Sometimes people say that water is5j)q mcsk+td.d iolj;4pm 4:wb *6de k removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this sdck4m t64w;dmkb.dqj o*e5sl ): pj+ itatement?

Will the acceleration of a car by4 vkxil: ifs6;vd4g/e the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the s6lv4 kv/fi:;xgd s4iyame speed? Explain.

Suppose a car moves at constant speed along a hilly rtkv hn i2/yb0)oad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom ofkni/vb 2hty) 0 a hill?

Describe all the forces acting on a child ridir o*x0stk36cx0nz gvj ;d,vf +ng a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the childvdovg3x6 tk nc 00fzj,r*;+ xs?

A bucket of water can be whiz domq 2gdi7,fp* /o4zjnn:g8rled in a vertical circle without the water spilling out, even at the top of the circle when the zi *o gq,jomn48z2pd d f7n:/gbucket is upside down. Explain.

How many “accelerators” do you have in your car? There are atansp* e4 jv2x. least three controls in the evxs *2p4.j ancar 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 o4uo 5a sb1pbr8h*eck/:da2sz7 x9lp rf a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feb*ubrsa:oz7pp 8 kcs1 45 r2 l9/adxheels 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 cur;wm p4i;iqmy /ve at high speed?

Why do airplanes bank when they turn? How)wpfzel im.g8-:;fhz would you compute the banking angle givenh)p8zw-i.; fe :mzl gf its speed and radius of the turn?

A girl is whirling a ball on a stdx+ oxu*ml2q1i cdm) -f,(zq xring around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the strin(lf2 zo+d, xuid mmq )c*x-xq1g?

Does an apple exert a gradx7,qr6., b.3 y/n omdgzyjxpvitational force on the Earth? If so, how large a force? Consider an applepzmry q7x n6,,d/gox yd3..bj
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wo ;mw(*rwpdq .,aqwct7uld the Moon’s orbit t7*q( wdmwq., acwr p;be different?

Which pulls harder gravitationally, the Earth okl:u:tt 3w9)b a deb/yn the Moon, or the Moon on the Earth? Which accelery: wl9beta t3)/b kdu:ates more?

The Sun's gravitational pull on the Eart;eau8-;a4njq , zte2.jeqhti h is much larger than the Moon's. Yet the Moon's is mainly responsible for the tidesjtjnqq8ahia e, 24e- ;zt.e; u. 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 ttepfz84/v5jgu1e++ yi ohy7zwo effects are at work? Do they oppo4p v 7y+1j8 thzf5+eyoe/guzise each other?

The gravitational force on the Moon due to the Earth is only about half the fole w1uav6++ 9b2joigfrce on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eartfj9 g2v 1weiua+ olb+6h?

Is the centripetal acceleration of Mars in its orbit around jy+dzip7eh-tu0)m 6jthe Sun larger or smaller than th +j 0hdye7itu p-zj)6me centripetal acceleration of the Earth?

Would it require less speed to launch a satoei.ii.1q i++ n; kyubqgjl3l-s 1*52 xbtcshellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation 3tbk+jb *.q 2y+iu1iii-lo g5 .xhle qsc;1sndirection.

When will your apparent weight be the ot6 kuagn6 m:4greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at cons: 6om6a uknt4gtant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affecpma6)qrg 61,*aagbp war-jf;ted by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how tafp)w,6a-6g;mj qg ab1 rpra *his 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 weig j8 qv.bz0f5idhtlessness” between std 8.0jivb q5zfeps.

The Earth moves faster in its orbit around the Sun in January than inmwsd0vv1)2a)n va r j2 July. Is the Earth closer to tha0 )v2rjw1avvsm )n2 de 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 its orbit.]

The mass of Pluto was not known until it was dl.*h e2hvpb5v iscovered to have a moon. Explain how this discovery enabled an estimate of Plutolvv*2h.5eph b’s mass.

