Sometimes people say that water is removed from clothes in a spin dryer tyl hpz 7jr4,3by centrifugal fojy 3t,plz4 hr7rce throwing the water outward. What is wrong with this statement?

Will the acceleration of-fagx g/n, ov3v,cyw0 ok-ir5 a car be the same when the car travels around a sharp curve at a constant 60 km/h asfgc, on y 3 0i/garovk5x--w,v when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hjhwuj*0v 1oa7j,n pit0wj4 d 1illy road. Where does the car exert the greatest and least forces on the road: (a) at the top ofn h0w1vtpjdujo4,1ai*7jj0 w 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 g szpwr, u9;x9horse on a merry-go-round. Which of these x ,uwg9 9pz;rsforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circl0t99 dv3akvqxe without the water spilling out, even at the top of the circle when the 0v9vx qtka93d bucket is upside down. Explain.

How many “accelerators” dz u n sna9kov2f1ep883o you have in your car? There are at least three controls in the car which can be used to cause tha382vu 8eos 9fnpkz n1e car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smal.pg9vb*s)3xix wmu 1,bo2ywul 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 his chuvy 3wus9b2*m b1xig. )ow, xpest 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 curve at high 4*wgppl ue /4dx,-vu rly6ui7d1 :yi fspeed?

Why do airplanes bank when they:./(kvsxqg 4v 2 an6llrnag q)jpd0f) turn? How would you compute the banking angle given its0krg g(qnvx 42 v ld6p aq:/s)).anlfj speed and radius of the turn?

A girl is whirling a ball on a string around he rjyw.l8/3q tqr head in a horizontal plane. She wants to let go at precisely the right time so that the ballqy t.rl/ w8q3j will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a g(73 dx a 8gl8rfdmrk8nravitational force on the Earth? If so, how large a force? Consi3 8k7lgddr (m8xnrfa8 der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double wu6rcce5; zuuuhve;( jb o; m*+hat it is, in what ways would the Moon’s orbit be differenu cuj(v;b*uoe;zh 5+e6 rc ;umt?

Which pulls harder gravitationally,1 6wiinjo-*s c the Earth on the Moon, or the Moon on the Earth? Which acce 1n jows-*i6cilerates more?

The Sun's gravitational pull on the Earth is much larger than t.5eqgwe 7kqizb3: s;she Moon's. Yet the Moon's is mainly respoe g 3iqk zq5e7w:s;bs.nsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at thzon6lgx f pbp *s--;d6e poles? What two effects are at work? Do they oppose each ot-pzpbg 6s- fd *;lxon6her?

The gravitational force on5d) ccbh/a2dr the Moon due to the Earth is only about half the forc a /bch5dr2cd)e on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or s0cs1ec9:;atr vorq t. :sr5db0 ltk 0ooo 4:ncmallersookrc:tta9 1 : r0 c.;lr:von4eosctq0 0d5b than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the ea 92q.( (ey0qk dwmxaxmst or (b) toward the west? Consider the Earth’s rotadk0y .2 qxwmm9(qxae( tion direction.

When will your apparent weight be the greatest, as measured by a scale in aob6nt;m9 rdf pfb r;*: moving elevator: whf;rdpo9:; b tfbr*6m nen the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lonw awx5vnu+a0 y,a /u+);mjr8 h e0zlmcg 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 (Fig. 5uh)v 0 mau+wcj, 85ar/mexy;wa0 nz +l–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 experienc7 c0gr:gw)pl pkh+;fy es “free fall” or “apparent weightlessness” between stepspwg 0prlg;h: f k)y+7c.

The Earth moves faster in its orbit around the Sun i8qh x;hcys- (en January than in July. Is theq-h(yh;cx s8 e Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discp3mlnik-6 /mpb-e fq vx*0 +eaovered to have a moon. Explain how this discovery enabled an estimate of Pluto’sn3p l0/b-xe ak6fp +m*veqi-m mass.

