Sometimes people say that water is removed from clothes in 0cy5i pyr*/yh8 y:625nsnn wk 8a tlyva spin dryer by centrifugal force throww ktv y/y:n6s5hypny2 c*l 8ra 50y8ining the water outward. What is wrong with this statement?

Will the acceleration of a caru/ol q(8vvw u- be the same when the car travels around a sharp curve at a constant 60 km/h as when it travelwu8/v-o q vu(ls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hiq5wan5j 3 o:2g7fzclmsz rz9q ++*sz mlly road. Where does the car exert the greatest and least forces on ths9 s5n37 q m gz+qz:w*z czj2+r5oaflme road: (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 forces acting on a child riding ar g4m- o:sbmwmk7/t/s horse on a merry-go-round. Which of these forces provides the centri/ wot-7m4 gbm:rkmss/petal acceleration of the child?

A bucket of water can be whirled in a verticalc:5-wn/ 1dt.wc p3 uerc2o gob circle without the water spilling outor/wuc2d-c5c 1p3 .nwgeb :o t, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have - /p2iaejh3fvz w 4m9oin your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleratiow/ ezij o-v m2ph3a94fns do they produce?

A child on a sled comes flyhlw.se cb 36+wing 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 chest ancwl.b3sweh 6+ d the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speed?v1 uzz0 t)l6jn 1nb(b,zhyif3

Why do airplanes bank when they turn? Hmd 9 f1mof,sb+equtbl/p/2q9 t4roq1ow would you compute the banking angle given its speed and radius qbu o9orq21m/t/b fm+eltqdp sf4 19,of the turn?

A girl is whirling a ball thdz3,i j3(6lhlj8a e on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of t 3l j jh8e6a3iz(ldt,hhe string?

Does an apple exert a gravitational force on the vo v m5*y;un68 p1ynxq te.t *ri,rvv;Earth? If so, how large a force? Consider an app5n vt1qo*;. u8t evypirv, n6m*v;xyr le
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’sv9 -zxa d/l3o5tm dx,k orbit be differx , xt5d-v/lo9 3mkzadent?

Which pulls harder gravitationally, the Earth on the Moon, 8 d h ;rpkba,r0)a7v zfyd6 q:q6fzji-or the Moon on the Earthd -)6jzfqb68paf7,za kh r0d :qv;yr i? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the M- sl76mz-t ukyoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one s-uyks-tl7z6 mide of the Earth to the other.]

Will an object weigh more at the equator oroc77, ge/ca vs6 ;tv ni5fh+rs at the poles? What two effects are at work? Do they opp;hc eostr n+f5sc 7vvg/6,7iaose each other?

The gravitational force on the Moon d e2 m0/umlzks.ue to the Earth is only about half the force on the Moon due to the Sun.2ls z e0./ummk Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the m1q.5q xgh8p, jzh9zis y0k*h t1d tk2Sun larger or smaller than the chhiy hk 52 kd18mx g1z0,s9*tpqz t.jqentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or akw(f .emeu 88(b) toward the west? Consider the Earth’e8.8fm ae(kuws rotation direction.

When will your apparent weight be the greatest, as measured by a scale innrcsf9hei y v* k,+f,/ a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In whc 9 yffs,e*nhvk+i,r/ich 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 co3g,b jgg cir3)uld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astcgbgr j,g33i) ronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” be wctryf/jvdla +2 : kpd,17* )a0czkdt*3rkcetween steps./dp*) t k31cj*dew yr7 avla ctfkk,zcr:d2+0

The Earth moves faster in its orbit aroundmd7k mbd pd.05 the Sun in January 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 the seasons — the main factor is the tilt of the m.0dp dd5 km7bEarth’s axis relative to the plane of its orbit.]