  The Sun's gravitationq*f l538zsqs8k/ mx rx7.k bksal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in 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 m k sr5xxk.3bl8q7s/qkzf s8*$\mathrm{~m} / \mathrm{s}$ . 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 j9;ul0e0u 5g(pkenpwqx g4k(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 +zgyb6 : , +j:dyvqwepits orbit around the Sun, and the net force exerte: ,+ vy+q6b dep:zgyjwd on the Earth. What 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 discus aiw+2l(lpz 2 gi:s 7uits it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the spe27s+ liiti2l:pg (uw zed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's suu 0+urwdqb) z9rmr:k7rface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earthq d:9 mbwzrk0 7ur)+ur's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay onq 2my70) zr h0q.kvaxd the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) ifx2qy0q0mz7.d rkhva ) the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verti t + fxx49tk9fgvzyb3v8x/d9scal circle of radius 72.0 cm , as shown in Fig. 5-33. If itsf t8xzv fv3xbdg/s4xk+9t9y9 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 s.to 5rlb)( 8pdndij*which a 1050-kg car can round a turn of radius 77 m on a fb *.nsrpti d()jl 58odlat 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 between the tires and t1 *i p+rl pl,gvj0xq:qhe road if a car is to round a level curveq q,rpvp0 *igl+xj1: l of radius 85 m at a speed of 95km/h ?   

  A device for traininbk a*xy 6;yvd3g astronauts 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 76ka3*;x yy dvb.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 aq wb.6t/qfs4ign. g4j rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the 4g /. jnqtfgi sb6wq.4turntable?   

  At what minimum speed must a roller :r+-c ,amx prv m.py5lcoaster be traveling when upside down at the top of a circr+.:r px 5plcm,mya v-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 mass 950 kg (including the qr /d2 vos;q(qdriver) crosses the rounded top of a hill (rv(;rq/qs dq 2oadius =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 wou ,lx;9deg 5m ,rq;jidvld a 15-m-diameter Ferris wheel need to make for the passengegld md;5j;ri9 qxv e,,rs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10oly tx/4eb )o/ m. At the lowest point of its motion the tension in the rope supporting the bucket4) oe x/otb/yl 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.)s hq1pm,m5+gk+jf vz00 cm from the axis of rotation is to experience an acceleration qzkf+)v mg1pmh5j,s+ of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated ihlm (qal6e ,+cc 3lme7n a cylindrically walled "room." eh(ecl6+q7,m al cl3m (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 6)eq+gw 7v r/ sq4mr.wo;6ssq 9jrtw u ) is rotated 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 sho6rqs7s9)4r/.; v+wemoqs w gwjutq6rwn 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 odh )f0eo ;ytt8 cva/y0f the ball which revolves on a string 0.600 m long. In particular, f 80de ytyt/ hoac0);vfind 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 trbbg98 ;qck1 urnj8:; gj nd,mwaveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses v vv0(n6ve 6qt$ 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 m i;6lj ntes--by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential andi0; qqcie k9v r5qf/ux avo6j5,a2 w(j centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its sp9fqa wa5v 6oqj;0i,rkj i/ ucex25(v qeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerwt 3u,;q4 gupfmq9 nb8ates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine thq;48fgu3mnw p,9tb q ue tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizonta8 el0)t 0:v yzqxj/eckp406sq 5gwcnw89pa oml circle of radius 2.90 m . At a particular instant, its acceleration is 1p c6yz npj g w49xo05tqsm e)0: 8a0vkec8/lwq.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 od0.wq(/nn n pju z:(zmcfk mko+s9c 87f Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ik8nnc: kq+mfmp(9(su jc/w70 zn o.zd f its mass is 1350 kg.   

  At the surface of a ces4q :j:q b(hzqyd p p(gmx8:8da6ap5qp( 8axurtain planet, the gravitational acceleration g has a magnitude of 12 mpaba z48mxu(dxq(5aq8(dyq pj8qpgs6: h:: p/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 opof6zrs m:wao/b/6 f6n the Moon. The Moon's radius is 1.7 o/fm:f6/6 rzoas6pb w4 $\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 t8 pys8 29lkxoljrt :w.he same mass. What is the acceleration due to gravity near itsop jlt: x8k.2lsr8yw9 surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thur5,4 vp4wegp e same radius. What is g near 45wreu,pvg p4 its surface?   

