Sometimes people say that water is removed from clothes in a / d id.co-3zmj* y6 l/s zltxcrnr) ay.,emj(6spin dryer by centrifugal force throwing the water outward. What is wrong with this.).jm/- dnrydmx z/ j ccl6y*zleat (ois ,3r6 statement?

Will the acceleration of a car be the sa+hcisnvz6 3b0;y 8 ggrme when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gzcsry;+ g n8hb63gv 0ientle curve at the same speed? Explain.

Suppose a car moves at constant speed al:ggzxij ec, 4k;l r.x)ys 3mjuz;r7l(ong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hil c j:jzl (mry7xku gei;3.xlr,;gs4 )zls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child nkb7cl)+49x/h qd5bdkuyp+t riding a horse on a merry-go-round. Which of these forces p qn+hb /tcpxuy4k 7ld)59bd+ krovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spilling-t4 z mlox1k(hi+ sj-h out, even j xl1hs+m k-hz4-(oti at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Therexgv76l( yh+rp:ky6x jfft a -2 are at least three controls in the car which can be used to cause the car to accl6h26-fr :p+(a yxt7xyjg k vfelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill,jwknxboav; 5v1k/37 r 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 thebw;v5 vn kj1kr7 3xa/o sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a ekq g0iew 0;8prrfb5w1/ikvxw0 h1z 4x2 8unhcurve at high speed?

Why do airplanes bank when th+j 5 ftr/x ytjm 95nwko-7nz:g)nv*u.nor m0gey turn? How would you compute the banking angle given its speed f0j/y9+on rm* rmjkgwot.n ngtvnu5x-7 :5z )and radius of the turn?

A girl is whirling a ball on a string awt q(b7zk.yjiak95h0(y 3r-l i i2pudround her head in a horizontal plane. She wants to let go at precisely the right time so that the bala.yd ih903zpuq (b5ii ky2(kw- rl7tjl will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a fo7a,42 zg3zmy;se if oqrce? Consider anaq;4 7fiozgsyemz 2,3 apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wer)zy n2z:/ukph5 vw8dw e double what it is, in what ways would the Moon’s orbit be different?yv:u8wzhd5w)nk2p/ z

Which pulls harder gravitationally, the Earth on tht* vju;w0+(q hgtq w;ze Moon, or the Moon on the Earth? Which accelu+g;qzt ; (q*v0wwtjh erates more?

The Sun's gravitational pull on the Earth is much ;hs f2 6t;,elcr: f+rl,dzauytly4 3c larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explaincyt3 +l:u4arcf,6ys;h edl2; z rf,lt. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more a/kx,)u d*)so 3oujv upt the equator or at the poles? What two effects are at work? Do they vs, u))odo3p*/j xuku oppose each other?

The gravitational force on the Moon due to the Earth is only about half the j()(n*c k)f kla fmjlfp9jp3q8*x bj(force on the Moon due to the Sun. Why isn’t the Moon pulled away fr mq j jc()j(b(* nf3xfpjlf98kp *kla)om the Earth?

Is the centripetal a0doq(f afd:a ;cceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acce( o af:d;0dfaqleration of the Earth?

Would it require less speed to lws,ar 9ngm4 )kaunch a satellite (a) toward the east or (b) toward the west? Consider ngwrs,9m4 k)a the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in aq k) 3q+c,ipjkb0p/ os moving elevator: when the elevator (a) accelerates downward, (b) accelerates ,o)0b/ kikqq+3 pspcjupward, (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 space co6d; rz d59 t8yrgffv(auld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) a 6; r(dfr dyag95fvz8tny other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weig4f (si*:pee / rbvl8sjhtlessness” between belrv( s:i84 e*/f psjsteps.

The Earth moves faster m8mk+k;m4 wgkkwjw+7( cyyz* in its orbit around 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 t w my8(z+gkckk7jk *m;myw4w +he 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 to have a m+te --tb2z ngxo)9 x:esct u-eoon. Explain how this discovery enabled an esu-t :en oe2xzb) -+9xtt sec-gtimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Y*3m ltlswgxe-gt.:fz9/ t1 3ccb-lraet the Moon's ilcwgb gxsrm lat/9t c- z.l*:3t13f-es mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from 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 travelind0gxjkps ( +8a7jp;vz g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratiom3 )uow4- 2ckn8e/.bf kescu on of the Earth in its orbit around the Sun, and the net force exerted on t8 ucwon 2b.34efe-kmu)/c o skhe 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 e2uk;mw* yiacvxu+b21*2amya 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s iu* cw myu1m*yxba2a2 k2v; e+length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km ff2pmy2 f hda**rom 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 Eayp2*h f2 m*fadrth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck u2szu r-nkcs0a w57+dof clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheew5zu n-askcs dr70 +u2l’s diameter is 32 cm?   

