Sometimes people say that wa0q5n;keo5z9 yvl w py8ter is removed from clothes in a spin dryer by centrifugal foe5; 9vlznk y8ow0qyp 5rce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tdy;;.j.hmk m b3.1jwiude0wxravels around a sharp curve at a constant 60 km/h as when imyjx.3 heiw dd mb;jw 1u.0k;.t travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed al. y+nxwln1.) xui)rmsong 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 dipw. n+xir. )1ny) ulsmx between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the for :ke8( )5igbt6kqvf o.a6rixpces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the ce 8.r)gvqp:6bf5tak 6o(kixi hild?

A bucket of water can be whirled in a vertical circle pg av2qt pa+w y jewo-lt8gu3a480p+1 without the water spilling out, even at the top of the circle when the bucket is upside dowp3+ju+0 8wqav- ewtga84loy ptp2ga1n. Explain.

How many “accelerators” do you have in your car? There are at least thrzff)) 0bdwhv6,. j grbee controls in the car which can be used to cause the car to accelerate. What are they? Whatz b)r)wfhfv b6g 0,j.d accelerations do they produce?

A child on a sled comes flying over the crest of a sma-vj px.6tekrdw* h3o8 xi/ q-mdmzj86ll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between xxde. qd8 rm8/h3-o6pmkz *-vt6jjwi 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 rounding a cufwb770jv1c6lu 4loh urve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angl5: -jekvhqx1a -; seqoe given its qxv-sa- eeoqjk1 ;h5:speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pmwa;hxe/1v/ kk:et/e 0yq; cnlane. She wants to let go at precisely the right w/e0 /e;h xyk1teaqmck;v:n/ time so that the ball 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 forcfjw-sdc9t 9)w e on the Earth? If so, how large a force? Co9c9)jfd-w t swnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass werew k1yvdd1 9y ko5o+2re double what it is, in what ways would the Moon’s orbit be diffo 5 1kyk9eoyr2+dw1dverent?

Which pulls harder gravitationally, the Earth on th.:occud +w, dke Moon, or the Moon on the Earth? Which acd, cok.:uwd c+celerates more?

The Sun's gravitationayo*(t:3 bc2vn:l 0e+ad 4arp7ovcs pul pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gra2oy a* 7vrt:ub l(34p0n:p +vsdcceoavitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What twd0 / kitix0+ogo effects are at k+00xiigd /towork? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only a /f0nru xrr:x5 btq-qet:8 q9cbout half the force on the Moon due to the Sun. Why isn’ xq tq:cq5e8trr:fr0n9x/- ubt the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around t(mrm r)c*hm5z;jnhw5 he Sun larger or smaller than nrhj w(c m5;mzhm*r 5)the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bez nq-)s0z1baqdxa. -ow3el 3) toward .b zza--ladn wxeqq s03e1o)3the west? Consider the Earth’s rotation direction.

When will your apparent weight be t9dcbe v,+( hw nojnvtqc7jkmg(n2-)2 he greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? Ih d g(n2t7+ emnvb-)ojc( ,qn2jv9wck n 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 longqr8,iba8kn cq-6og) o periods in outer space could 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 ( g8 iqrc6bo -n,)qa8koFig. 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 experience1 j9ejkr/nz(spx6 i- es “free fall” or “apparent weightlessness” betwee pk -e ji/9xs6ejz(1nrn steps.

The Earth moves faster in its orbit arouxjcvqg3vcr) pa/57ul c,9ne ;nd the Sun in January than in July. Is the Earth closer to the Sun in January, or in Julp5crccejvxlg q,9; n)a/v u37 y? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until itl m9s uggczz)k1 fr r(l,u:ctu1.(.t x was discovered to have a moon. Explain how this discovery enabled an estimate of Plur mlzkxt)( guuz 1rsct(.u.:19l,gfc to’s mass.

