Sometimes people say that watvi.wk7 5 zb:gk4cni esjz8s ),ln/1srer is removed from clothes in a spin dryer by centrifugal force throwing the water outwn8 kb )5i nrszwsks17l.g4iv,jec/z :ard. What is wrong with this statement?

Will the acceleration of a car be the same when the car trai hh241j, tddgei,1 h4m6 twgivels around a sharp curve at a constant 60 km/h as when it travels around a gentle w2i ,h im 141egg,d46hhdtjitcurve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the5a,brl t xl0i *q)4xdj 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 of a *, 5)dxjxl tqb0ria l4hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wh.glzsn+-rrhp c.2 ;1o cfbbbh d,dg) (ich of these forces provides the centripetal. corfs,nhr +d.bldp )bzggb-12h(c ; acceleration of the child?

A bucket of water can be whirled b4izhcl.l0qcuq w(5j:2pce8 in a vertical circle without the water spilling out, even at the top of the circle when 42cehwczpq58 c l(0 j.lb:iqu the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at l/ ci(6wj(;i a ul:bb7ubnqg/oeast three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they pw(ub6 ilj;/u coqagnb :/(b i7roduce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. dqa.+3 oeer,te 5a4j g5–31. 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 3rjegoa5d +q . eeat,4he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curst1)y3k .y 5 edcd:yfnisfx1kn;xb/0 ve at high speed?

Why do airplanes bank when they turn? How wrs7wpd8nw 63l o82ynn 7 hrj0uould you compute the banking angle given its78os r 03wd7n8 ny26prhj wnlu speed and radius of the turn?

A girl is whirling a ball on a string around her head in a ho e(if*tmdq5ev4uf8 (w rizontal 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 ywvu(f e(e id*q 4ft8m5ard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so,2u-)vi2;i, jfog tzz l how large a force? Consider-g i z;z2)tvi o2j,ful an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whi:p7p jfh.tn/,fs uu1at it is, in what ways would the Moon’s orbit be dif. jtf/uhs pu 7,:1ipfnferent?

Which pulls harder gravitationally, thqxgu v+gk sc4c4 he.:(e Earth on the Moon, or the Moon on the Earth? Which accelerates morqhusccg+e4v( gk .:4xe?

The Sun's gravitational pull on the Earth is much larger t -x wcvw auo5594np5dm0ess-than the Moon's. Yet the Moon's is mainly responsible for the tide5 -09 umxw4pv 5t5-aseo sncwds. 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 two effectdg7wx lz)tl7 +s are at work? Do they +tdx7gz7lwl ) oppose each other?

The gravitational force on the Moon due to the Earth is only 19r8cmm bzf3tdo ww+3 about half the force on the Moon due to the Sun.31rtzmomw89w3 cb+f d Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sl1n:xae s o y*ai1;n8mun larger or smaller than the centri 1 m 8lx*;nniaeoys:1apetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eas pp4zrr.tq(d*x.s 3d ahl 5m)ct or (b) toward the west? Consider the Earth’s rotation direction*s 3drd5c zql)4m h.ppaxrt(..

When will your apparent weight be the greatest, as measured by a scale nnji)in)ypa63alv /- in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speedly6)3a)pi n-ivan/nj ? 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 adversely8 t +(d5bwselr knfs+5 affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindric5t(s8+r 5nkw ds bfe+lal shell that rotates, with the astronauts walking on the inside surface (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 w2frbrhc *x ,l6hyt7 s8eightlessness” between srlr,h *cb68tfxy 72sh teps.

The Earth moves faster in its orbit around the Sun in January than in July. Is t of(*3wodp.r xqf;db- ph6-j pal94 eihe Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of -jwoqo 4fb9 (dl3.rx;-i6edpp ph fa*the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hav rf-;z k9iblw*,fv al)e a moon. Explain how this discovery enabled an estimate of Pluto’s mb;kal9)v , -f wrizl*fass.