The mass of Pluto was nf/,eml4 xr (wpot known until it was discovered to have a moon. Explain how(,/mlf 4p rxew this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ed xy9b.z :zlpz..m;tyarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffz;b. yy9dz.:tm xp.zlerence 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 travelingi,u)qve7kiq0njnz 7) 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sun, ic,1 q2*sceeo(ik(p o4(hpwm and the net force exerted on the Earth. Whc iie,p(c*h 1m (q2eo swkp(4oat exerts this force on the Earth? 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 exerted on a 2.0-kg discu2ejs ol;86urk s as it rotates uniformly in a horizontal circle (at arm’s length) of radius js;6lr2ek u8o0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thefs/u;j4)t 576zo vqwno q) fle Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Expre5 q4)j;nt7/q6vfwuf) oeslz oss 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 clay on the edge oflncw.qw h2q;8 a potter’s wheel turninq nwhq2.; l8cwg at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved a 2v4m:w7pnmkat a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33m7v4 mwknp:2a. 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 xf nj,:8vx yv; z-nvw7radius 77 m on -xj;v 7:fxnzvy nw ,v8a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwee:ya8uqo5 )bs r2(ihl mn the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ?5)y2mra h sqo8ubl: (i   

  A device for training astronauts and jet fighter n, 4oaj6o ;ranpilots is designed to rotate a trainee in a horizontan,r6ojnao a ;4l circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable -qhh(, 9yyzyn speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a yzq(y hh9-ny ,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 trav8goxp 4 vl0vt7eling when upside down at the top of a circt4vl0g v7x8op le
(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 massiy1jh+,7 tnrs 950 kg (including the driver) crosses the rounded top ofsyj7,inr +1 ht 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 an7p9l v;6aq ll 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmosla;9 vlnq l76pt point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. *rrlk k ;9dck(l1;*8;bc wjgcxpk+ pfAt the lowest point of its motion the tension in the rope supporting the bucket is8c;;c *j k;bkkp(xkr+pwcld1*9 l gf r 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 cm4bgfzgfc 0.i bb2 an57 from the axis of rotation is to experience an acceleration of 5fb7cfb0g b. i42gnza115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are roti4ie3 g+p5 mgmated in a cylindrically walled "room." (See Fig. 5-35+g5m4mp3i eig.)
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 fricti657oadwv( yfz4 vx-mi)ek fd-onless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling izd4d6xe a f)vwm - yk75vf-(oblock (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of q+etun//uxc9yql j sr: w.z2.the ball which revolves on a string 0.600 m long. ./qtqeycu.:n+/luwx9z jsr2 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 cxwg/y( y( :;cqvug k,tar 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 massesfwzjz8 ;e*xyul++ 3guvbe+ , u $ 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 verticali wmc+/(:yaf:b(dawk0s gt u )ly 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 tangenm yq0z4nl(,h ys v2bna s-o28ptial and centripetal components of the net force exerted on the cyq2ysa-8,n hs l mpn zov0(24bar (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, goin 8d+ 5qbsbt5uk-7e fhig 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 thro if+bk sbdh t5e57u-q8ugh 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 p f8hvy8s(/ )g,d8jhdc ia 7tta horizontal circle of radius 2.90 m . At a particular instant,8g a)yfj(i7/ct8d sphd th8v, its 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 Eq0ucdwy vod:jn o,3d ,9 ec4y32t8:ndk ,pcdoarth’s gravity on a spacecraft 12,800 km (2 Earth radii) ao,w3c 0ydc9vdn,j oqkdycd:e 43n odt8: u,2pbove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, t s1hsw +(gifp3he gravitational acceleration g has a magnipfs3hg i +(ws1tude 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 acceledn*(l: z(,bef dgmez v9y+8 mbih7g,sration due to gravity on the Moon. The Moon's radius is 1.749d, l, y8n 7m *beihzsggfmz(v+:(b de $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the s0j6gp; h;tl*gsu4 aq(zp mym5 ame mass. What is the acceleratihap45s z0puyg6;m(qlg *t ;m jon due to gravity near its surface?   

  A hypothetical planet has a mass 1.66m;t qise q9(u psbf;4+ times that of Earth, but the same radius. Wh+9ue 4qsf;mqipt( b;s at is g near its surface?   

