Sometimes people say yxq:0t)t9j9odho sz* that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with thiso sx0y jqz9 9)todt:h* statement?

Will the acceleration of a car be the same when 6 ).)xx uepmtbea720l-3i( ywahcgb(.tjonu the car travels around a sharp curve at a constant 60 km/h as when it travpu.i)(bex.h)tolwm0n3e( x bcga t67-ya 2ju els around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alon(k h4abe/nytpy)h. .vg a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top) /k(hph t.y.nvaby4e 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 aal: ;c;2jf0t ozvw +pwjtgx5 +cting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratwpzj;0 wg o+t cl;j2fxt5v:a+ion of the child?

A bucket of water can b: vqj( 8llvtf:e whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaivf8(vlq : :ltjn.

How many “accelerators” do you have in your car? There ar rl0(g9jf)cv):u-byuc k pxi k7;izw;e at least three control )7pzxu ; 0rbi:vguyc);i(kck fj- 9lws in the car 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 small hill, as sh(ivp3um/ggcnoa) 1h)wb 0z n:own 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 th(hac3i 0wvbn pg ))1mgno: u/ze 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 curv8w2st*e *1ipk mgf me3*soc7ue at high speed?

Why do airplanes bank when they turn? How ftnm(d1.mz)rr92cq jf r-irj sl ,-y: would you compute the banking angle given its speed and ir:nfl -(.r 1r,jc -j 2sd9y)fqmztrmradius of the turn?

A girl is whirling a ball on a string around her ghpif*5o ac 33head 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 f5c3o *ih ga3pof the yard. When should she let go of the string?

Does an apple exert a grav;:j.o rmq 1otbromy9s8yq)n y(xec4/itational force on the Earth? If so, how large a force? Consider an 1ocm4b moro /.; 8rxn(:eq 9j )tyysqyapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it g8f,9c h5asi)g3 r 7my cfcd2yis, in what ways would the Moon’s orbit be differ753hf if cg)gmd2,9r csayc y8ent?

Which pulls harder g* *oay .zy l,nql8w 280pumoovfvob .0ravitationally, the Earth on the Moon, or the Moon on the Earth? Which acceleratenovwyopo.88llozq* .20y0 mub va,f*s more?

The Sun's gravitational pul h)cm0fikrcr dy-m*(8l on the Earth is much larger than the Moon's. Yet the Moon's is mai*0rm( dhf m8-cik) yrcnly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What tlwa-w2m sfp7; m4sg s,wo effects are at work? Do they opposlsw7ma2 g ,wm4 s-f;pse each other?

The gravitational force on the Moon duex 67t2 v (dvabyfx(4gwa-bus,u8*dhu zbx:t 7 to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away2fx uds(tu xgubax4by*v778,zw (dhb t:6va - from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger dxz xwl4pex(6 ,u3u g2)he*z9oo sqq. or smaller than the centripetal acceleration of th6 gso p9qx,*dqwo ) xx.h4z(3uzue2 ele Earth?

Would it require less speed to launch a satellite (a) toward the east or ac 8xlay*y,i(sq )en-(b) toward the wesn* 8eqx( a,yslyia )c-t? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measuru/ gra6q++qaj ed by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight jg+a/a6r +qq ube 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,ri5yo0 n + a*t*iqf6 lld)/rxhx(szu long periods in outer space could be adversely affected 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 (Fsyfx6qt+/ln5uii , z)rxr **0doa(hlig. 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” betwpxdbw6j n; +3wwyxs13:ix;kzeen steps.wn3zdbi y:; 6 +ws1 jpk;w3xxx

The Earth moves faster in its orbit around the Sun in January than in Ju( aqp ac/6i5glly. 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 Earth’s axis relative to the plane of i( a65l cq/aipgts orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explaib 9, kas5*fcpjn how this discovery enafa , pbjcsk*95bled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mu3yaz0;ev5d ue4k-ef c95 m surch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A v3 -5s e0 94fze;cmeyu5kau drchild 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 travelin2u3paigi m(5q4thsr 4g 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 thicn(4o-rqp6/r9;jkt x oopa0 e Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that thno6 -;(jprpr4a/cx t koi9q0 oe 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 discus as it rotates unifor+u ggato(g3rn 9oadfoviv4 ).k(go,6mly in a horizontal ciat3(g. + 4foirn(ovuggv9 odoak6) g,rcle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, 6f .f8 smv;vvr:tiy8d 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 fmsyvt vf8;d8 vri :.6gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge o)* ajcqbu5324ywr f ugf a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is25q uw*3afr) b4y gjcu 32 cm?   

