Sometimes people say that water is removed from cloth/fvsoh,(v6q)3se.vn n:kwf 5 ohqk + ees in a spin dryer by centrifugal force throwing the water outwardv nkqfwesv3no +.f sekh( ,)q/5ohv6: . What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a .j3.arh22 sl v 4tmgkeo q++gdsharp curve at a constant 60 km/h as when it trajsa+ 4m2t3de q+r.ov2 h.kgglvels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed ap:jjr(tn-g;u +zc n 1p5u-wuvlong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at: 1+u(jpw-5putugz;vnr n- j c 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 riyug t2 hn;5a8iding a horse on a merry-go-round. Which of these forces provides the centripetal accnagu i ;5yt8h2eleration of the child?

A bucket of water can be whirlf,a4z.zv (l3wr: 7 rh cr*sxnked in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside downkcr.3z,v 7sa*xf w rl :zh(r4n. Explain.

How many “accelerators” do you have in youro dowtm08u1f dre( 7: zlsow3, car? There are at least three controls in the car which can be used to cause the car to accelruwooto83 dmfwld0,e s 1:( 7zerate. What are they? What accelerations do they produce?

A child on a sled comes flying ov xnhbsm4i2q7i ; ety/ t,kc,z-er the crest of a small 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 dsmzxihkti,e2b7 t ;4-, c yqn/ecrease using Newton’s second law.

Why do bicycle riders lean inward when roundingjpx2pkh*f(+2fvw +42khra m r a curve at high speed?

Why do airplanes bank when they turn? How would y;0g3 8 oby(ze:lj1c )hopp eu 1xuawq+ou compute the banking angle givbe810;cy( lq1p+ eh: ojao u)u3pg xwzen its speed and radius of the turn?

A girl is whirling a ball ov oc z:nbh7.8vn a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of thenvc .ho7z:bv8 string?

Does an apple exert a gravitatic(ucq(4(l 0 bpmnm:om onal force on the Earth? If so, how large a force? (l mqcbo0p ((mcu 4m:nConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit jzrv3 1zj9dw0y09ia m be different3 z1 d0z9mj ar0viyjw9?

Which pulls harder gravitationally, the Earth on the 8n(cj8 k79ylizhkp zo4(uz4i Moon, or the Moon on the Earth? Whoj zzpi4 c9iuk( y hk(8z78n4lich accelerates more?

The Sun's gravitational pull on the Earth is 4 ws+ vu3wb0ikj bi kd/q*4be2much 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 the4 bqbb0+ k/3jdie4iw2svwuk * Earth to the other.]

Will an object weigh more at the equator or at the poles? ge/ au5w1(bqi;ndf0 lWhat two effects are at work? Do the;adi/f0be( l nqu5w g1y oppose each other?

The gravitational force on the Moon due to the Earth is onlygyivd8g evgi/rup 9t-okihf41- 0;2a *df:fm about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the fg g y2fduoa8-*hk9gm:i/-0vf tpv r;ide 41iEarth?

Is the centripetal a(xkk92gktq8 q cceleration of Mars in its orbit around the Sun larger or smalle kk 9kx(g28qqtr than the centripetal acceleration of the Earth?

Would it require less speed to launc,u3;u d4 j asp iyp+:mnkdr3+vh a satellite (a) toward the east or (b) toward the west? Con :v,4syu k+m painprujd;+3d 3sider the Earth’s rotation direction.

When will your apparent weight be the greatest, as : x *i)d9nw iwzl em/,ohpcn3:measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upwainwx/9pwo*)m:cih: d3nz ,l erd, (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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer sp0v t 1+hf(hw s(+1ft;gfk fwktace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spacest gf tk(t ;vw1(ff+kh0+w1h sfhip 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 “7q 0xg cabvg(mw+i 1o2free fall” or “apparent weightlessness” between ax1( 7+qmcbw ogig2v0steps.

The Earth moves faster in its orbit around the Sun in January than in Julyxa. m -wammcvuq,bd /o,(:: ny. Is the Earth closer to the Sun in January, or i:y,qwvn, -mxd. comu(am/ba:n 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 ulzd/m 7g)fmtwq8r 5(dntil it was discovered to have a moon. Explain how this discovery enabled an estimate of Plud8r f/5wdgl zt (m7)mqto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t k2v-q-ogy her8o( vi.he 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 chygh(qo82vi --ko e.r vild 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 9it pz 2vai/0r )xk:xv1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 tezg,6dp;tc 3 qhe Earth in its orbit around the Sun, and the net force exereg;c3zpt,dq 6ted 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 disc823m*qqam.yhx:6 zl t gecsr.us as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of zmtcyhr.q* gql: m es38x62. athe discus.   

