Sometimes people say that4mjh0lk) xk z8 water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stateme0 l4 hkmjz)8kxnt?

Will the acceleration of a car be the same when+o ..bwjnjo *4 kxyk1r 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? Explnoo byw+.x jk.* j1r4kain.

Suppose a car moves aty46i ,fyn/a 2hw4ccyb constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betweenac w4, 4n2c y6fh/yiby two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child a.*k6j7+urdwst /dw* 3chgjm riding a horse on a merry-go-round. Which of these forces provides the centripetal accelc am+hdw *j.37* jd/ustrwgk6eration of the child?

A bucket of water can be whirled *kucqo-h11s +dfufw: in a vertical circle without the water spilling out, even at the top of the circle when theudwc1uf-f kso *1+q:h bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at+ytyo /zlx4- l- ft:ab least three controls in the carlfzty--/bl + xo:t4ay which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a c5hq va:tw9 a4small hill, as shown in Fig. 5–31. His sled does not 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 tawc59 a4 vq:thhe hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a 8 wwfq)39/4/jufdpn*7 ekxq3rdt edycurve at high speed?

Why do airplanes bank when they turn? How would you co +ficp;z4:kx.p1 4otm +1gg uzwwhv,ampute the banking angle gi: +o,uaig;zkw1xz pwf +c4gv hpt41m.ven its speed and radius of the turn?

A girl is whirling a ball on a strb; j7*ol zzj2qqzhvu3u 7we13ing 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 go of the stri1zo3qzuv bjw; q73*eh7luj2 zng?

Does an apple exert a gravitationamhcy4u tn9y 9q. 2fr-s+p0h5)wqihv al force on the Earth? If so, how large a force? Consider m 9riph04.h wac+9tv- qn 2f5qyh)yusan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would t :nvsq6njnx9p: 9(nri he Moon’s orbit be differisvnxn:n:(p nq9j6 9rent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on tkh.w;;q je./,n:8y bjikxe;uwfvdy;ol1 vu0 he Earth? Which accelqek0 :y.j,l fj;yi;b/e v dh;.unx1o 8vw;wkuerates more?

The Sun's gravitational pull om(qkr zctx- +h0 1q4uyh-- kp5gngo6ln 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 grav 5(16rtcqk4g mxp-uq0hzg +k-hlon y-itational pull from one side of the Earth to the other.]

Will an object weigh more a/n) zm )trk/zvt the equator or at the poles? What two effects are at work? Do they oppose zm)znv/rtk) /each other?

The gravitational force on the Moon due to the y xxc+7fgl1h 9Earth is only about half the force on the Moon due to the Sun1+xflyh 7x gc9. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larcef/ x: u4m22f,zbwof ger or smaller thf w feu:22xm cz/4fb,oan the centripetal acceleration of the Earth?

Would it require less speed to launch a satelli7 rqn8g-dg csyz1b 8;ete (a) toward the east or (b) toward the west? Consider the Earth’s rotation directior b n1dy78zce;s8gqg-n.

When will your appart) c(ebl8vv,d 7 oc2cqent weight be 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 ) cl, eqco27tvbdvc(8upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely afca1y, uiphgnd/e68.jj7 w xh*fected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any 7c ,/ jwiajhngy 18.*peu6dhxother aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwexn qcjwyxxdh):7w(ra f:99 /nen c7dyx)(x:w/n:r h 9 j9xqfwansteps.

The Earth moves faster in its orbit aroundf 4.ivjy(4p 14 umnxmi the Sun in January than in July. Is the Earth closer to the Sun in January, or ini v(.xp um4y1n4ji4 mf 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 discovered to have a a:z pv9wc /s27rb1xz2r r;qcfmoon. Explain how this discovery enabled an estimate of Pluto’s mas q1 x2v:r r/a7z;ccr9 zbwfp2ss.

  The Sun's gravitational pull o8 u fq4z;s n0o dcii1j+*m4dorn the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tidesj0 funoi *;1im4sz+cd dor 4q8. 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 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 :o .xw k,h7+rpysj+s c 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 ar-b 7qxcakjk, 2) -fdvcceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Eq -b ,2f c7dkx-ajkr)varth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus asqjbzure8hpa l;a a h*/5d29.x it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.; a*e9jhp u 5a/zdxlaq h.b2r8   

  Suppose the space shuttle is in orbit 400 km fro.nv edl -z-* zlt8ai35lchc3b; e(fcnm 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 terms of g , the gravitational accelera5e-c 3fil3vt.h blzec-znal8;d*( c ntion at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a p40w v*id,z btcotter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter i, *zd04ticv wbs 32 cm?   

