Sometimes people say that water is removed from clothes in a spin qb*yn0wby l)ma00. fwdryer by centrifugal force throwing the waterfb0qa*0y0 m.l )bynww outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a skp/1szom 0* efharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explai*/s mef0okz p1n.

Suppose a car moves at constant speed along a hilly rgpe 0oq0dem vf2/(jjh3sl 03joad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (cljhej 0jd3f0 3m/oe v2p( sq0g) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round.x9e z;e ,,(:4:zo+aqlmg: hjwbhpryf Which of these forces fpbzx; :zh,o:(m,:gyj h9 +rewqae l4provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withc h0: 2d4ahjiyout the water spilling out, even at the hy:4ah j2id0ctop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three conts+qn2q. en8k krrh09 q *hd)iirols in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prodi rdnn2qkq89+rq.e*hk shi 0)uce?

A child on a sled comes flying over the crest of a small hill, .f )l rbsj(;hhas 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 chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s sec)j.;(rbhfl hs ond law.

Why do bicycle riders lean inward when rounding a curver -3o*3a cxrwe at high speed?

Why do airplanes bank when they6v3bbu: i 3l3yzvak*a turn? How would you compute the banking angle given its speed and radius of the tur6bia3k:vy l3v* az 3ubn?

A girl is whirling a ball on a string around her head in a1v*9de)e w n1zhgkodzc rx 46(kj.yjm.y6 6fr horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targe(zcg) 6fovz jj.6en4d.wymy961rh*dxkerk1 t on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force *0vgm r7wci(w on the Earth? If so, how large a forcewc0(ir w7m*g v? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in g a1odk*q6gr/lp1sp-nw.7 b hwhat ways would the Moon’s orbit gn-d*hwsa1q.p7ork 6l gb1p/be different?

Which pulls harder gravitationally, thejru:6h iw-+hl bl9 6j8ui .svb;qz m/e Earth on the Moon, or the Moon on the Earth? Which accelerh 6/6svhme j9 :w+ 8zb.bju;i llu-iqrates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'unsn438yd: nl6v k//c ji6hzvs. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of thed6ujnk/vc 6n83 :hny4z il/sv Earth to the other.]

Will an object weigh more at the equator or at the poles? Wd/hnri rilt+xj6dp7 s68z .(xhat two effects are at work? Do then .iphld sz7j8xxr+/r66(d tiy oppose each other?

The gravitational force on the Moon p,li/;s* d*j:exyt mbdue to the Earth is only about half the force on the Moon due to theljs, y:m;dtbiepx/** Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration u 9xc6 uhi;-ekof Mars in its orbit around the Sun larger or smaller than the centripe-h; eiux uck96tal acceleration of the Earth?

Would it require less speed to lan8a6 ksi fgq8+unch a satellite (a) toward the east or (b) toward the west? Consider th8a8gq6 f+ksnie Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in h2q7r;p9htie mwel)i 3 ;e :hka moving elevator: when the elevator (a) accelerati9mt; : h;k2i 3rh ewhle7)peqes 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 adverselqas /m(na:zf nj eb,+;8d uk8ly 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 simn dezmqs/kj8+u,la ; fa 8n:(bulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bes8ve/w+h xtm8 4ww wx1tween step xmwwx8es1w/8vt+4 hw s.

The Earth moves faster in its orbit arounexe 3iwv1-c tq139kuj d the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of ajev1t e3 ku19xw3-q ci 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 untihafqps gvmm(3+um, , 8l it was discovered to have a moon. Explain how this discovery f(+mmuas3v8 q,h,m pgenabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon0:wqi.j43 uifrta qc5's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider t4q:qi0u ij fa.5rct3 whe 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 travelinvn kc3vj )0red;0zo yxf-ht.( g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal3dlk3tn u ck)8 acceleration of the Earth in its orbit around the Sun, a3k3)c lu8nt kdnd the net force 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 disssq5 u. *y;1b9p9 utvkhgz :6iqqou y5cus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discuyiqkptbv s:1s u.o9g56quz5h9* q; yus.   

