Sometimes people say th +t)f9 b*j6f7uidakt 7hol/a uat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong withdjtthof7 * 7ai )+lu6f9ak/bu this statement?

Will the acceleration of a car be the sameey) fau1/ g4akync4;h when the car travels around a sharp curve at a constant 60 km/h as when it n) fy;ga/chuy44 e1aktravels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wv vjexei;97f*6 a 7bcpd o37sshere does the car exert the greatest and least forces on the road: (a) *;p sfbd x i7677csev39voje aat 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 jq-; ,atv mm5rriding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratio-qarvj;5mt, mn of the child?

A bucket of water can be whirled in a vertical circle w9h;t bod)g u1dithout the water spilling out, even at the top of the circle when the h9b d1t )goud;bucket is upside down. Explain.

How many “accelerators” do you have in your1cj d. b*vxjp ynn+ nmi tq8*ze*f4;+d car? There are at least three controls in the car which can be used to cause the car to acnj i em 14zcpvydx +t;qfj*.n d8+nb**celerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smalq t61qt9ei9f jl hill, as shown in Fig. 5–31. His sled does not leav 9q6 9iqtj1etfe the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward wac);wjp9 (vvxd6;1gx(ma d y ohen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankin* f)ss2)/5ctw5sz nv5yy 7bg n xrcms:g angle given its speed and zn) m2y *wg 7s 5vt/:n 5bsfr)cscsxy5radius of the turn?

A girl is whirling a ball on a sd y13f8 m8ljg :hh2lobdr+:ib9j f7uwtring 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 tjd18u7: h2l:8w+ 9bbglij f oh3dyfr mhe string?

Does an apple exert a gravitational force on the Earth? If so, how large 1x5gj+mtqxe 6rpe(+ ocrl1f-a force? Conef re ljc1p tqr-5omg(x+6 1x+sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in v ,ikfb.p47nt what ways would the Moon’s orbit be di7n k 4tvbi.pf,fferent?

Which pulls harder gravitationallky; l dtv)v4yl7uu 8qp:i,xa 1y, the Earth on the Moon, or the Moon on the Earth? Which a):4dyuk vp8qay xu;7,tvil 1lccelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon7.w8weos,zq5se omra f *me4('s. Yet the Moon's is mainly responsible for war*o7.ozq , ee4sm es8fw(5mthe tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh moreju28/a c4wed1 id. ww ak.:lwb at the equator or at the poles? What two effects are at work? Do they /.jc ea :28wub.wdd14awlw ki oppose each other?

The gravitational force on the Moon due tq g3m*60pwtkgj,/ae e0 k(gal o the Earth is only about half the force on the Mo*/l ae3gw0kg06pge(kjtm ,aqon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or1zb 9lk5 c:lnr: oo4qy smaller than the centripetal acceleration of the Earthko1bl: r n l4cyq9z:o5?

Would it require less speed to launch a satellite (a) tzykjmbwt 8lot.uuwg scc j. -(d6(0 5*oward the east or (b) towayd g(* jct 5.ojsm. wc(6u8tkz-b l0uwrd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as meay;uwywfj88 :(bblr)nv0y abm2 20fxb sured by a scale in a moving elevator: when the elevator (a) accelerates downwarbx0) l2m(8 j;nufbr byba0: ww8y yf2vd, (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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend ln3caq94xv ;w (:;6b/co:st nstwc qob ong periods in outer space could be adversely affected by weightlessness. bs3qoct 4 vsco:;n6(w; bn9wt :x/ qcaOne way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this 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 “sw147e5abe xx y9,p ugfree fall” or “apparent weightlessness” between suypaex xb 5we9,1g 47steps.

The Earth moves faster in its orbit um,iykqh)9gfe5 yaz4q+2 t v5around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit. m f4ky5 +qug 2z9,ahtyiv5)qe]

The mass of Pluto was not knov8cbp nnc s k,k7;rhuvnp47s8 n 40)fewn until it was discovered to have a moon. Explain how7f)su,4b0kcnn n;7vpekps84 h nr vc 8 this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eartzs6y.r rbaq .ei l;cc1 *,guy0h 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 6esg0 bczlcr .yrq*u 1ya.;i, 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 1980 4,s6 e00nbsc/ce ivy i$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratio8skji+k:q k.8xj8 sbwd jq yq)m6:vik;)sy m6n of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's m:s8kiy8ijvqqj)d 86b+jk xkm:sq sw6 . k ;)yorbit 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 rox,yp pmp)) ea.tates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcup, .axe)m)p yplate the speed of the discus.   

