Sometimes people say that water is removed from clothes in a spin dryer by cq8+mn, t+fyow+i a-xln ggi 8.entrifugal force throwing the water outward. What is wrong with this stat wqi l g-8 +mgxtf8.iyn+a,on+ement?

Will the acceleration of a car be thov 5cbaw4;((xpvysj h,f3f /ze same when the car travels around a sharp curve at a constant 6 (fxsyc f5zp(3abh;4 / jovwv,0 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves acxm6x yfia0c,9 49ki vt constant speed 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 betw0kiyx,m cf9 vi4cxa6 9een two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting o0 4/gj rh;uly3k6i znln a child riding a horse on a merry-go-round. Which of these forces provides the centripetal 3/n yg;z i60rk4hljluacceleration of the child?

A bucket of water can be wkw79hyz9n te-5v r0rl hirled in a vertical circle without the water spilling ne-59h yz ltv9rw k70rout, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” d0r9fob(r js 7rfg2muw2k*xf -o you have in your car? There are at least three controls in the car which can be used to cause the car to f22b *f frko 0jrx7-sr(mu 9gwaccelerate. What are they? What accelerations do they produce?

A child on a sled comes fly1dshucn8epo 1y *kx /-ing over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does n8-*s/ohcdn u1kxpey 1 ot achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at ,vjvy6 xc/jx, high speed?

Why do airplanes bank when they turn? How would you compute the banking anuaop1h/c .lr0- vzr9r gle gihuv1/o l r zc-rrpa0.9ven its speed and radius of the turn?

A girl is whirling a ball on a smule i r*nwu;fl y6z77 9lr6yr3d9h/ptring around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let d76*r/ mn6 zhe3 9;yr7uyi 9f lrpulwlgo of the string?

Does an apple exert a gravitational force on the Earth? If s:;qhp/ 4jbt fyo, how large a force? Cbtph/yf 4;jq: onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, i/yp.ft .r 6v5la +ybi /wk)etkn what ways would the Moon’s orbit be difel.5ftb +./ kk)y v6py/wait rferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moorg0. 3rgy)+3 ut,ajfp 0 r4vfsh omg,on on the Earth? Whi.og r0g pragj0,vu3f),rmh y43otsf+ ch accelerates more?

The Sun's gravitational pull on the Earth is much larger than t4lv)35 pl vxezhhuk:5he 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 : u l55vh)34e phkvxlzto the other.]

Will an object weigh more at the equator or0y; bntz9gj935dafn b at the poles? What two effects are at work? Do they oppozd 3ybt; 9njagf05n 9bse each other?

The gravitational force on the Moon due to the Earth is only about v kw j276pvjzs)+l6lahalf the force on the Moon due to the Sun. Why isn’t the Moon aw6 jvzv)6l 7pjk2ls +pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arla jd(;ee .c*round the Sun larger or smaller than the centripetal acceleration of the Ea(*eac;jedl r .rth?

Would it require less speed to launch a satellite (a) toward the east orv9-goi *txl1r gx c,,r (b) toward the west? Consider the Earth’s rotartg-cv*xi,lor9, g 1xtion direction.

When will your apparent weight be the greatest,/l(2cp wj2fqxh :r(w q as measured by a scale in a moving elevator: when the elevator (a) acceljq lpf(r/x h(q2w:2cwerates 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 long periods in outer space could be asd8p, * tlknmf )-9lp51i wzejdversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspectss 5wjndzifme-l9*,lkpp t) 18 of gravity you can think of.

Explain how a runner experiences “free fall” or “apparenuh*x-chw :oe +f2s y;st weightlessness” between st;2e h+wsuxhc fso*y- :eps.

The Earth moves faster in its orbit around the Sun in January thci/md(sl(i 9- /9lxi*guhgv 9pkf to 8an in July. Is the Earth closer to the Sun in January, or in8gh dxii9p(il /kosgm(/*9c9uflt-v 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 discovered to0xy7su.y jr3p i-;u8nz82.vy bc mthx have a moon. Explain how this discovery enj .py s.u80u r7b3zxhcm;niyt-xy8v2 abled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth -iy qf-:yp9j/zf4c el/xl.h c is much larger than the Moon's. Yet the Moon's is mainly responsible for :-f i9z / /yxhcfqp- c4ljel.ythe 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 19a *kl+yt:nx:l2ko 3bp 7w0uqs80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ed.yt+adj hi1 -arth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on ydt d+jia-.h1 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 it rotates uniform1 izvtv 6h3,ijhdkglt3 ;:( holy in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speekh3ih 61ojiv3hvdtgz(t ;l,: d of the discus.   