  A ball on the end of a string is revolved at a uniform rate*lz09si./ yy5dmha b q in a vertical circle of/siq9 h5.0z dlb*myy a radius 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 rad, , kedgxtv671+mch2gx c 1nbbius 77 m on a flat road if the coefficient of static fr ,b2gh6tked 1 7xm1,bn c+xvgciction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tirescys47 o9d4ap r and the road if a car is to round a level curve of rasao cp74y4 r9ddius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figh)ahnxa mupn2hg,z9 4,ter pilots is 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 hua gxm4h,p n9z2n h),aer own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rota7n odzkic0rz w s00t7)ting turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate rok0s 7ti0n)dz czw70 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 mmb 4)t .gjv a*ek4deu:ust a roller coaster be traveling when upside down at the top o b4 *).tujkedeamv 4:gf 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 x4b fbe u+vj,+the driver) crosses the rounded top of a hill (radius 4+ub,ebj+v fx =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 1 7:kxufgc 7pf jk,g.zo37 g)h1tn1x bpb, f+cy5-m-diameter Ferris wheel need to make for the passengers to feel “weightless” a1u tfykf1 pbf7)b7,np: 3zg xg.kgc,c7j x+ hot the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ogk(+wx prmrr2mi x/x,d (7cluea) 6z3 f radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 257(gxu)lecx/k (,pdx +zmamr26 rrw i3.0 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 partb/ oks: fmq-60;zv oocicle 9.00 cm from the axis of s;/o-v:zkmfo0 6boc q rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically;rr kidcs x),9 walled "room." (Sri,xr; 9 k)cdsee 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 rotateuj9 rbjt/1fe4rc .0fhd in a circle on a frictionless air-hockey 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 bj c0fth f1ur4/ 9.jerFig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , prec: u h k-mm6+ceba*7ycmisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. maceyk6b +7muc -m*h :In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelinqoa18e g a0oiwba6;azc5 ,rt);q pv18 ub1gvtg 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 masseso6zojc ifh )/fy0j,;8 bra4i61b zx gl $ 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 :rlz)dpq9)w s 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 e 25)tl/ i hxh:),yupp7xnwop and centripetal components of the net force exerted on the car (by the groun5pwn7xo hi)ytehpu/p 2 l):x,d) 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 Indianapo7ru,s7ic)p: j mp oa2h3nfhf9lis 500 accelerates 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 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 witpfr3 2s7 njh9, ohfma):icu p7h no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rad1jh 4wm,7iqt k9a u 2we6z;benius 2.90 m . At a particular instant, its accelee 7kah4q1 i29wbme u,z;wtnj6 ration 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 Earth r9oeo6 aoi skgx3py z31q ;+go 7u13vndadii) above th odgy31n3pg9savx 13i o ouq+6 kz7;eoe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerat8d2u8qg0cdoodp,f d )e c-zw)ion g has a magnitu)c8dfw8o q d,0zec)- pogudd2de 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 gra1l kabxu +e8p9 gym,g0vity on the Moon. The Moon's radius is 1.79glg8a xe1,0bk pmyu+4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tiez, bmw c3kb))mes that of Earth, but has the same mass. What is the acceleration due to gravity near ikcmbwe 3b)z,) ts surface?   

  A hypothetical planet has a mass 1.66 times thj 4sawyvsg.aa8jz9hb,n8t 9gd j8xk,ev.* /mat of Earth, but the same radius. What /9dg,ykxjj8t,j s9m4aevs.a*8 w b z8nv .gahis g near its surface?   

