Sometimes people say thatq pta+y9- yvi8 water is removed from clothes in a spin dryer by centrifugal force throwyqvy-8p9 at+iing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp c 7)o 0lqfsqhq ei4flvx9s1mj7v5344unla0d burve at a constant 60 km/h as when it tr3j 4llqnu4q7 mv0fdbv7iqs e1 0lxaofs4)h 59avels around a gentle curve at the same speed? Explain.

Suppose a car moves at constacad 1b1 g7i7jg*c; dnhnt speed along a hilly road. Where does the car exert the greatest and least forces on the rghc;jac*bni7d 7 gd11oad: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forcg/4zi -akcsq 45 d sqw6t*e7ibes acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration ctwq5e6gs 4*4z-/askii7bq d of the child?

A bucket of water can be whirled in xzo1h t 5sb /hmf(ly pc*7v3s1a vertical circle without the water spilling out, zy3sh5 xo1b* pfht17vms(/l ceven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at eqnd 6h:l;c+idl r-d2least three controls in the car which can be usedild: c6+n-rdqh2;del to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comkvk2v-( tpf 0ees flying 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 feels the normal force between his 2kv-kt(pf 0ve chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when/m*y jka2iw-d rounding a curve at high speed?

Why do airplanes bank when they turn? How would you coay8 zmr5f03js mpute the banking angle given its speed and radius of thy0 sz3jm 85fare turn?

A girl is whirling a ball on a string around her heeo)5+t q)ivh ohk+hp1 e3ln.zad in a horizontal plane. She wants to let go at precisely the right tim.3nhz 5qlvhph+)i ee k+o1ot )e 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 force on the Earth? If so, how l 90f;nhg4 vahfms) :dnarge a force? Cons)nvdfn4 9g s;hf a0:hmider 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 ebi1m4 t1cew,fn5q *wcj./ dmMoon’s orbit bc.dfi,54 1w/t ejnb emwq1mc*e different?

Which pulls harder gravitationally, the Earth on the0tq1 iy l(-x(n2w aavm+bvz3g/q hr m1 Moon, or the Moon on the Earth? Which acceleratvy+q rt m2 -gi(1lma(qvwhan/0z31xbes more?

The Sun's gravitational pull on the Earth is much la0z y0h,hqn q9frger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the 0n y9,zhqhqf0 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? What tww/+f3nv yvi+m ie :-umo effects are at work? Do they ope+3wuy/m m:nvvi +if- pose each other?

The gravitational force on the Moon due to the Earth is only about h9hg(c* owf/mg5 eqag 2alf the force on the Moon due to the Sun. Why isn’t the Moon pulled away fro9og (gc/5aqfm2h weg*m the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar xfuys5r6m;-e 92afqz 00zm ejger or smaller than the centripetal acceleration o9m0 zy-xma fer5efjsuq 2z0;6f the Earth?

Would it require less speed to launch a satellite (a) toward the *sy szug55: q;* wcmolrzj33eeast or (b) toward the wecmw :sl5ysojz;q e**3zu53rg st? Consider the Earth’s rotation direction.

When will your apparent weighok3l c.mn.nkhuki-*0t be the greatest, as measured by a scale in a moving elevator: when the elei0n. lck khkmu. o-3n*vator (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 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 adv51ithn yzjxb1rp6 9t0ersely affected by weightlessness. One way to xz ir5njth019t1py 6bsimulate 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 “v;vi539) b wgnk1yf eeapparent weightlessness” between )ve; 31k5egf ivwy9nbsteps.

The Earth moves faster in its orbit around the Sun in Jaw,ql. cuw oizuk 9yf ayr8*y,1k1kb41 nuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing th uqw,1az,8 kfyk1o4k 1riclwyu*9 .ybe 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 .9 iowv gi6xwv3mue/: until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s massxvw vo e:3/6um. 9igiw.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yex0jod,d(lp- 4este mft;e7a4hd n4u,t 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 si,f7 el-p(n0aodsd;u, h e4jm4tdt ex4tting 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 1987 9ifro 2fimarr n:v,fv)/*g+iwdj k90 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 i)f *f/gspr m9e62hon8bxzx;p ts orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth?* x/ sx6p; mgz9 8n2)fhpeofbr 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 o nmx yp*7jh:q)f 210 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 speed of the discus.x*q)y:7nm h jp   