  Two objects attract each other gravitationao5wt-w 1cxmps: :xi5 hlly 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 ,rx+d ik w ;/(ik.sgq7o the acceleration of gravity, at (a) 3200 mo7wri/ xkqgd;.i+k s(    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ox1v*0 3 s4vtt+bksqur utside the Earth where thegravitational acceleration due v 4s3+ktsuxv1bq t*0r to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h ,jm0dp 5uhf+ ql+keg-as five times the mass of our Sun packed into a sphere abo 0++,djfp 5ue khgqlm-ut 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star a i4 jd/a4kv:,pp5qadlike our Sun but is now in the last stage of its evolution, is the size of our Moon but has a/ d 5ik4ppja 4qa:,dvthe mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weig aoydu3.r o-n3htless while orbiting 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 t d.n3o-ur3 oayhe 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. Calcuuiq k0b)a-/ hnb7p)g vlate the magnitude and direction of the total gravitational force exerted on one sphere by the h)b- pa/ig0u7q nk)bv other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up4 7u6)khvs ghl e++z)wuilch ; on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a 6)c)i+w+sz kv ullu;4ghhe7h 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 of ab6lkb,02r iy+ red2c Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, dete, 22r irayb dlk6eb0c+rmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun (),mki nkk+pfj5mu(ivns m*1 using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16ki j )(nip*k+1umsn(m vfk,m5.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a ;dlfn.6zwx 9v stable circular orbit about the Earth at a 9 .xf;wvl6nd zheight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 6kf:etg0 ktv (1noxm;s)a3l ; hyn)/ vd50 km above the Eark 1:yl; mkh at)fs0vt x(dv n/o)en;g3th. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupanj ss ph:z .5b/u3ytpqs(ewy(2 ts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and giv2bh/y s j(sety5z3(p.wsp: que your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eartdjfm 7y0ro;bf/9 tn*ch 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 compary 7f/d;c9f ojm*brnt 0ed to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wou/njmd9gl rn 1, nz);e7yk t5ycld a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around th t1l 79);drcgn jkz5y/ynem,n e Earth?   

  During an Apollo lunar e2zr-4 jdst63ulwmy1 landing mission, the command module continued to orbit the Moon 3lu rw4z 2je6tmd sy1-at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit 9lh+x)cf4/vvo4j rwb the planet. The inne +/wjlobvf hv)rx449cr radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once2sy9+vi1 yg ros19a7fmq ajy 1r0ni 3i every 15.5 s (see Fig. 5–9). What is the raty91g0y 9i1+r7 jaf3yrsvi om1qa 2ns iio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wei2q *zn nawd9a*ght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (aazqnwd9*n2a *) 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 of equal mass.twhgvj+.jn7aiegbz.b5 7t0 ;bv w*t2 They are observed to be separated by 360 million km and take g7 2+t.ebhgibjbv 0. wz75tntv w;* aj5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale rea43iss zy9nky6bf9w hv u+0o f(d for the weight of a 55-kg woman in an elevator that moves + hv9s y4zfswy(ifbn9ok36 0u
(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 elevator.hvd08(rir5b.yck m x6 w*2p*px lwzf: The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was th w r(ml *f 0.c*vpb hzw:irdyx8px56k2e elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits verf+r:kr3k gwif)n;1w 1oyau8x y near the surface of a planet with period T , the density (mass/volume) of the pln f)rx koa:1w3+uwky8 i gr;f1anet 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 therz o:hq+4 6lso Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth6lsoo+qhr4 :z ’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sudp)6o* ;m gbdyth ;5pjn like the planets. Its period is 410 d. What idg5y ;t ;dhbm6po*j)ps its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc-mpmh(x a *hm(t- ukc xp62d7bkue60w 2unm3h e of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close txpwao-*i o w 4p84 g.ywjc8h3jo 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?848pwj4.jyi w w ho*a3g-pocx What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cera8y gi9c*f.0d xna*b nter 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 distance2 er7e/i;rui;q3zpu ox.u-fvzz 55 qw for the four largest moons of Jupit.;e r/ fpzuqui5o- 3zrxe527 ;qzu wvier (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 Ei( :1vssgl7j3 zpj3qpbx0 li; arth from the known period and distance of the Moon. 3il;s iv0lp:j1jx 7gzsq p3b(   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, uwy:ksizecc6 1 ;5b,8tuh7 k onsing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3u7bt8sh 6;oieznky5,w kc: 1c. 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 mzzor50ms y -s7jj 0yv2kcoc20+ to:k fragments (which some space scientists think c 0z2 o j5c c0som0k+t-s2zvky:jom7r yame 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 tal9j ,ias x0l36y fe8+sik;h6 gm +usllqe describes an artificial "planet" in 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 tl ;ha8q6x+luf3e s+6,g9silj m iky0s he Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from ao )euw9*t- f0xo1qvg k 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 sout-qe09k w)fx gv*o1 wing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Ea*y1p;r (cxaxii/2)g fodi(kh rth’s surface will the acceleration of gravity be half what it ( xo ;fk i2/ r)aiygpi1*xch(dis on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal m owzjzp yife 3,* r7o+j;cgs(8ass 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 individuayp( 7 8j+erj3 z;*f ogwozic,sl 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 accelerateh7ig n ilg943 vi:n)v wtsp),ion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the 7ih:ve p g gi)3)4iltw9snv,nmagnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacsl2 wuou3 91iyzxpvx2 ,u9jc :ecraft traveling directly from the Earth u,yj3upx9l9csx2 z: 1uow2vito the Moon experience zero net force because 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 in an elevkw sp 8x; z;4v;f)urwgator, it says your mass is 82 kgvxw puwsf4k )z; ;;rg8. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tub.k6d f d30tvfxiihx --e 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 (revoluti th30 fk-dd-i6 xv.fixons per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical2awwd q i:+w;x 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 eb+kv 5oy/)5/ fmjqnfanet in terms of its radius r, the acceleration due to gravity at i5 m/ofk /ejn+fbv) 5yqts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected ft+yqb g8 fqnyuz 7504mrom the vertical by an angle t5nq gm40+yy u7zfq b8$\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeff h)6vzg mqx mnuc.hz xu. c)y3z6*2dg635ymhyicient of stazy6xcyy3)3*vgh 5m 2 hmud g6 nuz.z)hmcqx6 .tic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so f)l(r 2bmv* ur z:l3aklp ll)i8* km5bjast that objects at the equator wbl)l3 *)k8v*u:l(pmrb l5ijm2lz a krere apparently weightless?    $\times 10^3$s