  The Sun's gravitational pull c 2qrh a)j7 8abcj3nu0on the Earth 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 the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.83juhb7 r0n2 qaaj c)c25 $\mathrm{~m} / \mathrm{s}$ . 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 w b-t ed du8.ms96ok)qd;iyx - 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 Earak m luo.yc 5ng3l(8n(th 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 orb. o(l 3g (n8umk5canylit 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 rotates unrg5 wl6tu 6p0szb:u0r iformlyuz utwps:b 6r506rg0l in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space sho pwy*n.qyk- wakg/*( uttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration ofqg*opawkk (y * y-./nw the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a po)4kqjwmioq)lw2 8; 9 /bybpg xtter’s wheel turning at 45 rpm (revolutions per minute) if the wheelpg )mwib4 xko8 ;q/9qlb)y2jw’s diameter is 32 cm?   

  A ball on the end of a string is revdwn+f8 owgp9dxr zu y:32y16molved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5x 81wwu9dop23g6 r+:yndmyfz-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 su. 5 usnhd.(dcp7h zq3peed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Ihh.cd5qz 3 supu(nd .7s this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tir 6*6jly9lmx jtes and the road if a car is to round a level j6y6x jllt m9*curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate d/b.,kih: lc aa trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on he c /a:,bh.kdlir 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 11.0f7( v ryp-9qb6.ma xrf cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains mp rabr(9 -vf6x.qy f7fixed 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 cftn.b.ut; 0gn4mhmm r 0y e54when upside down at the top of a circlyh0 .rm. f44b gmntmteu;c50ne
(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 drivfhn5u/sj67 mpokzf h :1y qg4d m7t9(jer) crosses the rounded top of a hill (radius jf:m5ymtohn /q 4uh7gk19sd6z(fj 7p =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 mr18v qv6rikq7inute would a 15-m-diameter Ferris wheel need to make for the 6 q1rqv7kvri8passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.005 ikvt(2 x;e+ds4hujd 5fissm:;t4wf kg is whirled in a vertical circle of radius 1.10 m. At the lowes ; 5sejd hufi;s(dfkistx+v 4t5wm 42:t point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a parhi*et ;9:s)df*lqagj ticle 9.00 cm from the axis of rotation is to experienl d9s;afj)ehig :tq* *ce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivaldcipo e m(c7lew-7;q eg5bk8 *, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) lc(- w77o; d5ik8cgbqe*ee mp
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 ci39cugpfz4 0xdg um /p2rcle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (/g gpxz23ucmpf4u 0 d9mass 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 , preciseqr 7 zlya1to;v6fw y56ly this time, by not ignoring the weight of the ball which revolves on a strlywyf6zv7oa ;q r 15t6ing 0.600 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 radiusyyzxxk( 14ft.liv7 g- of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masse:6fxby+rwlxtg6w9if+ a -01wx2 eglis $ 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 evawfmx w0jsguvhex(o)rp .p u4ea9w :was *35 +.sive 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/pfz fk m92;3gbh6fg l components of the net force exerted on the car (by the ground) lmgff fgpb6z2;h3/k 9 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 unifbu r2 n9ayane1l3w9v4ormly 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 acceleration. If the curve were flat, what would avanr1b 9ye9u2nwl 34 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 aiz5v*i c1bk:. At a particular instant, its acceleration vabz5c1k*i:i 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 E t2(rob;iha a)arth’s gravity on a spacecraft 12,800 km (2 Earth radii) abovao ( b;ira)2the the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelera:va.zgjq 8cq(k3xf ; ation g has a magnitude o. ;(ka 3xc8vqf :gzjaqf 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 accelerationw-s v9m/w-5puo:tbw v due to gravity on the Moon. The Moon's radius is 1.7pv- wvb wmow59/ut -:s4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet cak7(q/rxq9e kx 3q3shas a radius 1.5 times that of Earth, but has the same mass. What is tckqek3/(x s 3a7q9rxqhe acceleration due to gravity near its surface?   

  A hypothetical planetjt;m6 tpiaqx4sc+ nu2lvvvr 5 9ow)6-kix3t0 has a mass 1.66 times that of Earth, but the same radius. What is g near i;xp6iv it4os0mnv+)qlwtrua kv 26j93x t5-cts surface?   