  Suppose the space shuttle is in orbit 400 km from the El+xse/nf 7wwb5-w xv+arth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbi v5x-w xn/+fw+l wsb7et. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clad abhq: lr/7s uz)2s,my on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) qdz:l,am2 urssb)/7 hif the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a 8i ii)bnvz8ro 6zj5f+ vk /ojgx)si0 ypg979 vvertical circle of radius 72.0 cm , as shown in Fig.fj 7giojoi6gvbn8/y z)8i v9 sv ir+x0pk5)9z 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 tukzweb*)i 5-pj ,ms )pnrn of radius 77 m on a flat road if the coefficient of statbezji -n wpsk*),5pm)ic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the t:/nl/ck t3an7iua pr.ires and the road if a car is to rou ur./lan/ ci pkan:37tnd a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet .bqts v;t tn,1 gffy lv0 4ydq11g4f-ifighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the ty14,i g df.vfsv1t0q4fygn qtbt;1l-rainee 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 fu-8rq 9no6f8i,abqll 9h::qm1x n ag(wpiqs0 rom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin sl6xl,pobnq9 qrqgmihl:iafu ( -08 sq8na19w:ides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster fkzvj 1-o1b *ng+h.py be traveling when upside down at the topp1hfj-1*zo bn+vy kg . 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) chkm+ 7ogsc+96z s tdo186(7 oqpg gxokrosses the rounded top o zo op sxc96o 7 q8+dg+kh71g(ksgm6otf a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel neez+hf+g jqg*ev;e 1za:d to make for the passengers to feel “wei +gevh:g*eq a;1zfz +jghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m.*ntk u.s xwxo7*) gg3j At the lowest point of its motion the tension in the rope supporo.kn*sw7 xj xg3t)gu *ting the 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 particle 9.00 8,wk b nordu :4znt+ od:-(w2yvo*vnycm from the axis of rotation is to experience an acceleration ofdw ,:yrovknvnu dwo-z4:28 n( +bot*y 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are r*3( -vutqhjzfotated in a cylindrically walled "rvqt f3(hz-* juoom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a friction kbe5-u 2e;v1o- 9 egux4tzrqoless 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 ikrx92 uegb5 1tuvez;--ooq4e n 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 weiq-f8 k +kkmkh l+x3)+tin+aksght of the ball which revolves on a string 0.600 m long.k+kfh+)nql3xt8+ +kis ak- km 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 bankz 1(2ucge xmi0:z x3ived 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 0,r( rscuk,c(hx :ma zpan.9d$ 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 vertic7n,0)u;e8scvepc*tele x 9n hally at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted on 8 l ,fxm.8xcs h/.:tzej tvc,fthe car (by the groue f ./8 ,xcf.v :8tlsxm,thczjnd) 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 gi;5iiwovm (eq;w0. k pit area, going from rest ei;wmv ;0q5wgiio (k.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 no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m p(*gdb9cy+b+, m8; tbsada gm. At a particular instant, idma+c ts9m+b8agybgpb;,( *d ts acceleration 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 12,8 6rjbn 9v6o,9mt4 ntmg00 km (2 Earth radii) ab49n 6r vtgt6mjnbo9,move the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, th ldo j rwkkg.:.4-)qfce gravitational acceleration g has a magnitude of 12 m/k)q k.-o jl 4frcd.:wgs$^2$ 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 Moon's radius 5.eod r9eyk:h is 1.74 erhek.y9o: 5d $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timety-4k/g+9a:rksp*ho (uyo 6 xa6hdpys that of Earth, but has the same mass. Whatxhsyd-tp *9 4yao+ug/k p (rh6:o6kya is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that o/;urg 5c/vud vf Earth, but the same radius. What c ; u//5vugvdris g near its surface?   

