Sometimes people say that water is removedxx u67mm2 t0nk/- pwkh from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stateme/kmxk0hxt6nuw 7 mp- 2nt?

Will the acceleration of a car be the same when the car travels around rr/ 5ty v1 g4em6wnjv:a sharp curve at a constant 60 km/h as when it tra et1/yjvrg rmn :4v65wvels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does yq5/* vofhcs) the car exert the greatest *y5o)fv/chsq and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on aeob0: o 9 +ex3fy( tuce,nyxf) merry-go-round. Which of the9 c eb,x o +yextny(3uo):f0fese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a v96qlgq 2: kokzertical circle without the water spilling out, even at the top of the circle when the bucket is upside doo6:9zqlg2 k qkwn. Explain.

How many “accelerators” do you have in your car? Tbbw7d p8ti(o*m67j x vhere are at least three controls in the car which can be used to cause the car to accelerate. What are they? Whbpix j6bwmv*o(8 7d7t at accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in dc:jvr4w1:886gqqod vj8 dt eFig. 5–31. His sled does not leave the ground (he does not achiev wo8d1dq dj:c4j8rv8 :e vt6qge “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 when roa62j cn8 xfp:funding a curve at high speed?

Why do airplanes bank when they turn? How would yovzj df9cq+6kawpaj bz* 14 d9(u compute the banking angle given its speed and radius of tk9djv p a1*zz6jbwd f+ c4qa9(he turn?

A girl is whirling a ba yx2.ksq caa9s70wjy (ll on 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 oj.q y90 ak(c7wxa 2sysf the yard. When should she let go of the string?

Does an apple exert a qt2cg93p7uw( 3 eucgd ih0 8q)cv mp;bgravitational force on the Earth? If so, how large a force? Consider an a p7ct0 pbch eq3gm8;2w) vqu d3ic9g(upple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whatn.,-e6 mer me k3ghb2:ycr,yn it is, in what ways would the Moon’s orbit be differentyb6n2 eeneh.m-, 3gck y:r r,m?

Which pulls harder gravitationally, the Earth on the Moon, or thx mzef5yw0kga/* -tazr,q;8 ce Moon on the Earth? Which ac0 m5tx,r z*az;ewg 8af/-cykqcelerates more?

The Sun's gravitational pull on the Earth is much larux 4tzt )8gi5fe,oj 7et-vr z9ger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differeg89- o5ir7 zxu efet t4j)tvz,nce in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator5 7 ,n ch(/gk 5rmt7fr,h1vpzbbm shi6 or at the poles? What two effects are at work? Do they oppose each otherh vkh1tm /gmr ibf 576,pb(z5hrn7,cs?

The gravitational force on the Moon due to the Earthztl8qb96ccvy pf i, 8; is only about half the force on the Moon y8v6c,;ifbl89zp t qc due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroux .w7wh qkvr3wpm;5 *)ir nsm.nd the Sun larger or smaller than the centripetal acceleration of) 5wp3 *wim;7vwnqrxskh .rm. the Earth?

Would it require less speed to launch a satell8n;fgj/qb5h gibz a55 c/m5 elite (a) toward the east or (b) toward the west? Consider the Earth’s rotati55bc n/g8 i5q zhm5jfbeg l;a/on direction.

When will your apparent weight be the greatest, ka *xffk+ ;pr7bjg4(eas measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerfxr+*kfp(4 kbjg;7 ae ates 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 long periods in outer space could be adversely affecte d 4i4wqnvx2,rd 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 simulate,ndv 2xi4rq 4ws gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or) if 0,wl7nztpwmyjhg4a8,+z “apparent weightlessness” betweenhfjy 4z +it8z,nwa )m0gl,pw7 steps.

The Earth moves faster in its orbit around thu94gpl+;p ipm e 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 i4up g mp9+l;ipn 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/e9 mfba2 3ygx known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass. 92 efygabx/3m

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet jti 0ey; ls1ut9m vou 2wx-4w;the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round my w0 j u-s;emxut1v9l; 4woi2toves 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 a;j4sj 8itzm+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 acceleration of the Earth in its orbit around the0vn *q 2wg iigr5pnjzs:t. 2s3 Sun, and the net force exerted on the Earth. What exerts this force on the ws g. snii0pvzn*j2:r3t5qg2Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it ro c ff5 -m/0xcl*;s-elpdduz1 uk 4pjf/(sylj) tates uniformly in a horizontal circl4ec ful(ljjdz )csp/sy f-kxuf 1-0 5* dp/;mle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, an3qj 3/ eabi) uvtkw2d9d 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 ackbjai e wu33v)/d tq29celeration at the Earth's surface. $\approx$    g