  Two objects attract y,i q-nr 5x k.sw5mnfy9o77c:vn;u dheach other 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 ohv. md8.h;n,ok 2vrn +lqu3nof g , the acceleration of gravity, at (a) 3200 m h.vk3;+ odl.qohnrm 8nvu2 n,   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centgh5w uz;y2lu /7 edkw4er to a point outside the Earth where thegravitational acceleration due to th e5 w;4uzglkwy7dh/u2e Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphevze6ik4ajq m05,a vy- re about 10 km in radius. Estimate the surface graviz-m 0,kaqvea j5i6v 4yty on this monster.    $\times10^12$

  A typical white-dwarf star, whng1zk(rs ,c 7fg9 24ldb wdgv+1wiv 6cich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mdwlsc6z vv1g4dkc gg 1n9+,(i f7bw r2ass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space eg4 v 14t6mdxzshuttle. Your friends r gv41x4 mze6dtespond that they 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 located at the corners of aqmdp b,ljxnu/vu+/ta)h uo.us 58 :,s square of side 0.60 m. Calculate the magnitude and direction of n/s :dush vp q8j/b5uxta)uo ,l+.mu,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 pl 9-y:zypj. yhv 1datlft6 dp y,/x,5ipanets line up on the same side of the Sun. Calculate the total force on th6/p y dyxhdilz - ta.9t:f,y p5y1j,pve 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 gr 7n3dyyx( mob5avity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars. 7n5dm3oy (yb x   $\times 10^{23}$

  Determine the mass of the Sun using the known value for ,)rn glu3 0 :cclxfqh+the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, ,:l cfq3 r0cgul) hnx+Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular ornh xut*+ui4 9u1l9npmbit about the Earth at a h1m*nnhu +xl tpu9i4 9ueight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kjm il85 8h6gpg f/(bbem above the Earth. How fa8lmfg6ej5 gp( h/bib8st must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotah e)68)ptisovbaw.za 60+r *c8bam yete if occupants are to experience simulated gravity of 0.60 gbcmvoa60 p 6ihrz) 8.y tbaa+ ew)8*es? Assume 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 orbit the E:ihdl 65+hvuhy +5r s oe)n(syarth 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 masssi:5(y+eu6hv 5h lh syo+ dn)r of the satellite?    s ~    min

  At what horizontal velocit sp4;zerr5a 2goez*;wy would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around th *z ar4;g sw;re5ez2poe Earth?   

  During an Apollo lunar landing mission, the command module continued to ogb8.bj)hntq 3rbit the Moon at an altitude of about 1bhgq8 jb)3tn .00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are compowxlh,/ oau m.)sed of chunks of ice that orbit the planet. The inner radiuw,.hmau ) x/los of 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 diz),+(qq(i5fcj e 1 p-ybmqkitameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real w kmfyb1 p-c)iq q+jq (z(,5tieeight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center ofp)uc o;+-)c-by 2nlgbh,6 p jdnvu(ov the Earth's Moon in a space vehicle (a) moving a nbh ynuo c;)+pj6-pbc2,-(vvg lo )dut 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 ofvlwa o bf//w * cvj;--i.4rhwu equal mass. 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 ma c4h-; wwwa-/u*ibr v.lvj f/oss of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator th: m 6swzjj:meelj f*:7atjj:wjef: e: *mml 6sz7 moves
(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 suspendednftp s+/tl:2ah,ze s ; from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Whalz,n:/fts+ s at;p2eh t was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wil2j cy+kbr5zgmywx p1hx+ ug d+*/11e th period T , the density (mass/volume) of ypy /lbeh+xc1jw2 ugg* +kd51r+x1m z 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 ((ojw* pw bbvu3(4q d)tsk. sf)27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s sur*bw4jfv t(w) 3b. q)spuko(sdface.    s

  The asteroid Icarus, though only a few 2cf ya3v3mz16vsze.8 7fcvn4-ukbb r hundred meters across, orbits the Sun like the planets. Iuv r1vna63ybmc 4fbkz.2 s8z7f -cve3ts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5a;8e;dln k;z uf)zfa 8 $\times 10^{9} \mathrm{~km}$ 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. It comes very close tlqe4rkjj 8x7u..fp2uiof :- qsv9 xk1o the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law 1l sorjxeq4k8:2jq..xfiu7pvu9 -f kis half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxzem j 5adrv7xd4b*6 p0y $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distan9p jsa7zhya6nw 3u0cx ,nkb0,ce for the four largest moons of Jupitew xyu ,,h00 j97naspna6ckzb3r (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 tve;i zdwt62j6/r .t pohe Moon. 2pr6v;6twje/ zitd . o   $\times 10^{24}$

