Sometimes people say that watd xxj2t-5fsy l:1ksxgz( nw0/* r2uvter is removed from clothes in a spin dryer by centrifugal force throwing the water outward. Whxt x x *fgzk(2y:50t sl/dr1n2-swjuv at is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a shn(7nm6a tj) m o- 1 r,5a:dtbkbs dlraitv96z9arp curve at a constant 60 km/h as when it travels around a gentle curveina(9dzat65lan9k o1)rt ,6vbr : ms7d -mbjt at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exu(/ ednj,gyg ;01 bgebert 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 level1 (u 0ybggb gen,dej;/ stretch near the bottom of a hill?

Describe all the forces acting on a h.c+r2rn v7tgchild riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerv +rhn.7g2rtc ation of the child?

A bucket of water can be whirled in a vert,b ny92xmui u*ym3yc neor51)ical circle without the water spilling out, even at the top of to bn crx*y ,)i u9u3nmy15ey2mhe circle when the bucket is upside down. Explain.

How many “accelerators” do you 3slc 1b itxeesz95 mah*r*is x-646dt d:aq x(have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they c-iddr (*3xx96xae h5mltqtzsas 61e4 ib s* :produce?

A child on a sled comes flying over the crest of a sb.9c-yq(uxx2eavjy(r bb o sc9 2 :r3ymall hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease u9-b3v (y9(j2r2 yc qbos ux: xabryc.esing Newton’s second law.

Why do bicycle riders lean inwardelb-b6/j1c a+fz 6gaz when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bank1m4pv2mxk2u+n me w +ping angle given its speed and 2x+wmmnkpvme412+ p u radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plgk(/*w pac,;w-5/jrmb*f7g h eugn v h5rv.mfane. She wants to let go at precisely the right time so *g g b;w(j-fm/f/ hrwrmg5ch.vekp 7,au 5*vnthat the 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 on the wcwf7o+wq,f, , xokx( Earth? If so, how large a force? Consider an (oc kqww,,,fwf 7x+oxapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways+3bzw((+ijxp hsg (r s8n,mqg would the Moon’s orbit be din ( +ix,(swb 8 j3sq(phg+gzrmfferent?

Which pulls harder gravitationally, t(/you j0bmk:s he Earth on the Moon, or the Moon on the Earth? Which accele:m/ s0kuo b(yjrates more?

The Sun's gravitational pull on the Earth is much larger than the Moon+brj l:fx 80eehh,3l h's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conside3h, +fj8el xlbhe0hr :r the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equato9pxre jou4p.r0 r2i1q r or at the poles? What two effects are at work? Do t09jprx1opqr4. u ie2r hey oppose each other?

The gravitational force on the Moon due to the Earth is only about hal-v:5bk2lr:mnv z c5n9z flf o/f the force on the Moon due to the Sun. Why isn’t n rlzcvf/:-v 95 om2fkzb:l5n the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroundh w;:zo6ozwwd62pz86wncue;9 l- fxv the Sun larger or smaller than thlfzow 6uv o w-h;cw;6:n z 82dxp9w6eze centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east mm)ihc:o 8xw0or (b) toward the west? Consider the Earm)woh0m ixc8:th’s rotation direction.

When will your apparent weight be the gre-nz8ft5 7fsel -zp;ryatest, 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 constant speed? In which case would your weight be the least? When would it be the same as ws8pnzf-f 7-ztrl y5e;hen you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ox1 jtx;c2*inb 2 aze,outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simu einc22ta,jbzxo;*x 1lates 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” di7cz gig*pyfbz6)/9or “apparent weightlessness” between ste*i7g zzc 6gb 9p/id)yfps.

The Earth moves faster in its orbit around the Sun kb a mp1(wijbcp/7.i(in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not muci w (cbb(am.i7p kjp1/h 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 wasccok4z r,usu,s mcp d 8-f62,m/ wfz/u not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of zcc,/ ,- mwprzkf ousm8 udfcs64u/,2 Pluto’s mass.

