Sometimes people say that w z56j7in1yrd**4wzu aj jxx/ water is removed from clothes in a spin dryer by centrifugal force throwing the water outward.d anzy 67wzxi*u/wj15j*4jxr What is wrong with this statement?

Will the acceleration of a car be the same when the car travelpz)0)v*m9 l)l 3(u aclhrj;oqr3ss gjs around a sharp curvear g luv(c rl3oms9 hsz3;))qjj )*l0p at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car efnl6c*5ojot7)ib.svz 3i6o n xert the greatest and lv o .jo6iltn s5o7i3)f 6bn*czeast forces on the road: (a) at the top 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 h1ky3q yld*s,so;ui- vp5gv*rorse on a merry-go-round. Which of these forces provides the centripetal aoyl,g*u-31ky *d;rsp v5qis vcceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sph:c3gknlb1ozptbq 42/zk 9 t,tb-5 veilling out, even a3b tv t e, z5n:h4/qlk-zo1tbbck92p gt the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There af nelcz9 zkf uqoa2:2h69b/7vre at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleqzbo9 h7k26/nu f9:c2 vazlferations do they produce?

A child on a sled comes flying over the crest of a smab)20nhe eou+h.a mnl:ll hill, as shown in Fig. 5–31. His sled does no eheu0: h2am+n .)lnobt 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 second law.

Why do bicycle riders lean inward when rounding a curve at hgs8a;op us uel7x*f,4 .c mr;.svcz2nigh speed?

Why do airplanes bank when tr22llwid ga- )hey turn? How would you compute the banking angle given its speed ial r-2 2dl)gwand radius of the turn?

A girl is whirling a ball on a string around hermsd;9 4 m(2tm9merlio head in a horizontal plane. She wants to let go m4rl9(si m mm2ed;o9t 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 forcdzlx g 1cl/u9;e? Cons; d/lg1ucl9xzider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whu87xok3e6p.yd,a uty at ways would the Moon’s orbit be different?e,ux 3.y8atuok d76yp

Which pulls harder gravitationally, the Ex-wk 1a1hx.na5v jr7 jarth on the Moon, or the Moon on the Earth? Which accel1h a5nvwaxr.7- j1xjkerates more?

The Sun's gravitational pull on the Earth is much largd 30rt00h-rsxepxw)xer 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 - d tx3sepxx0)hrw 00rto the other.]

Will an object weigh more at the equator mh+bo.zo:hm)or at the poles? What two effects are at work? Do mooh.zhmb ):+ they oppose each other?

The gravitational force on the Moon due to ) p )my83dcsmjthe Earth is only about half the force on the8 )c3mpmsy )dj Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit bowo4(s.3 b)es e:i iiaround the Sun larger or smaller than the centripetal acceleration of thebsweo3 b4eio)s ( i.i: Earth?

Would it require less speed to launch a satellit(rhu5pb l57uoe (a) toward the east or (b) toward the west? Consider the Earth’s rotation direction.ru7h55(p ulb o

When will your apparent weight be the greatest, as measured by a scale in a movi +dj8j2q:nphp3okvm, ng elevator: when the elevator (a) accelej mkh+82q, v3:o pnpjdrates 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 spaxk)c*2q rv-qusu x( /i+.ix okce could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking o+(q2 o.)k u-u *qkxxc x/risivn 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 experiencedt:uc 9ct:ne- ;segb6s “free fall” or “apparent weightlessness” between sub:6 t9- ence:dt;cg steps.

The Earth moves fasterp+7 +eh q,k)p- bydygt8s j7bs)a)nx s in its orbit around 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 a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its o7hy ak -t+7) yx e)dsbpgq,j 8nsp)+sbrbit.]

The mass of Pluto was not known until it was dis2 c5c(h5g zqivcovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass.cz ( 55chqivg2

  The Sun's gravitational pua 8q)iqony-c7 bi85g vll 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 pul7 ioa-nq yi58bg8q)v cl from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 3-gu uzcn dr8e:4 ep36nr rt*m1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetalr.3j/2lm+p k;tmjog w acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth3k.t/gm2 wjr+j pol ;m. 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 discundb, a2 :nzu6itc9( vzs as it rotates uniformly in a horizontal circle (at arm’cn6z :u2 ,b9viatd(zn s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is ivzylws92k: f8eh.e- zn orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space :hl 8sy2 efz ze-.wv9kshuttle 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 a qw;:rns(cm, of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) m nsw,r;c:( qaif the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cirb o eraiy5b,( d8n4k/-ev spcsw7kz0 1cle of radius 72.wnc5s-kb,1 y v 08r d4/e(pz7ibsoe ak0 cm , as shown 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 w354gr- yiw8/y mwcsxz hich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thiwi3-xyr wsy 85c4z /mgs result independent of the mass of the car?   