  Two objects attract each other gravitationally withfgbo,iiszohw 5 6*w q /)re.,gtk4iw8 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,,b *gap;vg5pivm *o1hci nof: ,jt)p) at (a) 3200 m mg5 ,c :pvifpojg)*t ova),ibp*;n 1h    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance -t83eozmpzf0 otx5l; from the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is 3 8pz tx0oz5meto;lf- $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our+ucev1dp4yi4u h9 q/ r Sun packed into a sphere about 10 km in radius.4vy ruei9q4/dph u1 c+ Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is cj.ii*osla, it /yu:up)7d zph63 *upnow in the last stage of its evolution, is the size of our Moon but huy l)ppd : z6 7*3p,usji.cutoi/i*haas the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in du2 w 0*vytlvop-9u6athe 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 Earthodu*-u p9a06vw lt y2v’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squb2yxp w:tok1uf 237mr are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphy2:b7ftr31po2w mkx u ere 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 side of the Sun,a j:;+z.zt idb3 .jmsn7pjhp . Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, asstj7np.d.;ipzm,: hbzjj 3s+ auming 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 the surfacezl3m y *.3fwwzvbs0:4y:.xyud aja 6m of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determin: 0y saz amv6wfmw.3ubd x.:y3yz4l* je the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perio2gqum6 h c;mrdm57 (iod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s rd(2mqi7m c5 guhmo;6laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a sta(pm ;6xoaaof , wdy6f/ble circular orbit about the E,offwp 6m (;aa6d/x oyarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satel:4qd7s6 bn f o+epn3/ebe:spplite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rel/qn ep4nb6f37ope bse: ps:+dease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants at 35dmm d imnr0c.*t.zre to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 dr0t .3mmnc d.5imt*z m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth ga9taa4v 9 +dyin a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the sura9a9y a+ vdtg4face 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 velocity would a satellite have to b0riz 4 8vajg:9krp yp6e launched from the top of Mt. Everest to be placed in a circular orbit ara6y9:4v8rz p pr0kgj iound the Earth?   

  During an Apollo lunar landing mission, the commc7knwo( 3m.l sand module continued to orbit the Moon at an altitude of about 100 km. How long dwo3l7skmn ( c.id it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The in.hlv6ph3csvzewp o88s79f 2 o zw+8v qner radius of the rings is 73,f3q hvps o+8 .zlev7 p6wz9vwh 8so82c000 $\mathrm{~km}$ , 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 x2blv17gk wtq z* 2bgvwmu ,9-m in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b)tz2 qxu, ggb-927 vvwl *m1wkb at the bottom?
(a)    (b)   

  What is the apparent we *2tkjsxd1 jup/gwr6 +ight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vej1w pkr+ux 2t* d6sgj/locity,     ----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 sw4 x9wxp- n-toystem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a poin wpwont9- x-x4t midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight o:/ ( zh z-jrzfkxe2d4ef a 55-kg woman in an elevator tharekfxz :jz e(-2/zhd4t 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 naudb:06tk,3/ muw a ga cord suspended from the ceiling of an elevator. Th uda 6n3m,:tbakg/w0ue cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very s7jnrd6y nno04 z1ai 3near the surface of a planet with period T , the density (moy3sn67j40iaz nd nr1ass/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 Mooni7 w* eoaf 9ef45ygb6z (27.4 d) to determine the period of an artificial satellite orbitizab6f5ie*74 yw 9goe fng very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits t0/c(;oay jgela m 52;-vhhskopl5. tdhe Sun like the planets. Its perio/ -gp l2; hoja0d t(sl.ceo;yma5hvk5d is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average 3zja q1 jax d 8d+ny/hubv+6d-distance 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 rohb i3uzd8; (wfughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out the3d(u8b; hifzw re? [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 tqm0e e95wvq u*z(1ta mhe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fo.p 9g/4kewvdnur largest moons of Jupiter (those discovered by Galileo in 1609p /w4 v.edkng9).
(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 t tuw0u0hl8d 6nhe Earth from the known period and distance of the Moon. t0 6 nuudw8hl0   $\times 10^{24}$

  Determine the mean distance from Jupiter for eac-k7/smgga (l1q g2 sarsdkhnz + y1q2/h of Jupiter’s moons, using Kepler’s third 1a12/m szsq+q/ g-grg hkal(7kd ny2s law. Use the distance 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 Jupiter consists of many fragmeq5pw2 .a;w cva m+i.avnts (which some space scientists think came from a planet that once orbited the Sun but wa 2+aivm;q5c .awpvw.as destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form ofnesdp2b/;, m( /ee.j;m hv syp 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.bden ; p/e;(/ s2jmvhempy,s . 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 hangwxyl 5agp1j) +ing vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N ygxl5j 1aw+) pon the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of jlvi. wzr+84: yuss +kgravity be half what it is on ths.vwzj 8ik+ly ru :4s+e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mav o fs b l2qvo6r1-d4bo4+.cvuss grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual ma loo1ufv44rc+2bv qo-6 sd vb.sses 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 grezcw :ek7q hg65 k5/gmavity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What 7g e:gw/me6 5kkqzhc5fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly55xiri p*r - rmu8.aju from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppor 5*8xjm5ir irpa-uu .site forces?    $\times 10^8$

