Sometimes people say thd isd( krh8hcl(,ca 5+at water is removed from clothes in a spin dryer by centrifugal force throwisd(rca8, ld5(k+h ching the water outward. What is wrong with this statement?

Will the acceleratione1;4 p sl+4oo, qbxwbl of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroundb+;4ep1x bls4q o,wlo a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed ala- xzkdf b2z,/w kf1.eong a hilly road. 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 oedz2,z-1k . wax/f fbkf a hill?

Describe all the forces acting on a child riding a honjs87mr. na odjjtc kf 5jx 27b8:z.0wrse on a merry-go-round. Which j78nj.s:f0x8 zj.two2b7ck md5 a rnjof these forces provides the centripetal acceleration of the child?

A bucket of water can be whirlefkpv/)4/qv aqrmi n (-d in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upsidrvaqif4) (mvqk-//npe down. Explain.

How many “accelerators” do you have in your car? There are at least three cob-czzi5 oqa(4ntrols in the car which can be used to cause the car to accelerate. What are they? What accelezqc5b4oia- (z rations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. w-5 -r:yrjea wd,1ea 9:iq*-bk .gwqnob 1kgj 5–31. His sled does not 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. Ex1 . jiq:kj naebkdy- o-a9r wr*b,5gqeg1 :ww-plain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a b3wsicgm0+u d1:ul s3 curve at high speed?

Why do airplanes bank when they turn? How would you ,c ojw;4d*0c z b:ihtccompute the banking angle given its speed and radtbdji4wcz ,c ;hc*0o: ius of the turn?

A girl is whirling a ball on a string around her head in a hork-*/+k wtjd h ps2e4p 9tivhd5izontal plane. She wants to let go at precisely the right time so that vks k9*i -pt/ h p4hw2de5jd+tthe ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force ofxt *w3kq-m ks7a a8d:n the Earth? If so, how large a force? Consid:*8k wdtma 7kq3fsa-x er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were8r)x 3cuw l8qoz, v.i5 e5jsid double what it is, in what ways would the Moon’s orbit be differenivixqc wolrz)8 5u53j,de 8. st?

Which pulls harder gravitationally, the Earth o:wrs 9k1 gh03uwo7jym*l*bo cn the Moon, or the Moon on the Earth? y*3mo ho 9bcusw710 wrkjg: l*Which accelerates more?

The Sun's gravitational pull on the Earth is u1si qy +*.yj5puf8(vm bjv,dmuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatiovs1y q i f5mj.byd(*,p+ uju8vnal pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the polc)pevs0o9 92cl66;ssmsg nohc c8(r f es? What two effects are at wo82c09o ;ec s(lvcnh) fm6orc ps9gs6srk? Do they oppose each other?

The gravitational force on the Moon due to :t ez9u.e:jw/ n* 1f*hexpdxtthe Earth is only about half the force on the Mn9wttjdh.:ee1p xef/* z:xu*oon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acce4lmmsro+)b:box2e7r 55pvk u leration of Mars in its orbit around the Sun larger or smaller than the cee2rk 4 l:ovs5r b75bx om+u)pmntripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a1 dp:m 8rh5ao hv8gh kge14b0b) toward the east or (b) toward hgm8hd11p0 5hr48 k:bbvoage the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale iv sy qrz5/0oav :umfns-gj:39n 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 be the least? When would it bejs5uv /zqf ryon g-3a0vm9: s: the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long perj6-v1 *xwv )nnmr;fvb) wth( zpqwd33iods 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 )6wv3vj1 phf)*3bwnvdqn w (; tr-xzmsurface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlesikvxs5 /vy7pa5b0 ;itsness” betweens 5ipvy0ab/kt 57v xi; steps.

The Earth moves faster in its orbit around the Sun in 9xvn1aq7s:pg:2d1spm g; dr yJanuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt qprsv7xa9 dg;s p:dm2 1g: n1yof the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was d2 spfkq/ px-c(iscovered to have a moon. Explain how this discovery enabled an estimate of qps -/(pkf2 cxPluto’s mass.

