Sometimes people say thatg mvl6i s4x+6n water is removed from clothes in a spin dryer by centrifugal force throwing thi6svm l4n6+ gxe water outward. What is wrong with this statement?

Will the acceleration of a car be the sdyxz5 .)e in+7x /edvtame when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same ty/nx5ed.i 7 )dzvx+espeed? Explain.

Suppose a car moves at constant sp lh 6bo228ldyb .ph x5bz2u4doeed along 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 betweenhdbh86pdy xlloob 25 4.2zub 2 two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child;3 k)kverxh j; riding a horse on a merry-go-round. Which of these forces provides the cenk)jrv;3h xe; ktripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle witho( :i)k)i()zhs x8tf7tflek wy ut the water spilling out, even at the top of the circlihfk8 )x7)lfty:wkt()(zi e se when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are atpfzd /;jn56m s least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleratio5 z/jnfm p6s;dns do they produce?

A child on a sled comes flying over the crest of a smr rm+ddep(frfy7,2 b ,all hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the mb,prfd,(d7 efy 2r r+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 inwa-ckkzi e/g60-hrj4x kx sv/dzf701j vrd when rounding a curve at high speed?

Why do airplanes bank when they turn:ioq - guuf4)b? How would you compute the banking angle given its speeuiof)- gb: 4qud and radius of the turn?

A girl is whirling a ball on a string around her head i(g 5okple clar*m3p:; n a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target 5;cp: ogka(3 pleml*r on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force onhs 2)g6k 2ocwp the Earth? If so, how large a force? Consider an appleoh ) wc26g2spk
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double w4+)gm-cwimuk3( ylu vhat it is, in what ways would the Moon’s orbit be different? mu+ )yi-mk34luwgv c(

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on th fgn4x n(zb:x,e Earth? Which accexx:z(4f, bngn lerates more?

The Sun's gravitational pull on the Earth is much larger than tha1.al*e:fg 1tv a jq5ee 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 othee.*ea1 v qjft: 15agalr.]

Will an object weigh more at the equ-begu) 1(vrllator or at the poles? What two effects are at wgullrev1 -() bork? Do they oppose each other?

The gravitational force ow fr/1t* mmkcof.y/yv/ 0ly1h n the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t thkt/*/yf.rvm11yc0ofm w /hy le Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its oe e,u,iyt*wab qf1 u15*ukj5nxpew*e1r: u6orbit around the Sun larger or smaller than the centripetal acceleration ofik,1*,r:nato up 5e *fqj wyeu5eb* u16 ux1ew the Earth?

Would it require less 9vtqvkp(dz 28snla5 .speed to launch a satellite (a) toward the east or (b) toward thevqda .5kp(2vsl n8tz9 west? Consider the Earth’s rotation direction.

When will your apparent weight be qe777;i. wlpn fvu5 bt in,9vithe greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates u ne7 qifi57n w9,.luvpv7;bti pward, (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 ouu;s5 -(vu4oawueoq oy /s5yp *ter 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 (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall,/yup-a(e4 oyusvuoqwo;5 * s5 (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner ewwup lla )6r.qe ,9yqbz a7w37xperiences “free fall” or “apparent weightlessness” between step 6up7rwq .,3w )laz7w eabqly9s.

