Sometimes people say that water is removed from clothes in a spin dryer rv:0gif q( stq)yu7c7 by centrifugal force throwing the wateg q(y7cqu7 vtrf) si:0r outward. What is wrong with this statement?

Will the acceleration of a car be the sam+, deqaj9sfj1e when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spse1 ,+f9d jjaqeed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does t s +o8jyiy3 m9ss7aj.vhe car exert the greatest and l mvs.7i soay3yj8j+9seast 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 hill?

Describe all the forces acting on a child riding y-)*b ,w08qol xejxxja horse on a merry-go-round. Which of)bxjox* j 8 -weyxql0, these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in3l k+q(9tc3b ospacw6 a vertical circle without the water spilling out ocs+w(93ab p6qk3ct l, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your ca9 ,/rk:k+xaki:2med-s mnz hi r? There are at least three controls in the ca-k : ehin/iaxs, mk92z+r:dmk r which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of,dufw plq+g t; 1 kx:*a4yuhb0 a small hill, as shown in Fig. 5–31. His sled does not leave the gro+twaqxud4u* l 1k: gf bh,py0;und (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders leansbo0 fxf 6 mczih4d2oa7 ew*09 inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would d3tvit/040twf jsn v) you compute the banking angle given its speed and radius of the turnv i0w34 /st)fjtnvdt 0?

A girl is whirling a ball on a stri )3ntrdc ,u:rhm*m l;lng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should shed3c :;rhr)*n l,u lmmt let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hocpf4j h:ahj/w-hm m,; p; vd3zw large a force? C:mdcw,4 fhzm3hv-p ;;ja h j/ponsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, inyeu6pg)q0aoi n q6q.tf;;p,eq r :ap 5 what ways would the Moon’s orbit be differenq ;ap:typ q0qp.fng u),e6;iqao56ret?

Which pulls harder gravitationally, the 0*rx ;gxf)lf ht/ 0ezo 7ga2jyEarth on the Moon, or the Moon on the Earth? Which accelerattex f ; h0z7yg xjr*/f20)algoes more?

The Sun's gravitational pull on the Earth is much la,)a8tslhx1(x1uk q 0vy3 ng1lk odqt6rger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from61x0hl)ksk q g1ut qlon ta1,(8xv3yd one side of the Earth to the other.]

Will an object weigh more at the equat xdh ;mdm)lq7 :,4yvflor or at the poles? What two effects are at work? Do they oppose each odlml7,f ; )4hxqvymd:ther?

The gravitational force on the Moon due to the Earth is on+yf olvii/wqe z,(m19ly about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eai +zq9l,fe1(/ iyv mworth?

Is the centripetal acceleration of Mars in its orbit around,mp 0jh ct;7ius1gb 0k p)5hpv the Sun larger or smaller than the centripetal acceleration of the Eartht1g0hj ;v,smppcp7)0 u hb 5ki?

Would it require less shs/a bqp51 el:peed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direl bsa:/1eqp5 hction.

When will your apparent weight be the greatp ,(bht,d i7chest, 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 when i(bh,pdt 7,chyou are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affyn4 znpd)9nkd 9+j.nlected by weightlessness. One way to simulate gr+n dky9lj4 pdnn9).zn avity 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 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”l 59sx wfo 0ysp1n6y-d1p -q4rlghsi7 or “apparent weightlessness” between steps.qhf9-l-rx6l s5osywpnyg 0141ip s7d

The Earth moves faster in its orbit around the Sun in January than in Ju9r,tj v6y.ushly. Is the Earth 6.hjrt9 s,vuycloser to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered 7l9)bzhtw p bs. /,n kh6vzi;rto have a moon. Explain how this discovery enabled an estnsz lpv)i hw7,b zt9/6 hbk.;rimate of Pluto’s mass.