  Two objects attract each other gravit2gdh4lria ufk1k /*r ;q+ o9xtationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3q- ;+ xcob+x+wr6rpzuk-ys+ u200 m c6x+yopr -+b uq r-wk;xz+us+   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s )va7e/ ryk g-t fqq) zrq3v4/fcenter to a point outside the Earth where thegravitational ac/)7 rqqyrev)a-/f tkgzqf34v celeration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timbhmoqv7 (60ui ckwa:o yk)6r+es the mass of our Sun packed into a sphere about 10 km in radius. Estikv6h)kqir(m+7 6b o0owu: yc amate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but6 jm*ajwurn1+ is now in the last stage of its evolution, is the size of our Moon but has tr+wa6 j1u*n mjhe mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feedp4)k0yp t +ipl;sj7 gl weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker uk 4)py ;ld0tspp +jig7p 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 sid 15n/mnk0f dpde 0.60 m. Calculate the magnituden np1 5f/0mdkd and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of hlwd2qfg29u* the planets line up on the same side of the Sun. Calculate tlf2 hw29*guqdhe total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleratio) /3dqn2:x; oi shaityn of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 :q2)od;x 3hin /iytas km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knownd l 0ewind+.7v value for the period of the Earth and its distance from the Sun. [Note: Compare your answel+i7e.dnw0dv r to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cot-7ylc 60y 0pbdu-h fzwj06bb :u ;eqircular orbit about the Eart--:6y f bb 6j0wl; zquyc 70detu0bpohh at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 8k+5krg +llbv0q )ufd650 km above the Earth. How fast must the shuttle be moving (relativeu k+q+)r0d5vlglf8 bk to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyli5aib cmvded3p zj (n./o.:wn3ndrical spaceship 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 Question 21, Fig 5–32.n:/w5d ( ad me3.i3vpcb. znjo)   

  Determine the time it takes for a satellite to orbit the Earth in a circu cln5pucf f:xfjs/3z;y3o:*o -z9vvi lar “near-Earth” orbit. A “near-Earth” orbit is oney nfiu/:9c *5:xf3cjpsf3v;z-o zlov at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from tok *smxx* 3 6b)bc9m7n)nufqqhe top of Mt. Everest to be p7 x*n)6fmb q*)bx kn cq3msuo9laced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to o,t 47d5c :c6vhc l6ro*qd jf; yu.zdbvrbit the Moon at an altitude of about 100 km. How long did i564y,* f .t:;d7udd6v jrcbvochczq lt take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plh) be4xr0nay ty. 6uq6anet. The inner radius of thr. bny x66yh4t)auq0 ee 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 (seral( (sjfcl3p y: ;,ele Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a ,yp:(r sfcj l3;e(lla) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 7r;z)wdwrs8t * 5-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving zdsw r;8r)t*w 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 sy6;z96 dffviwz stem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years todif6fwzv 6; z9 orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman y-v,nal-jrc yikx97v/5 dt i4 in an elevator that m9i/k,jxv7vaycil 4rdt 5- y- noves
(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 thrhk.;e1(z s1qqnw 6fr+6gip ke ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (mapkr;w+.e zk ( hr1q1nigfsq66gnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with peg) *; v 02nm9g:u,tv a6cwluivyqtb* zriod T , the density (mass/volume)2ty*n)uu:m6 ltw ,g 0vbg9va*i;zqc v 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 anjrqf + xs2)n3dd the period of the Moon (27.4 d) to determine the period of an artificial satelli+ 3sxfqr n)jd2te orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred met cvjuw*;cxv;1ers across, orbits the Sun like the planets. Its period is 410 d. What is;wc 1 ;xvcj*vu its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance pt51 6ctz4yoq5icwy0 of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once el66j8e )zg d9 bpg)uxyvery 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” )d9e6 bxzgg 6p j8ly)uthe 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 of4l.6o gn. omdhaqst*: 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 distance for tb ca2 8 -ud9g8jpl3p-6l3y.v ezuglbf he four largest moons of Jupiter (those discovered by Galileo in 16e98u3 dlbv fzu2a-ll - c6bpjy3 8.ggp09).
(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 ujrf.(gcv4d iicywg9/3 e7r:Earth from the known period and distance of the Moon. 3je9 gi:uirrcg (/ d 7f4y.vcw   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupn mg l/)w0:;kcpdsxo(iter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the v0c (o/plxwk)dm nsg:;alues 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 fragmentsfm(0os6y z 0av dk,k)srbox/ ) (which some space scientists think came from a planet that once orbited the Sun bks r6)z oo0,ybksf) m ad/(v0xut 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 artifi kuze b0 rc5c8*+clt2ucial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it crule+tk8 uc2 5zcb*0is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hangimp0f 6wg c(psodj(w2 (ng vine (Fig. 5–4jcw 0p((wfos m6 g(pd21). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleruc m yng;, 9g7p3vpw0mation of gravity be half what it is on the sur97,gc3m u npv ;wgyp0mface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua(.i(( 3u be a;zg3fumhquin*bl circle once every 2.5 s. If we assume their arms are each 0.80 m long and their i g3i*(ua i(;n beqfub 3hm(.uzndividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the cod38t h zn0:uapparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate th83uh 0dnt c:zoe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the us1h2mo8ttx *1iu )lhEarth to the Moon experience zero net force because the Earth and Moon pull witm uxtti1lh )*h2u8 1osh equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in m/u n aaxid*av4et54b5ak:h2 an elevator, it says your mass is 82 kg. What is the acceleration oft kahenm4/bx2 v5u iada4*5:a the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a 7;.qufg3/ rrani 0:pb s- uc4i5xziflcircular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) 30gcrxfu7.-z4 r/ pifiiubans;ql5 :is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loy5(0xtbj. /bbar: z/dpglp6 cfpo7 *lop (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 planet in terms of its radius r, the accedhfq +rbf -pak07h4fw;o0y o; leration due to gravity at its surface and the gravitationoo4awpdh;-+ y 0f;7q0hfkbrf al constant G.

