Sometimes people say that water is removed fro0 s(zq5,ex* lalihiyhz3 i *a+m clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this staiyl sxqea *z0i*lh,a53hi (z +tement?

Will the acceleration of a car be the same when the cx ,u46db7r6 vklzd1nyar travels around a sharp curve at a constant 60 km/h as when it travezy 4xbd1vlr,n6 6d7kuls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alo.yn3p4 8,htei/ zhtp ing a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hhpez/nth. , p8i 3iyt4ill, (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 chi civa0f rf31)*raes3pld riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerie *fc1v sfr a3pa30r)ation of the child?

A bucket of water can be whirled in a vm+spqy2s 2)*rv o 7pndertical circle without the water spilling out, even at the *d ry n2p)7vop2smqs+ top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lea/vii rpu5 8xrs). ykxz +0dq 4m6:egkjst three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do xju i8zi y6 :r4kk.+d )g/50rpxqsemv they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fi3npd -ra2gee fmc,yqsn hw)k.(ng ,65g. 5–31. His sled does nqyhc.g6( n n-5ng)rem,,2kpwf s 3edaot leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cu gw2 bal)(,gj hiax5a,rve at high speed?

Why do airplanes bank when they turn? How would you compute the bankinfw6cq ,cgjm;(alt2e glf 8yxmf2+t 3+g angle given its spfcc a jx+g2f; ,mq (ew28tflg6yl3+tmeed and radius of the turn?

A girl is whirling a ball on a stnc( lt9 jcz3)vring 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 tzcjn( t l93)vche string?

Does an apple exert a gravitational force on t 88gqvxoisj 89he Earth? If so, how large a force? Consider an appi89qovjx 8s8 gle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wou0ci( l *oa7xgold the Moon’s orbit be different0*(gci x7laoo?

Which pulls harder gr3oemm+b9 vf**1awxi tavitationally, the Earth on the Moon, or the Moon on the Earth? Which accelbmi*f*3ae tvx w 9m1o+erates more?

The Sun's gravitational pull on the Earth is much larger than);a xicuo/ g,m the Moon's. Yet the Moon's isa ux)/gi, co;m mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at38bg6 cw3h*ij4-qd k* tvgltn the poles? What two effects are at work? Do they oppose each other?3i3n6h*wbk* cltj gt-8vd4qg

The gravitational force on the Moon due to the Eak80x1qm bvuj k(fhnvm6k97 d+rth is only about half the force om7(x9fdvnju 1 kv0 +h8k b6kqmn the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accel yg b0k/v 2sls4kj/y1deration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleryk s/j/1bdk vl2 40ysgation of the Earth?

Would it require less speed to launch a satellite (a) towzyhrdf- a7.w 2ard the east or (b) toward the west? Consider the Earth’s rotation direction.w- frdz2h.a y7

When will your apparent weight be the greatest, as m1oznxas( e,e:fd/sv/ s( l) vfeasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) des of(ev( lxa:1z sv,f/ sn/)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 spauv0aep 6ko(r;,othu rcttps51 h8)3 ice 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 (Fig. 5–32). Ee;hvut8ctrohot1a srp p 0 5 u,()3ik6xplain 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 “apparen aktg :ch5:a ovv,)lg7t weightlessness” between sta gk,thc o:5v7av: lg)eps.

The Earth moves faster in its orbit around the Sun in January than in Julyz9i giw2xf ff .zb 7o;bo0 h*,0c,qgfl. 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 planwg. i;29,oqo blh,f*7fib gz0zfcf0xe of its orbit.]

The mass of Pluto waftmhxd5ac ; .u2h8,ift *lq6xs not known until it was discovered to have a moon. Explain how this discovery enabled. 5*muxxd,hitah8 l6qft ; cf2 an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earsfmcx191zhdop 5 1e,rth is much 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 child sitting 1.10 m from the zd he1c,9r1psf5xm1o 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 19fh(y 5l5pqr* w80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 arou(m-v* t7d/gemlqor5h nd the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a ciromm5 l(detrqv * -7/hgcle 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 izp+: ) pk8.xeirbhl 7gs exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m.g +p zp kb:il8e7x.r)h Calculate the speed of the discus.   