  The Sun's gravitational pull on the E pbkoi/erhsgdk6w1axi.4ji9y6em ); )6 ,mp w arth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explainkaier4ks6bpi m6ow he1j6x/ 9 i)dmw g;.y,p). [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 1980e9 /dptva.*u6xv3 whv yk/op/y hu ebb85yi// $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 qcdi;0qx7 g6f or-*st Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts qtx0*gfi ; 76roqscd- 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 a mnv:7hb/y5st s it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.v t:b sn75my/h90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fromteo3a,p t/jz : the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surfac3pottz/ a ,:eje. $\approx$    g

  What is the magnitude of the acceleration o2 9kuo1v0)0iuztcktx f a speck of clay on the edge of a potter’s wheel turning at 45 rpmiz90kv tu0ko1ct x2u) (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate io+duz-at7; v qn a vertical circle of radiu;z7outq+d- av s 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 spee4 dvfvn3f )i:rd with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indeivfnr 3v: )4fdpendent of the mass of the car?   

  How large must the coefficient kb-8hjw h7 ji:of static friction be between the tires and the road if a car is to round a level curve of radius 85 m-7w hjhi:8jbk at a speed of 95km/h ?   

  A device for training astronauts and jet fighter piv, -d0pba q,bva:biy ,lots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trai,i bd yva-v:0 bp,abq,nee 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 rotating turntable of va mha f(aruog,ir8 *o8,riable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm isofaao* 8ri,r8,(mh g u 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 co,d 3u h0au4pevaster be traveling when upside down at the top ofd au,3 hvu04pe 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 rounded7y;h;a;ezdp*,hyo6 . rxi3vibe by sei3 ja41 top of aii1e;xriybj*6;3o7 sd4b,za3.vy;he ya h e p 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 would a 15-m-diameter Fer x),vemf4j)p dris wheel need to make for the f,e)x d)4pmjv passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 yhff1gqtu-k;*udzcg)c 7 hs /-) (fznkg is whirled in a vertical circle of radius 1.10 m. At thq;czz7gf(dshgy 1-t-u)nfh f*c/)k u e lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a ce9a:wf seppqa v /g9g.ino/;u4 ntrifuge rotate if a particle 9.00 cm from the axis of rotation is p/ei9 ansqwp;u/4of9av :.g gto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrical70 xjaf1 +1or/ erlrydly walled "room." (See Fig. 5-a d71e jr 0+xfor/ryl135.)
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 :-rk qm8g(w9aaaxfy;c7t9par p (p0o a frictionless air-hockey tabletop, and w;: taayx qpf rp (a97cagm8-9(0okpr is held in this 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 t7lq u lce;m*hfhh l4(4he weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude o mh7 e;llf h4(4lcuhq*f $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 1w6*ex vt,obobanked 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 , rvh)j+4 ix0(poi kl,p(jpec$ 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 vertically at 3rm/m3 v94qu qs10 $\mathrm{~m} / \mathrm{s}$ . 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 componentsqwmrc(,wvn -5ejg) j7 of the net force exerted on the ca 7,nm(jej)gc vwqw-5rr (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 the pit area, gmwn1u -jl t0fn4* i(pasto8 7ioing 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 acceleran4tom -paiji87*fn(tsl 1w 0ution. 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 c/k d)vru,ts64tvt/ kq ircle of radius 2.90 m . At a particular instant, i/kru k)v 6st,4qvd/ttts 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 hr3oz /-wmr z3a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.-3m/wo3hz rzr   

  At the surface of a certai6 * gpafzw1ca 2ftfzsjxja;2y q.:.:mn planet, the gravitational acceleration g has a magnitudefp yf j1.awsagcta 6z mzjx;.q:f:22* 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 is 1:k bw ta x.h-,h(xm(eg.74 h-e.xtxhk ,wa(bmg :( $\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 s yzl 8ad1et wx91.0gjhas the same mass. What is the acceleration due to gravity near itsexl z.d 1awty sj19g08 surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. ihdfo 4 w3vxcn6 po((hs1yx:5 What (13wxvon4 f5 pcyo6xshid (:his g near its surface?   