  Suppose the space shuttle is in orbit 400 km frm38fd pml.f*f om the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at tffdl*mf p.m83he Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of aha9i;q k qwudgx2+qio;* m u4/hf+x m0 speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter ismqui0g2; xhh iq*wd4uao q ++kmx;9/f 32 cm?   

  A ball on the end of a string x 26jtoh dz7txqjv )5a w2.m84thew(xis revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp(tea 6xwxoh 2.2zjjht478w)xvq 5 dmteed 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 cub ;+oibf )it ydi:c78n-9grzar 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? Is this result independent of the mass obcn79o +;d gu8i)ir-zib: yftf the car?   

  How large must the coefficient of static friction be between the tires and t7)yixxr a8e+v7owc rn7r h1d /he road if a car is to round a level curve of radiuix87 )hera nro 7vyd/xw+ rc71s 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed 10 qqxyqz+89ydlo8tm 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 is she rotating? dq8z0q lt my9q yx1o+8   rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable sp(ga9ac+,6 mw dfkl d s/0n2yxmeed. When the speed of the turntable is slowly increased, the coi dd6afnx9sgy/2(m c w+,mlka 0n remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when 8jex*33)hc3wtpi+spl2v j w y upside down at the tw ix) tjel8w 2vp3p33*shyc+jop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 95 th8gzy u0q94v0 kg (including the driver) crosses the rounded top of a hill z yuv84gtq0h 9(radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-d5yay: ki9eqi2 qxh5w5hr7xbn:n z;x7iameter Ferris wheel need to make for the passengers to feel “weightleewi 9h5:b 7r7n;qk xzxixhqny25 :a5 yss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ratak4sinkwg(wj1* )7eh l,t.0cgxp 6hdius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket i j.t6h0 tp *a)kcxhi4gs elg, 7ww(kn1s 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 fre52bo q+jg-f bom the axis of rotation is to experience an acceleration of 115,000 -f5 obq2jbg+ e$\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated w 3d6 s-vca 4wqnbq hu;zh++*uin a cylindrically walled "room." (See Fig. 5-3q *awu4z+ nwhsc6+d hquv b3;-5.)
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 a2x;i.*fhvbm: r6k1 dhen;in+ t fw xl1 circle on a frictionless air-hockey tabletop, and ixriwxf;;k+ vdhl .1 tb6hi*1fm2: enns held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring th :xa( 9sr3v2 zftkrq l-yj*iy .:lipt5e weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude -xl*: (qp iatr32l frvszy 9.y5tk:ij of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelin3 g,ci85 htdpmg 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 massehd t /csbb8 ;vb5i4w*n6 ov.cls $ 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 vertically at 310x 1f;m*g96fbdvjbrq9pm.dg 3nnm h)* $\mathrm{~m} / \mathrm{s}$ . 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 compa n mk3c9eb 06:-infom+gny5wa2 ,vhionents of the net force exerted on the car 63v kn2: w+,aian59mie-ng fhcy0 mob(by the ground) 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 )*q ii.,tk tntu,ryz*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 hai rtqz,tuyt,. **kin)lfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal a9 n +adi9ksk7circle of radius 2.90 m . At a particular instant, its acceleration isk 9a ak9si+n7d 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 1h uc lc1t9iwj7g kk27:2,800 km (2 Earth radii) above the Eai9wk1772cg :hju k cltrth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gr0c)hf7ah(m sdavitational acceleration g has a magnitude of 1dahcs)7 0f m(h2 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 acceleratio6etziebua5b a9yf 7x(m./ae.2p r.vyn due to gravity on the Moon. The Moon's radius is 1.74 eaaua/fy75 ( me26 rvep9 .tb .ix.ybz$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiuj9m yl ws/8+qjj;d. who8psl4s 1.5 times that of Earth, but has the same mass. What is the acceleraly4lm p8 j;/w.ow9ds8q jj+ shtion due to gravity near its surface?   

  A hypothetical planet has a massaa76o.p3rs/ 1 ay+nki,eukqy(b+oc7 z s mo 2z 1.66 times that of Earth, but the same radius. What is7b, z 2iyos+k3+aoeqmz 7 o a pr61sy.(knc/au g near its surface?   