  Suppose the space shuttle is in orbit 400 km j,i. dh if6 s(nf:y8vntrdfh8 ,g */agfrom the Earth's surface, and circles the y.n/(hddjsi6gf ,vi *afgh rf :n 8,8tEarth 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 surface. $\approx$    g

  What is the magnitude of the accelerati *v)hmi2cowh9r+ 6b u hnkt2*/szs)g zon of a speck of clay on the edge of a pomb9h**c t2)h2/hg)znksoi r us 6zw+ vtter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved atsmhwc.h,n14 v3js2nyqvh* m. (y1a a y a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed im nj. vh1a1c. hqys,*wa(y43y2 smnvhs 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 10yteh82ic8phby6ky m+ tb9:v4 50-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 independent of the mass of the86b i ky: 294hhmt+tpyceby8v car?   

  How large must the coefficient tl0.k07c/iyiut+ 2n v3p pam tof static friction be between the tires and the road if a car is to round a level /+t3k.u20cnp0 pvl7iyttm iacurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rot 4 o evlg0sfwg*h 9t)kw2u5y6eate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own w * kug se 295wg0v64)hlyeotwfeight, 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 2x j m7juqrk :. 0)oxyaxf5vb88 u2ilvaxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until )2ji2u.uvy q7 bv:8xo a8j0f l5xrxmka 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 upside down bnb-dl+ zd xa46tzd -4z0dms u:g*c- eat the top o-a0-dbedc4 +:ntldb*d gzmz4- u xzs6f 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 drive- :hdczms2e , yju:ofr5 a61mor) crosses the rounded top of a hil ed,yuf6or 2zm:a1 msj:c5 -ohl (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 r -pl-xr vrq .dqn8jx bo lrh:;8:2z4ya 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlrnlzr4x 8b r :dhx28oqvp;. yr-:q -jless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertig;t tj72y 2e+;xbs vfzcal circle of radius 1.10 m. At the lowest point of its motion the tensiot ;2jytsebx+2fvz g;7n 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 wo2an u4;ean4efls1 k 17td)n centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accna2nunde1k7; et 4ol 4w1) faseleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c4xedb+gdwfj 009iu m5ylindrically walled "roomd00 95xju 4gi+fe dbwm." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on 16n is3t1igb+ft0arl a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangl1 bt gnf+60tsai1 i3rling 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;po-fb)oa/7vyqq :l v, by not ignoring the weight of the ball which revolves on a string fy;- ovv p/baq7) o:ql0.600 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 88wl sjh-l56*rz( cxyz ) m is perfectly 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 /ouyu*0 reyfs3r, ur/ $ 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 evasivq jh1bvif:t/t+ncn u5 )-deo o8i)wnjd*4wf 3e 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 of the net force exe kmgm fc1+e*ua 0k,c-krted on tu agm,ckc 1k-k+me*f0 he car (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, going fros 2/.1cgzle+:1ipriy r 2ws vim 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, assg/1wp rss2 eiy +1v.zli:ric 2uming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radineoc3zs9jyr 0;(-yq a us 2.90 m . At a particular instant, its accelye;qzs n0-oary9 j 3(ceration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (hv-8zowodvi1p 131e o2 Earth radii) above the Earth’s surface if-hw8 eoid zovp13o1v1 its mass is 1350 kg.   

  At the surface of a certain planet, the gra xkhx0 upk :-hsnu*r rf)1i-h tc/pt/6vitational acceleration g has a magnitude o f *-h/0:nu hp/ )-xsxutrkkhtp6 ci1rf 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 r 2uisk/9 se*j:mg aa6cadius is 1.74 gs:ik 2eaj 6m*/asu9c$\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 Ea60wn737:xmb)nk za* xzi gzry rth, but has the same mass. What is the aw b0mxnx73:a)*nzgz7z6r ik y cceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samlg9e-/ q6)hir qtg8ule radius. What is g near its suu rit8hqql /- eggl69)rface?   