The Earth moves faster in its orbit around the Sun in Ja.tv1z4zmrp m , 4+nawnnuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a facr, amnv4z1mz4wt+pn. tor 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 knv2 ah *av0g)6a4pwuhh own until it was discovered to have a moon. Explain howauahp2 6a w4hv*) h0vg this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on tq y4ywmz -e(at :-zh-lhe Earth is much larger than the Moon's. Yet the Moon's is maewyz ( z-ql mat-h4:y-inly 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 traveling 198a1q3e:icsy: c0 :lbn sw i8,qm0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbituu1km bzmxo30cf;. 1 l around the Sun, and the net force 1m1 focux3bulmk;0. z exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as itqr1+evxfaq . xle 3s9. rotates uniformly in a horizontal circl vq r39q+1ae.ls. xxefe (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle ut .a5 lyhd75e vnd. (bsy)(luis in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your ans ntd.b.y e)a(7 ll huu5sy(5dvwer 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 mhj4, nzf :zsi ,qb x.+omy3i4on the edge of a potter’s wheel turning at 45 rzox z,s +bym:f3m.4ihqjin4, pm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical w:5ch/zo3z h4ngnel +u6tc 4vcircle of radius 72.0 cm , as shown in Fig. 5-33. If its suv4h6nz4z on/c letg5 3cw:h+peed 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 tur6j4mi*fer*0 fvjg /v fn of radius 77 m on a flat road if the coefficient of static friction be**vv4 f60frmgj/ i fjetween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the/4u xnha6 r;y3bg1 dnn road ifxn/b a;nr 4n3duy1hg6 a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighk 8bg 1w2b8tvtii)*pv b.l am*ter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast gi **mitl bw .1p)2bbtk 8vva8is 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 o7g;dqs -f5v dy(yr1 yeo e5op:f a rotating turntable of variable speed. When the speed of the turntablev5e:; gyo-y f5d( sq o7yedrp1 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 static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be t0tnuk,b )0-gduu4at traveling when upside down at the top of a circle kt0,- tganut4bduu0)
(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+cq8 bz,jck6 p the driver) crosses the rounded top of a hill j,bz+c68kcpq (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 wdwa0nh fi/i*/b x/oppc1/ t7d ould a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlehfb /wn d/*iait0 p71/pxod/css” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. tocuta;34o 1-h2n r;)dxavq q At the lowest point of its motion the tensruox4o3tc1) 2 q- avn ;;ahdqtion 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 particle 9.00 cm from iufzr 1-ro5yh86pf5pthe axis of rotation is to experience an acceleration ofr5rfu ph f5618 -pyioz 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carns : vh/yels1j3ex75q wival, people are rotated in a cylindrically walled "room." (See Fiw57vseq3 xljye1: hs/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 M ) is rota2vzw)) vqe+p+m i*/bvgr*mxh ted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected twive*+ g+ pmqxh)2/m*)vbvzro 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 time, by not7hkc0vehf4- wl vqs2( fpl2)t ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, findq022e)t lc(vp fhhk4- fl 7wsv 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 perfect2yxf y2lgey7zk-/ 8 i0vpyceuv -c4;aly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses r9ci) au72nvt7ly47kd 0ycn p$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vz,ltz g2r 4os9i ph/x/ertically 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 componen/a ho9baz:n0nts of the net force exerted on the car (by the ground) in Examp9zn:/aba oh0nle 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going4(-nvj wehu0)sk9 n sp 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 th(hnjus)s e0p9n4k w- ve 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 hor *tfldim9 a;-+nq yo.vizontal circle of radius 2.90 m . At a particular instant, its acca;v*oli. tq -n yf9d+meleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth rax; uxdwx 0 :;c7+o1j(suhqilzdii) abovexdq;s 71ou0h:iux ;cw+j l (xz the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hap599jdh gq n4ds a magnitude of 5dp jhd9gn94q 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 caq,)t(qp, ysto gravity on the Moon. The Moon's radius is 1.74 t,cys(qaq ),p $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same mas9 l4hicwkaavu;k 7u i94xl+e9s. What is the acc xuv49+ c; wliike4la97k9h uaeleration due to gravity near its surface?   

  A hypothetical planet *cxefyxc t;fc (c sdfp/9 +:1bhas a mass 1.66 times that of Earth, but the same radius. What is g ne*;dpcce f c1s9( xx/ f:tcyfb+ar its surface?   

  Two objects attract each other gravitat- .ma)ngmhql*t( lgt4z1s+xcionally 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 wk 2o o0tc+1zdgravity, at (a) 3200 m 2dzw+ c0t1koo   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr yindd9w.i5lpy3l91kij 1 fg) s ,3djfom the Earth’s center to a point outside the Earth where thegravitational acg. yd95y,njf1 d3ipsk wi1 fdij)9l3lceleration due to the 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+(qd nmjfm+3x sphere about 10 km in radius. Estimate the sux+jm q3m dnf(+rface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once*ag-hn7 e6h 8n. ghwtxrse /r6g,lr7xdim8,e was an average star like our Sun but is now in the last stage of its evoldhlnh8x/7g t*nia -wrms66 8,eg,rh e 7ge.xrution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the sp xk59yyae-3xi fr/k8 en ocas/gj87l+ace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculatinrag8 y/jx5 fe /7k+ k9 o3sniaxcly8-eg the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squz81in4h:*hz 1e wrm4gjmrf*iare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other t*wrj4mz *i:m hrn18h4 fg1ezihree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sunab 1a6yvd+w0 c6wvp7b. Calculate the total force on the Earth due to vpb1y+7 b660dw aa wvcVenus, 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 the surface of Mars istaq75j p d.lno/o; xtg 8qb;-u 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.b/ q;t-p toxjn.qgodl75;ua8    $\times 10^{23}$