  Two equal-mass stars main y:wc74xrae*hvbn m) ryo50- etain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of rl:0sx1.jfw 5cm06i 5bfkbwpz adius 235 m. A lamp suspended from the ceiling swings out to an angle oc01 zj bwiwsx5p5k :lbf0 .m6ff 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Ear*upp xift9;x6th. 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 experiencep;ufx 6i*x 9tp 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 an extrr)le;wl s 38vnemely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the spe8nrvsll) ew 3;ed 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 traversepa0j pe 0o7 i;kkbr/8)luar/r s the hill and valley shown in Fig. 5–45. Both the hill and valley 8au bl00e/ 7op ia)rpjk kr;/rhave 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?) 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 S*9ti , (hvtp8-mrxlfj ystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits,i t8phrxm(f-*ljvt9, 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 (NEARnms:7b -;x w49 8el v+fein5eynaxzm0), after traveling 2.1 billion km, is meant to orbit the astv zam0 :ynse47+wmnebelx- ix 85n; f9eroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite innzqw4*v 4ygs: need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the wn*yvqsg 4:4zEarth), 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)9 b5vm e xq8a42cbbx3z What is its mean distance from t3x5v4c2b8 mxazq 9 ebbhe 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 vall 0d6y.j7ajo aue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make rea ayja6 .7d0ljosonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-4vyxvsk tegtv3 pk*s )k,y+a8 *4x3m1 y6) at a distance of about 30,000 light-years from the centk kkp**y3ty8g,s4 1xs yx+v evmvt)3 aer $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the co x:)7prc a4z(lg: cpnsrners 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 the bottom side of the acxpr lp7n sg::)4z(c square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kyknn9l+i fjl-9 z7eq5a vhb)0g 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 theckx2)vxh0fd 0bc n-z+ tip of the 1.5-cm-long sweep second hand on-c )bh2vfz00 x nck+dx your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wepgy3vc1nsz+u t9 iuki c*:+t 4ight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50*vcptcsti+43 g :u9kizy+1u n 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 newcgi7c-r4ig1g.h 2 qvt*e ctv( highway is designed so that a car traveling ce-4t1 (chivq vig2.7 rtgg*cat 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 carud +3 m/mwp0lgs 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 agai/g 3+m p0lwmdunst 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.$\approx$    $\times 10^2$