  Suppose the space shuttle i.tete w;n v2f-s in orbit 400 km from the Earth's surface, and circles the Earth about once eve-;.2fevt nwtery 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration ml qo.zpcqp- drv,-5r1a3jn * 0j /5omq7tpdo of a speck of clay on the edge of a potter * -ad55qpvj q31mopr.od rn,omjt p /c7l0qz-’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical rk( 4bil 8bwf*tixle;03tr g 4circle of radius 72.0 cm , as shown fb4 r3tl (*g0r ;iw8t4kl bxiein Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7jc;,uha 0d3n .9:oivgj4 gaiv7 m on a flat road if the coefficient ofg3;i0:. ,dino aaujvcvj hg 94 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 between the tire zx86kkezf:u)zeyw5 2s and the road if a car is to uk2 f8:wx6e)zz z5eykround a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desigwp0aut.q bwd5pf t- 3;snr v uzk*e49-ned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own we- vnq4rbedaf5puwtz3-u* .k0swp9 t ; ight, 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 5w . alzml5n/a8 l/ )lacmdw6dturntable of variable speed. When the sam)m/dn w/ll5za 5c awdl8 6.lpeed of the turntable is slowly increased, the coin remains fixed on the 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 downf(faean 30t),l 8ipl dbsa0 .r at theli r aas8f)n,bef(. pat0ld 30 top 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) cros-f/18p8 0i w+)vme bfpowzl pases the rounded top of a hill p/1wf )zpew -8o +8ailv mfb0p(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 wvs+.a4m i:wg0lzgpi;y (31prhde - z yould a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?p:+yp1im igzr40wyvhl3 e;s- zgd .(a    rpm

  A bucket of mass 2.00 kg is whirled in a vr ;7x.fz* c5to*po titertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope *rifzco *;7ttx pt5o.supporting 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 cm from pfvz8o;v za.( the axis of rotation is to experience an aova 8.z(;fzpv cceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people 9m,m3i d1r swkau9b:lare rotated in a cylindrically walled "room." (See Fig. 51mwib :3 9dm9ruaksl ,-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 rotbdi5pa .j.6s w36 jysmated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord cby .6.mwd s 5j3p6ijsaonnected to a dangling block (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 the *c w chfz 3:;,vtbue.uc-uow5ball which eo-c * fv;u.twzw,uc c:3b5uhrevolves 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 car traveling z .*y *p1*a jyd6ny9,u opuzaz 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 massesp9wos; scv.h bq 9-9yc z-ak3g $ 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 dtb5,uk ia,sfc,-sq: civing vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centrip( ni6qicf y;x8etal components of the net force exerted on the car (by the ground) in Example 5-8 whe 8ci(y fxnqi;6n 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 uniforma0 of .*o(dc il5euxj2ly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the tf(lcado0o .xui j*25eurn, 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 (b6.sb4:ghsmu4 o tbb a horizontal circle of radius 2.90 m . At a particular instant, its accelerb4b4sot(gu: h6sbbm .ation 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 Eartkf5kt5yflj0v9rmlrs7be(ll +e0b , 2 h’s gravity on a spacecraft 12,800 km (2 Earth radii) j krb5l tyle(59bfkev,r2l0ms 70l f+ above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnicv3d o n5y eh;:dh.1:ty.ytet tude.d hy3.ct oettd:n:v y;y1 5he of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due 6*mf8 p; nluc.r;a eknto gravity on the Moon. The Moon's radius is 1.74 r* ;f8 kunmapc;nl6e.$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius +:4rxsz :1zqh9hllzb2 c *sq w1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its:1:ls czqhbz+s4q* l2x9w h zr surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but -rk;x;nmxsanoxx(8)-rxeg : the same radius. What is g near its8mg;(xrnns- -o rka x);xxex : surface?   

  Two objects attract each other g:4+pj x zhefw2ravitationally 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 o ecl;p2c t4 eub.zz6t7sh,/8 zmux 5tsf gravity, at (a) 3200 ms74 ptm /z 6lx2s,.5zbue zcuc ;t8hte    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance ze(nae4:h3 pv9s4 ; :5d cdlpa6dtqtmfrom the Earth’s center to a point outside the Earth where thegravitational acceleration due tltqha3sda4c(4 d 6: e;pz e:ntdv 5m9po the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass j;nxf5ohgwjs,7d+a0*5w, 4wmmo brh of our Sun packed into a sphere abomm onx w5jhbdh0r; sa 7j5,,wo4+gw*fut 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, wf hn79h6 ehx1which once was an average star like our Sun but is now in the last stage of its evolution, is th1 h7fhnhxw e69e size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitin3mo a,7mz6g cvs/3xkp gc;qr/g in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Eqk/xa/pzr3c v6,s;o3mg m 7 cgarth’s surface in terms of g.   