  How large must the coefficient of stappjtgawu,8is94p.k/js( h(h tic friction be between the tires and the road if a car is to rjsp( jh /8k(.w ,uptaig4sph9ound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is d4(2buk kp eyp7esigned to rotate a trainee in a horizontal circle of radius 12.0 m . If the (pe2 47 ubpykkforce felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a ros 3,sn kcz7lgao-93yz tating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntablka3sy z-ocl zgs37n 9,e?   

  At what minimum speed must a roller coaster be travenodd ok 8q8(x l;n4w/nling when upside down at then8dwlkn;48n oxodq(/ top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the dri7x frf gza)82hver) crosses the rounded top o8hf )fx72 azrgf a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferr4,bjjt,pl sf ,is wheel need to make for the passengers to feel “weightless” at the topmost poin4s jj ,pf,t,lbt?    rpm

  A bucket of mass 2.00 kg is 0pcjw*l a(r3e ..b- ukrk euk/whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope eek urlac3b j.r. w-(k* uk/0psupporting 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. u +p/7*cr) wpnmjruz the axis of rota+.pnj wu p/mu*)rz c7rtion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopleu w4gw:r/gbm(k s :-na are rotated in a cylindrically walled "room.w:wrms :4ka/-gu (n bg" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a fricni(, /cijur 4jg +f1(gznsn t-tionless air-hockey tabletop, z r-,4n(sn/1gf+jj(ug c tnii and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely n0rd:nelf6gct/ 0g c4 this time, by not ignoring the weight of the ball which revolves on afc lnr /gt:40 0eg6ndc string 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 radius4b4f mlrxwy 62f( ta)r of 88 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 masses:(etlzq 5;gd 6um5hltvu55h :cps-qh $ 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 o :co*bbl(a:quz q0l4 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 cfvgowtzomkh,f8 1( c i +;*z8ientripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15 fo g;iok+zwf1,zch(8 v8*imt$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goiw pzfosg7 : *:2o+tdszng from rest to 320km/h in a semicircular arc with a radius of 220 wpd7z:o2+:sfg to*z s 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 with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At ;s,aj 22u6nlngpjh; p:) komaa particular instant, its acceleration is 1.05ja 2k ;g,sp ul:a62pno)mnh;j $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii um s17;xp5yud) above the Earth’s surface if its mass is;u57uxp sd1my 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g-i3mq5( d;s6e8s 0hvrmy 3 f jlbixro: has a magnitujsiqiom bv3 8sr:fh- 35xemdy0r(l;6de 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 d jko3zmcaas p(fl;s/i6r 500(jra pe.ue to gravity on the Moon. The Moon's radius is 1.7(l/maiaf5rep0;3crpss( 6. ja z kj0o4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planerqtc /g3a1d o0t has a radius 1.5 times that of Earth, but has the same mass. What is 0grocat3q d1/ the acceleration due to gravity near its surface?   

  A hypothetical planet hasahx0mf ;gm em8oi6vx 9,( i1gp a mass 1.66 times that of Earth, but the same radius. What im8;im xh gep9aim 6v, 01gox(fs g near its surface?   

