Sometimes people say v7o p:1ibbpia ix 6x+/that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong o6+ p7pib1xv/i :xabi with this statement?

Will the acceleration of a car be the same when the car travels ar 3yk/s0.b ztzp-y zsbbve;*qki2*f h,ound a sharp curve at a co ssty kb 20q.*zfv/ze;,kh*pz yb-3ib nstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at ck7rr p6h5b uox0l6o-gonstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the tor7xo0 b6-l5rkg 6 ohpup of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-g)bfanu) ofbr*w3ku*u 2*qn 9round. Which of these forces provides the centripetal acceleratr)nkaw* 3og)*q 2u *fnfubbu9ion of the child?

A bucket of water can 2w 4ag. 6bmn sh)5xlzhbe whirled in a vertical circle without the water spilling out, even at the top of the circle when the buckws b.42x)l am5gnzh6h et is upside down. Explain.

How many “accelerators” do you have in your car? There are at leasjfa34n(/druy 2bcsjo:z.o-i 2rana: t three controls in the car which can be used to cause the car to accelerate. What ar2fo4crru:abj(:z oiyn/nj ds. -a2a3 e they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smal yw(s6i/p gdx*k,yi. g56gb ell hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal fo*/ xdbsg pke( .65i,gwgy il6yrce 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 roundins*dcq wq*4 82lk*pvilg a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankin)nx yc6o a,b0cp:cxn 3g angle given its speed and r0xbn p63cy:n ax,c)oc adius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pl:66m vn;f4mn qea0qi (k dfmx;ane. She wants to let go at precisely the right time so that the ball will himn6fv;(:n4diq 0qf mkm6; eaxt 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 forcrk:2jhz+x vmg*k yw(z 4si jr 78dtl4.e? Consider an appv m xj 2ztgs44 kr7l+*:zhwi.r(k yjd8le
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wha2jp,cok( gtvh+uxx8 (d1 * tkft ways would the Moon’s orbit be jgp*8dh,cv o1f2 k+kttux x((different?

Which pulls harder gravitationally, the Earth on the Moon, f5l 6,npeu 6aaxk7tk04qox.zbkj2 m5 or the Moon on the Earth? Whioa2nf6jq6 e.lxkkzax 5k7t5pb u4m, 0ch accelerates more?

The Sun's gravitational pull on the Earth is much larger tha 2d5vb wv2vu2mn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in u v2w5v2m vb2dgravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or /rvqc2-u mh(y at the poles? What two effects are at work? Do they o2rv-u(qh/my cppose each other?

The gravitational force on the Moon due t5,ot+t.tucz y4 1v egto the Earth is only about half the force on the Moon dt1ce 4 tgvy uz5,+t.toue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su f1m gwtou/9 ;ccg-:qmn larger or smaller than the centripeqtmf-9mg1;/wg c :uoctal acceleration of the Earth?

Would it require less speed to laun+,ktq t7xh 1qoch a satellite (a) toward the east or (b) toward the w tq1,kxt7 qo+hest? Consider the Earth’s rotation direction.

When will your apparent weight be rrg t9 m((kd,9mys1 gxthe greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it 99rx(g1(,d t mksrgymbe 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 oa fby82w/nb bv+zle* /uter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a/evl8w*+y znf2bb/b 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 +z1jw .ab tgcpmy-st2pr 2o38 experiences “free fall” or “apparent weightlessness” betweentw231y+p pa8 -m.rcgsbtz2jo steps.

The Earth moves faster in its orbit around the Sun in January than in Julbwpctzc956o1 y. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the stpwz65cbc1 9o easons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knownw-35j egp7-l -vjcg8uh7pz e x until it was discovered to have a moon. Explain how this discovery enabled an estimj7e z 5wl ujggx7vp--h-p3ec8ate of Pluto’s mass.

  The Sun's gravitational pull on the *0e q6ha(8mx 6tlkfslEarth 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 side of the Earth to th(8klql 6me 6s*faxht 0e 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 1980sw/+c5zckzr+0d;uek $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around4s9ck 8qpi1ng3 ber k( the Sun, and the net force exerted on the Earth. What exerts thi1 9cg4e 8 kp(3iqbnrkss force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it ro6lrc*74n,zlfmdwcoe2hytm) )3 3j s otates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. e, z m)ltco r4ljdcy3o h72m) f*3n6sw  

  Suppose the space shut u-5yw8siles9 tle 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 , theiu sse8-w9 yl5 gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spec(,:bjh pmhndd.x05 ; 8r xofdsk of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if hxf:(j;08mx.rh bdsdn5o p, d the wheel’s diameter is 32 cm?   