  The Sun's gravitational pull on the7n5f1r7 el w3ak s3 my+jlk7fe 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 3kkf 7rw5js n3 fa+7me7l1lye 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 198l49b p -oxhg.6sbj5 wn0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbi 6itk,)9x qgnhfqz8rbsn1- .ot around the Sun, and the net foxb )9r18kngqih6os.-qt ,zf n rce exerted 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 as it rotate0bv -rn9v n.cxrj j1t1s uniformly in a horizontalcvjv nj0b t. n1x9-1rr circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit s, hu8s9y*nn9 .ehfqa400 km from the Earth's surface, and circles the Earth about once everyq*9s. h, fynehu8n 9sa 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of co +8or0pak)uid1-b o flay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute)ob+a)fk 0 uid1 r-po8o if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniern0 -fzy*el sf3ha+.npy5 6 bform rate in a vertical circle of radius 7 +6fz0e3l* nh-sabyr nep.5y f2.0 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 which a 1050-kg car can round a turn of radius 76st3).h csalb7 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this a)c.6bhls3ts result independent of the mass of the car?   

  How large must the coefficient of static fricttn4uikq t:zgu837ihf r * re:,ion be between the tires and the road if a car is to round a level cutrqit::f,z * 8gh4 3ruekui7 nrve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet g:rtmi u4fnlb8 4t9 1l9(hsej fighter pilots is designed to rotate a trainee in a horizontal circ ntmh g94r4tije1llf us9 :b8(le 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 from the d;6- hjc h843 ofgtrfaaxis of a rotating turntable of variable speed.-h j a tf4h;g6ocd3rf8 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 turntable?   

  At what minimum speed must a roller coaster be traveling when up2/3e6 d0/br knykn-svkw 9uotside down at the top of b/o-nkw9dusrk 63nv2tk e/0 y 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 (includi 3x ktr7ys:v3ang the driver) crosses the rounded top of a hil v:xr33ksy7 atl (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-di4 )yk1 d3 r,qhwd vdp12aqf(fpameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poi2yp d)w(dvqhr31 k1fp a4 qdf,nt?    rpm

  A bucket of mass 2.00 kg is whirled in a verticj* ;d g(rtwt0nal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is w dr;n(gj0tt* 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 cmlxxbs 7 5sq(h u;par3x9 van-, from the axis ouxba 5a xn, v;s7 l3(phqs-r9xf rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrical0j 9ce5 e3kei 39iapwlly walled "room." (See Fig. 5-3l95pi 3e w ke03a9eijc5.)
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 rotahqlso ;y 9fy)x1,7jcm ted in a circle on a frictionless air-hockey tabletop, and is held in thiy1m fc)j97s , ;qoxylhs orbit by a light cord 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 time, by not ignoring the weight of the b xd3pfg9zpgr 3*b.imf4aa/ , fall which revolves on a string 0.600 m lon,g.fzf39 f prpd3i 4bg/xa am*g. 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 perfectlygg f3 i3cs,ek* banked for 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 masses ic3 n3nwf(:u j$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving ve b5*hq z,:kitw4ee b89s7q.mf av wv7crtically 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 of tor+ afjem )bve24;h.z he net force exerted on the careb;.fj2m4zoa rhv e+) (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 o*-hu9yxit4k9lkmatfot 1/z -(jfl 3 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the aj/ 9k ft h* 9lo3ly1kmf(oz4utx-it- 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 2xz)qf t.h5qb5 / o9:;tn*kq h(cyr76 haximed.90 m . At a particular instant, its acceleh)f: q yrqtxo5/ h nitc;z 9k5bh6x.m*e7(qadration 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 12,8jb5;v - o0o5kg8qduwu00 km (2 Earth radii) above the Earth’s surface if its mass is 1b- v g;5 o0u5wojqd8ku350 kg.   

  At the surface of a certain planet, thef*l.k0on0w9 ;uoy;ypn t 9nyy gravitational acceleration g has a magnitudo op u*ly;n;n.yf9w y00 nky9te of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius(h9lp)aow+ rz6(hddz.d *ulke2uoo) is 1.7r2oz.)6ud (hw 9+hkulealp o )(*o dzd4 $\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 the same 2pzo th 7qw9d-mass. What is the accelerat2wo7thq dz9p- ion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ea,0:gkqbu q6 7 ugrqc9ldf(e9h rth, but the same radius. What is :996qrlk qf(qeg7dhu u,0gcbg near its surface?   