  Suppose the space shutt(p8ib:u 2auwt le is in orbit 400 km from 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 Ebu(: wapt28iuarth's surface. $\approx$    g

  What is the magnitude of the accelerata.4rgiz6e fde;; sn)qion of a speck of clay on the edge of a potter’s wheel turning at 4eq)a d;nf;zi4rsg e.65 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolj pp.gf,c yuqvy +.g7+ved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0u ,.pv y7j .+gqp+fycg0 $\mathrm{~m} / \mathrm{s}$ 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 rous-/3* xgndmrux8 wwz(nd a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road iswusx/ m- g*rwn38dz(x 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tir28bfz5),mzamcxmmr at 0 -o/kes and the road if a car is to round a level curve,zr-8)cm/xaoam25 mk0 tfz m b of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to r+ ox4*pdjc*/um4;wlcwp / qvr otate a trainee in arpw4 */l/d w;+4qmv xoju*p cc horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variabjt ivn7,1bln05 -agcj3 io x 9;z)accrle speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm c7 3cxbcjj5tn)ro g 0l1 ; 9ia,-izavnis 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 trh *a5/smv ge4paveling when upside down at the toem5h4 v/as* gpp of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundxqzj4ymzcq: ueo m(.t .q0 :4ved top of a hilz(jqv.z ou:m0 :4qy4e ctxm.q l (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 mi+zu2sb-d h5 lpnute would a 15-m-diameter Ferris wheel need to make for t lz-d +uh2b5pshe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirle 5e,1aotjjs9- p0bti6uu epd.d in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2,-ap 016e5.esiu9jobtu dtp j5.0 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 o)re5+y n)oq h:d8wmv a particle 9.00 cm from the axis of rotation is to experience ano8v qd5yo :+)m)n rhwe acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricalq wfw6m e-(;ssly walled "room." (See Figw6 -qm(s fwes;. 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 al0jr; ism-2ckq b; -zt frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as show tj-;-s2z m0kcr; ibqln 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 p04 eei/ktdm: e9bdw u.1s-nmthe weight of the ball which revolves on a string 0.600 m long. In particula- .mst u:e019mddip4e/b enkwr, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 75cq -,s*)re mpxs vt/*q hqdf+( $\mathrm{~km} / \mathrm{h}$ , 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 w/n:a:ns)xa2 u 7h jgr$ 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 q.-;h+5yuyv2w0r *qbxa p5ljr9 ar n vvertically 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 centrcq3-z 4sr6s-ng r.ofeipetal components of the net force exerted on the car (by the ground) in Example 5-8 when6r-go3 nszesfq.4-rc 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 unif3 t ea:krj(lu7ormly 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 accur(l7 ae:3t kjeleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partiz tb1co7c2ojjz jg/2,cular instant, its acceleration zjoz2c, 7tcj 12 bg/jois 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 -lg8f+ge 0g+jnl4 q khEarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 k j nh+fkgll +eg84-q0gg.   

  At the surface of a certain planet, the zhb* 5r/uwsce 8:weu0 gravitational acceleration g has a magnitude of 1b0e r uc5hs*/u8z w:we2 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 acceledqe cp g dc2bd+4yzec13l/i91ration due to gravity on the Moon. The Moon's radius is 1.74dc dzqcyli+13/cb1ege 4p d29 $\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 hytovyph1qvpzi:ko,. a8b im ;v7509 das the same mass. What is the acp k :1;7qitzm,dyav .5i y0v9bpo vo8hceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same 1v9yza4g-,) . hnpwy4wc 2wxu*fl ipdradius. Whatcp *14wx-gwl az2pu4ihw9n ,d v) f.yy is g near its surface?   