  The Sun's gravitational pull )j9 qr7qd fn:pon the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the dq:fr jn)qd 79pifference 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 198qh8qy 3i7 ;.hm6jiaep0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aru:2g5z t +pjg o1p3gyhound the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the E uhztyp gj 5+opgg3:12arth'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/z 1eho0 u pgav4rwi.0-kg discus as it rotates uniformly in a horizow40g e 10+/aihozurvpntal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in o)phs0 cp 9i+gxrbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acc9p0 g) i+xscpheleration at the Earth's surface. $\approx$    g

  What is the magnitude of the 6s0 )cbx8+ gzhfxjn5vv. z.fo acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per mijcv )sh.b +xn fg.fz6voz 50x8nute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string iya ly,i3 ;sr.o+cy+d 5h 9avois revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is c5ri+yavih l a;s.y +oo, y9d3 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 eb4u*rqpjn7j(/2 b :cq 7xjm k1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of st7 en4k/2qj*b(:cx j7jpu mqr batic friction between 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 pwlx4a mj c19p6t lb1t:oz;+yand the road if a car is to round a level curve of radius 85 m atpo91zlta x 6blc;4:+yjw t m1p a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designedow e9ix84roi cbfzu7n2 w+g(-kqqw1 7 to rotate a trainee in a horizonta(i74o wuqqn 7- kfc+2r wgx8z1woieb 9l circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from zjb2:n0cb c /8;6vqcfyb1kd d the axis of a rotating 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 static friction between the coin and th db61y b82/zcqndccbf;kv j :0e turntable?   

  At what minimum speed mustf pw :o.kj+lp8 a roller coaster be traveling when upside down at the top of a circle fw:j 8+ .olppk
(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 drive +ek3 jlw;hg m:layhp-g:g7i3r) crosses the rounded top of a hill (radwg:a7-lgh3i 3ekhp+ j:g ; ylmius =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 woad *j6+cmsm ws+j8o sh*vh-,duld a 15-m-diameter Ferris wheel need to make for the passengers to feel “we+s8mahmj ,s+ 6vdcshojwd **-ightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertichs1 7 fm.c,wspal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket sf7w 1.msch p,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) muz 3-wjrj)l7jm ybs79rst a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an ac3-jbj zr9y m77r jswl)celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walle9*.wh: o tddjhw8sy-f d "room9 :fowj.whsd 8d-yht*." (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-hocuk(in6/ mts2x3q5lu 7 t9x7 xkp5qbi qkey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole asi3xti(6l q x np752t qk9/u5bmuxk7sq 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 , preciseyctih)( .mf/n+j) fvvh,g,kf: (s+cm f ut8zuly this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In cv z .ffhf/us+knmj8i (f mu:tt) v)(h g,+cy,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 perfectly b 1 t:vzz6sj8lfanked 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 masseu g7cdoq*/ 4g6hnhc,je3s* zrs $ 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 verbq9-(nz:y h nitically 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 cenr *c5h-4oq+ oa;zxz) iw ty*kmtripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speyt;c )5-oz*q zkrxo+ m*iw4haed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapozdy2dg 26p 7wjdp3qu0lis 500 accelerates uniformly 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 the coefficient of static friction have to be between the tires and t y 7dwdq320pudz6jg2 phe road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of(8 sw e8mw4rro radius 2.90 m . At a particular instant, its acm88row r4ws e(celeration 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 rz0l5h xgcj s02b6c jr+ qs07nig y 7jpzk*u*9cadii) ab0zkp60 * 7jcnr gu 092cxb7s+i5 *ghzjycqjslove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravicc: t3ki06bun(mz w0ytational acceleration g has a magnitude yn:k( iczwu6 b00tm3c of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon.q,h s+vr3o6diqa dxt/ls:o (4 The Moon's radius is 1.744 3qd,qxoss+i6ovdr :a(htl/ $\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, bu,qr4ds *ak7z oj3kd5u .(lvpo 3-rgnd t has the same mass. What is the acceleration du3u4(j,n vk3odklq-pdr 5*o7. rgsdzae to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the )la5)oiwmr h )cfs5h7 +plhx -same radius. W5hsxh-)o+ h7c)m) ilw a5rpf lhat is g near its surface?   