  A ball on the end of a string is rg6c5t3mv +d6o7 ztkbwevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fit5dwm vz6 37 6kgo+tbcg. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with whb*w:,gsx0 d ,;c731na4 ztauqhxbtwnich a 1050-kg car can round a turn of radius 77 m on a flat road if the coeff,3,0gu:dbbn*w a1txasn4w t c;7xz qhicient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of staticg(z 1i;2;bg*v,c mrctll *xbqr 4svo ( friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 9r(b ;vrqg v1*cz(4l2mtsxb* i,;g clo5km/h ?   

  A device for training astronauts and jet fighter pilots is designed to roopgh/jjv(v(7nal :nza9k 7n 8tate a trainee in a horizontal circle of radius 12.0 m . If the9olh8g jvvzn n: 7n( (aapj/k7 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 ,um/kjb3n6f i)m(n13tkocjavariable speed. When the speed of the turntable is slowly increased, the c3o jmanbf /1c)(ij 6,m3nukktoin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whx8dwsq0 sa;2j en upside down at the top of a circle8 assqdw; x02j
(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 (includin-43 -3w7op6dltnshct gfkc 7.h7 lo peg the driver) crosses the rounded top of a ocwnp ehfo.k l34td76t--3g7cl s7hphill (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 Ferris whee(cctev 43 :n(,nxemd j,rdlqj-ve 9.tl need to make for the passengers to feel “weightless” at the topmost pod,eemjdx vt c:c(tr3v9 4q- n,n(.ejlint?    rpm

  A bucket of mass 2.00 kg is whirled in a verti9 d,b + csuxkkxsw4)r2cal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket +sxx k dkc)u2sw49rb ,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 centrifuge rotate if a particle 9.001 0-c*uy,rival9jr)*wnylpb cm from the axis of rotat vw *jyi9rl-0,yua )lr1 n*cpbion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carni/r *a/mjoelcqd hm* ).val, people are rotated in a cylindrically walled "room." (See Fi/lqhc) om.e j/arm* d*g. 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 Mo t -fg+(-elii s6gc+3+0wirkigqu l( ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord co+c g+((g 0i il6 liqsk3fwg --+rteoiunnected 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 + ezx1 9,-3hotw c5 olkutog,stime, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In p9z-ko,,5ttxo3cg el1 uo+swh articular, 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 caka18rpn+ucij +b/ )ffr 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 masseni7v04*ty u nh hzkfr/r0b) .qs $ 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 evn c*xicp 2tn17asive 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 exertedroz 4t7kh5u,* * rvstl78f nyc on the car (by the groun*7f *4sknr8 yc,trothv 5zl7 ud) 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 x8ao 6a(qiz.n9uuyt , 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 qu.69yt(8 xz,na uaio the car when it is halfway through the turn, assuming 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 radius 2.90 m . t6so un1;i3)s lduvadq n9+ u/At a particular instant, its acceler d;nu93l/d)u utova6 +siqsn1ation 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 ofd* ; :7+vqu csnxh)noj Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the hc 7u ;xv:*o+)nnqdjsEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration4 s4mack hu ic:eov8 .c*0j4dn g has a magnitude o4 jcam .uchi48kc:vden4 s*0of 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 ;2wygl3:ac+5po f:dm g)l vik eg /g-aon the Moon. The Moon's radius is 1.74 lw lgy o2;v:kp/ecd5g3a:i -)mg+gaf$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planeb)/n rcbjm- mh5.7oe2rbf/izt has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to g )h/b-b nz errmfo5. j/b27imcravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radi,/m;vke nfim 9us. What e,nfk9/i m;m vis g near its surface?   