  Two objects attract each other gravitationally with a force gd jn3yk,i:-w7i+j m aof 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 acceleration of gravity, at cj elqc)x. tv4)2ok sx9l a3 4nmme0.f(a) 3200 ms clv2qo ))xn 4lce.3txm0 9aj 4km.fe    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wkvn 2a1;puefo kq3o4 2here thegravitational acceleration due to the Earth4ku;2oqavfn31 pe2 ok is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere d, q7+79 g0avnn/ l.fflgnlqb about 10 km in radiusn0.gq d7+ vnqbf l /7anlf,l9g. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averab593j uwmx o6awx,vlf) 44xrkge star like our Sun but is now in the last stage of its evolution, is the size of our Moon buf4,ja v wbwxr 64ol9)53mxxku t 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 ga gb)cku,,3r )pb),k:zrsz ain the space shuttle. Your friends respond that they thought gravity was just a lot weake: ,czsp )krza b3,brka)gu)g ,r 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 lomznbd+l l*i-c q/w+1ocated at the corners of a square of side 0.60 m. Calcublwz* c+ m ol+qd-1/nilate the magnitude 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 planeob) lt6culy-i4xh9 c4ts line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiteu)tb4l6ycilo94x- c h r, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38h6 y, 4h)mplk+n jt-l0rxvl)q of what it is on Earth, and that Mars’ radh6l+tn lm 0qykl,rj4vhpx-)) ius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthv v( h,2. )chmnnky/nqx/v:we and in m(vn: /h,y2h/xn cqk v)we.vts 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+ nu 4uq1i. wwlapkb+;n q(;vv a stable circular orbit about the Ear(wqu+i4bw +kpl vqn1nv;u;.ath at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitetq, a()i g+rau into a circular orbit 650 km above the Earth. How fast must the shutaui+ar(t q g),tle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshipvdd9 0ejx 72) -qbynv gfhgj71 rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, hggnq9e1jxvfj d-y7 7d2vb )0and 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 the Earth in a circula3suq g rl;cb tl153)bir “near-Earth” orbit. A “near-Earth” orbitbril;l 1tc3 q bs3g5u) 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 from the top 7a9( d saihez1of ias9 7(zh 1daeMt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar d wfv60xbx-5d landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take -v 0x fwd6xbd5to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Ti 4 by rypwr,r:yv1i,6r,o.f the inner radius of6yywr, tp4ir oyfi 1r r,v,:.b 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 15.m4 qrjpb,s )tw8;zxj35 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at ths3z)8 ;xjtw4jmbrq ,pe top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weigh:w5oqcjfowhkc gm0/l964 3t 7sgx1crt of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehi5ww9f ctj7 3gm xqrkg o/16c4ol0hs:ccle (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 two3:nn ar9qdg, /m1wrqo stars of equal mass. They are observed to be srdw gm3an: /qro q9n1,eparated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevtkxk0)) uiic g); w1fgator that moves kicw t0)u )gx;)figk1
(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 zhud0x. sbq1mm-ei 019j:frefrom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accel mj1u m9feq0-res:x1hz0d. iberates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfa(t.8r,jaynha xbp42 2sr5dylce of a planet with period T , the densihpnya8 jlxrs22d ab.,(4r5ytty (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and t5yz/ adba nh4u2 3gvy:he period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near thb2azy: u/ayndh4 g53v e Earth’s surface.    s

  The asteroid Icarus, though ej.+) bv-rs x .mlf9caonly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its m.+al.rs)x-cb fv e 9jmean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag3h9.)xa -pwsmam + h *x va8;fyizt:bte distance 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 every 76 -**mfiy) sc,om r vth5years. 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 poysm5im,h )vc*t*f -rlanet’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 qqx(-mz3;obh+ 6i fkxn 7ukpq3 df-5 f 4olm3hof 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 dyrp/a0rk-i1qh1fhg(dh nq + b 0-i su q9*4fdfor the four largest moons of u qf14-/di10gnqhdd r-a*9h0+ri(p b qfs kh yJupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period anjdnawjlzx x/7l j i+d3l) 79*yd distance of the Moon. 37*7a +njd )lwl d /yxl9zxijj   $\times 10^{24}$