  Two objects attract each other gravitationally with a forci25)( vltc aw9:eszjpe 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 valufqw74yf n,5jw 8fnum5e of g , the acceleration of gravity, at (a) 3200 m8mqnf ju,75fy w45 wnf    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside(g, cbwxsk4 5k the Earth where thegravitational acceleration due to the Earckskw5bgx( ,4 th 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(+vz0c 1nn cqd into a sphere about 10 km in radius. Estimate the surface graviczv(0n + 1cqndty on this monster.    $\times10^12$

  A typical white-dwarf star, which onc-gf(( 532o hbiiivw mhe 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 thei 3-h(vmiig 5ob(w2hf mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitin00ptyps36keiw76 l;z p f- osig in the space shuttle. Your friends respond that they thought gravity wke s36f wst67o p0pyi-p;li z0as just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calv poug (*vr+mg5maw7pl/ 5ijk 9 s:t3rculate the magnioi37s9l *w ragj vp:mm(g+v5 rtupk/5 tude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line upf x3*qe +ul4h;lfn)q qg*5 ueq on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming +q;uf uehx5lge)qq 3fl**4nqall 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 gravit8k4suf. ady yf3c/i;l xw7: rwy at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deter.kx;lsuy:i wy7 f8 f /34rcwadmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usinc3)i 9ku ,b +qxsxn)xug the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer t)+cxun3s bi9k xx,)u qo that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabws7)72:ez9 igvpd ;ancph pkoj -un5 ,le circular orbit about the Earth at a height of 3600 km.sopezd2wg-a7p7 ;n5:p9 )ic un,jk hv    $\times 10^3$

  The space shuttle releases a satellite into a circular5n4x( hpb e9cne2s u:i orbit 650 km above the Earth. How fast must the shutxui52 s:4 henbn(9pcetle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants j crgx5h r*/4t)vx,vux0 k c.iare to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, avvruh5 4x /r,)kgxi0cc.x *t jnd give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sate(/nhi0ud. n-60dduvyxs (gd w llite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above0(0 h g/dd nyudu(.6xs-wv nid 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 launcheg+( -nhkuf t ,j7cf7qed from the top of Mt. Everest to c7q h7+ feufjgt (n,k-be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing , m*kuk(ss 6vls/9l+*qtn eqg mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it taksl9les6k *v( n +tq*g smqk,/ue to go around the Moon once?    s

  The rings of Saturn aqrra;.ak )3bq l-f:)fl3l5kjn 3h k bsqj k)0lre composed of chunks of ice that orbit the planet. The inner radius of the rings is 7ajjkqn ))3qsrbb ll :h -.l3 kl53fakr)q;f0k3,000 $\mathrm{~km}$ , 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 onc/ 1g;6yk(p hplxar bb(e every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weighb;ryk6h bpal(1/( gpx t (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 center of theq6u 2m5ssr7yb,o 8/ l/w ixrce Earth's Moon in a space vehiy2osw8sl5 6r7qri/e, m b/ ucxcle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars/sp3046x( ky:dmw s*y ebncds of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mabxw*0ms dd6nyky/ : p3s(ce4sss of each?    $\times 10^{29}$

  What will a spring scale read for thf /ss,2;jp smue weight of a 55-kg woman in an elevator that mfss;,2p/ s mjuoves
(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 the ceiling of an eemodcl,17 p7k2 lgzq3; v 6kcvlevator. The cord can withstand a tension of 220 N and breaks as thed2m6ov 7l,cv7 qck1e3z ;l gpk elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a yf+ww6 c/)-y+x p ba3ugz7 otrplanet with period T , the density (mass/v7/+f-)ag+ybzwwt x curp 3y6o olume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the z lu ibw6f(egjcs0,).period of 0. ),lzs(fbwuj6c ei gan artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, v0n+h3f hwu:qthough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?hv0+qu:nh3f w    $\times 10^{11}$