  Four 9.5-kg spheres are y;vc,4v4nmp-ld*l* sg (7c4ovsl yn clocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitatiood *-7ncpsl ys4 *nv( l4vc;mv4c y,glnal 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 up on ther 5g6.iukj3m, .e* ri wd1wzte same side of the Sun. Calcue6i z31 r.m.jw duw5 ,gkier*tlate the 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 ofhhvyi r: 89ox,f+du2 w gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the ma y+h ,xi:8h9drvu2 owfss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun us7 5z vm)d4uhxeing the known value for the period of the Earth and its xzu5m47hve) d distance from the 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 stable ciroh jm,0)cxg/r ;s* zmkcular orbit about the Earth at amxsh/),*co jkm0; rzg height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular q4.3nror4cqf- -wn ez orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?3nrq-z orw. ne-4c4qf    $\times 10^3$

  At what rate must a cylindrical spaceh6nzsvx:* y6 eship 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 v6e y *z:nhx6sfor one revolution. (See Question 21, Fig 5–32.)   

  Determine the time i9/g* jr20h: h6haroh hgzy+fgt takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius y0g*2: 9g6ghf/zj h+roahhhrof 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 the tusjt37 sl5h6 -d.gttc ,lwqv)op of Mu ls73s . hwc6g)dt-t5qljt ,vt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbi lwxypn.n)ly xzxehm**,c qn46 5z/r*t the Moon at an altitude of about/xh.yx5 )zn*rlznpmwe*xy n4* c6ql , 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn ar2(qsu+ 2mtb* tkcbp a6l2o7jaak6.jue composed of chunks of ice that orbit the planet. The inner radius of the rik.m*psu u c j 2bl2t+(qj7atab6o6ak 2ngs 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 t3fu,6nsmv f k1l80fum in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparens 08,vnf6lm fk1utuf 3t weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kmxx rp4a86 bf9mz (1dvg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constam4dxpxf( 6 mvb a81r9znt 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 0,t z u xln)xa 3zm8(dnk)ng6 elfe-/kof equal mass. They are observed to be separated by 360 milli) ze0n,6nlmxkl)z(gf x/kt- ued3n a8on km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reatfl3u 2uz9 /nrc5vi2 (7miiw od for the weight of a 55-kg woman in an elevator that move3i 2cft2i ovurwl95 7/uz(mnis
(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 hang khj:mp)pi )b/mput7 5s from a cord suspended from the 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 :i5k m/u mp)tbhpj )7p(magnitude and direction)? a =   

Show that if a satellite orbits very near the surface ive6+o.2 h p )/cardoj*1sb-h .uesl gof a planet with period T , the density (mass/voe6+j.2v.dh o) saiuls p/ohe1* gcbr-lume) 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 perny78w3-x 2lv -z ;idq xt+uzryiod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near t38n w +y- 2zdlux7 qryivxtz-;he Earth’s surface.    s

  The asteroid Icarus, though only a few hundred m 2.,nmltl +gjueters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance frj g2+,lmtnl.u om the Sun?    $\times 10^{11}$

  Neptune is an average dista5exe / joem:p8c 6kzvkt 68l)wnce 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 Sf+ou* t rd6qum6zy1e 7un roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s thirdoe f mtz1quu66yd7*r+ law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galax9 v, /roybbcw++ml46;x to oaey $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, ani,ll . c84nyn uwkt4r(o0;hde d mean distance for the four largest moons of Jupudkh0ni(r c 4;tlw4elyo8 n .,iter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earxjuk: (c )c9qgth from the known period and distance of the Moon. gc:j)uc(xq k9    $\times 10^{24}$