  Two objects attract each ipp*41s2 hw fmother 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 value of g , tha:k2t h) qn ry)dg/u4we acceleration of gravity, at (a) 3200 m 4uwakht q)rn/ d)2 :gy   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth n81ml6fv(nq g’s center to a point outside the Earth where thegravitational acvnn6 f(qg8 lm1celeration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed in1p5n5 v8cep.kd lvt;pto a sphere about 10 km in radius. Estimate the surface c;v8 p. ep klp5vtd51ngravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average9yqk9ver* 1.k9f+ x:m:a tbysweo0 w e star like our Sun but is now in the last stage of its evolution, is t9 e :e0v oy yeasqfm+9rx9 kwt*:1.wkbhe size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in thjf. l /k;e;vxr)u- njse 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 acceler-fnxrj) /k.;lsej;uv ation 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 square of sid -n 1q qpmz1c2c6/cshhe 0.60 m. Calculate the magnqnpcc chs -621mh 1z/qitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lindzs )fx4bq/6u e up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuminb )sxf4u6 qz/dg 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 graiq rayjcm3q o+6l w -k/wuzqb)(qz:.8 vity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mjryzmblq w z /6+)q:wkq8 i q(3.uoca-ars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value frcnsae3j(2w 26nwh d bvjf48l/ 1)yxgor the period of the Earth and its xl (y18/3acgjned6vrw fh2 b 2 )sjnw4distance 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 moving0ew a vz*9;e9b9dx auu in a stable circular orbit about the Earth at a height of 36*u0aebvawexz ; d 9u9900 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbdk0i* i;q tt)oit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releasqk;t i0it* )ode occurs?    $\times 10^3$

  At what rate must a cylindrical space. rf,6whv hm0lship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revoh, lvfw60r.mh lution. (See Question 21, Fig 5–32.)   

  Determine the time in3o 8g;pk 2 06eshaq ,fie3ybet takes for a satellite to orbit the Earth in a circular “near-Earth” orhiqsyo ;e82pebk 0,en 3 3g6fabit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a sateeyofq8(n*d 8i 8cp/jc f-l6d nllite have to be launched from the top of Mt. Everest to be placef8 c68 idlcdypnn 8-*(f/oqej d in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mpd(yp yg1oq0*odule continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon ond gy( *ypq0po1ce?    s

  The rings of Saturn are composed of chunks oa5 6;*j(c nim cv9wjtnf ice that orbit the planet. The inner radi6 ta;wi(j5j9 vcnn*mcus 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 rotates once every 15.5 s (see Fig. 5–9). Wha yhj1ctfr -7.qt is the ratio of a person’s apparent weight to her real wei1hq y7cftjr. -ght (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of n4*rn8hilnz 0t;s kia*5znmi .,m :sfa 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veloai.z5n,* m ihn0fr48li:zs nts *;mn kcity,     ----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 ofhb2 ks8-8przohv 5ci( two stars of equal mass. They are ob5ozhk(h8p8ibr -sc v2 served to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read:vy7moomh6 jv, ,off ;:d 0loc for the weight of a 55-kg woman in an elevator that joyomodv07mvcl ,ff: ;h ,6o:moves
(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 6aunz7f xte- u/- ;wfh)8a17ysx owansuspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was z 1u6--tuns/ naa h)xwxfy77oa fw8;e the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface ofogg56 ir8hv r/ a planet with period T , the degi r6r8gohv5 /nsity (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 peri(vri/l 1fo:sq od of an artifi iolv(/1: rqfscial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sunb/xzdi04uvv 0z.v * 73wk ze8lnbxbu8 like the planets. Its period is 410 d. What is its mean distand*. nbkxx07vu0v4e3v 8ubb w lziz/8zce from the Sun?    $\times 10^{11}$

  Neptune is an average distw8u;k apla;u. ance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very cldyli9 0 rhbp+6 90phcrose 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 pb0rhp 9h 60ydrli+9corbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga tiz(nht a;;d8laxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 massrzuqw 3*,,nc.,qzhvj -gvg 8 h, period, and mean distance for the four largest moons of Jupiter (those discovered byc-vhrqq8,,zgn .w 3vuh*gjz, 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 there b +al1x.*vixko e)0 known period and distance of the Moon. a.e+0) bxkori* 1xlev   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mo;q,b uq7(ealdl+9crt ;ez4hc u6w1r lons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3.ulul6ar,l(ewqt h; d91 rcze7;q+4cb 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 consists of mav4dnkk - lj2 37gulb*pny fragments (which some space scientists think came from a planet thatkg-4nl*k 73blp2vdu j once 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 an artifi tgh4 h3) :lbq4xwntx8eba0h:edw41 xcial "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 tha w )b30hhxt4qe:48 : 1texbwh dgln4xe 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 in an arc from a hanging vine (Fig.ow wji0 2o1 .cpys,0qi 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the max,w.c0js1io0 yp2q iwoimum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratim : i7twrho4ilblb9 0(on of gravity be half what it is on thl 4itmowr i0b9b(:hl7 e surface?    $\times 10^6$