  Suppose the space shuttle0uxod;6 +q e-xwgi dn1 is 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 answer in terms of g , the gravitational acceg+ d0q xuonex;-i 1w6dleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of3 47 dzvom/,llva,yag clay on the edge of a potter’s wh,,a/o3almgy4zvlv d 7 eel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is red4 clc+mjj+6yt f 9r qt7g,6ktvolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is6kctd tctg6rl m, j7fjyq49+ + 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 rounhf2 q3j :lokc*d a turn of radius 77 m on a flat ro oq:l kchj23f*ad if the coefficient of static 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 and the :yf lg6si.*sz8tzu6 kh96/rlwi*y we road s 6y6t*u:8eis.wyk*lzzfg9 i 6hw/lr if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training qabl jmwxs s0.l1y4-0 astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt bymsj-qw4 xl.alysb01 0 the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating tui np5zb*a3fpg bu1)v :rntable 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 stati1zp3pu* abnf gi:b5v)c friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whe9zf fh22ff1/ug9erq y vl/5lcn upside down at the top of a circleglf/ ly1 q5/fcv9 f2hrz2u f9e
(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 (includik.wta41x:0 miz rxan/ng the driver) crosses the rounded top of a hill (radius tixn1 kaz/mx 40 .ar:w =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 wjfw q)at w ypayp2+k6:+ ef yfbk4.:7iould a 15-m-diameter Ferris wheel need to make for the passengepa:qwy+k.k:ei fwy) 42 jf6abpyt +f7rs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m dybe0r4/7id: +)bcnaz/ lmab. At the lowest point of its motion the tension in the rope supporting the buck70ei a+b/4ad:c ybm zblnr)/ det 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 b .qb,y3wstg. rotate if a particle 9.00 cm from the axis of rotation is to ,tqswby .bg3. experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "0usnr usbu 6,mh, s.3aroom." (Seer,nh6 .,suu 30ssm aub 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 circletl3 w2r8vo nv4v0 vom+ on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling bloc0t + v43ornvolv 8mwv2k (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 the weight (*xzb56xv0)yni i ok (ea1ogk of the ball which revolves on a string 0.600 m long. In particunk)yzki*1v o60b5 x agx(eio (lar, 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 banked for a car travh9yy2 rkbahr ,4 .4bqmeling 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 massex(pg;2psys(9z wuz tv i+9ci +*ny t7hs $ 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 310hq:8 2+asv qft $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exertx1q-31gji lzg 7ce )b:tgg it7ed on the car (by the ground) in jz )iq c-t1b3g7igex:l1 7gtgExample 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 acceleratexhu2: 7mds av8ajfz3tj my3gcpk8 +jk//a4 8bs 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 the road to provide this accel4v3bkpacx 2f 8u/ yz :7h8+ a3gsj/jmkma8djteration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle f+gkd,o+cylzo ( ,5.w lwov*rof radius 2.90 m . At a particular instant, its accel( +yl woc d,r l5+zkfv,*ogw.oeration 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 op9yj0. mymh7eiq 2 3ewf Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ifmmw.y37ejqyp0 9 h2 ei its mass is 1350 kg.   

  At the surface of a certain planet, the gravitam -zalqdz l ;8-szntm.txbv; +t/ 02tational acceleration g has a magnitude ;a/2vzt sqt m.- +l-0t;z nt8xldmbz aof 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. The Moon's radius 4t/ ehys:,0ajmnv 2x ic +arw33n:y tnis 1.74a4:ascn /3i2t0vj nth+mn:y3w xyre, $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiinrip38oaz, 5 jb+s m(us 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfomia38spjnir z5b +,(ace?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. b4pf*ya3 un 6/wg9yd,xt1njmWhat is g near its suu1dx9 jp6a t3gn/*m ywf,b ny4rface?   