  Determine the mean distance frop ;n p*vg*gcyfb(wx- szjv6.3m Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and thg3j.;swx*zb* v - (g fpyv6cnpe 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 frag1cnv*t 5 wjqh+ments (which some space scientists think came from anh 5 tvj+*q1cw 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 artificial "pwlpsa8mrdu huby2 lv k01g7f2. 60m0o lanet" in the form of a band completely encircling a sun (Fig. 5-40). Thm f0 1p6rg0 l8su vdb02homa7wk2y. lue inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an aawq5hkwz: (3s rc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a fo5kq: shz3 wa(wrce 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 accelerp0q klh;(:ax/izwf7m ation of gravity be half what it is on the suh l fami/ p(;kzwqx70:rface?    $\times 10^6$

  On an ice rink, two skaters of 3ejn*m+/q :re2g hhbat)2 bbe equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 q enj+ mg3 :bbr) *2ehhb/a2etkg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravit,w8+ekf + msa pmz e8tokn96(xy at the equator is slightly less than it would be if the Earth didn’t rotate. x+8w6o mes nmf(9ap8z ,tk+ke Estimate 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 from tmt)bo7 7dwoicn0a7 e3 he Earth to the Moon experoc)3etbmo7n0 a w 77diience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,tn2 xe3ka tse 9e6mn., but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is e e2,e mnsaxt9n3 t.k6the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate14ss +q 9s endet+cwd7 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 rotation9qs4 cs 7+nds+wtee1d 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 verticaph;7,ff p9l q/i3bte ol 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 :5-mhbz11dnalsw2mz mass of a planet in terms of its radius r, the acceleration due to gdmhzl-: 1bszaw5nm 12 ravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verm8u3d38 o-py )msahqoo:fu c 7tical by an angle uf73ohqaodo mm8-8)yuc3 p :s $\theta$ 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 ip*3yj68rrf q:i0e ian s banked for a design speed of If the coefficient of static friction is 0.30 (wetfir n0 :r8*iaejpy6q3 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 th0dw8/ z(-inaj 4s:cve.ffia lat objects at the equator were apparentld4(ze nwjc-av:l siaff/0 8i. y weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dis+)n:v8 kt bxmntance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius +23j(uvov7 m j* putdsja4 da*235 m. A lamp suspended from the ceiling swings out tdd*js+j7p2ov(a u j3uv ma4t*o 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 Ea a54dcjop3r f8rth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size84rpoad3c 5 fj of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space c, d:2nnpo (lvTelescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that c pn:v( 2old,nit could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it d0w)wc g,afs 9traverses 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 feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with thecf9a0w)d, s gw road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellit/pw3 5ihnh84o zb :cb2 5xmvxqes orbiti:vp4 hhb 8 oz5m2qiw/b3xc n5xng the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 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),f;wp )qjis/ h; after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros ih/q w;)fp; sjis roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of pj+ pk dw* 6j9d1wm-iurepair. You are id1j*j-m+pdiww6 9 kupn a circular orbit of the same radius as the satellite (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 r5hol5rvc7y / ,v2wcl a period of 3000 years. (a) What is its mean distance from th2 5/ly,ho rrlwvcv57 ce 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 ;p7s*a w fmk 9j4yywk1actually "feel" yourself gravitationally attract4w7 y;yk*s 9kwp a1jmfed 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.a us4, g,nwl)e 5-46) at a distance of about 30,0wl4, )g,easun00 light-years from 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 c8c yg,vp8tywz. )fsz 1orners of a square 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 fw stv8.ycz,p18yz)g bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits p29g*yj)dsk8a 8oe jathe 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 dm42ns*uhzm3sweep second hand on yo* s4hu2dm3zn mur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swinn.v6l nvsj7c7 ghn ,w(g 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 vertical? [Hint: See Figjcgs6 7(.7,hnv lwnnv. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a.qa7ueax )c 2c car travelin qx.uaa)ecc27 g 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, utilin92 ,szix ndn,zes 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. 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 n s9d2,nz,nixthe 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.$\approx$    $\times 10^2$