  Two objects attract each other gravitationallts,-oa z7 s*oky 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 ac cvr7(pn5aat+obg,9 f celeration of gravity, at (a) 3200 m fot cvna(57+9pgrba,    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthr0w (a1 wt*ivue:ux- c where thegravitational accelerati1 *ww0uarutc-: vx e(ion 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 pac2tb5 q*je m5, xwbdwr yl 54/wed*7yjoked into a sphere about 10 km in radius. Estimate the surface gravi*obxwyt55q7 j drl5 4,2b*wjwmdy / eety on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averag* 8qd 9ad.bf pxy6ptln+y17gq e star like our Sun but is now in the last stage of its evolution, is the size of our Moon but h 6l8qbtyfpgn17pd dx+ *9q.yaas the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightle43xy+v))oq y x1 ekwwlss 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 calculating the acceleration of gravity 250 km above the Earth’s surface in te1vx3q wo +exklyw 4)y)rms of g.   

  Four 9.5-kg spheres are lolmfvi) -d w7w:cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gra7df -wi wvl):mvitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sidebnot2vht y05a+r(q l 1 of the Sun. Calculate the total force on the Earth due to Velvn b qya+2ro(t0ht51nus, 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 is 0.38 +o8 bmnywep42w7y)te/r c3 sqof what it is on Earth, pe+qe) bc3mow4yw8 2 yr7s/tnand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of th jddo(7orca7 5e Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s la7d5ro (jcda7 ows, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a w )o+4lywrey;cohy+ho ,5:gqsatellite moving in a stable circular orbit about the Earth at a ylqw,o+) ;rw:4go5hhcy+oey height of 3600 km.    $\times 10^3$

  The space shuttle re ak3o,dha14zy leases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? ay3zdo 1, ahk4    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are t-eb 5j5 8swljbsf:78ijrpd h )o experience simula w5phb:sji b5r-flde8)8 jj7sted 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, Fig 5–32.)   

  Determine the time it takes pi )vo(8a7f oifor a satellite to orbit the Earth in a circular “near-Eaivo7 o8()fipa rth” 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 of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top7 fknk r6)ets+ of Mt. Eveetfkn) k76+s rrest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued n u0e4b5pd cr6uf+1crto orbit the Moon at an altitude of about 100 km. Howrpccu164fr+n ued0b 5 long did it take to go around the Moon once?    s

  The rings of Saturn are composed oyh,h5 ei hi0l lxbta8tu99x o8u3xk -:f chunks of ice that orbit the planet. The inner radius of the ri5iibtuko9he, 89:-x x 80ltax3uhhl yngs 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 onc*r7oh8 (15wntbwbh+kx2 tu 28jul/z rig r4gwe every 15.5 s (see Fig. 5–9). What is the ratio of a perg 7otwi8krl4r ru jg2 x8nbh ww1t25h(*bu z/+son’s 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 ass) gz./q9ukrstronaut 4200 km from the center of the Earth's Mo sg)qz/ 9ruk.son in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars/(ax4g iu(o26l ul kzv of equal mass. They are observed to be separated by 360 mill6av( k2u ouxg/(i4z llion 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 xyla uji 8 y/q(bi1u:ep4p7s4of a 55-kg woman in an elevator that moves i8ia uusyp4 q p(e7/jl4:b1xy
(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 suspen jfa2ya5f5c6a ded from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitufca f556aay j2de and direction)? a =   

Show that if a satellite orbits very ni.k g +zk*ts6near the surface of a planet with period T , the density (mass/volume*6s+k z.ngtik ) 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 thne +*)d8. bzw9)eavdh 5d spdee period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Eartevddha 9e )n sp+* b58dw.)ezdh’s surface.    s

  The asteroid Icarus, though only a few hundred mr)asz (a a24bjeters across, orbits the Sun like the planets. Its pes 2(aajaz4)br riod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanca x6x3snn-z1 5hf( mbje of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years28n; o/ * ;omisqsnr bejeyh*:. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate ; j eimy/soenn*8;:rhqso * b2the 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 cer1nhnng5 ie)3nter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance fs u2rluro.a4f s8g/* qy.zae5 3scy;jor the four largest moons o;rs jye.4z*ssu5 a2rac qul gfy83o. /f Jupiter (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 d 1lvnplg.qgmzmw :5/2istance of the Moon. n1q2l.:w vlp5/mgz gm   $\times 10^{24}$