  Two objects attract each other gravitatio18x;v53l0r c e swhnlmnally 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 valkv,l6 *i2vvpoue of g , the acceleration of gravity, at (a) 3200 m6klv,2 vvo* pi    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eaup:py+m-u d e)rth where thegravitue)-yp+pu m :dational 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 / kctynyu9jt6 t: 4i1ypacked into a sphere about 10 km in radius. uyj:9 y 6k4/tci yn1ttEstimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star.q.16zxvvqwn /2p q zjkpiq+: , which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our M.wik zq :q/1nv z6.2j pq+qxvpoon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbdynx;*evs6 o t7n7q n6iting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the accnqxnnvyods7 67e; t6*eleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locatedaj )u*1wuxp mz q2n.f( at the corners of a square of side 0.60 m. Calculate the magnitude and directxp.nu mq u(*)zw f2j1aion 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 planets line up on t8 nj xdeq3.u5 7k1ivoghe same side of the Sun. Calculejd no3x .5ug 1ikqv78ate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Meu5:5z1kw xi* gtjah2ars is 0.38 of what itkj:g awx52ethi1 *zu5 is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known v7yr015slq f98pqy5cx (p 2ozt dfeqssys,3z)alue for the period of the Earth and eq1dzy pr( osf8cq z,5 t)9pxy3ss0 7qylf5 s2its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a sl 1 8xo11kwcbfxh(l 2de6j: j0 4 uhmrcd/u)grtable circular orbit about the Earth at a height of 3600 km.juh g(6cm od81r1) l: 12urkxfw hx/ 4ecdb0lj    $\times 10^3$

  The space shuttle releas :e1,0 mjc1pq5fyeabl es a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the 0q,5ejma:yc1e blf p1release occurs?    $\times 10^3$

  At what rate must a crf 4 p6nl;9t xml xvw/6q 7gkmgym,:.pylindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter7k/vx46pp;m9:lm w l6 ygg.xft, mrnq 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 satellitoy k5.r at.jw0k; q pp2eiqc.-e 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 p.y q0wkace ik-p ..25or;jtqof the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fr(oa1vss7 im 9yom the top of Mt. Everesv1s97 oim( ayst to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued 4n4xc2wc) jd9bcdo7ybzy kt-lv0. 6gsd 72bg to orbit the Moon at an altitude of about 100 km. How long did it take to go arounddkvyxy9g7 nb )bb2tw c.62ld 4j-o4c 7sgcz0d the Moon once?    s

  The rings of Saturn arejbz euiss. 8s/nu)fh.37n 3p b composed of chunks of ice that orbit the planet. The inner radius of the rings iz f.u7ubnhs8s.pe/3 j3i nbs)s 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 15.5 s (see Fig. b9q)q/qia i 2 nfce;a3 g9b.nv54ynyc5–9). What is the ratio of a person’s apparent weight to her real weight b;y )fvg5eq/y29a q cb4nni.c3 naiq9 (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 fvn(nqlce+ :bipq o 9 7qe2i15km from the center of the Earth's Moon in a space vehicle (a) moving at constan:97nelv q2ef+pbo ci 1qq(i5 nt velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal m/hs r+x2 gio+cass. They are observed to be separated by 360 million km and take 5.7 Ear/isc 2h+r x+goth 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 elevator tha)9bf /d3;oslbdct mw,t moves 3b 9/)l wdof;d,ctsbm
(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 el vljakm46bc+ zyyu+9 )evator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude +c9yzj l+6 )mbu4yv kaand direction)? a =   

Show that if a satellite orbits very near the surface of a planet wiz uj22ai34, jviwxvr6 xr 20mvth period T , the density (mass/volume) of the planet is 4u,r2z xrv 3imj 0ix2va6 j2vw $\rho=m / V=3 \pi / G T^{2}$ .
(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 the p) ;kao g*vsp1period of an artificial satellite orbitisa 1gvp o*pk);ng very near the Earth’s surface.    s

  The asteroid Icarus, thoj-3roi54gk1+8kzu cjf:y z t nugh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance jkgck3:j1z4-yfz un i85tor+from the Sun?    $\times 10^{11}$

  Neptune is an average distance k3i*wqi8rxqg8 /9oq:5tr( mxq onu +nof 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 everyr v x(g/xnc+8y 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 plancx8 vx+/y(g nret’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 abou0n/ s jnr,x7qat 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 largest moons zv rtsv(3w65 ry;g9 ymw5p4 ynof Jupiter (those discovered rwn9 vvyrw5y4 y5 s6(m t3z;gpby 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 thep o,:s3pb v2go 2tnio/nhe6;s-qqwwd)w0 aj0 Earth from the known period and distance of the Moon. wnp) 2wo;dqns 3hg -i:p6w 0/tbveo a2 sq,o0j   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupfek)(z+0dv ffn.zk xu :jsf7,iter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to .0dun ef f7 f)xvkzf:(skz+j ,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 fnzkz7bk+iwbxcuq 9,iz 9- 0m:ragments (which some space scientists think came from kx7n:z0, bu b+iz ciwk99 mqz-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 describeu0m7y8 mkpw s+7(vzxl1abp.3ep . exjs an artificial "planet" in the form of a band completely encircling a0u exysmmppz jv.lw(+7k17.8 p3e abx 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 crosy.7+ nd+z9f7xc5fp nhwuv og-s a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vinn cyfnf+79xvd 5h.uw7zpo + -ge is 5.5 m long.   