  Two objects attract each oth c28j +bvxgb2*j6xuyaer gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 32;bm/h r o:qtn)00 m m)/q o;t:b rhn   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earfh 6+fsqfe,ymnlx/f ,n4 3xi 0th’s center to a point outside the Earth where thegravitational a,ifxnhfnlf+ m6,f/ 0es3xq 4 ycceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times th4n-t+p i6f 3he yo:ofdh; pf6be mass of our Sun packed into a sphere about 10 km in radius. Estimate the - yoth;+fp6p43 h fdbio:nf6esurface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star ltd ovjp.r swku+2;nh)9 * 6bybike our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the .j r2)wd+sy6h;9v u kontp bb*surface gravity on this star?    $\times 10^7$

  You are explaining why astronauf- hq mamu23j8ts feel weightless while orbiting in the space shuttle. Your friends respond that tq8j2h 3fu-mmahey thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locatv 5)crnwq:-jw ed at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational forcern-wq)c5 j w:v exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets li7e l u;4oseq 0v; bke-n)oyax;7b a0udne up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming ale aq 7ubyb0k7ex-; sln;40uaoev do);l 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 gie li/3gxjj- rb.ju (q +k,(wsravity at the surface of Mars is 0.38 of what it iswe/ii,b(j(kj u x. gr l-s+q3j 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 value for the periods8* s3o71m7+o //gl-:rus6y rld uqjtfmgwij of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.8/7f3 /iw y-+ ugs *j ts:or1udsllg 7oqrm6jm]    $\times 10^{30}$

  Calculate the speed of a satellite moving .ra)x(9 xy lb:lp6yqft d3c3sin a stable circular orbit about the Earth at a height of 3600qy) 9tsb.drc6: l xypafx3(3 l km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ea h54x viln,wr98 hn24ae/tlnmu0cet 4rth. How fast must the shuttle be moving (relative to Earth) when the release occu hx rn8ecmtal ,0vit4 /42en5u9h4n lwrs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants a-ingrqacv+ ek.+2 1u ore to experience simulated gravity of 0.60 g? Assukorav+ -n.uqic2 e+g1 me the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to rmlxqhl 7+00g orbit the Earth in a circular “near-Earth” orbit. Am0+lqx 0rg 7hl “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be f, ln0f9wtl,tj; bb:tf8 w(drlaunched from the top of Mt. Eve dbnfljb:89w, tt 0,rl(ffw;t rest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the comm wn t;j q.5adizv2+)dkand module continued to orbit the Moon at an altitude of about 100 km. How long did 5nqtadv2iz .;+j ) kwdit take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet,hte,) c39tcmu pf z2(ubo my:. The inner radius of the ring 2)tczpyeu:3ou,f9mh (b,mtc s 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 diame nv9m3c6 hqiit:rb4x)ter rotates once every 15.5 s (see Fig. 5–9). What isibx3 itmv)49 chqr:6n the 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;kb o q,.sm4kx a 75-kg astronaut 4200 km from the center of the Earth's Moon in a spao ,qmbk s;x4.kce 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 syszky(vlpk30tkm22 q b ,tem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5bkvm,0 tl2kpq(32 kyz.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 elevatoe3:7 sa7m3mmlzlpg a,a) d lr(r that mov7sam7l,egmdzamp l :)3 rl3a (es
(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 c ha0+1ndd yyg-eiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator 0d+d n-yyh1 agaccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfac1 4d+wxi 5kke -wgdeg0zv8d z3e of a planet with period T , the d81 zz3d dd 4vxge 5+kwek0wg-iensity (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 the period of the Moon (27.4 d) to devq8mq;btf* a 9termine the period of an artificial satellite orbiting very nea 8tmqfb;a* 9qvr the Earth’s surface.    s

  The asteroid Icarus, though only a few hundg( a2xpsmknm* 1.kd m4red meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fro( 4 .xn m*12mkpkasgmdm the Sun?    $\times 10^{11}$

  Neptune is an average dis11j5 ve(vztphtance 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 years. Itaomm 71s gtg +8n8qfdi73p0zz comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from a0dzg1i zsotm mpfn3+q78 8g7the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cennlc .ewdc7n*(sey.o o +1 g2hoter 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, andaeyqt+3qvg*9 mean distance for the four largest moons of Jupgev3a 9*+tyq qiter (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 perdoa1wh4xv g,+ (bw6og :lnwfux mfceq 88j,3)iod and distance of the Moon. 8wmqho ,6 1w :gcb)4e,lan+owu x8 (fxfdjvg3    $\times 10^{24}$