  Two objects attract es+ m66.nvjbyett c.3bach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valkti2.t9f wb0owd6dvhp nu. 6( ue of g , the acceleration of gravity, at (a) 3200 m60bwd wvh9ointkf .2 dpt6 u.(    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earkxcp*g zzoa wb1)v3i 5 3z2uv)th’s center to a point outside the Earth where thegravitational acceleration due to the Earth isv)gz3 b2 c u)kpiwz3xaz 5ov1* $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of5-bz2ptv(e oj our Sun packed into a sphere about 10 km in radius. Estimattj2e bzp vo(5-e the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a07w8zk+vm uqdiy neak tp7-- 6n average star like our Sun but is now in the last stage of its evolution, is the size of our Moonadztky8+v-m0-q7w ike7 up n6 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 w- uu s8i buw1cbknz fk;i9kjc6o799)orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and91zsc )67ukokk cbjb w8nf9-iu9w;iu yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squ01wv01)5 wjw7e mkv*fyecfj0 kl n( xoare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exert0*ocvejkjwlk7ne0f0 )( f1v1wx5w my ed on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets tm gdknn/0)e8 line up on the same side of the Sun. Calculate the total force on the Earth due toknt/80 )edg mn Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0d1n ym .s0h1nr.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the sym .11 hndn0rmass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perirwuo,5;p3 hs-z ;aybdod of the Earth and its distance from the Sbzd3;,p hyr; su-oa5w un. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circul4t1;*e amktfo+)gif1ml6ij5 ozu x wj+mb.)t ar orbit about the Earth at a heik zt)1o.t*fe;wol4ijg1u5j)mat6 +xfm i + bmght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit x- h:f20iq5ej vm;yxa 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rel j2:a-hixfv ;me0 yxq5ease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experi)gan93x ax) czence simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed anx)g93zc a) xfor one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cp-f2zve9 hwf )ircular “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 depv zfpe9-)f2w hend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from tu7d 83lpvetl -cxc,9lhe top oeu9lctc l- 8vd,3pxl 7f Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module1rvz o93x ;vkm continued to orbit the Moon at an altitude k19 v; 3mrozvxof 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 pjnj+r*q lylig n31 1+that orbit the planet. The innerl+ryj+ 13p*qgnnj1li radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rifwhfrr j9x0d 8,,ps2otates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight tojxfpw0 ,rh, fr9 si82d 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 frwhz: -,tur6 zt.df/z dom the center of the Earth's Moon in a space vehicle (a) moving at constant velociwtdh,.:d6z/u -tzz rfty,     ----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 equawqi2k/uc22 vkub 9c w)l mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. Whavq2)w29 b 2ukc ikcu/wt is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevati3 :r2fu9id ocui44o aor that ifrc9a:oou i u43i2d4moves
(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 ceilin5 )ubesqs68u.yz ,cveg of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleratios ub58e)zuy,svc. e6q n (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of.doabgk ;8n xbcv** ;qh9wxzlel m/(8 a planet with period T , the density (mass/volume) ofmbz*8nwohk/8;(qav lx.*e9 x lgcbd; 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 periolvv vf7 2/d,+p l(l.(r c9uo3ieq gppid of an artificial satellite orbiting very near the Earlpp(/7pirv q9o.lev3 gucvf(i+,d2 l th’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th2/2j ,ud1 jb8j0qfuy e4dtyqt e Sun like the planets. Its period is 410 d. What is its mean 14j2y jdb qqye t/2u,f8tu0djdistance from the Sun?    $\times 10^{11}$

  Neptune is an average distanceb4;xeds 4wvq:u uphcy )7 ;)7eyw/h rd 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 :csi)z6b - zquonce 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 qu 6b)sczi:-z 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 m:h9y x*u/oeg 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, ansmto7 a (7zc.ad mean distance for the four largest moons of Jupiter (those( c77atza s.om 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 an,jevjjh s7+h 2d distance of the Moon. +s2hvh ,ejj j7   $\times 10^{24}$