  Two objects attract eaup /ahn-x*u2ji a (t2tch 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 g , the ahu c8tz g11o,6zchq l,cceleration of gravity, at (a) 3200 m61z8q hl1g,cht,u czo    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s o 1a)s:q+) znui/lzkhcenter to a point outside the Earth where thegravitational acz1 ksz/ni uol ):q+)ahceleration 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 mvm* 1klks;li,ass of our Sun packed into a sphere about 10 kl;kl ism,kv *1m in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avp(:y,rz wyl:ec :ycp4erage star like our Sun but is now :pyrc4 e(wp lzy :cy,:in the last stage of 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 wfa 7 bn43zakl+hy astronauts feel weightless while orbiting in the space shuttle. Your friends res4lbazn 7kaf3+ pond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of qs6vxoi f)z96 a square of side 0.60 m. Calculate the magnitude and direction xzqo) 6is6vf9of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of cdts**mcajdzn 3q 9,c+31yhs the Sun. Calculate the total force on the Earth due to Venu*a,3+1dyczj s d cm9hq ct3sn*s, 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 Mar h5p fz,ehc6:u/juk )ts is 0.38 of what it is on Earth, and th/t6j f:h5 h,cpu )zkueat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun lbm+4+b8f krcg6q 5z q+g(hneusing 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, Exa+ 8 lb6grh +mncgqe(4k+f5 zqbmple 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular org8y.3x ,h 8/on fatazrbit about the Earth at azx3ot n88/,ryg f.h aa height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbiv dhj1(+txg wi6-p -vut 650 km above the Earth. How fast must the shuttle be moving (relativeitdxj 6vw+(1 uv-hg-p to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if 9buc q/)zqg9i occupants are to experience simulated gravq9z9/gc uq b)iity 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 satelf )-/y7ba vtf)l yzu0mlite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earthv- f/ty)ly abfz70m) u” 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 satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from7fpgr (ipz1wx 48 *kvk the top of Mt. Everest to be placed in a circular orbit around the gk7v4 r* 1zkfwpi 8(pxEarth?   

  During an Apollo lunar landing mission, the command(fh0b7)w;ln 5b6 jn vv u/-xw zpffp1l module continued to orbit the Moon at an altitudewn5b fwjp/vb(z7vf1 ) nllh;p- 06xfu of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chutwtp1qi f/u(fw7l/ g/nks of ice that orbit the planet. The inneg7 f(wipt//1t /lqwfur 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 once every 15e;u5byz5ao 7p vx)v1g.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the ybuao 5)xe17zv5g;v ptop, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the 92zulgu-avn8p g3;gucenter of the Ea329vuglna; ugp g zu8-rth's Moon 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 v,tpvrs o b/.;equal mass. They are observed to be separated by 360 r obs;p,tv/.v 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 an elevatoi 3a made4d:i02*b; jz4:vgrybhk fq/r that mdai32fdm y0jei g; b 4qa4/*bv::zhrkoves
(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. Tmraoaj.w-403 v idcepsr 7ig48g6l4v he cord can withstand a tension of 220 N an3cr l4v60ia 48jogwige asprm4d 7v-.d breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite or4ue.x 1 b*se fh6mrf9 po8ch5ebits very near the surface of a planet with period T , the density (mass/volume) of th85emhu* s6e9rxef1.f4p chbo e 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 of the Moon (27.4 d) to determine theq8c zynk8qw3pteu/r 6rt+)2 y 9cm,ebc)mp6 o period of an artificial satellite orbiting very near the Earth’s s6mp krmzo9t 3t u )ny+c)8 bc2e r,/qeypw8q6curface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits thjujfd ga5l )2qo6y1 f-e Sun like the planets. Its period is 410 d. What is its mean distance from t udlfqf jgyjo -5a)261he Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.3u;o/lexn2-mprv: 7 y,yjm en 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 c erp /756erazghu7z/ oomes 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. eer5gzuz/7 a/6 ohr7p 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 about the center of the G1i3h od jc+z5tmlz x37alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 largest w)zo5jq)p9qomoons of Jupiter (those discovered by Galileopw) )9o 5jzqoq 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 from the known period and distance of k7fat9cd 9s +ho+d9jo the Moon. s9+j9dcodt fa7 k+ o9h   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Keor,.m;0a ejbnwn2 cp,pler’s third law. Use the distance of Io and the p, j2nro,0 neabpcm w;.eriods 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 many fragments (which s7jjvexnn4 bp9f; v /2/vf2j ks mei6)iome space scientists think ca j )i2vv6s p7meefvj2b9/;nj n4/kxfime 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 tale describes an artificial "plane63o :l-3e( i)i3 devrvuvzq tqt" in the form of a band completely encirclint(i u:3e-v)3qoe d6z lrvv qi3g a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig,akbk*vs j*4 g. 5–41). If his a,a*b 4kjv*kgs rms 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 long.   