  A ball on the end of a string is revolved a7q fn a/;iev)et a uniform rate in a vertical circlee)nav;f/7qe i of 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 n4hv6hz.sd kuh8 5 r4hx0y3gwspeed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coeffi0hnhhh5vy6dusgx8 .z43r kw4cient 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 ben9d9o6z,,r rpe zc 5cu between the tires and the roa59,96 zrdzn,rcpe c uod if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astro5v;blt0 ,x -fd1lj jpfnauts and jet fighter 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 bv ld 0x jl;p,ff-j5t1times 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 fev+nqh6 a/n* 5md/ mydrom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on /evy nh*dm6dn/ mq+ a5the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside wqr wrx.,.cl (lr9s o2down at the top ..ws29llr (r,oq cx wrof 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 driv qs(no f4s 5:zn:4-qkgva2vnuer) crosses the rounded top of-:45 u:savgnsn(z4fvkn oqq 2 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 need to mawctrx.96:zuki7 t /nr ke for the passengers to feel “weightless” at the to/xiuwzkt7 n.rtr9 6c: pmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticemave. 76k (ntv( 0zbeezo 5e.al circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supp( a5e7btz(. ko 6.ve envem0ezorting 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-.j9ab6 or8oykmevrnb*.i u 4 cm from the axis of rotation is to experience an accelerati98u.oej-nr6 b ayr 4m.i *bkvoon of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatk: f,hh: (gzfred in a cylindrically walled "rgkr:,h fh: (zfoom." (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 rotatbmo 3bg)r ;5vued 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 Fig. 5- rm v3; b5ubg)o
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 ignor8e 2s efkuzgb 2 4.mhoc*cq2y/ing the weight of the ball wh 4yee2.2bcc2mfsq /uo z g8hk*ich revolves on a string 0.600 m long. 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 9mwldf2ywz8c ;(t zu+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 massec/ qwe5gng), c+m0 kays $ 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 v:y5p5ikmg dr :ertically 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 b+0ds9 (f,hx+t wirswcentripetal components of the net force exerted on the car (by the grou f+(i +s,d hrbs9xw0twnd) 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 fromx8: f8 e 0axoxa 2;utmak,9czd 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 thx8 ta,x8cfm aek92xz;ou d:a0 e road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pax.785yneo*zor z w:y ,uvxy.drticular instant, its acceleration is rx u.57n:8 z ,y.xowyyvz*ode 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 spacecrafigcoq)p vko;* tj,bm *107 skat 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 13tbk1m7 )vo qok,pgcs0a* j*;i50 kg.   

  At the surface of a certain planet, the gra;-tpzct8x6taa 9a v;rb9nv mdu :8n-s bd2h+lvitational acceleration g has a magnitude of 12 9dr9+v sxau2tlb6m; t a8b ah -cp-n;t8zvdn:m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Miaao 5u3uutl:i1o -:.v2nfd x oon's radius is 1.7.- ado 3 x51to: u2ifaln:viuu4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet2pghr l19 pis7 has a radius 1.5 times that of Earth, but has the same mass. What is the 7 ls2igr pph19acceleration due to gravity near its surface?   

  A hypothetical planet u ciq810 qlaaah 4v+ktd,3*pahas a mass 1.66 times that of Earth, but the same radius. What is g near its s,a+3pic0 8qkhala1vqu* d a 4turface?   