  A ball on the end of a stjah,k4 ;x.sg)akohnktp2 jv2e j1we;6 a(4dyring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shoj,;vx eh k )wjyse1pt42(kgh6a2;jdn4aao.k wn 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 3saz +esxrrb 7.w1xq 977 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this resu7xrqs9szwb .3 xera1+lt independent of the mass of the car?   

  How large must the coefficient of static friction be bet 82:d rw+jz/(snom-ppe,fksbween the tires and the road if a car isk , p d(p/+n8ows: m-fjerbz2s to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and j39o7 9ktiw9sofad+sfvp.. ek +fml p.et fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own w p p.of9 a+f7def.93v.istl9wsokk m+ eight, 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 turntable of vayp58 :p)hu e sim6h7lwriable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until 6hlp7yue5i)w :h mp8sa 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 upside down at the h-5nu- k5ucxp( wvtk* vr1dv0 top of a- w5vu51r*n- 0 (hxvkc ptvduk 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 (including th j nk.:1ezpv*ce driver) crosses the rounded top of a hill pz vkc*.n1 ej:(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 per769mul4 z riwj minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poinu6 9wji47z mrlt?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of r9:3za kx9j2 xxa8yw efsp w9w,adius 1.10 m. At the lowest point of its motion the tension in the rope supporti p,zs ew2wjx 9989yxa3af:k wxng the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axis hgpzg .6:cl:sasqm mm- l96l( of rotation is to esp6-mmgslag6 h.lzqc:l(: m9xperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are r*7,e1; exu+g-v 7xtn vlsqy2 r oeij4potated in a cylindrically walled "room." (See Fig. 5-35 l o+42xx qe-g7e7yujt1sn,rv;vie*p .)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on nc5um4n *:sj3zf7ddq a frictionless air-hockey tabletop, and is held in thinf*3c 7 zqn5 :sdmdju4s 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 ignorin sy qw 7.j y-/suhx3z-vzwip61:u3 hfimpfe 2:g the weight of the ball which revolves on a string 0.600 m long. In particular, find thex: ph2izyfqi3/763u : s1uehz f v.wy -jp-msw 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: -coc5gonm) 1j ys9po m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massedi ..wz axb9m*s $ 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 maneuvet zjo, d-livs9 ,xgtz ;m-6(ngr 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 centrti. 4py..ro9fuz,jo ;gicuqjh (iy-7ipetal components of the net force exerted on the ca otgp9zu ; ci.(jufjr7qiy y. 4-hi,o.r (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 ac2 g z; fy*4oy8/j (l6asydvlxecelerates 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 acceleration wito d(lxy ;yfav 4gj ez/86*2sylh no slipping or skidding? $\approx$   

  A particle revolves in a hori c7vnmi)d37)fe e ;vrfzontal circle of radius 2.90 m . At a particular instant, its acceleratn; fvicfe377) )vmderion is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (h /qln5o,3doz2 Earth radii) above the Ear 3,5 /qdolnozhth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accawr- ek45tta 9eleration g has a magnitude of 1 94ateaw kt5-r2 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 acceleration4q -ij( 2ri*omo/ zgzh due to gravity on the Moon. The Moon's radius is 1.74 o/rzmj iio-z4( h*qg2$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that or)3s,q1q j6.9ay e nqf.zqi nbf Earth, but has the same mass. What is the acceleration due to ibn qz) .319sqja.qfyn6 qre,gravity near its surface?   

  A hypothetical planet has z p8-rw1+yeel9n fa+aa1uka8 a mass 1.66 times that of Earth, but the same radius. What is g near its s eakya8w8+a z1 npl1 au-re9f+urface?   

