Sometimes people say that water is removed from clothes in a spin dryer by cent:lu86kw z5 xegt0q3u mrifugal force throwing the water outward. What is wronw6u 3m qu:t xke508zglg with this statement?

Will the acceleration of a car be the same when the car travels aroundw;r6:kr ie5 ih a sharp curveh5 : reri6kw;i at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at cop: *ffmjw*g 4e )w(apunstant 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 between two hills, (c) on a level (wfgmuewa4:f*j)p* p stretch near the bottom of a hill?

Describe all the forces acting on a child rid+utw8r 8:pf4 uk) a,vb md3dlcing a horse on a merry-go-round. Which of these forp8 cbv)fdlrta d,:4 ukmw3u8+ces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vepzj 1f1g.qma+l.b* j brtical circle without the water spilling out, eve*1 jbgpmla f. 1zb+q.jn at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Therx xcg3m:l+d e0e are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations d :l+dg3ex0x mco they produce?

A child on a sled comes flying over the crest of a small hill, as shown/g7eo x2no+7dlg *lzf 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 seco *f lo27le+zox/d7 nggnd law.

Why do bicycle riders lean inwb arq3m6ze(1 ebihln)/:s snf:39g -8ainbsqard when rounding a curve at high speed?

Why do airplanes bank when the 23 (jwt 2u byx-l g/rrscz4xn6sv)0dty turn? How would you compute the banking angle given its speed and radius of the r3n )c rsy4xvd- x(stl6z b0 wg/ju2t2turn?

A girl is whirling a ball on a stra -rm7 (cw ,gqb8k/s7c33fp nzt oib.ring around her head in a horizontal plane. Sheki wqa7on sm-8(3cz3.t7b, cr/r bfpg 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 go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a u,ane2: x y96/ ; bavdkq6uui;ftqb1l 7jj/yuforce? Conqb/2;u6:/tuujx;qb7vu ayk6 1 fedny 9a lij,sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublet75 qj8t*nss/iv*kuoskfc3 2i h)h m; what it is, in what ways would the Moon’s orbit be diffecttk )ifo /kh8 qus;2i s*5hjsv3*mn 7rent?

Which pulls harder gravitationa.pb g2p ub . 93epfx.ylylqr**lly, the Earth on the Moon, or the Moon on the Eartg. pbxu ly.2lef.bq9*p3yr * ph? Which accelerates more?

The Sun's gravitational 8j k34eoc5qhzbp ,f4hpull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one q hc4kjf 53ohzpb, e48side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What cypp6q; vdz.v/m ta;) two effects are at work? ;z)v .vdyt ;/p apqmc6Do they oppose each other?

The gravitational force o)0mog*jdzbhvd b 43h *n the Moon due to the Earth is only about half the force on the Moon due to thh4*jg0 v bozhdb)*m d3e Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbitzyyx ul7mr )4tv( 8o;n around the Sun larger or smaller than the cez4ln8vuxm(yr 7y; to) ntripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eb2 r;z4 g*s15owo;lfxp7kg f sast or (b) toward the west? Consider the Earth’s rotat; f* sgb2g1x7wos zf4r ;5olpkion direction.

When will your apparent weight be the greatest, as measured by a scale in a mo0 sl5n 3u-gfwsving elevator: when the elevator (a) acsfs3 g nwul-05celerates 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 a:5f;:wgbvvcqe esa - ,7nx80v5kudxwyi4 b+periods in outer space could be adversely affected by weightlessnesuv4i-c8vf7:wxwy5 n qgadseb,0x+v;kb: e5as. 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 aspects of gravity you can think of.

Explain how a runner experiences “free fall” dq0:vmd8ph*5 fd +fll or “apparent weightlessness” between stepsfhvl*+qd:md d p085l f.

The Earth moves faster in its orbit around th/-ua;hhopjefs35/x h0a y x4qe Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This ishxh/ ;pu y-fe04xh 5aas /3ojq 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 u ngl gr*/,8ypto have a moon. Explain how 8u lry*n/p,ggthis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet )0 dj2j9)lf j;dmqvan ;fin q)the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round mo ;am)q)f jfi;2nd0l9)njdv j qves 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 travelingil-07chsl9 fcid hu45 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth i1:tvy92l m7 n,l a o8mze3pmbjn its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the yel z23mn1mj ,: a8pm7bot9 vlEarth? 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 5 ch0 l1hzq/ pgq;qf4eon a 2.0-kg discus as it rotates uniformly in a horizontal circle (at armq0/qpfh 1qz ;4 gcleh5’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface,t+s xjtf4t :w. and circles the Earth about once every 90 minutes. Find the centrip+ftjw4 :.tsxtetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge j3d;ntz gzvh2fq(9v :of a potter’s wheel turning at 45 rpm (revolutions per ming3( 2n; zz dvf:q9jhtvute) if the wheel’s diameter is 32 cm?   