  Two objects attract each other wukvb ) ugbi-,zg31,s w, pk;rgravitationally 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 acceleratiow *7s. sdtdqa9n of gravity, at (a) 3200 m .9st*w sdadq 7   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s l i8p-(e: p;2xlg hkekcenter to a point outside the Earth where thegravitational acceleration due to the Ea e2lx( ;:-e kl8pgkihprth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timet oux( q,w.ksl.3jg m4s the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface grav. j,x.qtgm3solukw4(ity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average st s+x3gyqqu/ )rar like our Sun but is now in the last stage of its evolution, is usyxq3 qrg+)/the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting /c+jmpc-jg w* in the space shuttle. Your friends respond that they thought gravity was / c-cgpj*j+wm 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 a square of sjfsa8* zsbt r31npl2xj 77a/mide 0.60 m. Calculate the mabaj2s17 t7prs*x 8/mazl 3jn fgnitude and direction 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 lqyprp9-.o-uq mg hzg1l1*o 1on the same side of the Sun. Calculate the total force on theq9.-o1p -r*umyql z1hp l1ggo 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 acceleratioq26 cpcnh 1ue((tin9wc7mp z0n of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine th(0w e9m i6 czcp7nht pnqcu21(e mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using y9lg 9y+1avuj1 s6yyy the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer t9yyys1a 9y + vjy1ulg6o that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of 6eqb m vy1okdsf 57w7*amev14ubx3 (g a satellite moving in a stable circular orbit about the E as167ewk5mx 4yq *mv7 (b3b ugf1eodvarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitez ja6mq .gq:.mro7kl6 into a circular orbit 650 km above the Earth. How fast must the sh mr. :7zmjl6ao.qg 6qkuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrica6n/wb6d jzr 9mqkx,a ki t51o1l spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, ao5ni 1qa w,1kz9 kdbrj6t /mx6nd give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit thebr:yt;9) 0 d)gibr rux)+r gvs 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 depenrr) t9+ :ivsg)br0ux ;)bgrydd on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to n geg0g uzv)53be launched from the top of Mt. Everest to be placed in a cir)g5 nzg30 gevucular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to 4qe8)fce-m;w3h9qtiwy4g th orbit the Moon at an altitude of about 100 km. How long did it take to go c4 f9y3thi h;weqmg4q e)8-tw around the Moon once?    s

  The rings of Saturn are composed of c u7/v6mhv7gh qu:,fsbi*3er bhunks of ice that orbit the planet. The inner radius of the rings is 73,00b6 sf*3iv :bguer hu/7h7qv, m0 $\mathrm{~km}$ , 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 ev o0 5;gb-g6tyg,htt9j xll*qf ery 15.5 s (see Fig. 5–9). What is thettl lf,t*jh g-y b9qg; ox60g5 ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg ast,u b;n1q 1xgqaronaut 4200 km from the center of the Earthxn;11qau ,qb g'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 e( a flb93,keujqual mass. They are observed to be separated by 360 a3j ub ,9fkl(emillion 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 woma:3cvauepfzh4r* :c5 pn in an elevator that hpzp 4 *c:3:urea fv5cmoves
(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 hangs47i s o(geux)j from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelera(g4jue xo)7is tes. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periortj*tbp.t9inqe: ) 5bd T , the density (mass/volume) of the pr5jb .iep t* qb:9ntt)lanet 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 determio35t )i1vroh 80qayvjw:qnnw6b y y5/ne the period of an artificial s aw oy:b oyq3ywt8 hqi/n5 v0)j156rvnatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the yiahmff h3)k9w072 feSun like the planets. Its period is 410 d. What is its mean distance from t9f0f2wi7ef hh )am3kyhe Sun?    $\times 10^{11}$

  Neptune is an average d hrpx /1:jyvf.istance 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 i xrg9un3o8el:a) zg6 every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.] o u:ae ixzg9)8rl g6n3   $\times 10^6$

  Our Sun rotates about the center of the Galaxy vz maig1-(;m-8kcv8p 7txhd o $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, n4)r6t/bk 1 yrfqyyds l7c *2kand mean distance for the four largest moons of Jupiter (those discovertyc s2d6qk14 r/knyy7* blrf) ed 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 fromy ;rr2)tv7 bfvkq.fkb7p(xc* the known period and distance of the Moon. .ky 27(f*q vk;ftbcv)rpxr b7   $\times 10^{24}$

  Determine the mean distance from Jupiter for ucy bd) 4qkko z5yn81.s-d uie*sxp 19each of Jupiter’s moons, using Kepler’s third law. Use the disuek .1idky1sp) d *b59qux o4zyn8-cstance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentdv0 aawr6qpvx87 4v b:s (which some space scientists think came from a planet that once orbited the Sun but was destroy4w:86xv db0arapqv7 v ed).
(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 vnl ;t/gm(zw- the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sunl(n/ mtzwg- ;v 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 *5mmcjy 2/c5i4 6fn .vpftuoww c pu-;hanging vine (Fig. 5–41). If cvn./jiut oycf mc- 5m5up46w2;wf*phis 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 long.   