  Two objects attract each other gravito1hfhd p.+ si7ationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravx1z nyy(raasxb9;(4rl 3s + lsity, at (a) 3200 mx9 +ra y ;3n4s(zlbsasly(xr1    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tvng,qap1y3i)8 nzf/j q9 ye *lo a point outside the Earth where thegravitational acceleration dlyapjn)nze v3f ig 18qy9*/, que 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 o8nucn1y rvzhoskf3 y7r32 (p-f our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thso- 8yh znv(3c fpyu17nr3 2kris monster.    $\times10^12$

  A typical white-dwarf star, which ow ezbz v/ax5tucw v6g o4(4655bl/r hdnce was an average star like 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 surfacet /z6cbe g(w4/rzd wvxu55b45lao hv6 gravity on this star?    $\times 10^7$

  You are explaining why astronau muh) d9)-eb t; le l/emt2)fq.qbg,njts feel weightless 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 a.g2 njeleuf9-lmhttm))b,d) q/ b;qebove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a sq4 pxgk rzl*a 06)bnr9suare of side 0.60 m. Calculate the magnitude and direction of the total gravitational forcrkrnzal4 g *p9bx)06 se 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 side of thbc j3,gjcq iru;0s.l5 8vvgu9 e Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a lin gur ;sj v.b 0ljgq9ci58vc,3ue (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 /tozkzgp-y eqh8mybcpk7( w 7,m.,,g of what it is on Earth, and that Mars’ radius is 3400 km, dp8oyycz-7 gm t,, e.wbh q 7p,(kkgz/metermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the2kx4b g3k,jvi3g*enbwjn+2 p period of the Earth and its distance3*,e j+xpk bj ggnv32i4b2wnk from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movin7xd xbx+d jaj/)l5xew 86q kswxi)(1ig in a stable circular orbit about the Earth at a hj8wbekd i)q +wijx5x/(xl6 17dxx)s aeight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 u1.g(ha 6i, (nnwdnbqdt,3 rq,zua6zs; r:v v km above the Earth. How fast must the shuttle be movingzn( , wqnat,3(1n, 6;qgrirh a:d vz6u.ubvds (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyb: z:u6:b* upx09c bkr:vz odulindrical spaceship rotate if occupants are to experience simulated gravity of ob x: :zbp: z:vb0u k9udu*c6r0.60 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 for a satelrqfqjb c )u80-lg k2o:lite to orbit 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 very small compared to the radius of j 8-l)rqb 2of q:g0cukthe Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fromn:0ce19 xx. aeld 4e;jpf4a pa the top of Mt. Everest to be placed in a circular orbit 4xac daapfe4l9nex pj;1 .:0earound the Earth?   

  During an Apollo lunar landing mission, the c laen4dyxig 7c 4w(q t1,to77eommand module continued to orbit the Moon at an altitude of about 100 km. How long(eeg4y,741qtowdai tlc7 7xn did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pllkv+ 0ihxx(b* cl08lm anet. The inner radbh(+*vikx00 lxlmc l8 ius 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 rotat g-2.xe q :poq8j7)5gngedbvees once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to hen)q . 8e:q evpo52dgbx -j7gger real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronjll;j qlsqxz v) w8zu*a+4 k/ky( t+x4aut 4200 km from the center of the Earth's Moon in z+xs*v l+ jt zukk jq8wxl;/( 4)l4yaqa 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. They are r5 e6x)gg6 pmp76veqo6rz lk.observed to be separated by 360 million k6mp7 lqp56 r 6ggv).kxroe6ezm 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 ofuo7+ 6pd9d3ygm:rm h pm9lel6 a 55-kg woman in an elevator that m rm9o d7ygh+ep3l6pm9u:dlm6oves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elezr, r;h)) rfqusv5 0vvvator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magni q; s5hrvz vur,)rv0)ftude and direction)? a =   

Show that if a satellite orbits very neaxucn8z+me 1, kr the surface of a planet with period T ,n cem+u18 zxk, the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the 51ev9q-1ttn,m c dxyo3 n;vwmperiod of an artificial satellite orbiting very near the Earth’s surfacee139d5 qvxmnmcvw ; o1t, nyt-.    s

  The asteroid Icarus, though only a few hundr5 i:a8692 /fgrdhnj0y *l emb8hi+oime yh9yyed meters across, orbits the Sun like the planets. Its period is 410 d. What ir58h:6*i 0yjmdany9g i 2 +i/8 oehh m9yylbfes its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ky od,,2z m-btof 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 *lu/jval) 0l dp8 rfz7years. It comes very close to the surface of the Sun on it ju)v *z7all8f0d lrp/s closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of zld0 (;y0c/gyzlv:yuthe 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 for g j6 ky.tc 1phbouvk,s*c ..7pthe four largest moons of Jupiter (those dipp.6ov1j 7s .ygb,kcc *uk.htscovered 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 periodcm 8mx.vliu )( (:ehdw and distance of the Moon. mehw). :(mvdc (x8uil   $\times 10^{24}$