  A ball on the end ofj vn e(2f0cg*r a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as f0rn (2*vjcgeshown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of radius alt6nj nns 1g)8 ;nor677 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 of the car? rs ;)nntn6 jon6g8al1   

  How large must the coefficient of sgc7opj9/ kb8fd 2fba (tatic friction be between the tires and the road if a k do/cgjb(ff 978 b2pacar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rott j *x+q6gr;-/n ht+4at(iqdaz0 zirtate 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 r4t ht-*x(/+ q+6 djaizzatigqrtn0; 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 /xeuzeu 5(v x(from the axis of a rotating turntable of variable speed. When the speed of thvx(u/(uez x5ee 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 the turntable?   

  At what minimum speed must a roller coaster be traveling when upkj1 gny8iydpz. l:.j:side down at the top ofd z1pjy.n::yjg. il k8 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 950 kg (includi z5:yms8r0:at u;tfz cng the driver) crosses the rounded top of a hill (radiumz 5z 8;:rufysa0 :tcts =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-diameter Ferris wheel need to makpi)jk koh:a11e for the passengers to feel “weightless” at the topmost point?)h1j ko:1pa ik    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi7q*:/gnk 12gdx*yarh7* x5hae tkcjius 1.10 m. At the lowest point of its motion the tension in ay/jkh retdn:*k7 c5 xgqi1*gha7 *2xthe rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrif:q rsc*(ssmz8 uge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,z (crs ssq*m8:000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "mtt6w*nque,il6v, 92o7e cexroovo* clneqee ,m9 i w7x2,tu66tm." (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 5+0m-hq6jx2pizg jm.vzsj f 2 ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connectf2j2sm0 5 g ijx6-z z.vp+jqmhed 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 the weight of the bzs1 ( u z:.squml8e-j(ti6n puall which revolves on a stis(8quepz js:zlm( 6-n u1t.u ring 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car trau6) z*0 tt :wgiaqwb02blzuv7veling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses* nk.5 -bdinfm $ 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 maneuvd/o l.l2dv y;oer by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exertea8s g9oj,xggspwrk) gx62 piz;:-o :ed on the car (s8pw o -z g o);,9g: pgxga6:xir2skejby 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 Indianaw 8r 8c. v pio8n9vkmr;jkp(mva((hd:polis 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 9m 8mvvp(hapc(( n8jrd . kr8:wvik;oacceleration. 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 hori o;qm95,hbrt 00ts*kgysne.h zontal circle of radius 2.90 m . At a particular instant, its acceleration is kbrso e0ht.5gy 9t;0n m,qsh* 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 o,xs1-hvmh qr 7f3- lkbn a spacecraft 12,800 km (2 Earth radii) ab7v s,lmq -1xfh-bhr3kove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelera8r ri xj-6jhi9tion g has a magnitudr6j -ri hj89ixe 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. The Mors j-hosvsg 0.t *m7f1on's radius is 1.74sfs j 1ohsr*-tmv0.g 7 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a raquj-+ 5bp7-b saw(laydius 1.5 times that of Earth, but has the same mass. What is th- 5wa7uj+baq b(sl p-ye acceleration due to gravity near its surface?   

  A hypothetical planet has a7x90mrliomm ww l3zb9 74g8we mass 1.66 times that of Earth, but the same radius. What i z7r9wolwi97bmmel8g w0 34mxs g near its surface?   