  Determine the mean distance from Jupiter for e(vv bau7put l 6+/fja3ach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabljv+7b (t3pu6 la aufv/e 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+q f(l:+0y*yk,q oe oublk4vx consists of many fragments (which some space scientyo : 0+(flbo+eq yq,k kvxu4l*ists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artife0 p0rp:xrlb: fv 4pym. ,gke+icial "planet" in 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 sun is exactly like our own, that the distanck 0 p xr p+b:vler4pm:ye0.,gfe 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 hanfix ;u8,mv-pe:m4s;ae ch b8 nging vine (Fig. 5–41). If his amsxb:hp8-ee;4inufa ; m 8 cv,rms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration .ofoqv4+i 3leof gravity be half what it is on the surfaceqfe 4i o+o3lv.?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands ai4zotb n kvn5l(4 /uwp 4.r:zpnd 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 60z ( v 44iunowk.5pznrtb:lp/4 .0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, tos6alzwlc+ a y0i)qhf6 + p2o6he apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of thow6 lqfil6oy2 0c 6+ +z)psahais effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling y0d+ y)b+nzrudirectly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppo+rn ud0b)yz+ ysite forces?    $\times 10^8$

  You know your mass is 6bpt+cb+-r: mc 5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is thecrpc++b-b:t m acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cirx m .7qb3mdk.. x5obmicj, x0-(smttq cular tube that will rotate about its center (like a (m .-.7kd 5mxbs. o qb0xmqm itjtx,3ctubular 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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. ) d9v3lz.bc buv djga .ve9,2p5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the ac tvrrs*90w3rtlbyw4; celeration due to gravity at its3sty;rw 4rv b0lw9rt * surface and the gravitational constant G.

A plumb bob (a mass gbuqi6ckpc*7pq /dc ;l dt5 )+m hanging on a string) is deflected from the vertical by an a qd i6cl5;cgc/p+tu 7kqp)b*dngle $\theta$ 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 wm+-5ld,u4st*p6lpp0li * +bxbqvk c of If the coefficient of st wbpimcl*qvpd5l+0 46tk-,l *xbs+ upatic 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 objects at k i76j+k5 qtidthe equator were apparently weightle k6tj7d +ik5qiss?    $\times 10^3$s

  Two equal-mass stars whz7:7k t9j474arg pihsc s( d0d p*ocmaintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at357zog nv wwb0 a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5n go5w7 z3bw0v$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as toos 7;k-tdvq* he 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 following data for Jupiter: mass *;dt ovkq7o-s =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremelph 1 99*5nl- ggkwlqnc-o 8neyy 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 core to be k-h w9c1y 8-gqnll*p gn95noe780 $\mathrm{~km} / \mathrm{s}$ 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 hill and valtr w- ow4(9:z sbyziq6vxs/pry7 x91pley shown in Fig. 5–45. Both the hill and valley have a radius of curvature (rqv:9 sp 47opy-z 1tby9w w6xxz /sriR. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gr.sn 0gs2qi7 rpjy4jgtr u -/stp.m.g.oup of 24 satellites orbiting the Earth. Using “triangulation” a2m4tygr i.j p .ss.gg/sq.-u7r j0ntpnd 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 Rendezvou4.ktv ab rf96ps (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid vf4rpt6 ba.k9 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 space shuttle purs4:zm,(ve3g3xyruxd duing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above (43x red3 ymx:ug,zvd 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) What is itsnk1n bv; l0+wrop6qsomq 4+z: mean distance from+r q; v1o: onbqkz6l0s+np4w m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" you+ /o.cmkpcacyl566g( q 1 rgsdae)nq0rself gravsl0 ac( c6k+drce.gpq5/6 1onqa) gymitationally attracted 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 Galaxy (Fig. 5-46) at a 5v9qk c8pi3n,cu*i jrdistance of about 30,000 light-years from the centecirn,v p9i3uc8*jk5q r $ \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 1y;wh bj;*a4--ozs kcvfuh+s side. Find the magnitude and direction of the gravitahs;1+jksu vocb*a wfy4zh -- ;tional 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 k, ry)az;rl6o,0d t,rgwd wj(yg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long si1e(c1al0j8 lhu( mmnweep second hand on youre0 8jhncm11(liu(ml a wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing tmvzjhev,98xsw f ql hb0/32,: xbp2k a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What iwb 2ej8v9mhhzpl:02xq fk/ xvtb3s ,,s 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 ;(ourk asj,/s, *pmolthat a car traveling at spes ao,*,(rl;um/osk jped $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiat-oxpopwks 7/ s db)o( r*ym0z5ing curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal forzb0 r) xkd/ (pm7p*wosooys5-ce. 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.$\approx$    $\times 10^2$