  What is the magnitude of the ;r+obd374 atx(v+hva hh;g lp1g be/m acceleration of a speck of clay on the edge of a potter’s wheel tu;bg+pavdvre147t;bhgm/l ( a3 +h xhorning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a df2e0 8gn af;guniform rate in a vertical circle of radiugf8 ga0dne; f2s 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of p 5wuzs*1my)bradius 77 m on a flat road if the coefficient of static friction betwee*b)u1yp5ws zmn tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frictwaf hm a8fuf0q6l//xqr2 ,ak.ion be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of u /qwf /a2 x6k,f8 r0a.lqhfma95km/h ?   

  A device for training astronauts and jet fighter pilots is designe7rdeo rm-j6o) d to rotate a trainee in a horizontal circle of radius 12.0 m . 6r m-) o7djeorIf 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 ez(og ,jn 7mefd*-f--fllfo 5rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of foome5gn -(lzf-fd* f7jl,e- static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dow c3;s )gwugy*kn at the top of )kggyw*uc;3s 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 (iuwsudn4.w98 u ncluding the driver) crosses the rounded top of a w9uud8 4nw.us hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fehgunk 7z43)vx rris wheel need to make for the passengers to feel “weightless” at the topmost poingz43n)x7 u vkht?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At thrfzd hb i4/wpl6vt/goi19p ;3e lowest point of its moti4fil/o pizg b6h;vdp1 rt /w93on the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cent ).nu qk s)kunpx6nkk8w :grcz f)3o0:rifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 1w)q83 kk 06pzgnx:sn:uk ou. nr))kcf 15,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walle(3lae,r wsx 9qd "rox9eslqa w3,(rom." (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 a frictionless air-hockey tabf 8t xh.9a;puxocg/ ji d-3mr9hkc2ul3lb; x1letop, and is held in this orbit by a light cord connected to a dangling blo/lbl-c3ip; fho.83hr x cmut1d 99xgu;x 2jakck (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 tisxm+1 mi*qopl ton-ij-s*( - hme, by not ignoring the weight of the ball which revolves on a string 0lsohmj-( mxs io 1n -i-p*+t*q.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 88 m is perfectlymog e/;7b1puv 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 massesfm5 pi:z hbct iq*)x:*k,bis / $ 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 b m0 3nvxo0ue5by 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 exerb9+4( rhtlzyn ted on the car (by the grounzr yl(ht+bn9 4d) 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 them r/lgmfu.cv p/o 19l ;c8:tpr k1mh,r pit area, going from rest to 320km/h in a semicircr.m/k8hrm9c t v1 :o;grppl uf,1/cmlular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the 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 par 16buyut4 v41ez,qu j+yx*jeoticular instant, its accelera4j 1z* 61b,vyjtu +4xqeuyeo ution 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 gravityzo 2pljwk niq:k4-s5-qaj7u+ ks h9 1z on a spacecraft 12,800 km (2 Earth radii) above the Earth’s suqqlz9sp kkunjas7wj4-kh:15o 2 -i +zrface if its mass is 1350 kg.   

  At the surface of a certain planau5 ys j4k3ey6h1qn ,egc/)cs m+r,ouet, the gravitational acceleration g has a magnitude of 12 mucrc 6k+ey u45qsha 3nmj,y/,1o)g e s/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.qw z rak+6;yx. The Moon's radius is 1.7xr;qz+w .ka6y 4 $\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, b5 pzpr 1f1ljb1ut has the same mass. What is the acceleration due to gravity near its surfac1l11frjz p pb5e?   

  A hypothetical planet has a mass 19tbm(e;vt)/hgq estp 7 mk: x5.66 times that of Earth, but the same radius. Whp)mv e xe7(5k9 : mtst;hbtg/qat is g near its surface?   