  The Sun's gravitational pull on the Earth is much7:90 da+rzsxtdsyvcj/ra0 2 q tfdy39 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 speaq0 sd : sydc+9rfvyd30r29t7 j/xtzaed 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 travelinp6s4;rwy,/ khvzg+gw g 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 1cdv5 e7n0yfvacceleration of the Earth in its orbit around the Sun, and the net force exerted on the E 1fnv70ye5c vdarth. 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 as it rotates cquf s0. 8t/eiuniformly in a horizontal circle (at arm’s length) of ut/80qe .s icfradius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ciexdvwi(p(0fm2 h7(v ;4rni e qrcles the Earth about once every 90ir x;nwf v7e4hq (v((2ip0de m 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 accelerati v p/yls00arfq;rt 90ion of a speck of clay on the edge of a potter’s wheel turningr 0;iy v0lrfqt9p/a0s at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a tmt f8m -hv bc2-z:kd/string is revolved at a uniform rate in a vertical circle of radiu-v/kfdm2z8 bhc:-t t ms 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 speed with whiciys/hu4b4 rka *;)s.l yl9 rpeh a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of strl 4uar.yie;*py b/l)sh94 skatic 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 tt8qaf q(9l4m t( ovgex0:ds ;between the tires and the road if a car is to round a level curve of radius 85 m at ag84qmtotfvs(l;q x:9( d0at e speed of 95km/h ?   

  A device for training astron;obblt ek2+ ( 6zeyk;dauts 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 trl kbt;6eyd;+k(o 2 zebainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rot6kifivv61kb n77jfyu.-b7e s ating 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.. s j17vb6u-fik7ey6 vi7nk fb What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must /7 iv9 fo-qngcl5k1g ,q. eneaa roller coaster be traveling when upside down at the too/e1cg,fl-a9enq i5g7 k .qvn p 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) crosses the lirl cl2+9 d82xl63sb06el ,8ayaikya n3mdcrounded top of a3dell b3n 82l6i2 0,xslmlc aa6dck ry8+9aiy 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 wou v2o( oalbo * s+ky7f5v/-ie exahgd10ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost pofaxydl o 27av 0*igbkv +se/-1 oeo(5hint?    rpm

  A bucket of mass 2.00 kg is wtu tfqt0,; ,,j j giu/md-pv;ehirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope suppor,g/ jdi;,-eq vt;0p,t umu jtfting 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 t4cu ye,4y a9eip8 ue;fhe axis of rotation is to experiee uf;9ye4 4 c8,ueaipynce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a t; wj q5tk8bs;tex +/vcarnival, people are rotated in a cylindrically walled "row5q ; et+s/b kt8vjt;xom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in u1ke0 lc .r1 b8n*cpiev,:d xca circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dange1d :uxrnlc0,kbc8.e1i v *cp ling 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,ozkqe7 v04t3 g by not ignoring the weight of the ball which revolves on ae0 7 v4kqz3got 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 r hf9k*(faa-mq dwhz1;z*i ss 0krw- r, kw-2c 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 v2ha*v6ozz 5z $ 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 o 1/y+app6 kveby 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 and cf 84df,,zj*4 llzrq3dv g6l7s5 fkrk:y/oo n dentripetal components of the net force exerted on the car (by the grs,fko,f6j 3odg5zdvk4r*l rz:lndy/q8l4 f7 ound) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, x 0zwb3l pt;6.wmzj )egoing 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 the road to provide this acceleration with no slipping or skidwb.xlp m z0jz63)t ;ewding? $\approx$   

  A particle revolves i; bwzb(f *av1 fou20ksn a horizontal circle of radius 2.90 m . At a particular instant,w2z(uf1; *sfv bbok0a its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radiu0.yrkwazt-o i ;urn//5 5 nkfi) zy;r5u0.tw5n/kf k-no/aui rabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gr. p eia,nd3hov*re4 )ravitational acceleration g has a magnitude ofea)v*r 3o.ipe4hn, rd 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 to gravity on the Moon.ld,tch2w 0qzg 4uf4f4 The Moon's radius is 1.7l044 h2zqc,fdwt 4f gu4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet zq3jr/be 3ury;,rt6sm i3orn /r 3p.vhas a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gra,3mjqiyr v63u/e3p tzr n/ r s3;.rrbovity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,;rws0c q: e*( fogbahp9 dm,u0 but the same radius. What is g near fpo;9h,rm wues0 (0adq*gc:bits surface?   