  You know your mass is 65 kg, but when you.9 f7nrmqnfx;h *wim 1 stand on a bathroom scale in an elevator, i. nrf;nq* im9mwxh1f7 t says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists ofnwdmehmywn4;;u is ro,u.:y .b3p8a8 a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What muui8y.ho4.a w,mwsdn euypm 38 nrb;:;st 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 in a ve vmev cmr:u:p* /-gyafj0,+s krtical 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 mass of a pvvdwk6-:xxfrw,2j 0 c lanet in terms of its radius r, the acceleration due to gravity at its surface and the gjwwv xcf0,-6v dxr: k2ravitational constant G.

A plumb bob (a mass m hanging on a string) i jqaw5 .z0 eken/g8s;us deflected from the vertical by an anguees. qa/0g wj 5zkn;8le $\theta$ 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 674lm 85 kdayeq- m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range oe-45 yk8lq madf speeds can a car safely handle the curve?

  How long would a day besg/hg:+g+rf ta7 ,1tk 65v9tgz tb xxkj7l2pk if the Earth were rotating so fast that objects at the equator were apparently weightl t7a 1txhkgg2, r: s+tj/6zfpg9k7kt bg5 +lvxess?    $\times 10^3$s

  Two equal-mass starsdab)9+x .y row maintain 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 consa, so(ty1f b+ozpq1/ t0z a-putant speed rounds a curve of radius 235 m. A lamp suspended from the ceilin+-ao,ta(o1 py p tz/0fszubq1g 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 thm awyl6chj4 v1ck8 a89e 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 person would experience at the equator of such a planet. Use the follow8cwyk1v lj9c4 6ma h8aing 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 Spa5m d95xwus327n6o p v/qhycm (fm *uhxce Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting wnhoxx/v 7uuc(5 53dsy f*qm2h9mp6m 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 ixv pp 5e 6;tpuzkrv0w v41,w3ct traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) Howzve tvpr3 kxw5c6w,4v10p;up 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 (GP t66sun+h yc8 -i80ymxpe, tigt dx3n;S) 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 sateltp-, 6xi6dc3 yismx8 n0t;t ny+u8gehlite 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 4wp y/ep e,h,rux1pcw,/ f;pj 3fb m,c(NEAR), after traveling 2.1 billion km, is meant to orbit the asterrfubc emxe,/pp cww1 ;, f,p3,hp4/jyoid 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 res5b ;4rbi4 +f3nn cnbzpair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth)brb n5nns;i+bcf4z 3 4, 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-gp8bhvda1 v) kdj 7 xf5)qd:s mean distance from the Sun? 75 fqgjbd vdv8xp)d h)-:1kas  
(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 c- - 5f 9fczi9mrjss;pnould actually "feel" yourself gravitationally attractf;99rni -jc-psz5 sfm ed 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 Way q6,5-; gdyk tigsak 2kGalaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center ;k- gtayi2 d sk6,q5gk$ \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 side.n aon d(dr2qktw,/0t) Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the mi( wa2dn)r/ntok,tq 0 ddpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ejkzy47k ;u piqewx:5rdl1n65arth $ \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 acceleratiby*;gtl gs6l /he 7zt/ i6l1qjon experienced by the tip of the 1.5-cm-long sweep second hand on your wrist tig//7 j ;ge61y*b6lhztslqlwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in nueartyp)s 0jqz7y59sw0221 o ebj2 b a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [9azto j20 u 152) bpyq0nrybj2esews7Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tra(a+g3 5zozvkz 2esdb2veling at spe32akzg zszd(ev2 + o5bed $ 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,q9y, i*bhc 7li the Acela, utilizes 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) Calculalch ii,y7q*9bte 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.$\approx$    $\times 10^2$