  Determine the mean distance from Jupiter for each ventnsb55h: : k:3e mlof Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the m5 l: tnken:vsbh:5e3periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consist +zfuz6q )m1/s 19-7jqug(stlnu; v5sivbezxs of many fragments (which some space scientists think came from a planet that oncj 5-z 7msgnbiq )+x u9z qf61(v;zsu/u1vle tse orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes zfvk4gy(t 13 pan 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, thaty4gt1pvz3k (f the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a g;0/ mamcf8 ha.ntz1no s;q wj 3s6h.tqorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowestaa;zt6;mt n3shsnj 0.qw8/1 qmf.hc o 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 gravity be half wds l2g2/dz..ov qab z.hat it is 2qga.d. z vlb.zod/s2on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in gmo9 zn j)7,po3f4pep 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 f 4 7no9 pgj,oe3m)pzpthey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparen:+je l3,k6kg qz e.sevt 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.,.kek gv3zq :ee6ls+j What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travel aynij z9 .: n:;aiimjipo*t-.ing directly from the Earth tjii nmo:;z tiip .:y*n- a.ja9o the 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 you stand on a bath 9 0dqr0ivw zc0:tykw0room scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, ad0q zir kw90c00vyw: tnd in which direction?     ----待选择----upwartddown 

  A projected space statunx2-- 0)gcoj(tfv(mjnf: l/th m1 bsion consists of a circular tube that will rotate about its center (li)f(0c2 ntts / nuhxm1b(-o -jjvgfl:mke 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 (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 (yf-9 riec;t k37ueg*a 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 o ukyd8 (xiygq ;jv/4mp *ig+a-f a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational condjp;4*mg8i(+gy-au vykx/qi stant G.

A plumb bob (a mass m vw6,vwjkmmed. 2a1/thanging on a string) is deflected from the vertical by an vwkm j26va1td/m we, .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 j-yt(-5r:-pi0dofvsk )c s pqm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hv- :(fis5 )prk0 jdqp--soty candle the curve?

  How long would a day be if the Earth were rotating pkfs :c 3(7ljvmih62i so fast that objects at the equator were apparentvi jc h2pi6 3ms7(kf:lly weightless?    $\times 10^3$s

  Two equal-mass stars 4fuoy mlz-n547h t;womaintain 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 curve of radius (3sqj+ 3tqzd w*1laoy 235 m. A lamp suspended from thez 3q+(josqta1*dyl 3w ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, .bx --4 ;l;m, qe(eha/rbnyia .kcnjpit has been 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 's a person would experience at the equator of such a planer4n jahnkm,q;i-ela ybp;.(bc- e/.x t. 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 deduced the presenc+kwpqs d57u( h::sio re 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 i+rdwshsp( :7 ko5 :uqcore to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valle. kd4 h;e7udtyy 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 u; d4yt he7.kdis 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) utsxv wzwv9j 3qwm8o(-3 30q b vfhm93yiilizes 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 withiwv0z(9ism q3v mw3fw3 v9j- 8yoxh 3bqn 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 billiooy2,na8w*k-l,tl5u rsfpsonbd 5 3h(pt0 b)w n km, is meant to orbit the asteroid Eros ath3fybstp5,lo2) n,k (ao- w*0l8busd nt5rwp 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 shuttlov2:5r l qzwe-0b/n yme pursuing a satellite in need of repair. You are in a circular orbit on0-qmov5l wey / zr:2bf the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Whd +ut/lyd-l4rr 2ugv*at is its mean distance from udvd+ur*tl4l / g-2ry 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 n*-+mx m:0c3 f-cq uvz dacyk:xeed to be if you could actually "feel" yoursel*xa:y:q-zmfv3u +dcc ck0 x-mf gravitationally 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 Gala5n. lo;w3x kluxy (Fig. 5-46) at a distance of about 30,000 light-years from the cokw3;nul .l5 xenter $ \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 cor.gv7wtr/ix( f . bkghy570ollners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0 gty0.lb 5ik.gf x(7v wor/hl7-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 orbits thbo +7jct 0h pr.1p8gdzk 7iqkf+crz(4e 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 sweevr7l ds) ,,16ojzn rpup second hs6o7l d1puvrn ,), rjzand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cir.qhpqlgi k 46:cle below you on a 0.25-m piece o6kq:4ghi q.lp f fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway ikz8mt z)(:ar cs designed so that a car traveling a)c kmtaz8z: (rt 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, xlo, wsxi6.e.ar b8o0utilizes tilt of the cars when negotiating curves. The angle of tilt isors0o.. wl xbe6ix8 a, 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.$\approx$    $\times 10^2$