  Two objects attract each other gravitationally with:nd4tnywd -i 6k,f dl; 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 acgv0+mstr,9 xtvw6 w hzpn 12.eceleration of gravity, at (a) 3200 mmnwv 1vp 902re.h x6tg+tsz w,    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinn bp 7( wlm(*6psk7cmct outside the Earth where thegravitation 7km pcl7bc(sp*mw(n6 al acceleration 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 s0yz y5gz, j2,n2vovxrphere about 10 km in radyv,r ,gyj52 n02xzvzo ius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avecxcan*5 e :4yzrage star like our Sun but is nowcnzca y4* xe5: in the last stage of its evolution, 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 weightles; z h17h,exefus while orbiting in the space 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 calcula 1 hzxh;fe,7ueting 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 sq, pgv5,rqfmi0uare of side 0.60 m. Calculate the mmp,g0fq,5vr i agnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planeps j,4p0i.b 9uzx d*xuts line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sxpdzu 9 0pj*ibxs,.u4aturn, 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 gra2( :m )k)g+oesuo yfemvity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km,)e eg soo )+fumy(:2km determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usin w4)dawnz/hg 4g the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lan)44zwdg wa/hws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabl qnbt/-vf n(efw6/ly/ e circular orbit about the Earth at a height of 3600 km. f yble n/f-6//tnwv(q    $\times 10^3$

  The space shuttle releases a satellite into a circularnzwx04n uw rj 49*b/nl)rm k0u orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rr)w rmun 90/4l4 knnbwu*j0 xzelease occurs?    $\times 10^3$

  At what rate must a cylindrical sphbp r,--dnliydfv)9 1aceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as yn)bi, 1-lp-dfrdv 9hthe time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular dfw2g;kzwls8378 h fb “near-Earth” orbit. A “near-Earth” ord8l f bz8f;3s2ww7kh gbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launchedd,h)n 3jcxqb7u4 ;enwi-tph,* uu d1l from the top of Mt. Ev,x n4;1j3htdu *u7 pwdblq-ceui,h)nerest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, thetovljupb)5u,b+ 9 s v0 command module continued to orbit the Moon at an al ,l0pbsvojv9ub) +t5utitude 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 ice that orbit the rxtv60qry-m m :*gh g(9r 4buuplanet. The inner radius of the ringsgmy*g(q69m-04:b vu hrrtuxr 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 onceh pyw*yi ;ohbu27 -tk+- jsx . nqgk2ojv:-r8l every 15.5 s (see Fig. 5–9). What is the ratio of a person’ss y-hh:;r*jj-k 72in b u8 pgvxl-+yoot.wq2k 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 4200 km from the center /chcf yi9 +j86yj4ir:nq.r lwof the Earth's Moon in a sp :r fj/4 wi 9hcqjlcyny8r+6i.ace 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 mass. They ruf78 wv7 th*mare observed to be sepaw*u r7f 7t8mhvrated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevp4vdwz mk.bz.3t dxnk)bq /31ator that moves bddnv b3)k zx4 m3tkz/q .wp1.
(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 han-h2v;yeifiw 5iq(ip/gs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 5yiqwi2v fp;i/h- ei (N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wi3louwoj hta j/a2z wrqz178 b* ;k4g)hth period T , the density (mass/volume) of the planet i2zqhjat4b z)r;oo7 aj kg1 3lwuw8h*/ s $\rho=m / V=3 \pi / G T^{2}$ .
(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 period o6dj3w6jp::iwe :k l pvf an artificial satellite orbiting verydpk e3jv6 pw:6j:l wi: near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun litax.07 cjez2t 5l0 hqpke the planets. Its periodhtcxt j0eaqlzp2 . 570 is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dk .tesx400po7t3 krs eistance 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 0 1xg9h xs)oprexr -a;gm42gjroughly once every 76 years. It comes very close to the 1pg9 2o4r g-m)je sxh0x;xarg 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 is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gala 6ql2zbk:;/ y) l n;4zjyvthtexy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 four largest moom 5hhl(r -f:g ,8fb80sf0pzapvyk8muns of J8s (v -08 fmp0yupkzm,8ha b :fhgr5flupiter (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 6mj)w3 zpt(v2s ljlro ,s 4qy882 uqyithe Moon. rj68s l ,piywuqj4v y8st3mql2)2zo(   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s m: xwe5plkh-2rst ai,.oons, using Keplerp5 wil kr,ex2t:h-s a.’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 betwry( iw,fj yo;u s9(/ ho0uas(neen Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited thuri(9yu/s0yj n s ( f;hwoao,(e 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 n cac itl3y*5rz;+*wsp.t5o yan 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-Suywtp c ;+cl*r5t*z5a yni.o3sn distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanginmw, sr;ltpepl/ .p 2h*g vine (Fig. 5–41). If his arms are capable of exerting a force mllps ,p*2r;.he/ wt pof 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 gc 8,egcp-qa hxkm;l14 ravity be half what it is on lxcgmapq ;8c14, khe-the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands anu;d3hu;01istry px7l + ( njspd spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their in j13il;yx;sp(ut n u7r 0+dphsdividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appays9fm )9qme2b8mi gf+(rsdq+ o k5 kq7rent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effectq mq+ob5si(9 e+8km yqs)mkf2 d7 r9gf. What fraction of g is this?    $\times 10^{-1}$