  How far above the Earth’s surface will the accewi6( yoxc*-)*hghawr ls fp61ma 5wt ,leration of gravity be half what it w*wwxp,)1 tio h6 rh(gsaa-fml y6c5 *is on the surface?    $\times 10^6$

  On an ice rink, two skaters of eq-e) + llwezto+7wtpnx00 fg4 zual mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses arewt n 0o+l0 4pwz+7f-gze)xtle 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 ip6w hx23)qg3)xjun uat the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of gh3q uu63gn2)w i )xjxp is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fro,n+w(e r 0bg24hcclhjm the Earth +c(ngelbr0wjc24h,h to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 653g3vvnf,qh ,n kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. Whatn,3 fg3,qvvhn is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationp2 b 0zju0tge) consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be fel u20z 0gbj)ptet?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43(qlqd0d9*izb wnd5w: ).
(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 accelfblm2(buouzdl .+3- f eration due to gravity at its sm(-ffl b23 bouz l.u+durface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vp2x o*223n pj5nllbezertical by an ao b n2*jx5llzp2epn23 ngle $\theta$ 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 a8+i *bj86 2-c5ixgsvtxlm bu the coefficient of static friction is 0.30 (wet pavement), at what range of speedsb 568jxs*i g tm-c x82b+avliu can a car safely handle the curve?

  How long would a day bd ;toyf0w3 eu jp raad*a*c,d,jnt/:t/+tm+ce if the Earth were rotating so fast that objects at the equator were 3cdn:,*dtaw+; 0pttre+, / audojyf/ ajt m*c apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a coql4*wq ( fzsab+ka6o3 vk yk((nstant 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 spees7mo7we5u + xud rounds a curve of radius 235 m. A lamp suspended from the ceiling uwu ex+o m5s77swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times a1mm,clt 0s):u(sjkp5f ;s dovs massive as the Earth. Thus, it has been claimed that a person would be crushed by the5(tds0 o v)js,fmc :ks;m pul1 force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the 1 se g;gdak7f+,dp2vp presence of an extremely massive core in the distang g p;,+kv2d7fpd1s aet galaxy M87, so dense 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 *,rfaokuv 9.d1r 7 udbspeed 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 do9*d.u1 arf k7vb uo,dr the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gro;tzix owjs-ixa (l e99zy3-b/up of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 na- bi-t(w9j/izzxa93s;lyx oeutical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rbtnsin 0uynpl4;.qmm0 bb/v u(+ k01yendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Ero nv mb(sbbuy; /t0.iln 4 y0u0nm+kq1ps is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of9 ew.veg*+y yd repair. You are in a circular orbit of the same radius as the sategy +ewdey9*v. llite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Whaty ocmb1a( ozx2ac3vx*l53bk, is its mean distance from the Suny3(k bca1*,25xz clambo ovx 3?   
(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 8v.xeh xp ,:pw G would need to be if you could actually "feel" yourself gravitationally attractedp,:p8x.x vwe h to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centh1q: k ex qkd6e da5s2m-.gy6ler of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years 5klqheek qxd621dga-m6y .: sfrom 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 locatq2 wa cutw- 7zxvz92t;ed at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravita zww9t7a-qvz cxu2t ;2tional force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orb:4a: d 2rm ,dgn;wxrlp(z2a lrits 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 thioxf)8 /* l kldvm9cns4xdz 28e tip of the 1.5-cm-long sweep second hand on your wriis 2dl 8xod*k9/nvz)4c xfm8lst watch?    $\times 10^{-4}$

  While fishing, you get bx tk9-c7j37i//oh7vz sjyc s no ;9qlwored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cz;-hj/oc93k7 l qysi9snv/t7x jo7 cwircle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travel6i)lk ,u3hgs4luq3 3h fo i4zjing at s guo 3k)lulih46q34siz 3,hfjpeed $ 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 p 5 pfw(vv:er )fur4tfvh,x 63Acela, 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 h5v6x:vf)4fv( f,rew3 t rpu pcentripetal 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.$\approx$    $\times 10^2$