  Determine the mean distance from Jupiter for en,d++z ripsb8k9u0l o sed0k4,7 wkvvach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuesvrb zs p4k0s ,v +uoke89dw+ 0,ikl7nd 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 fr fm l5 z/owww76n0cu 5df57yvaagments (which some space scientists think came from a planet that once orbited the Sun but was des0 lcm7 z75nw6w fva dfu5y5o/wtroyed).
(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 describn;1i f2kpot29te-adi3 1g bwres an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of 9d-koit2r2a1ng1;p wibf3t e revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge rln8 eomkr;wn+.a+c4 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 speelcrmr;n.+ akn4w+o 8ed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerat.w0cyh h89yqfion of gravity be half what it is on the surfhyf.wy hq9c 08ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circ5xtgn-b: u n2b)n2yexp;en ,xle once every 2.5 s. If we assume their arms are each 0.80 m long and their ; b2g5 :yu-, enpe)n xxx2nbntindividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dabcg muurixqn 5j0(*u(h17 t,u y, 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. 1ht((qr b*cmj7xiun0u5uu g, What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly yfld/uv(x2d(v4 xu uc-1a uy 4from the Earth to the Moon experience zero net forv dl(y( xud4u/au241y-x f vucce 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 baniif5b/ob6rxh ,-qsl 6 nz)s 6throom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dis/lq , 5n)6b6oxi6hfrni-sz brection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatu,-da 7qh 6bkm(cqkp +e about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tubpch(d ,k7m+6q ab kq-ue 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 (n6s 27 eo)b6d.goddtu.p9 l uxFig. 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 ro9s1;xyu tw* c, the acceleration due to gravity at its surface xu s yo;t1c*9w and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical/fjm,r i )/;vdsf w9bf by an angd/fb)m9v,sj f wf/ i;rle $\theta$ 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 coeffic*x;kedj8 )yppqa8+pkc b,u3a.g f;e uient of staticu 8;pf*8k3kada,+g xyq )p;cpeejbu. friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotsk c.8lbh- n-zating so fast that objects at the equator were apparently weightless?ls- 8- nhzc.bk    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparhfk 5-:uw0.p6t eq no 99pujhnt 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 rouh5 ;e71dulths2alz .pnds a curve of radius 235 m. A lamp suspended from the ceiling swings o1sude5 hh;zt.a l72lput to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times asov/ m2n g;t.xz massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravivoxmg/2.t; n zty 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 .f et 9*ly)dz tdyv2n8Telescope deduced the presence of an extremely massive core in the tflndtz8 9dvyey * 2).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 speed as it traverses the hill and valley shown in w j-.n,n/tr.kjwd 5iyvm k*b ;1ftx*eFig. 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 roajvwtrxi;yebj,.*tk dmn* 5f1 -nw./ kd at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellxc0+ h4b hg4iqites 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 aroun0b x4hq4 cig+hd 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), af2qvvs ip)qo ;-ter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is -)2v;v qsp iqoroughly 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 shu82cbub op(90p bw4 i ur4y7iqyttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. bqi8o9pp4y ubiw74cb (y02ur
(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 300e6u+:9 n9yennxf.ayj;amu+ a0 years. (a) What is its mean distance from the9y:ennf amxu 6+9.eyau ja;n+ 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 wouldp)g3vhy;z5w8 5 d ddox need to be if you could actually "feel" yourself gravitationally attracted to someone near yo8vd5ohpg yz5 ;)wdxd 3u. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mf1srl4 o 8w9h ebp7-ps+.;asws l d,mdilky Way Galaxy (Fig. 5-46) at a distance of about 30we.lmssl1d 8f wb+ps 7,h- 4dpa;sr9o,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 0.5.2wo ly; yfmawzng71:0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint .2nw1f7a:y m lzy;owgof the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500ri : yikquu/1( 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 experienced by the tip gtfyu.7dmk g , cb1y/3of the 1.5-cm-long sweep second handc dy,u 7kt./bf1y3 gmg on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arount(b :1i9gl sfwh8sf s/d in a circsg b f /s18(tisf9l:whle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rz7.t .spidp(e adius R in a new highway is designed so that a car traveling at spp (stpi. 7.zedeed $ 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, utilizfcp rdd 0:2e um3ej2u:es 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 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) Calc0m duj f3pe 2reuc::d2ulate 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.$\approx$    $\times 10^2$