  Two objects attract eacnc8 *rwzoj d-7i0k7+pivx b2ch other gravitationally 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 gp(j qeq-/x i)p , the acceleration of gravity, at (a) 3200 m ip-pqx(e ) j/q   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ear2g net4i,y plg86h ;yv1m shr9th where thegravitational accelerat yn9m84 y;g,hpvshg le62 tri1ion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere e7 ebt;+h:l/myjra/ t about 10 kyt/: ; tb hmjre+7ea/lm in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwar /n: wkssz;r5jf star, which once was an average star like our Sun but is now in the last stage of nzjskw s5r/ :;its evolution, is the 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 we(ojq*9q:wiuv 5txqw* ightless 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 xuq( 5*:*w 9qtjvo qwithe acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are9 .1kkrr z4j +a4cwchdtdysp : hq8);n located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other th.k41tj dkh9: pd8c;r4)cqnra h+ sywzree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred ye ci 11y;k wx +thccte;,x;j *rds7o:uxars most of the planets line up 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 line (Fig. 5-38). The ;c k *;ur1xie;dhs+yx1tj:7,tw x ccomasses 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 l, :3gqi600k hdcyt1enp nyu+Mars is 0.38 of what it is on Earth, and that Mars’ rade+1yy3ghic: tn ql0d ,6n uk0pius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the eu;8q; dn.; 6do- 9et4 wtwkkm q-ptnha/pc2 qperiod of the Earth and its disq4 cp;-;.-aehwtp n u m8dow;e2k6 k/tn9dtqqtance 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 circular orbit about)c.cr1*n/bsfbspxkhi (*.vv the Earth at a height of 3600fb.)s/ sr*ckc.xipvn (h 1*bv km.    $\times 10^3$

  The space shuttle re+p0io9fmhpe- 6u wzelz9,9. xalho: sleases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) lm9eu,.azpi:+-9xp96z0 fhowl s hoewhen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship+7o1 xz-edz6*gdx 7 lxbeo6me rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.) dz66+xx *eedeo -zxg1l7m7bo   

  Determine the time it takes for a satellite to orbit the Ear, vvi, po(p4qvth 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 compaip 4,ov( q,vvpred to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satelt*thi)jc/ e, jlite have to be launched from the top of Mt. Eveh*ec i,tjtj )/rest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t2rgqt-ek6u9 vu a7n m6he Moon at an altitude of about 100 km. How long did it take to go around the Moontgumn62 e9q 67kr-u va once?    s

  The rings of Saturn are composed of chunks of ice tha4+65 sv ewpjqit orbit the planet. The inner radius of the rings is 73,000 p5q+6si evj4w $\mathrm{~km}$ , 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 rotates4f6 1e)c:in0ic vwu6s br7a bl once every 15.5 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 b71alvfnr4si )ub066c: ecib wottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of/v n:unk uk,8v the Earth's Moon in a space veuu v:/kn, kv8nhicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star w r/)tx+clz26 hf 0soisystem consists of two stars of equal mass. They are obseslro6c)2+0 tzw xhi/f rved to be separated by 360 million 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 read for the weight of a 55-kg woman in 2(y0r1 uk.l,2pamt6cggd kso an elevator that mo(6 m.ptklgy k2 ac2ugdor1s,0ves
(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 thss n,ml*p-a(r ()wsyme ceiling of an elevator. The cord can withstand a tension of 220 N a n(a*,wy(s)lsrmms -p nd breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite hcq wc761alzhnd/9 xv8vd7o 4orbits very near the surface of a planet with period T , the density (mass/volume) of the planet is h/cwqv46xvn1lhd9z7 7cdo8a $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine e.uya;is6 tg+ ii7bd )the period of an artificial satellite orbiting very near the Earth’s surfaceesd)u tb +i ig67.ia;y.    s

  The asteroid Icarus, though only a few hundred meters across, orbits t xz mv.0 .0c8vdm y4xidy9usc6he Sun like the planetssid vdx cy y0 4z6vmu8cx.09.m. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average di vyyq4( w.aul7stance 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 *+lkg/z-v) j/ 5(ermcehrpvb 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: r/b5plmz -vgv*jheekcr)+ (/The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Geezw9 d g5bx2xz-a;7 xalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fet g sdol./,m2m,dpgxlds0j 8 4rm9:your largest moons of Jupiter (those discovere :ej0ry mdlm 9dssgo.t, lm2g/x4pd8,d 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 E p3q +6wb k.,c3ny:nzuogor) parth from the known period and distance of the Moon. bngrn o6 ,.uz:yo3wcpk3+) pq   $\times 10^{24}$