  Two objects attract each other gravitationally wnrvv5j z7 8x8mith 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) 3zh,qq,5k: ja7f7e vu o200 mqqeoh,7 a7j,ukz 5fv :    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the7:lwhgp g75czv8m )b i Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is 5pl )g7mihwcbv7 gz8: $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mv 5 .cu*+5rgstwl8teqass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravwgtv+qe rs*55.tu 8cl ity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lykqvb-:aq+1 yike our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of ok:1y+-qa yvq bur Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining whfkkc ihyq 3(n);9c ;fjho (7j ;elf)5cx dl9kqy astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourse7 9;ckifj)ec)k9 olhdqk(; fxl q5jcn;(f y3hlf 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 ar-vok0-we t1; l3eamkve located at the corners of a square of side 0.60 m. Calculate the magnitude and dk1a3l oe0v ;ke-wm-vt irection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of tgf2-s2i2 xx eohe Sun. Calcuo22g xseifx- 2late the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at 1(e j+h hwwlf ;x,o ron;ct.ciejo80* the surface of Mars is 0.38 of what it is on Earth, and tfoh.( *cj;; x 8o+ te, 0wilhjo1nerwchat 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 period of 5ripuk0e1 . dqgs- crnx2(rdvb*y-w, the Earth .5brirq-ye pus0v(,-12nkcxd g*r wdand its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabc1dpwm. xb8ltd(y.t c8: ri.ble circular orbit about the Eart.iy1 m .:.x(brl8b8ddcwpctt h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the2knm5m(wxa wa7z9- xl Earth. How fast must the shuttle be moving (relative tmz7mxx9al25w nk(a w-o Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricarb6.h/g amcdn :ok3y*l spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assdc3m*.gn ob a 6/yr:khume 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 satelc5 op4o-v38c +jmmpsrejq+n0lite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the 3m pmpocej+j08+-nq cos 5r v4mass of the satellite?    s ~    min

  At what horizontal velocity would a satell ku2i-ukclc39 t7 8n)fgijx5lite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the E 7 cifu9t-kcu gl82x5j)kni3larth?   

  During an Apollo lunar landing mission, the command module conti26z fb kkquh2*dy,vdqx x , ,zk,*ns/inued to orbit the Moon at an altitude of about 100 km.hi2 ,,*6xq/ks*qukk nfzd2by,vd xz , How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plt k21o c-0po2cz(jc hlanet. The inner radius ool c 2k(jo 201-zptcchf 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 d .ayk4y+3kbin 9v cby*3ci7r7enwa/ diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’ski a/.by*k 7wciy4e7dc3 9vy ban3r+n 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 astronaut 4200q+lug9ap 1bx;cf -; c1ys)kic km from the center of the Earth's Moon qsfbc lag1ky 1pixu9- ;c+;) cin 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 equal g,v 3x(pfe/h w(c z;tfmass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?pw gxff ;/,c (hz(3tve    $\times 10^{29}$

  What will a spring scale read for th,rwo/l tj6bw ,*7 za2yix,nc2c;aos 8ztrp) ke weight of a 55-kg woman in an elevator that movebyowijt ,82 )c/a,7a2cl xrzwz ;pnk to,*6rss
(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 fro (gr+zd58 imuum the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acuimd5zug( r +8celerates. 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 periodqvk ++n)kiq. ow8bt8eox *8w l T , the density (mass/volume) 8v.)lo+tqb kw8xe oqik8 *+nwof 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 determine the periodzd / ztcbv166v of an artificial satellite orbitizcvb61 v6zd/tng very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, o1zhj(vi )mp3 l2q +gborbits the Sun like the planets. Its period is 410 d. What is its mean distance fr2(ib)lq3mpvhz 1j og+om the Sun?    $\times 10^{11}$

  Neptune is an average dix0bw .56j)nmbd62tavnsor s 2 stance 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,.vkwh/zfn z k /s3i z 1pg4qmall8bmu-6hc() 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 thiwlz hz- (lq4n.mv18c )6iapkzkuf,mh/s3b / grd law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galax+a0)y u,kr3npq w4iony $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fourvpbjns(;, )dj largest moons of Jusjv(,; ndp)j bpiter (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 and distance of the Moons :*bdl7i u (,i ;6kojmy5itiq. ld yob56 iim:j7ksi u*q;,(it   $\times 10^{24}$

  Determine the mean distance from(f( :clprd pn7hjgfa/ l1n;* t Jupiter for each of Jupiter’s moons, using Kepler crpnjl; :t*a/ p(g1l7d nhff(’s third law. Use the distance 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 betwee0m) g6.rno o6 1meuml1dcie2zn Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destromcu n1 ed)mg i2l6o01.oe 6zrmyed).
(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 the form of 0 du(wzme -*1,,ke z hdsfxbufe zx--4a 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 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 k4 udmz- hbzef fx(-ex1dus z*,-0we,year, in Earth days?   