  The Sun's gravitational pull on the Ec25rjku f./vnch6nt5 arth 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 frch.r/cnu6j k 5v t5f2nom the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 8wb0bxvt ua f07e.owrj t31:v$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerat2j6:wfn) uofib cx,3otd -w8 aion of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit : cwa-6f8)jotfw3 noix,ud 2bis 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 exrefsu*e9;8 8 t4y 1,sry mhf9gxh -e/l(npcbgerted on a 2.0-kg discus as it rotates uniformly in a ho4;s r1gh *mny/9g8r l(ex- ct9e8uy e f,phfbsrizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, andlu w g2fxvt4(9 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 , tf4t9 w(2glv xuhe gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the 8ksivi-d /3x 8lte6sy acceleration of a speck of clay on the edge of a potter’s wheel turning a- i6xsv8i83t/dyles kt 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 ratsth3a3z)os9 gf , m6wze in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If itz,6so9z)gs tm3 aw3hf s 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 withvd0y2)hq7 ted which a 1050-kg car can round a turn of radius 77 m on a flq2)vd e7dy0ht at 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 the rg, ro:um k12kv;u/ o.fsorq0zd,ob6s oad if a car is to round a level curve of radius 85 m at a s:rro /,1fb60gz.ku o, v qsudmkoos;2peed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is d a w(qow1)teh3esigned to rotate a trainee in a h)oh3a1qe wt( worizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm+ico0ez*0 jdj from the axis of a rotating turntable of variable speed. When the speed +0e*d0jjzic o 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 coast73(aks2vmue cer be traveling when upside down at the u73(c sae mk2vtop 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 950m b*i .gk1w:du,xov7z3 3oazk kg (including the driver) crosses the rounded top of a hill (3 3g iukd z :oaombk.1z7v,*wxradius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diamet9i4s4xd pbc9x lr 3-ozer Ferris wheel need to make for the passengers to feel “weigxsicr3dzb94xlo4p- 9 htless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Ay va*rm ijz/3*t the lowest point of its motion the tension in the rope supportin3j z* *yr/vmiag 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 s,qwas*w ( z4rn/mb,)xu h:gbcentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience :w(,n,4ua* q gxmssbr /)zwbh an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotaikr7bg 9i1hz*t /k51fl 1: vetxoe)duted in a cylindrically walled "room." (See fbi 5d uh1t lgki/vz1* tre)k9e7 1:xoFig. 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 a circle on a frictionless air-hoca 4smycp91p x1oujpb2)3 ro5ckey tabletop, and is held in this orbit by a light corm4pp3 xyc29ocr11b )ua5jp os d connected 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 t ;sh,h;r/fqn+hcn oe9ime, by not ignoring the weight of the ball which revolvehqo/f cn 9e; rhhn+;,ss 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 fo nt-9 8jer/3h7xlhl mnr a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesidia8:p5 sn,4o bj7hc $ 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 evasivezbrlbj r.rr6g(- *ve/ maneuver 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 and centripetal components 4u ihtm;)9yc k*rtd(hkti -:ehgk) ;n of the net force exerted on the carir)k( ;h;y gt*h n9c:m ki4eht tku)d- (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from th5l oe krs 2mbv0-*i-nne pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleratb2-s*onlv5r i-e0mn kion. 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 horizontal circle of radius 2.90 m . At a particulzyc.a/ag-ld2 m(nt+l ar instant, its acceleration is tlgynd c+l 2m(/-az.a 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 Ear g5j2v0p3rm5;dg a tsyth’s gravity on a spacecraft 12,800 km (2 Earth radii) above thdpym03 55jv2ggast ;re Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, te,j 5qz:e5gm ahe gravitational acceleration g has a magnit5e,amg j5z:eq ude 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 dl p:f(ypf r(jah1p9-due to gravity on the Moon. The Moon's radius is 1.74 rh fp l1p(f-d9pya (j:$\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 4f)k xo,ov,ai of Earth, but has the same mass v4xfk ao,oi,). What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timw,2k2l 7z s(mk lp0ijoes that of Earth, but the same radius. What is g near its surfac w(l 7lk si22mp0zj,koe?   