  At what distance from th5zk r(hzw0r:yz rrf:r1b 1qr (e Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Ear rwyqf1h1b0:zkz r r:zr(rr 5(th 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 elevatk8q dn9q/e x7vm hso72or, it says your mass is 82 kg. Whan kqodsexv m/q7 7h928t is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo)uvc.4/; hj8ocihjyao 8 .uaeut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube ha. hvjoc;e 8).yj8hu/oui4ca as 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 vertic+hoat/pd bes +,g0775np h mltal 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 tl.5 ax6q:yy mverms of its radius r, the acceleration due to gravity at its surface and the gravitational constax5 :y6lvmq ya.nt G.

A plumb bob (a mass f99cjn+88wbt k. jnvrm hanging on a string) is deflected from the vertical by an angle.f 9njk tcw889rj+bvn $\theta$ 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 bang gq zot8cx).5ked for a design speed of If the coefficient of static friction is 0.30 (wet pavemenxc)qt gz8.5o gt), at what range of speeds can a car safely handle the curve?

  How long would a day be 9v6 2 o.:m/v0j g6e2c1buf mfic mbiyuif the Earth were rotating so fast that objects at the equator were apparently i2ob1ucu 2imm fc /jvg6:bvme f.y906 weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart zm 9vt566jkmdc1bv 1bof 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+j:bzp c7gsp5xuy ;7t yftq k(3ki i)p6bh09v a curve of radius 235 m. A lamp suspended from the ceiling swings out to an jy9quv7;sf+k:3t5z 7g()kixbh p c itpbp0 6yangle 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 b14xl24syhv;f )dyi0sm6 zkpd een claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 2 zdkysm4i d1p6)fx ;h0vy l4s'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 Telescope dez7fg:cd.e.bt : q,lgv duced the presence of an extremely massive core in thegtd cl:., vg z7:e.qbf 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 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 consw0gl* x2qs-whm1kd k( tant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lighteswks whg dlq1(2*-xk m0t? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sc4p(hzlb c6z 7ystem (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 satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” Thzcbc 4(6lz7p he satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travel o0)m)7 xa7xvoljc0ffing 2.1 billion km, is meant to orbit the asteroid Eros at a height of abf7jm7)of)0v0o lxxa cout 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite ,yhh)13av -qolf zm,fin need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behinl yhffv,-o 1hm),z a3qd 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(y.1taq9+ang z4 bm- p p9qwda is its mean distance from the Sa9m.q4 dgn-(+b1p9qwtya az pun?   
(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 woul:jaurx* 7 l9jsd need to be if you could actually "feel" yourself grarj:9s xj la7u*vitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dipa0pvh ik:)(wvp ft8w i-nf 5-5v6qzostance kw-:5vphz5i6 pvq8 -ifw)oafnt0 v(pof 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 on each side;ix8 +d0kmc+s sdm*bp. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bm;d* mi+p kx sb0d8+scottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg )b6oeo;5x-l/r hxgfe orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep sq8d oz erj.pxe7+ e(-second hand on your wrist watch?e87. sdeq z+- joe(xpr    $\times 10^{-4}$

  While fishing, you get bored and start to swingv1oae4vheobg05/2.b d)/ d.miq r zay 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 fishinga bq vbz )od1 y/.oe2d4m/arhv50.ige line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiusg736( *ioe6h u lz fu;0vi akub.yb.qj R in a new highway is designed so that a car traveling at speedq0zeif(hu 6 l.ju3b7 buy*i avo;kg.6 $ 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 7 * c.q.(ohda ys6op23 ufzbbythe cars when negotiating curves. The angle of tilt is adjusted so thb.o.bhzy*f6qs ay do2u(c73pat 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.$\approx$    $\times 10^2$