  Determine the mean distance from Jupiter fosz gfdq ;r6cc6i s+)+er each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and+s6sc;c6efird+ qz ) g 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 fragments (which soj9*9f8l tx oy0eti9tbme space scientists think came from a planet that once orbite8xi 9o*t b tyt09e9fjld 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 describ 7ndr6* e)znuges an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the nu) 7 6grz*deninside 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 hana 9- ehy+ygj xym-k7b8ging vine (Fig. 5–41). If his arms are capablj -eb+yy9yk mh8a7xg-e 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 w yuawtc/upt orm4.)84ill the acceleration of gravity be half what it is on the ru4/ um)ocawpyt4.8 t surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab :gxaauf hs3/bh/on*-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 are 60.0 kg, how hard are they pulling on ouh 3f/a:gxh-/*nsoa b ne another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent a/r2) tnf2 blzfkd6rqp 9c:. gbcceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estima 9r/2 zqb6dpn.fgt :2lr)c fkbte 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 /evm1im6:xl s(51y *s mkyebq from the Earth to the Moon experience zero net force because the Eart:b/ mye6qs1* sxvmlm (5ky 1ieh and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but(z p -ya++ tdoehq;k*u when you stand on a bathroom scale in an elevator, it says(py-eu*a ;k+ohqzd+ t 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 sk. jo pi--+ qsk6qb3yood2:w 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) .: +bo3ky -wk6-qijspoqsd o2is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical l/yuiesaoo4e u* a10 j*oop (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 aq00ld+c0 pgv z planet in terms of its radius r, the acceleration due to gravid00 cp lvz0gq+ty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected f sa6kpr /uqs5rut;o/8rom the vertical by an anglr 5u/ 8s6sk poa;tqu/re $\theta$ 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 +yi6s z)kcun8 If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a cay+zcik)ns u86r safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectubi+6 na a.,e )wfs:wiee h2l-s at the equatohaul,wbeen6 +ws -if2.i : e)ar were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of f7* +y3-0hlo h rcoz ss00ddjb 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 spe zd)d:re+quz1ed rounds a curve of radius 235 m. A lamp suspendeddz+z) du1 q:er from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times yl)pp+0 op-d79mys qzas 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 of g 's a person would experience at the equator of such a planet. Use the following9o 0 ps y7qp-lymdzp)+ 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 pretz*p7ccckk0 niey 4f,7 g17u nsence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the corc ,e 7zykn4k7c71tni0 pug*f ce 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 consta8hks:j pv;u gj e7u2smqqv3i0yb8 r94nt 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 feebv8e jjmur 4y0q ;i32u hsq9g:vkp87s l heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utijek5o.8p1g7v y: ic pjlizes a group of 24 satellites orbiting t7 vep8yg .o j5cpi:kj1he 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 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, ixmp1hd )(f *vao: glzv(d+aw 1s meant to orbit the asteroid Eros at a height of about 15 d()la 1vz w* hoagv:xd(pm1f+km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a vaevkyud 1x ,9u0m )9o0l wxr/satellite in need of repair. You are in a circular orbit of the same radius as the satellite9 9vml)auy v e0 xw1oxuk0,/rd (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) Whxjj o5j vxqrb20 z00gfe2 9t9unfx 9(lat is its mean distance from the q0n(eoftxjlzj59r 0j0u2fb 9 x9x2vg Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actkpsx) 5j 9lc(kually "feel" yourself gravitationally attracted to someone near you. Make reasonable kl(5)9 k pxsjcassumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dik xjf)ey/lia-/0 /0u eiz k*jzstance of about 30,000 light-years fromkx )f 0 *0/ya-jjzeziu /kie/l 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 each sidc0mdxo; pgbet5luj (jqn*6 *.e. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottjc*meul j;p* g n 0(t.6oqbd5xom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi+ ryui9p qvg tp b.hv:ix9ea.9/jpj35 ts 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 exye6fnyx7 d)z* perienced by the tip of the 1.5-cm-long sweep second hand on your wrist wn)*fe7 zyydx6 atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cirlb:mf0s; dwqt,u6,o ncle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the ang6;: d utqwob,fl0 s,nmle 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 tracmw-k. uuk) s9 s56designed so that a car travelia)6ku-u sc sk.5mwr 9tng at 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 t et:j1ofx5 un)ilt 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 forco5u)nfx:t je 1e. 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.$\approx$    $\times 10^2$