  How far above the Earth’s surface will the acceleration t nii7u,mofi+be9gubet7l 8, xv f6-/ of gravity be half what it is on the surfac,+il/ mo6ib,euv- 7x7t ie gutffbn98e?    $\times 10^6$

  On an ice rink, two skaters of equam qeav 66 sob.4eqz6c6l mass grab hands and spin in a mutual circle once every 2.5 s. Ifa q4mbs6cze6o6 e6 vq. we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity at9b .xoyq+l.ml the equator is slightly less than it would be.+ll o9x bqy.m 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 directly from the Eawdr1hp89) sgf cej 9)irth to the Moon experience zero net force because the Earth)g ps dw9 cer8)19jihf and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bdjxnuba6: 3)4kyn 9hjbt1l tkika;03 athroom scale in an elevator, it says 1aa k)n: lu nj3kt4d03yk6 i9bt;jxhb your mass 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 rotate about il32)va m v2nalcvou,9pf9 m* np lst4:ts center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal,2l octlu)49 2f*9pvann a3lm p:mv sv 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 vertical lvk k5cg3r-m 2aul k, (pkitf61oop (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 radius r, the a.i+jjjcq, g *i9kl3qfllg 1 q7cceleration due to j kj9qqf,l.7*li 31+ gqic jlggravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflect4k(e5a;* qyr-5bkmpt az9r pted from the vertical by an angle teapt;5 p* m a5rqzkk4(rby-9 $\theta$ 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 thwvf2xj7/wqe* e coefficient of static friction is 0.30 (wet pavement), at what range of sf 27x vq/jww*epeeds can a car safely handle the curve?

  How long would a day be if the Earth 98wdj7ym o yp*were rotating so fast that objects at the equator were appa7*mw8ojp ydy 9rently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di,+t;qu b+mytdjncq: /8 nh(kastance 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 radius 235 m. Al 6s5*v3 fmp4v,lqhxz lamp suspended from the ceilv53zqm4 v*fslpl hx 6,ing swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiver2cxza rd+7*0dlxl-s6 iuue- m: mo/ r as the Earth. Thus, it has been claimed that a person would be crushecza os 2/er+dx0-m:l- m6x ir*du rlu7d 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 tn+x hx-7 -wev,lyxep/ he presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no /,+y nplxx-ve exw7h-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 cor32xp)h9u5ia t - cdrrq9q)cb nstant speed 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 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)a9duci-2hc)q )35rqr9pxr tb How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioni x qcpga;um 25ss 5pf0tuqj;,/ng System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangu 0;suf5/j,utq pg5x;sc2qp malation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “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 traveling 2.1 billion km, iq0jgw ws) jj2,fgyy5 juys 9)3s meant to orbit the asteroid Eros 5,w0w g))jjs 3jjuy ysq 9gf2yat 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 shuttlehp*vnhlv49;5cq ib 9l pursuing a satellite 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 ich5hv 499lp*lb vq; nbehind 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 hasj27hue)h* q*lt5:bmwwry ts3 a period of 3000 years. (a) What is its mean distance from the Se uy:hbqt*7wt5 lsh3j*2r)wmun?   
(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 tnogu ys+33avm;+l9oz8wmn au d2w:r 2o be if you could actually "feel" yourself gravitationally attracted twozym+ou agnwn;8l3 :3rd22a smu+ v9o someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ujd ), 5 dwf2a+t7mdhhof the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years 7, d+ hwudd)mt5jfa2hfrom 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 square 0.50 m on kf;go zqv7vgb -(ui98each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of th 9iob(gq;fg -7ukv8vze bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5 fc jl+p5i)zfqn+s 1h6500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-v/o wc(ylm7r6cm-long sweep second hand on your wris(/6 rym7wvcol t watch?    $\times 10^{-4}$

  While fishing, you get bored and start to shb o,r3 (g;dvcwing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes h 3(,gvr;obcd 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 ca63-ol 2wqlh-/eaxb k er traveling a a6 eloe2-3 lwh-qbk/xt 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 nencjn .3g 994fvsqoo- ygotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does 9 -y4f9go3 jsnq .ncvonot 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.$\approx$    $\times 10^2$