  Two objects attract each other gravitationally with a force of 2.xm9yd ss 85k(i5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) cd 5/rh,6m)yv qx fmr*3200 m vhmfqm)/d5*r c,6 rxy   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a yj.a*yc j7k0qpoint outside the Earth where thegr 7.y*ky0qjcjaavitational acceleration 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 s 6g9w 4.:ohby)lhi eanphere about 10 km in radius4 hohl96nbya)i .ewg:. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likf*dev2g 6pnly7eky(g a p gf),,+0etqe our Sun but is now in the last stage of its evolution, is the size of our Moon but has tha(*g+fgng0)2typk76fv , ,qd eleypee mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting*.gvv)hp vvh/ in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it vv. v gpv*h)h/isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of s 6(cn7 iiwfy4bide 0.60 m. Calculate the magnitude and dicw6(nf 4 bi7iyrection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the a x4p6cl)rkt0planets line up on the same side of the Sun. Calculate the total force on the Earth due0)x4rl tcpa k6 to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is eadug, jdx0 )ap;t6 -h0.38 of what it is on Earth, and that Mars’ radius is 3400 km, ae0uxj;d p6, t)a-gdhdetermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth: 2)2n3rdkwt9 h wilv/cfrqumz3w2o2 and its distance from 2luw/w:ri 29on 2h3 cqtmw)rdfz32 kvthe 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 circul w*h*/ *gwm+ tftmcu8jar orbit about the Earth at a height of 3j*h+u gwttc*/*m mf8w600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circumfk+bf 3;mmz-lar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Ea+-f f;bkm3mmz rth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaces t0*qxbme/eypv)r 2z(hip rotate if occupants are to experience simulated gravity x 0rez2mpyve/ q(bt)*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.)   

  Determine the time it takes for a satez 0 bgsmwr1ma+3,fq;x llite 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 of the Earth. Does your result depend on the mass of the satel; +zfrw q3x bg0,mmas1lite?    s ~    min

  At what horizontal velocity p8 3kd::kp5jpt kadc13diuw 3would a satellite have to be launched from the top of Mt. Everest to be placed in8: kcd3pt1wk p3jdpuia:5 3dk a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the commwja0f9y;yo 86qr bs.land module continued to orbit the Moon at an altitude of about 100 km. How long did itoqr9 wyly0fb.j8;a s 6 take to go around the Moon once?    s

  The rings of Saturn are composel k b,)i/spckot y+*:n4/f-tsqsz- mvd of chunks of ice that orbit the planet. The inner radius oqt*mfz)oc --:bkt s / y+,/vli4sk pnsf 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 ro r13nt*fed 5t0ngga y(tates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her 0(*g fyn d3g5t 1eratnreal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg )m8+ my5hph lohsv0n6 astronaut 4200 km from the center of the Earth's Moonhm np56v0o+ l h8yhs)m in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of eq1a3kq9 9bd.0xg 7 zg -bjdlulzual mass. They are observeab-.x 079z dbq13ll kuzgj gd9d 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 weiw ra/zbax+v d:g/r3y t g,3os7ght of a 55-kg woman in an elevator thatg7oxg+/ 3,d zt:wbyv3a asrr/ moves
(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 c g2sg7 pdx1v+yord 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 (magdv7y xp2 gs+1gnitude and direction)? a =   

Show that if a satellite orbits very near the surfac4gvt br87zsn 68dit5re of a planet with period T , the density (mass8si bdvrn tg7456z8t r/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period vjpp *g+c0,mg8 nni,y of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near theg,*, p g+jv0 8nypcmin Earth’s surface.    s

  The asteroid Icarus, though only a u t(b,jog;gn*few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distu,* ;ojng( bgtance from the Sun?    $\times 10^{11}$

  Neptune is an average distancevue8pkxzo t: u;/p d-dp):jr3 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 evmtuq b:fq/knb-2h6 wv,n* fw0 ery 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greab,f/hqf tw6uq*bmw:0- 2 kvnntest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abou or+3dd4sxkt(t the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four labgv3 zoeofgnq; 7s xs88uzsvj8dj k9d9*b 6+6 rgest moons o 9fouo88de7 vvbdqn+s6*3kg6s9z ;jzbj xs 8g f Jupiter (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 Earth t.pm5k c 4-mpdfrom the known period and distance of the Moon. mp4c-5m.k pdt   $\times 10^{24}$

  Determine the mean distancebbvx/ 9e,mh1o from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3.he x bm9bvo,/1 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 J)epvl0 svv l93upiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was deslv plvv0) 9e3stroyed).
(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 fnx ) szt8m7s5g8vkxi 8orm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on E z5gxi v88)8nmk7st xsarth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by -o( a5 q/ -tv8pthjy b-npeoafti:d0n9ov.f4 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 swing? His mass is 80 kg, and the vine is 5.5 m y v-nj 0 b o8vpdoti9.oaf:f-p4 t-q5(aeht/nlong.   