  Determine the mean distance from Jupiter for gl)bic:yucyn 5/p)x 7-dg1g neach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5 yg)ldnbgc /yx)pc5: n1ig7u-–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which somo rb0 zldx:t))e space scientists think came from a planet tharlxd ):)zob t0t 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" in thm*-(wtp hjyi x xe5c:8e 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 sxhce(8xt *mw:jp -5yi un 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 gorksm0d *m)rj6p9o 8bmu ge by swinging in an arc from a hanging vine (Fig. 5–41). 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 swkp8 m uros0)b9m6dj m*ing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accele 3yxz9-qs)vzk*2cckx ration of gravity be half what it is on the sz)x zyc2 sk3-x9qvc*k urface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab han4sx gv0t1d5qjzz0,z: 5c erxhds 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 a 0v5,tzc1sh4e: zxrgq5 0zjx dre they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, tl2oy arl:(sed 6r;ciog3b +;ihe apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractio do;o32(l ebsir6+:cry a;giln of g is this?    $\times 10^{-1}$

  At what distance from the Earth will at5s:fvn *rv*fwi z.8n spacecraft traveling directly from the Earth to the Moon experience zero net force becaur.*nnfvf8vizt* 5sw: se the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale)pj b4 +vfjoq2vo;m*d in an elevator, it says your mass is 82 kg. What is the accelerat ; p* f2+qmodv4jbj)voion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about io7;6 xwoy c:6ks qn-fuv1p )yb;uizc2ts center (like a tubular bicycle tire) (Fig. 5–42). The circle formed kyfz ;:u 66)i qbou2wvcy;1pn c-ox7s 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 be felt?$\approx$    $\times 10^3$

  A jet pilot takes his airck- (4hh:-ejyuss/mi n raft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of itsvcde l(i 73 y0u.usbe* radius r, the acceleration due to gravity at its surface and v3s*u uce07i( . ylbdethe gravitational constant G.

A plumb bob (a mass m hanging on a strin;w.*p3ycsi49mekrlv r0 d* b sg) is deflected from the vertical by anm4vyds r3pircs bkw** 9. l0e; 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 ml jkbe qp)q+j)59dkr7 is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the c l)jdeq 95qb+ jrk7kp)urve?

  How long would a day be v nw2rk)o2(g e7ahe7bif the Earth were rotating so fast that objects at the equator were apr 7ag7o evwb2(khn)2 eparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant : b,o -snka hpen1dxi*;9qsl3distance 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 curvji qnb*1/9 wige of radius 235 m. A lamp suspended from the ceiling swings out /*i9qgnbjiw 1 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, it has been clyj7tv,/8q5czwr p *w haimed that a person would be crushed by the force of gravity on a planet the size of Jupiter sincytw/wc7v*8zjrq5 h p,e people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of anm4uunxceexe-- ;l ;h5 extremely massive core in the distant galaxy M87, so xxm ;n- h5ce l-e;uu4edense that it could be 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 speed as is h0u i.ot n(c5m;jlg1t 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 compare? (Which is largest? Smallest?) Exp gioj;h ms .ul5n0t1c(lain. (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 sy o*7gksm6u 4rn b/k*group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixe *n64ors bsk*7um kg/ys.” 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 tra cu7gkr58 /vho4+wx syuf ,qs6veling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughlyrgfk 7su4c,xy+ w q u5o8/6hsv 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:ec(;e6zrov 6s.vl4 jba,wa;dfhd : i a satellite in need of repair. You are in a circular orbit of the same radius as the satellite o::6h6vdze a lisj;;4vfwb.dra ,e( c(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) What is its mean distan*cl; 5,le2t)dhlq/ ww6rkc wyce from the Sun? c /,2;wcyr)*5twkw leld h6ql  
(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 beof9dcl tz (6bbpt2q2 ( if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptio(od(zbbltfc2p2t69 qns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around tv.ffsffmny7 3 )r8 c)jhe center of the Milky Way Galaxy (Fig. 5-46) at a distav ).3nmfr)f8cjf sf7ynce of about 30,000 light-years 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 locatile, tl5 fbr3-ed at the corners of a square 0.50 m on each side. Find the magnb r5,-if tlel3itude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth * ipf0crrjjb h *fj0m598n:qm$ \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.h.u1,m fwam w25-cm-long sweep second hand on your wrmm2auh,1f.w wist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around 8ugyh /-mk q.4gxh2ej in a circle below you on a 0.25-m piece of fishing line. The weight makes a j hy/gu-khe4 .m 8x2gqcomplete circle 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 R in a new highway is designed so that a car tr+ddd+ki 0- esmaveling d-d m+0ske+di 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 Acel;we9)(qpt dl*7da i bva, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction for) 7atiel ddpwq*; 9b(vce 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.$\approx$    $\times 10^2$