  Tarzan plans to cross a gozn z 10;tfahyg hd.0zky6zn,2 rge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and , g1kyn; ztnz0z z2yfh.a0dh6the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whatubooc 8.s*c 1e it is8ou.s bo ce1c* on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a muthm4olmr tg(maz9 x),p b3v1 d1ual circle once every 2.5 s. If we assume their arms agml(xmd9p t mbov,1r)3 a1z4hre each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity at pght/6e,hjam:b;d/5ld 3 avptu; y ;jthe equator iym5/; lpdt 3a,v e/ug; 6;pdhhatb:j js slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a ow5ms2zr p9k u0h)x kt+g +f2xspacecraft traveling directly from the Earth to the Moon experience zero net fo tkh5sxpxo+k 22r9+ u )wgmfz0rce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elgm9d utmn ypr:sx 7ma/a8bsj 0:l12a6evator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which y67l1r9pasm bgajau8t2/:md: msxn 0direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube th7hnqscv( p :2rn4lb16jsa ( aeat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circ16:nr7c(he4np(jqavsl bs2ale 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 vertictsvmfqm*4boqtq ;5 -4al loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acce ;.jrkk ;crm1/ uv4ik1 gjk0vkleration due to gravity at its surface and the gravi;0/vg 1cu 1rkkijmkrv4 k;.kjtational constant G.

A plumb bob (a mass m hanging on afq ;pevqk14uqo:7d3 a string) is deflected from the vertical by an ang4p:3qk dq fou7ve1;aq le $\theta$ 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 0 ee;jpc3b a*ng9zl-lthe coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely p;*a3g9bcelz0-lenj handle the curve?

  How long would a day be if the Earth were rotating so fast that objao49hmiuo8 6s4o uq/ n ;yun,5yjn+roects at the equator were apparent6iono4nm594o uh u;8a y/ourns q,j+yly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cocb0(wafwo7oop k(e.) 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 c- :1l w-mxiu9emwv53 dscyt4wonstant speed rounds a curve of radius 235 m. A lamp suspended from thewws431m t y 9 c-:dx-wmliu5ve 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 as massive as the Earth. Thus, it has ,pw */i 2* c8pip pdlsrut09mgbeen claimed that a person would be crushed by the force of gravity on a pltip p i0 rwpld89pmgs **/cu,2anet 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 n hirtwt0 rho:hw5n k7t131,(wy g9f psyja0*Hubble Space Telescope deduced the presence 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 core to be 780hy0t: 7ngak0 ytji r1s( hnf1hr*wo5t9,wp3w $\mathrm{~km} / \mathrm{s}$ 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 valley shown inba+:e)bg+,nwq;q exvyok 7y2 Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normaln, q: kv ag)we7e yb;qb+o+y2x 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 m.jba5qfd5 0f(j fc.dqr a.4fb,u aa-(GPS) utilizes a group 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 satelli fc aj mju0bqrf.a4q ffbd.5.da( 5,-ate 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 R ,+tyrz 9b4kjr9dfrt(qxw )3x endezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros ist+ y, x9rkrw4dr)j zftxq3(9b 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 cks8xc1)hw5s the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abs1)skc 58hx cwove 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 i+2ss5 -nn hlli,fs 6lac-( qeyts mean distance from the S - n+6esshyl,nql(al sf ic-25un?   
(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 a21l9i1/n xawio a0 ygneed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Miay ial wo/1g2x n0a19ake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galgujx +o p* .tph8*/vztaxy (Fig. 5-46) at a distance of about 30,000 light-years frtpt.8ph/*zg v +uoxj*om 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 squareup,ww zt,- v1e 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the z e, -1wu,tpvwsquare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earvv0sjj; *yh*h th $ \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 ex6( vrnj d.rw-)shw 1ocperienced by the tip of the 1.5-cm-long sweep second hand on your 1cs hd-rw(r6.jo)vwnwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start toc:z) ktkei6w3 swing 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 is the angle that the fishing line makes with the ver: )k6wi3ctezktical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in aj p+b3(u2qi9cyi e j9:jqx-du new highway is designed so that a car traveling jcj9-i edu:p3( xj2bq+yiuq9at 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 trife+7x zc78ukain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Considec7e i7 xk+zu8fr 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.$\approx$    $\times 10^2$