  Two objects attract each other gravitatu pdc18uw3 ms nb/b3p6ionally 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 grij*i9 iek7v/k avity, at (a) 3200 m eji9iv*7ki/ k    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frt ut0i 1sq39q5 ezqfzk4l,r0yom the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth 4qtkz sut0y10e rq z59lif3,qis $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timt(ghqd3, nsg:rbl1 4ces the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsten13q,lc gt:brd4g (hsr.    $\times10^12$

  A typical white-dwarf star, whoy6lhq.p25y p 0e8iaiich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface graviplp68a2oi0i q.5hy e yty on this star?    $\times 10^7$

  You are explaining why astr c2**y(4jj:ixu,oim k* heaqxonauts feel weightless while orbiting in the space shuttle. Your,jj *eomi2k: i(hq*4xy* xuca friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a b7o/ hex2 l mw0g0oyi,square of side 0.60 m. Calcu02/ woi,o0mg bex7yhllate the magnitude 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 linem1wv5*lgpx v 4*1l/o3moity o up on the same side of the Sun. Calculate the mv1 *1pyv4gow3mto o5 lx il*/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 acceleration of gravity at the surface o; :(6wt6 zu1ym uu0dwiufgx .ff Mars is 0.38 of what it is on uzgxfd uf0:umw6.yt ;u6i (w1Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass ofyi 4fj*mji; 1i the Sun using the known value for the period of the Earth and its distance from 4jif m*;i1jiythe Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a scmri 7s 8(x0b xrxfh9 )g,6bjgtable circular orbit about the Earth at a height of 3600 kxfc96b)ris0b j7(x gx8 hr g,mm.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit8wa -) ibt*7mm9wkmv7xa nnp- 650 km above the Earth. How fast must the shuttl*7 nv9a-tb)i ma7- kmwmw8xpne be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindriw1eg76i u 8.onfh 3zh4nxia7.m3cr vfcal 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 Questioni.niro fzav7fe m gx6. 7c u3hhw1348n 21, Fig 5–32.)   

  Determine the time it takes for a satellite to o6u/,unjj uk(t o l,z-i:vras5f;yg9 arbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the i:ujj5l y/za ;vuuf(skn6,g9tra,o-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 velokv hx4n20vu1,x4ermqcity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the u1,mxe 40khvrxq24nv Earth?   

  During an Apollo lunar landing 2umz v -j/gzs;mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take /zj umvz-;gs2to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.3+q 1e1bnjt vb The inner radius of the rings is 73,nqb 3etbj1v1+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 kq5 kcsf +0sehp42*qy 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) at the bottomqfc5 *4ph0s2k+syk qe?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the dsr11 x, 3d .4zwyomyscenter of the Earth's Moon in a space vehicle (a) moving at cw. 14r 31z dysdmsy,oxonstant 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 of equal mass1ur: iouz ao10. 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 o ou10i1 azr:umass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5 ks7e hc;qd3o(ds- eo;n62mk5uag6pj 5-kg woman in an elevator that mov2s;j(e hgkpk5ao n 6-osdu6 qe3c7 d;mes
(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 suspengiws/bfi7+ o x,pi ),vded from the ceiling of an elevator. The cord can withstanoigi+fi p,s 7w,x /b)vd 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 orhv;q d29y9 dbxf8pr4g bits very near the surface of a planet with period T , the density (mass/volume) of the pfvd d29pq;b8gh4y9r xlanet 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) y6l 8w*9fx pwdto determine the period of an artificial satellit9lwx6 pd f*yw8e orbiting very near the Earth’s surface.    s

  The asteroid Icarus, d2vzq:t .b6r ux.rqe6 though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fro 6 u.ber. qtv:dqrz62xm the Sun?    $\times 10^{11}$

  Neptune is an average distance ofg9tmjmo( j. 9pr *o.c te03srn 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 year1zvu76yxj m5l s. 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” t 5lxjy1uz 7mv6he 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 tazf0b64uu (kb he 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 dis e,chwg jmba.q6o8:;i tance for the four largest moons of Jupiter (those discovered by Galileo in 160,me.;ji6wc o:gh8aqb 9).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance ob y(mm p)7r:kpf the Moon. 7y (bkrmp mp:)   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jwyfz 6heho. g.q+m65u upiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table 5qo uf6..hegwy +zm6h.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of tyefd*c7p4 04bvz0 oomany fragments (which some space scientists think came from a planet that once orbited 0 7*pbvot4d4zec oyf0the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in otnkp va0+rq3(ukc: 1the 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 revo r ok nva+p3k0tuq(1c:lution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vinay3 4,oyn xs9ei,:lbhe (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maxims oh:x lyba9,,iy3e4 num 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 su,2-wy j:oktt yrface will the acceleration of gravity be half what it is on the surface? o y2tty,w k-j:   $\times 10^6$