  Determine the mass of the Sun using the known value for d..tg iy/3u,uef*it g the period of the Earth and its distance from the Sun. [Note: Compare your answer to that ogeui gtyfu*./tdi3, .btained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinbjefi-9l6 ( n ss+rv(qg in a stable circular orbit about the Earth at a heig96(rejiq (bls+f -snvht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above tht58ewlu75y, ov rech8m h7) bve Earth. How fast must the shuttle be moving (t8 mhw y7)ohe5 r l,c8vue57vbrelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occj-bm1 oxy yh.vh:2 1fcupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, - . 1 o2yx:h1fmcyvhjbFig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circu6s3j *pz)w6idn2+zg7,j7 qi)d1 xbug oyxqea lar “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 mass) za37juxxs e2yonp1d6)jdg+q *wzg6 i7,bqi of the satellite?    s ~    min

  At what horizontal velocity would a satellitefp hx zq.z 7k1m /fgoq.s7o8w. have to be launched from the top of Mt. Everest to be placed in a circular orf .7qs8.zq 7kxpow z/og. 1mhfbit around the Earth?   

  During an Apollo lunar landing mission, the command noabj d o/83h:vkbe .l- 3/vvrmodule continued to orbit the Moon at an altibh3-jov:akov ve l.8/dn r3b/ tude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of iy- 1c kzz1i+,km1bqkxce that orbit the planet. The inner radius of theky1i+qxc mz,k 11-kbz rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fitx89h:sfszet-rbd/ykz*z k/ * w i4g7g. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b)z7:i dt4-et* s w/kb9*zskyx/8rfz hg at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200v/j r (6a) 9uz-krvmeln i48sa km from the center of the Earth's Moon in a space vehicle (a) moving at constant vela /)rne arvzu(sv8l ik49-6jmocity,     ----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 mass. t/7p,m3bjd1eyxo-e:q m f 6rqThey are observed to be separated by 360 millifrj- e:o y/q6 bmqmxe,713dtpon km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman;42g c9myxddo in an elevator that moves;xy2m dog4c 9d
(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 ceiling of an elevatr,:y:.lvtcp p or. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimuyp.l vct,:rp: m acceleration (magnitude and direction)? a =   

Show that if a satellite orbits v hmd1yayo:o+p jn91p9ery near the surface of a planet with period T , +onodayy9h :9mj1p 1p the density (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 determine the pf l6 *5bqj:xtmeriod of an artificial satellitlmfxt *6b qj:5e orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a : s zcp4 2p-tn;ba;wnjfew hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun? apz4npw;s- b cjt; 2:n   $\times 10^{11}$

  Neptune is an average distab q66xi;kkwt:f4d o5y pk/k9lnce 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 mare) :rm wqs)vs4k+el79;un once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s thek nssvm94wr 7)rmla+)uqe;:ird law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of 7snjzu1x(mo2 the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean dist.z)m+mlq h nfo c8c+)c v2dqmmti9/a( ance for the four largest moons of Jupiter (those discovered by Galile( )d2t+va/c )co nmimfqlmm +9q.zhc 8o 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 distancet j;)f+v :vlrl of the Moon. ;:lvf + vtj)lr   $\times 10^{24}$

  Determine the mean distance from Jupiter for each oo ax(x,r0misx f4(g 2cf Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuesox4 g(x0i( ,r2xcmsaf 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 Jup*zwjxu(3, s vv)esut 7iter consists of many fragments (which some space scientists think came from a planet that once orbited the Sus3 vuez*ux(wjs7 ,)vtn 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 desdc2oo )4k8t un jd8r;jcribes an artificial "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 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 yeaj 2ooc4ut8kjrd n;8) dr, in Earth days?   