  Neptune is an average distance of 4von9lsc+xnj* /t;bf 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 rou ylqil1-0 xay2* tta be1o0s(nghly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Figsx1lli*0qbo1- ne02aa tyyt (. 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 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 thie3rzw*dhmx z0p +9)je center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean d/agvlq ,qq 6hp:r+e6psx4n p5istance for the four largest moons of Jupiter (those pp:45q +6,/n 6 rqhgae slvpqxdiscovered 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 Eart;fjlnlq06 li lve p)88h from the known period and distance of the Moon. )levf6il8n 8ll q0pj;   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepljv 6 fjpq0kl)j. 2c9pvg5bl q1er’s third law.g v90l j.qkjjbp62c5vlq1f p ) 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 Jupiter9o:m g0mawl *v consists of many fragments (which some spg*o aml 0wm:v9ace scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" inz o8)xaada4-5oz 30k9 wdt djh 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 the period of revolution, this d5)o0az-z t89w4ox3kda dj h aplanet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc fro gdu5 1 .s/tcnhpce;cy;7s1bq m a hanging vine (Fig. 5–41).5e1ccdctqyb1sg n/hu. s7; p ; 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 acceleration of x; r- 9viji7s ggpg w94:ojn-xgravity be half what it is on the surfacevj4g ;ox9r--: wx jn 7siggip9?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands:bk1*cs l(7j1r antil and spin in a mutual circle once every 2.5 s. If we assume their arms :1bct7aij ( r1nkl*ls 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 acc3 hpia5lkimrvs d1 zkj:1y,14eleration of gravity at the equator is slzijh4k,al rsdy ik3: 51vm 1p1ightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth w,;nq/ w rigayf(h- e6eill a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mo6/(e ;wrn, -igafe yhqon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in -xsda4ui;xvx o* 1au*an elevator, it says your mass is 82 kg. What is the acceleration of the eoa- advus4 xu* ;*xx1ilevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular +eyv t7ug00 20rnjqr otube 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) is to btjy7 rqn0ev 2ugo00+re felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a5o lg+ (kydyezsti22: 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 mass of a pl ,9fnk; ftvdqqpm/f9/ anet in terms of its radius r, the acceleration duq ;f9 /npk,/fv9fdq tme to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m nfi9e bszs/0a5 7z (snhanging on a string) is deflected from the vertical by an /sz5isnbfn9s(ae 7z 0 angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for .3pkmdlc q-znu ;xq/(a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds canlz3/c up;q x(kn -qdm. a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that 3rw 8qur5elr:objects at the equator were ar r3r8qwe u5l:pparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan*3lts 0hmebclow0,8dnu 5 q+ vce 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 sq b44q0nac7z i(ij8iypeed rounds a curve of radius 235 m. A lamp suspended from theq784bayci zji(q in40 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 the Earth. Thus, itdam0ly;s )c)l has been claimed that a person would be crushed by the force of gravity on a planet the size ofym;dslc)a0 l) 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 Hulbo/jqc .5 e q/3rr3eubble Space 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 l rc rjo/u33bqq.ee5/ 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 hi cllnzsha56q 8 c5a*,eybn++d ll 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 one*z,nh nal5da5l+6sc+8cyq b 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 a group of 24 satellites oru-+xfovt1 itp27* ldvbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four sa-d 2tf7 oi*ptul1v x+vtellites 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 billidg 3f+epiv+ 9mon km, is meant to orbit the asteroid Eros at a height of ae+i+ v9dmg3p fbout 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 r;dq uskbu03j*p t8or3epair. You are in a circular orbit of the same radius as the satelli0k q;3uru b*pj8sot3dte (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period o dq8ahsg5b ;4)zu:ruq1qlgkqb.jx ,:f 3000 years. (a) What is its mean distance from qlu rq8gq)ax4: jsq1 .; kz:ubdbg5h,the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the valu,,b.jdntz;k ctame e(m-nv62e of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assu6( dn-ntc.,z v,; 2ee mjabmktmptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig* wo9m9thfas 0h-v ,qjjhl.e; . 5-46) at a distance of about 30,000 light-years fe;th0ma9* 9l.qo, jwhh jsv f-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 locat 8gw)xt pq5;u:3xn. k;,myl; lyshwlked at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint nw3u; l;,pl;swhmq)k5x8x l.y:ygtk of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits theou9.z 9 a3orjs 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-.g)) k.qkto:w , dvd hub.gg-zlong sweep second hand onozd.tv )bwqhd- .k, .gg ug:)k your wrist watch?    $\times 10^{-4}$

  While fishing, you getu5f zxnb7xq.*r g6s 4y bored and start 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 is4s5fy6gxx 7qn . *rbzu 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 20vvvz1qcs1 nthat a car traveling at sqcv 0 n1zv1vs2peed $ 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, thefm+sbkk4n+xaz c nso5c .4*b2 Acela, utilizes tilt of the cars when negotiating curve+fa2x*.c nnz4b5msk + 4koscbs. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not 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.$\approx$    $\times 10^2$