  On an ice rink, two sotgq.;xegc :4 q (6tlnkaters of equal mass 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 masses are 60.0 kg, how hard are they pulling on one another? 4n:tqlc.xgo;et qg( 6   $\times 10^2$

  Because the Earth rotates once per day, the apparen nha3jj 4 ,xiz4dbd9+pt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estbd ap h 9ijzd,44x3j+nimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling diryw:tm x68x rn tsy*l.xn6r3/yectly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal a63:nxrr xslnm wty./y8 y*t6x nd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bath0 gyz+qi bho)n0i7vg, room scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?ghiy,)zo 0i qnb+v g70     ----待选择----upwartddown 

  A projected space station consists of a circuu; lmbt)i) .xflar 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 t) f;tmi b.l)uxhe surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.ui,r:gzk9 85 opy1, )vzwi.9 u txwdpe 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 massxf5-ugmj/ drd (1dio. *obz s5 of a planet in terms of its radius r, the acceleration dug sudo/midj.*d5(5 f 1-b zxore to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) i j30 )wmy:6fonsvc:iw bk4sf.s deflected from the vertical by an anglecws3bff . o:0kmy 6nv 4w)ji:s $\theta$ 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 ( csfwts(.i4f If the coefficient of static ( f(4isf. wstcfriction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be ifm7o +hbbjxpvis6v/* 9-vmh9o the Earth were rotating so fast that objects at the equator were apparentl6vb99* /bmo jspo hh 7xvm+iv-y weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart y1w3*;xl :hzaay xg,x 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 cu f+z.;uk.f o g4j0pshqrve of radius 235 m. A lamp suspended from the ceiz;o+f kg0upqj.f4 hs .ling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 t s.+m )v59bbx wxj ,5(gbhwznqimes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planetbqxjhxg+ m n5s9w5.(wb)vbz ,. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an 7rvku*,n zb )wir zm90extremely massive core in the distant galaxy M87, so dense that it could bm0zr7w ,bur )v9zi*kne a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant spet(n lfgf2ph05o* y/qa ed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvatur2fq5(yp0* onga/ hltfe R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizesg qu3q78w-e rye(ucv3 6bwyy* a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the wby7gu8ce3q (yvqw *3-ur 6yeEarth 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 Rendezvous (NEAR), afte 62ammfas8n4 dr traveling 2.1 billion km, is meant toaf s2md 8nam46 orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle purs2-ksv9d* jj-lgjx a)cuing a satellite in need of repair. You are in a circular orbit of the same 2-x sjgjv) *a- j9kcldradius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) u z4 smi/dj5u8What is its mean distance frommudj sz4i 5/8u the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually3k2hew9mpsbo luz u4c i,*xvr.(vh6 3 "feel" yourself gravitationally attracted to someone near you. Make reasonable assuvbr*m(2op 9 zc43vwsiulh,6x he. 3uk mptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5- iikhny:weo;xz 5ql4v :.4p :j46) at a distance of about 30,000 light-years from the ce: .44oiilvhkw eqzy;pjn: 5:xnter $ \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 are0f s6 xx;rwt54w,nm tl located 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 of thrfnm50,4t wlt6xw; s xe bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kgw88s n *xycwvn8ol 3m8 orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long s+t- *w,nfr .obu0pktu pj* 6ftc(2h3bhd dp;z weep second uno;kpb df +j2t*b*dt.60(cwz- rthpfp3h,u hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you geo,/12habvze 4/) hc+ kw :6tsw, dnw- zyefgsyt 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 cir6s:ez-w,a w2wh1gyknyv)4cb,de/ zth/ +s focle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R7*g xo7:1 sxg cgcdc2t in a new highway is designed so that a car travelingtxx*ggc7cc 1do :2sg7 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, the Acela, utilizes tilt of the cars when negotiating o.mz: dun1q(x curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the 1d : mx.nuo(zqtrack 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.$\approx$    $\times 10^2$