  Determine the mean distance from Jutkn jgq8diot*qxv*x8j4b 7 2kjn: 7z/piter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the8d/8t*k42bzinqq*jgvo t x k7nj: x7j periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of v;qe 9xnsyu96many fragments (which some space scientists think came from a planet y 6sneuvqx;99that 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 the form of 2psg(4 yloef:r- ipx9a 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 offy29 -rp(i eox p4:gls 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 froncut5 w-p)bz 7m a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vinbu7pwt-z) nc 5e, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration l-ay /x89bno)b.cxt8z adzm 5 of gravity be half what it is on the m -bta5 8d xl/z9)zcx8.anboy surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and2p3p-kp;-xfx c ote*v 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 on v*-3ptxcpx- 2o ekp;fe another?    $\times 10^2$

  Because the Earth rotates once per day, the appso65 no7 8;qb6mn /n9up8yir9bxbwsqryn6 d 0arent acceleration of gravity at the equator is9sr 8b 98nn60 o buny/x76mn r6wq5bsioqp y;d slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling di) 4/2jgl zd2 .sbqlv7efd/be;fr wb x4rectly from the Earth /4rwbe.xbll)s;def gbjd4q27 fz/ v2 to 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 sca3qm2 (jh1tncr le in an elevator, it says your mass is 82 kg. What isqc3rj m(h n21t the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circula(:9uxpzoj/6ts o n4m) icww(ir tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circz6ou p(iowcn )t(ijwxs4 :/9 mle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in p*ge* ix/ 9z4o uh1sera 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 its r7qr qdyd /g j57l.v )qrhx6a,aadius r, the acceleration due) hyd 5gl q6ax7 qrjrv./,7qad to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from djg368hciez rh,8yy 5 the vertical by an ag8h8cyr, 5ied yz3hj 6ngle $\theta$ 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 kc0xk5q08iogr8*vuu l c9.eq speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the x8k5vc 8lg0u0ir*9q. u c eoqkcurve?

  How long would a day be if the Earth were rotatingfu ec or:d48d, so fast that objects at the equator were d ,8coe:fd4u rapparently weightless?    $\times 10^3$s

  Two equal-mass stars ma0(2c7c negfi ij1rjb 0intain 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 constanre ,ohdk.pjik+6. 5 svt speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings vk+p i6drk.s, h5.eoj out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as th k7ua9+0umunf-2sqi se Earth. Thus, it has been claimed that a person would be s7sa f+q 92umunkui- 0crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of af c ,f 2e ugsd:he/jw.nqyi1.2n extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by 1i ed2 qhf:/ u.nfsc,w.2j ygemeasuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valle .f3 zi,eqwvu 6-9yrczy 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?) Explain. (b) Where would the driver feel heaviesv q,cyr6.93iu-fze zwt? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS)u+o +otj -,1q upjgm+m 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, allowing continuous navigout1+-ummjo,j+q p+ gational “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 Rendezvousuglkj8 *sk;(:he g gk* (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of agugeslkgh k;*kj 8: *(bout 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 ud8pq9k 2(7uk4)q xl kqr/k dgthe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the gpkq7qxk (k9dr4d/ l2q) u8kusatellite (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 d,ww2d6q4 zkr histance from the Sun?,r4w k2d h6wzq   
(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 actually "feel" o8 agcmw5oaj+-a *5 ksyourself gravitationally attracted to someone near you. Make reasaoc m+g -5o5kaj*aws8onable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.. y,ktc/2+ l: pdpkjia 5-46) at a distance of about 30,000 light-years from2td, p/akjcp.y:li +k the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squ md62d .lfrh mtv7;8rrare 0.50 m on each side. Find the magnitude and directi tr8 rr72m6vdhdf ;l.mon 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 Earthn vua8a:wx014lu r58oe5y us f $ \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 si) dh;a jd*4unweep second hand on your wrist waidd4*n)h ua;j tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinw)x/;jzgj+x7g1+qk ry vj gg/ker weight around in a circle below you on a 0.25-m piece of fishing 1/jggjyg) x7kg qr+zvjwx+/ ;line. The weight makes a complete 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 traveb, i ny58ow1qvling at 8w qyo51v nbi,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 negotkkw ;agj7nw +(.8 fx;..k jxl:o hjzouiating curves.xj jl;ao.j;n8: kh 7ufo.zkwxkg .+w( The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$