  Two objects attract each other gravitationally with a force of 2. yqmxjc4(:v (l5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravwc3 d+j) zt8akity, at (a) 3200 m cat zwdk38+j )   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ebeok qq3ut5 b ph 4)3v4r8-kmhk4v,o barth where thegravitational acceleration duek3mhp 4vb3bk4 ob-4 tqq85uo erk)h,v to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivshpl 51n 1tc jy2 /iy-rfw4.gge times the mass of our Sun packed into a sphere about 10 km in radius.fg tw.n5h-l rpj2yg/cs 14 1iy Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star li( x d(zw8/a .tgorxhq7ke our Sun but is now 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 o(gdhxo 8a qw. /t7(xrzn this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sw x2,s8pzob z/huttle. 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 /8zwp2 ,zbosxabove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sqf4p8z)dn3 h m-j/p kyide 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on on ppnymj h/dzq3 )k48-fe sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on tht5 lmazh*6fm9ah yp),e same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (p*ma5hy6 t lmz9) ahf,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 ozc,d 45xs 5fvmf gravity at the surface of Mars is 0.38 of what it i 4zfv5 c,5dxmss on Earth, and 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 tnjtuv- *)fn2f0h-( 1 akexhkg he Earth and its distance from the Sun. [Note: Compare your answer to that obtained usinnhkkx( tnf2ah )-f0 1eg v*-jug Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed ob3 ii z5o4b5yqiy 1i pl0a w/o8x5z-uhf a satellite moving in a stable circular orbit about the Earth at a height of 3600/5i5l4bu-5izwo3yz 1 pa q8ib 0 ihxoy km.    $\times 10^3$

  The space shuttle releases a sa3zmltf5 ud2nvc0p9p b+p:a7p tellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative 3pa pp tpu:nbfv+m7l9d0 2c5 zto Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate n) k f9co/to gez9dul0 zl8n,8if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the zkto 08 f)9ln 8cnzodge9,l/utime needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbix54od lp /ek0nl t4e wl510mest the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is veksd5l/0e4n1 o0xtmwp 54e llery small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal vel1 (rv +o iqi8m*;s,ugttt-uuuocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aro(-g+;q uu*1 sto,miu8tvti u rund the Earth?   

  During an Apollo lunar lfg.q5 lzcbab,sy0 v-x/ r0bg+ -oa w:randing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How lonrqz:rv-x,+.a ayws5/ fb0b-logb0 c gg did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plantlis)) ( p 2*yf-06 fmgtadkmtet. The inner radius of the rings i d6t-m fm katyf0i*gs()p2 tl)s 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 rotat)h i anymq8. p ts9m8yklo3u3/es once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at t aqty o)3 83k8h.ps/ni mmuyl9he bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 (h0rv6 sspb7v fy*mf9km from the center of the Eaf60sph9vfvs y(7 m r*brth's Moon 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 of equal mass. T82fkmnv3 +jddhg+ x ; 1mb7kabhey are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is t2+mfdvhk bb7djg3nk;+ a 1x 8mhe mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a r;8:f hoek ;n+lw,y p9g0wg/vqhz;dm 55-kg woman in an elevator that mo;9d/pv w,l r q;g+zmy 0efnw8hho:gk;ves
(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 frz- t2jvebckfv a6*+j*ot pl.p5q)g8 wom the ceiling of an elevator. The fj*.zp)c2gqvbok65 p w-+v8tle *j tacord can withstand a tension of 220 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 surfacex 4/zocof fx4k0v1 o:b4)ykaw of a planet with period T , the density (mass/volume) okxbvc 1/fy44k:axof0)o z 4wo f 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 perio+b/a 0w:53 nkb (zk6xsoe /g/szqwc smd of the Moon (27.4 d) to determine the period of an artificial sat+0n q/5/c:zs aw( b6ek/w3xzsogbms k ellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a fsyiy/zv26 cdb qx8mq1b )3-m faos23 zew hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is ii2qzv3y )qsza3xm6-2d/1b m osfcby8 ts mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc7 )a)qkzk6eb oe 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 orbit5ogm hu/rt* q3f,iw o1)ur-dps the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is h*g w ord omq-/ )hu3,up5fri1talf the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy ) /lg2x vpioo8ilr8y/$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 moons g qdbz4 9o,eg)eqd3s4of Jupiter (those discovered by Gale s43, e9g qb)gdoz4dqileo 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 o8u26f4ue bp 1efikdpf3 dh5w8f the Earth from the known period and distance of the Moon. f351h u e8uwfepdf2id k 46bp8   $\times 10^{24}$

