\times 10^3$s

  Two equal-mass stars maintainmp f0nr .mr au5jug5. lre4l l39nv2)n a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve ofqkh (.+do1g. p(e(g opj:ndyz radius 235 m. A lamp suspended from . (ypeho +oz1g (dqnkpd gj:.(the ceiling 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 thu--nosvx gb a7of() -ue Earth. Thus, it has been claimed that a person would be crushed by the fors-(o x b- u7f)ung-oavce 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 pres +allc:aind ,o77 kj/gence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light kgaoa, jc:7l7i /nld +escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and vall+falk- 6 mrql-ey shown in Fig. 5–45. Both the hill and valley have a radius of curvatua6+r -l-kqlmfre 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 w6k)j9qn1s ydxq 8wicxe fyq 44u 0i;8a 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 sate4xduiqqy i6wq )snj8kcw8 ex 019y f;4llite 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 i pkz8t483 efukm, is meant to orbit the asteroid Eros at a height of abou8 8ikz3pu e4tft 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 satelo.p1 m5rq,qe/ pz 0-ihsgni/ya u0gq9 lite in need of repair. You are in a cposq . rgpq-/ 5e/ziia,qm009 gu y1nhircular 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 asfk of* ,;ou 2vwb 2v3f1cp8n:ci k3gr period of 3000 years. (a) What is its mean distance from the Sun3b 2f k:1c ovni*pvc3fg2frs;k w8,o u?   
(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 actuapy z y4s1/)acmw4f)u jlly "feel" yourself gravitationally attracted to someone near you. Make reasonable assuu/pzf1)wm4j4 s )y yacmptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkytqnhe76b,o)p, lh5 r y Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years f b7ryp6th,o 5elhn)q,rom the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each siq-gn:u bjd; s8de. Find the magnitude a-bd j:8qg nu;snd direction of the gravitational force 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 kg orbitq3ma1dj9qf7z3 6tu uas 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-lo+4ogz7m- 4mkl bxu7t0pd hqp1ng sweep second hz-lqdgppbtm1+om0k47u 4x h 7and on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and s998:raj dp4izxe yol0 tart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What idj4rzle p9aoi8 9:y0xs 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 trata ;kxe(-7- rhzxbb p1veling at xz-b7xa ke(pb 1hr-t;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 om8apua8mutciue6) 8 3 f the cars when negotiating curves. The angle of tilt is adjusted so that the main force exertim3)8ma pt 8uu euac86ed 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 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.$\approx$    $\times 10^2$