  On an ice rink, two spxc1cxc0 7 h3jb.w3tzca 7 jb0wh r3y.katers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their j 7wxrj.c0x7cyc 0bhhpct.w3abz 313arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity at.i eb cg,f:(li the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is tf i (l,eg:icb.his?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direcfsbgy4gug0c 4g 6b+ q*tly from the Earth to the Moon experience zero net force because the Earth and M+gb f ggb *g4qu46s0cyoon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in;vvl2p owo /,c an elevator, it says your mass is 8oo2w,pv ; /vlc2 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station con.8kggkn - -jj2y5hcdt mo99rnsists of a circular tube that will rotate about its center (kjg5 k -m ohg8nty. r-cd2n9j9like 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 (Fig. 5–4ti dz v-q*z5/-g:hc sixu c((w5du41hadh)a e 3).
(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 iy kqb6k0( tr )-d(pjh2kj,hi /nutt;kn terms of its radius r, the acceleration due to gravityi n;jjt(t hr) -bk20,/6q( pu hdykkkt at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is de e0ew;jt5z- meflected from the vertical by an anglm0t-e;je ew5z e $\theta$ 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 ag9m tm(izp92ax+y6g design speed of If the coefficient of static friction is 0.30a 92 9+6(ztamypxm igg (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at qi5uw,4y:8tt 0ucyrnthe eqrui45n yq 8t0,tyuwc:uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cjk yy 2(k;5tna6/se+ izeffd4 onstant 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,zh; +)yjefea lb n 2()hur7ni a constant speed rounds a curve of radius 235 m. A lamp suspended from theere jl7h na h;+fb2 zyn,))iu( 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. Thues+7r 8jjtyp 4z,xknvd1 0.gp s, it has been claimed that a person would be crushed by the forcepp0sr ,k gvd.et n7zjxy41j8+ 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 tfwpytss-e/,877 r2v - a itxwj0 f0ohlhe presence of an extremely massive core in the -v - fw0alywrso8tp7f0/ hs7e2x tj,idistant 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 a 7x2wuo, iau+yqoz. izl8c3l7s b;4c1ilw t6snd valley shown in Fig. 5–45. Both the hill and valley have a radius of c21sc.lay4lx8wzc,utb wiz ;q7ios+ 6 ou li73 urvature 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?

  The Navstar Global Positioning System (GPS) utilizes a gr3 ylcme5 )lujp: 4*0/xxpttyioup of 24 satellites orbiting the Earth. Using “triangulation” and signals tlxm:/* j04ic yx u)53typepltransmitted 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 orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km,3ac/ym(fb/ dwx +cjp; is meant to orbit/fc+apbmwy x jd3( ;/c the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in t)+ me f g 8hmn.(eai+xy8oysy1he space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite ).ioxyh eym(e+n88ga m+ ys1 f(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) What is its mean distmz7rq 71wi r keu)rmksv1. j;-ance from the Sunw7 vq7ku-krsmize ; m)rj.r1 1?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be ifre w a0ni4*5el you could actually "feel" yourself gravitationally attracted to someone n 5ln0w4aee ir*ear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) atyx1b pp4pu rq9l g+z,8 a distance of about 30,000 light-years fr+p8l z1qgr b,4 ypxpu9om the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each lnsmkvktm lj qvw-49:*b)a 1cg7w83 bside. Find the magnitude and direction of the gravitational force 8 wkvm7-:lgq 1vnbmb 9)ljt4*w 3kasc 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 5500 3mgcl bbeozs (m;,8nwly 3 0-*nga2 gbkg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-p1x+wf w*6u d ,jdcwlq1ny(j d05sfx-cm-long sweep second hand on your wrist w(udws yx 0lf fw jqd*1+,16c x5ndp-wjatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aro)tpx3.ymyskyp(n6dz*d 94h*zlfx6 j und in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hintkf6x s3y6l(xd* 4n 9jpyz )pt*zd.mhy: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway im30n q- nwjvnntce23 o3 fo1i;s designed so that a car traveling at 3 nonvwmtj0ni fe-oqn3123;cspeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when/m h+ppuqyh 2; 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) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train doesqp p hm+u2y;h/ 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.$\approx$    $\times 10^2$