  Tarzan plans to cross a gorge by swinging )xyu. h5yks+min an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a fmuysy 5kx). h+orce 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 of gravity1rmncj 6* dm dtu w,6u-/h1(u ;18qluarpciiw be half what it is on the surfa um(, jp cu6c1n*mi;u68riqdt1lwda ur-1/hwce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cifgzd :1t7 (agmz- :wnyrcle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard aregt(gaw-1m 7z fd:z: yn they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appar62j(e bgtzam3+y (z/ 8 curyoient acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractior2mgy ju (zocz(ab6e8/y ti3+ n of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Eao c1uy3 5sa:ewrth to the Moon experience zero net force because the Earth and M5cw3oy: 1sa ueoon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom+ lh x6led36wh scale in an elevator, it says your mass is 82 kg. What is the acceleration of the ellex+l6w6hh3d evator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circh9;,scz5b8xc,kufp b ;qa 3jcular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. Wu,h cb8zc;,;sb95k xj f ap3qchat 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. 5–43).kmzt+i,/w d5;x o, vmc
(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 forxlst: xt-dcs *g pcb+/o ;32s+hh4wul the mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitatio2lxbulh st g s;:to++4/pc -dw*x sc3hnal constant G.

A plumb bob (a mass m hanging on a string) is dgmwe 8k:fuv.i 8)db +qeflected from the vertical by an +buv w:qkdf.i8 )meg8 angle $\theta$ 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 the coefficient of s4 co ey68cu2nvtatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle 84conuv 6eyc2 the curve?

  How long would a day be if the Earth were rotating so fast that obhiey p8xq :,fppwclf)dt ;3+q72y( qbjects at the equator were p fxyqe8:pt2)qfdq;7 3b+ci phywl,(apparently weightless?    $\times 10^3$s

  Two equal-mass stars t6. /q6x.y+s(wek ym v6uxpnc maintain 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 at a constant speed rounds a cy/oun qa (y b6-uzrvs54f9q (iurve of radius 235 m. A lamp suspended from the ceiling swings out to anqs-u549(nzy ybrquv(6 f ao/i angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massu40 jfnhzelu ) h;g2j)ive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gjh )hjgnuu f 0z2;e4)lravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space 6k+ cmqd0ivgzn6wh82 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 tw+ m k6q08nchi6d2zgvo 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 :hzuw)) v3zc l as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curv3z wc vz)h)ul:ature 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 the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellitei wi)nj0 md5gja g9q4pmx;.5 ps 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 accuracx g)5wdi ;an j40g9m.5m qjpipy 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 Rendezm6ye .84lwz*k +khxg 4 x3bz v5gej+qsvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km .4jz.ms l+ xyw* 85xezh4+bvgk 3kge q6 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 shz;yf+w 7)2 viazp +eyuuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earthivy +zae+zu)72 pwyf ;), 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) Wh)bu25n1ijpq n u 6xzx.at is its mean distance from6nxni5xpu21uz jb ) q. 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 ojadhqk,q*aj6 bjf8* b:4 txup*:oj :if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like Fu6 ,aopq *dok:jx48jjq:**:f ba jbth $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46zar.o ae hh f0r:,fdnq3 .:752 zrdrpd) at a distance oor:7d.z0 d5f f,hehra: pqnrr2z .3adf about 30,000 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 corners of a square 0.50 m cg(y+ 00xesqxo .k:bfon each side. Find the magnitude and direction of the q(koxy00gces+f. x:b gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitnkyh2)7f.jtsh 1ts ;hn ,5sdps 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 t ftfjnjd+.n9 ivqi(zfc1)v71gtmx5 * he tip of the 1.5-cm-long sweep second hand on your wristj if f.x1dt9f*cq 1nm7 5zn+vi)jv t(g watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around wf()llk*tux 31xtf +wr0pdy r9x h-s4yf5kw - 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 anf -yr(t k45d- syl fwh9 x*1wfwk+3)tp0rxulx gle 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 designedc p1e2yv6c tqlw,4wpn sb+j06 so that a car traveling at spespwew10j46 p+, cntc 6ybl2qved $ 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 whezivy:/ j . 3bx llv6rd0ii0yg2n negotiating curves. The anglevil :l03rb vyy. 2d6zji0i/ xg 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 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.$\approx$    $\times 10^2$