  Determine the mean distance from Jupihy+c)tyx2y5 (0 drdphter for each of Jupiter’s moons, using Kepler’s third law. Use d hdyy5t(+ h 2yx)rc0pthe 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 between Mars1jttg sa zop3wf5)5d5 and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but 5f)swgpa 5tdoj 3t15z was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial rq6)p aow.,mv"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 q.6mwv,a r op)own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging iufn3 8*mguy 3yn 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 ca3yym f ug38*unn 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 acceleratio/vsgg d 4g-d/l(,,kb ms q8rq+vva4ron of gravity be half what it is on the surfacel4,+ 8sdmg//vr4r-gg(,q kvqv dbaso ?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutuo :(c:eara ag9al circle once every 2.5 s. If we assume their arms are each 0.80 m long and the e:a(a9gco :rair individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotat.q(z. l.ahxy*cve xk-es once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction o(kh.v-a.x xlz.e yq*cf g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s6:-lvw qr*-9ud cf plspacecraft traveling directly from the Earth to the Moon 9rl qps-c * -u:fwdlv6experience 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 bathroom scale t0hj2r89pi :o : tunn(ozhgr+ in an elevator, it says your mass is 82 kg. Wh8+ho (oi:ruttn :hg0pnr jz92at is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station f5dn3uj 0ts.s0d h0dvconsists 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 (revolutio53jf0d .0 u h0dssvdtnns 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 aircrcu 2t+svqqu/,1ooz a vbax,/0aft 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 accel i06mw3az.z sseration due to gravity at its surface and the gravs.wz a0z63s imitational constant G.

A plumb bob (a mass b1 eckjzh(2m 3 m hanging on a string) is deflected from the vertical by az1bkhem23 (cjn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient ol5lui1iny( l2p4t6 0dqw:zws f static friction is 0.30 (wet pavement), at what rdp:squ llizn4 wy (6205tlwi 1ange of speeds can a car safely handle the curve?

  How long would a day be if the t 7pdc0l8 d,9odm;ti8bivm ,e)my-es Earth were rotating so fast that objects at the e)-mvdd,t0si 7lde,ib9m ;o8yt 8me pcquator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintainw6;puwq(h:a hulw(( xe*j f3o 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 radiusyn tszh nzf )+d x4q6:m8mf n6dr+:+ub 235 m. A lamp suspended from the ceiling swings out to an angzd+n: 8fd )x4 tq+rny msuh +bfn6zm:6le of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times am yjb0vh -7lt+s massive as the Earth. Thus, it has been claimed that a person w+yvl-jb mt h07ould 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 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 deduced the presence of an extm-.)5 le:jh qreaq8)u boc*uuf(wyj;remely m yr*qj5-f8wohelubq.)ca) uuj e :m (;assive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core 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 q+8+ikoc/rc k 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? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A? icq+ 8kro+kc/

  The Navstar Global Poh7-ov5(m5 jv2lsd1. pf*)oxvx t jm/g god u(xsitioning System (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.” The satellites or5 1(jh.vtgov-jlxofmo5u2s/( xx g*7)dvmdp bit 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 km, ir 9);hrk/fwf rhn6y*b z+rj -ks meant to orbit the asteroid Eros at a height of about -9r6f* wrr;+knh )rfk/jbzy h 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 in need of -0xu4f-b5k cq;sgohrrepair. You are io h fb 5;q4kxgs0-cru-n a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period9vjlknfft /qke3y w+(;kszf 3g9 ,, hi of 3000 years. (a) What is its mean distance from33esz i,9ff;wh/l +kf k vy9q,(ktngj 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 vaet1;l xi ;8tb* xzbx30 9edlsblue of G would need to be if you could actually "feel" yoursel;b xx3zlbtx0ei bslt e8d*;91f 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 Gi, t*re08qw ( egwy9tdalaxy (Fig. 5-46) at a distance of 8 9we t(ge,wtd *0yriqabout 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 o6 -.ao9aittba. xa6l mn each side. Find the magna.ixl ta 9mba.t6a-o 6itude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 54ah;pp0by1s+ ghm tb7500 kg 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 dc: tlf. srs.2twrv4c-t vt):experienced by the tip of the 1.5-cm-long sweep second hand on your wrist wat twrv2l)vr:c4dt -tt :c.ss.fch?    $\times 10^{-4}$

  While fishing, you get bored andql stwn. 8)hk39ov +jr start to swing 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. Wvl tjkw )on+q83s r.h9hat 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 highwadv9 pp)9skid*y is designed so that a car traveling ap* d)kvisd99pt 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 traix nnswk;:6 ac1n, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers expers6:n; xc wkn1aience 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.$\approx$    $\times 10^2$