  How far above the Earth’s surface wio5x,c/frp9w0o iynd)06 hm ,ghbjp :ill the acceleration of gravity be half what it is o:mo, x 0,6 b)po5ipyw c9ignd0/ hrfhjn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual c s47o:+pae jko kq4x l+yl(bh/1t bxf2ircle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual:ybk/t4fp(s+ obh 17 k eqaloj2 xlx+4 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 accy vu dn2ktjc;3. wr7)eeleration 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 f3r)wun .2dvk7yectj;raction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travfd jp6(r8:ek4 w05boasn cx+ zeling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and o(rx w:5k6 boc+sf4j p zedna08pposite forces?    $\times 10^8$

  You know your mass is 65 fcdgi;iu7p;j5 1gcib/1( ot ukg, but when you stand on a bathroom scale in an elevator, it says your mi1o/u1g7c ui(dc5 ; if tg;pjbass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotaj) 1km;sb yxx( kdo+)wte 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 rotatio+ wkx 1;)dyb)m(sjkxon 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 aiy rcjc ea536)td6r46 zl0*,pd ncb5a wt5zijyrcraft 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 ma+) ot5y( zjv cpfuhe,6ss of a planet in terms of its radius r, the acceleration due to gravity at its surface anuc o6 (j)5f+h ,ytevzpd the gravitational constant G.

A plumb bob (a mass m hanging on cwka 5sg *ahn++yv22 ha string) is deflected from the vertical by an 25y*caha+ v2kw+hngsangle $\theta$ 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+a88gxvq.tz y coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car sx g8aqy t.zv8+afely handle the curve?

  How long would a day be if the Earth were rotating so fast thajj90l5*u tvs))hbwp +tdh nbbf4u1h : t objects at the equator were apparent bj9 hwl u nv*p:t hbd)sb0t)u+h15j4fly weightless?    $\times 10^3$s

  Two equal-mass starsei imz1f(/c :;exrx0o maintain 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 cu6feo:gxu d zk a1471vbww9;uzrve of radius 235 m. A lamp suspended from the ceiling swingwegd1z6oxvukw f 14;7uaz9: bs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tir8*5uk5wa5 u igz 9yoanl,m7 cmes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. C7nu8ou kyza, c5 55i9wra*lgmalculate 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 an extremszk-i9i / qez-ely massive core in the distant galaxy M87, so dense -ie/ zqki9-zs 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 y 3ezvv3v 6/dalpl5h/;g ;rtm as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do thelhdp5 z v/v;r y/;gta6lv33me normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes ybua k4rsn .lr2(nc wt39r8l5a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmaltrkwy(cr bul n5382sr .94nitted 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 “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelingxq17i6 kplrjdpkrel z1 1o60b )6e d-z 2.1 billion km, is meant to orbit the asteroid Eros atxbrd6zpqe e l10 6il61rzkj) 1 o-dp7k 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 sate j(o 7ro2ff4+xa *la2qe ws6ndllite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km b o*qofn62a4fja (+w dx slr2e7ehind 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 ye8smf3c) r 5zyiue5wl9ars. (a) What is its mean distance fro8 zui f)5 3wr9me5ycslm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could aczi8.2)lkx+t m qg b0go+/eoi vtually "feel" yourself gravitationally attracted to someool.2v+egzxtkgiq+ 8omi 0/b) ne near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galax- x ph;vd4d4i yxc2+3ojhcw(qy (Fig. 5-46) at a distance of about 30,000 light-years from the centv cpq +4 d4xc(o-2jwhd3xy ;hier $ \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 locatess a*ip mu31p*d at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at*s 3pam*1 upsi the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits a17wzl y-.4dqfd q1i cthe 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 exp shy,4g- a0kyv/j* 5elc lhxv/erienced by the tip of the 1.5-cm-long sweep second handk * /0y h/v4h5xysj-llevga ,c on your wrist watch?    $\times 10^{-4}$

  While fishing, you gezyodtp+d v/kvztwge3 );.u 9 7t bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight;ztde+pg 3k)d7 w.y zv vt/9uo 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 ne icuzc21 ,+s:upwrwx4 w highway is designed so that a car traveling aui1w2:wc sux zp r4,c+t 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, utilitc0)+z0sr 8/th nuq hlzes tilt of the cars when negotiating curves. The angle of tilt is adjust)hq/n00u slc h+ztr8ted 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.$\approx$    $\times 10^2$