  How far above the Earth’s surface willg6sj,b5/n9 *zt cgwqx.agd9 w the acceleration of gravity be half what it i x /gs5j9. zqtad9wcn*,gbg6ws on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands andztb(qgtez75.i7inao + 7ob 4r 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 one anothegb(btti 7 rqez7+n .4oi7az5 or?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravit)v eod;,gl8 ufy at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of;eo ldf8u,v)g g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly 0cud-u8g f5gj from the Earth to the Moon experience zefgcgudu 8-j05 ro net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bl 4yb. g)hmg9kut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accele)bm.gykl4 g9hration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatekq1 v/a j40qgh about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal aqk/qg hvj 140to 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 loop (Fig. 5ll4zp n:j*d:o 5e tz*m–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 ind3wt.pl t0g ce/1s3yt terms of its radius r, the acceleration due dt1ce/3l0t.3s ywgtpto gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b75j0.pu5lep7 oqh ibfk -rbd8y an ankhbjipeud p7.70lr -b5qfo 8 5gle $\theta$ 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 fool4u70f xmwku3 ;.oyjr a design speed of If the coefficient of statik. l7 3; yfoou4ujmw0xc friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that o8ex . ubeyoqz g- xc+(qk;.p/xbjects at the equator were apparentlyqpgkx exu-.c(./zqx 8b;oye + weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of,v35 3k2.jca rpwecd j(gcas 6 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 atcr 5g 2(h /okjvnuwm1er+ew/ )7wdq*m a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5rj*5u q)/kwo+2/ r dcneh(egm 1wwmv7$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 gdz8+0*s b6 adws y7sy3.p mh blfe,v:f*7rbgtimes 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. Calculate the number p ,v lf86wa*zbb d73br7.emghsss gy0d +f*:y 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 ;jk ju 1n5+vn;ti5 5pusm-eie Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it coul vm j5 e;u;inej1pu+kns i55-td be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hil/3vacv+pirmq v00 ph*l 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. a0 i*vmv3/h0pcv +rqp(c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioni;zrqi/wxz:6 /5 aosysng System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position :ws iqzxyz/ ra6 ;5o/sof 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 Rendeziq a ipg-(co84vous (NEAR), after traveling 2.1 billion km, is meant to orbit gap4(-8ci qoithe asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the sp 4q-foxffyg:uw lr8*9ace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earthuf9l-ow qffr 4x*g:8y ), 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 out.zlwh*ju z, y5(ye w6 thfm41jn2i5f 3000 years. (a) What is its mean distance from the Sun? wht4yhm f,t2z(jlyun5j5 *ei16uwz .   
(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 s9 -ip ysr59ee;s.typbe if you could actually "feel" yourself gravitationally attracted9y-; p5s syr9ee.tpsi to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy0 qzk4cb4llg6 (Fig. 5-46) at a distance of about 30,000 light-years fro 6cbz l40qg4klm 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 each2)vd *ab1z t2dfo)xw s side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint ofb)oza2 wtv d1d2f )sx* the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg oregquwvh t64blr-5bk1w2s, 5 zbits 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-cm-long h8 mwhad 9d 49)cxn2wkqgc91k sweep second han24k9 qw ckg)chd1 wdxn hm998ad on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cir4pmk 9 wmtgom x85av2.cle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the anx495m wtm 2amg.kovp8gle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwaz+omb o8awss7 1v5 3zxy is designed so that a car traveling at speezaxz5o7m 38 1w+sbs ovd $ 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 k u/zi66ipa 9cAcela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus fe6 9pz ka/cii6ueling 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.$\approx$    $\times 10^2$