A plumb bob (a mass m hay.io9u(x8 skg nging on a string) is deflected from the vertical by an angle o(g8 y9x.ik us$\theta$ 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 *m.r0 gbreqk6i 1b-rrof static friction is 0.3b-im*g rreb rq6k 1r0.0 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast rra3*)ii-sxgx 9yu 5h -lfs2athat objects at the equator wery-29s uxr ) a*-a5shf lx3igire apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a const)ti(ovq *;rxf:lo, d xant 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 of r+o knxde 03o7n /(quwfadius 235 m. A lamp suspended from the ceiling swings out to k3x 7n(+0wude/oqo fnan angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed th:utd7ipc jq 2.6c 5dxpat a person would be cr6p u.d72x dpj :cc5tqiushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Spa) qal e;+ql5zq+qyob -ce 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). + bqo ya-l+;)lqe5qz qThey 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 spz/tuuj +5;u we( ak)zwxhkk 0jsj))q:p,bad:eed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C wkaj: ;qjz)/( adt)sk, jex0u zk5h u:+u)wpb 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 p./*l8pw cyria group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitte8 *l wci/y.rppd 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 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 Rendezvousxu+kdv a 1f*o n1ab07f (NEAR), after traveling 2.1 billion km, is meant to orbit the aster+bn17 ud1 vkax f*0faooid 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 i3mw shj8r:og( n need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), o ghs (8:jm3rwbut 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 yearyq9(;er .xur qs. (a) What is its mean distance from the (9q ;ur.qer xySun?   
(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 needfg ;hf 3is298va6wt lp to be if you could actually "feel" yourself gravitationally attracted to someone near you. Ma i; f3lf 8wp6tv9g2haske reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of th271py ccerub0z ihit7f)3g d/e Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years1udfrct3 p b7zi y 02)ehc7ig/ from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.5/enxd+1db x9 : vhsww26 lbk9x0 m on each side. Find the magnitude and direction of the gravitational force on a fid2wb ehl9xk+n: /dsb 196vxw xfth 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 kgm,wg/z bt/*gm 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 ex i-0:ocz -tmpxbonk7/ perienced by the tip of the 1.5-cm-long sweep second hand on your wrist watcp-zt xbn :0 k7m-ic/ooh?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinmh+rh5g1 nmz1az *mih5 lv. ona*-(gk ker 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 is the ang*+mh( n5m . r1algaivnm -51 zh*hzkogle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway iszqoc3r9ybe /ha1*h+of7 r6 sj designed so that a car travelia9b*h6rsz/h f+3orcoqj7 y1 eng at 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, om.oyzywje 3c; 97h/zthe 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 againse/.moh 97coz 3;wyyzjt 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.$\approx$    $\times 10^2$