  Determine the mean distance from Jupiter for ea9jl3nhdvrm (i;f8(g mch of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare tidfv 8( (r;h gljmn93mo 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 fragments 35dx/llnf o+y (which some space scientists think came from a planet that once orbited the Sun n+5/l do3yfxl 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 de+aby dz7i16h rscribes 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 za16 ibr7+yh ddistance (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 frominb4-,h w;d lx a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the low4;dih-nx lb,w est point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface w/1z8hl3/sxt7 g4i vhvch nh5o ill the acceleration of gravity be half what gl zv1/hh8h siho57cxn4 vt/3it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands vdcm* :jfvj,5q q,an2 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 kg, how hard are they pulling on *qc 5fv,q2jnd j va:,mone another?    $\times 10^2$

  Because the Earth rotates oncc ax72) cn5pu5ujv.y ev:dpd3e per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotv :7cxue2py d jnc)5d5uavp.3ate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from th us0 q .da)kn).:upu mxqeo98le Earth will a spacecraft traveling directly from the Earth to u l9:q.nqsuu ) a0ome.d)8 xpkthe Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yvz krm(-l .5kdou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which km(dr-5v.z kl direction?     ----待选择----upwartddown 

  A projected space st* q uv 5abz8/,8lk44pmpmhd ccation consists of a circular 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. What must be the rotation speed (revo mqpcu/4p54ab8dmclvk,z *h8lutions 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 air6 ex*cfr (* ke x+m9cvzhqz 55(gu(suncraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the af/7 -ssuazw :+mvf9qwcceleration due to gravity at its surface and/z+sm u f vfwsaw-97q: the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected frp s2 qu12z2 er)jr:umcom the vertical by an angle 2r :)spqu2 cm2eru1j z $\theta$ 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 coefficiz4o;m9:bght : x -vt1dpkrv2t u1/ tvaent of static friction is 0.30 (wet pavement), at what range of speeds can a cut1: /vp2mtag thx1;-z:rkt94odbv var safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at stv kk 3pmc,w3 :4q0vithe equator weret,3:kpc sv w4k vqi0m3 apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanceul.tvl 7 cz,h 5wj1.ypg(ew v2 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 round 9sf23 n,tpdcggj9p z:s a curve of radius 235 m. A lamp suspended from the ceiling swingsstgd 2 9g3p: jnzf,cp9 out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thp bjx4cf9pu:r x5) ph6us, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since peoplu49xfp pc)xh5pr6 j :be 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 Spacy89ry z3yw -ob f93eete Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so d9yyft -33ywobe ze 9r8ense 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 constant spe f,tnpcex4 f7xhq0s+ )ed 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, 0cx4+7hqsnefftx p ) 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 Systv l;/y1h gsj c fg9js7s7cgzs)isd*.3em (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satel7s*g.fh) jzy9/c 7v d1lgs;csis sj3 glites, 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), after traveling 2.1 billion b)9ld.. cyjc ikm, is meant to orbit the. )i. dyjl9ccb asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle v2b7r;;bb ye m7* qjlmpursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abo;b r lv*b 2bq;em7jy7mve the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yearmu/zxu*qv/kbm*,5 b x s. (a) What is its mean distance from the Su*5,kx/ub /vmb* mqzx un?   
(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 app tfcdv 2f+:7ctually "feel" yourself gravitationally attractedvfp +cp2:f d7t to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cenc db*8tpfqs 9en :sir4 sx,q5+ter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 9bs8 ,t*sirnseqfqx:c54 d + plight-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 cp:9.pvgf accj) o k9l,orners 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 aa:)kp .f c cj99,lgvpot the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earthfi -bn+lmg ezoe5s ( /p+l)vrx2s v. +b1wcrq( $ \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 q v9ha+m7oyyar 87x 0j1.5-cm-long sweep second hand on yov7joxyqra8a +9 0my7hur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ac 9:+6nzcvtpebt * vbxhxd/4/round in a circle below you on a 0.25-m piece of fishing line. The weight mbccpx6 /t / tnbxeh:vv94+*zdakes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in ajmj.pp 4)92,wa rjazu new highway is designed so that a car travel4)z,p9m2jwpjar .uajing 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, utilizes tilt of the cars when nm f297zh yd7rki ve6:uegotiating 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 experience7uiefhm:v76z dr 2 9ky 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.$\approx$    $\times 10^2$