Sometimes people say that water is removed d- m:ah lw-.jvq*bqh8 from clothes in a spin dryer by centrifugal force d.-qv-a q8w blhm*:j hthrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a g5qvx5 m5lk:*xero2k sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spee xvkq x2gr5m*o: 5le5kd? Explain.

Suppose a car moves at constant spl zk (up51j8oq p03 :ikpj;lxob05sqh eed along a hilly road. Where does the car exert the greatest and least for 50kh1qo p0;3qbj5zs xo p8pj k(lilu:ces 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 ridluoyw(lq.c ;te ).gj5 ing a horse on a merry-go-round. Which ofqylo get5. .jlc;w u)( these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertik 4zr0klh0)rm o 5s2oxcal circle without the water spilling out, even at xrk 0kho2l5s4mr0)ozthe top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three c. qzg)g;jp-7a o)aw jnontrols in the car which can be used to cause the car to accelerate.qo) w. na;)zgga-p jj7 What are they? What accelerations do they produce?

A child on a sled comes flying over the crest20fhg / nwa 1k 3ay/yy 5fmrp5two1q; ,2hlllo of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieomn,py5/ 3owy l21tfahfry/kq5lhg 1; law02 ve “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 roundin d gf +p/dk74o9aycsd1u0y; uog a curve at high speed?

Why do airplanes bank when tjikidn eoip3-2:ic64i pe n) 3hey turn? How would you compute the banking angle given its speed an3 o-inij):p3pie 2k46ed i cnid radius of the turn?

A girl is whirling a ball on a string around dcc h*kyo:90t her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target ok hdtcyc* 09o:n the other side of the yard. When should she let go of the string?

Does an apple exert a grau*-wt.deu ut+vitational force on the Earth? If so, how large a force? Consider a.uw *edu-utt+ n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moonk)ha*n*mf t8m6 +c xzx’s orbit bm+azkxc t)*f x6h*m 8ne different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E q-ly n1y zedcc3 eht88.8j0fcarth? Which accy f c8 d-y.c80thlne1ej3zqc8elerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'su6mk0 iby n dp-8z5e (n-ag+bm. 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 the d +nkz5ymeminb - 0pgab-68u (other.]

Will an object weigh more at the equator or at the poles? What two effectsbtte a)m3j9f b:.dep- are at work? Do they oppose each othb.3m9j tf:et )pbade -er?

The gravitational force on the Moon due to the Earth is only about half u gk15f 0y/0uvepcem5.no u s)the force on the Moon due to the Sun. Why isn’t the Moon pul05/.)neoeg y 5uuv1sm u c0kpfled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the t 3tzxs2,pi k9Sun larger or smaller than the centripetal acceleration of the Et sixz9kp 32t,arth?

Would it require less speed to la cx zt43ww o0*gi)m b1,7xhzvbunch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation d1mvwiztxhbw 3*z04xbg7 o,c)irection.

When will your apparent weight be the gre,)w*el zk4er catest, 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 whie4cz) l,w *ekrch case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected h :hk :+ 4eq1)a2mwnyiruyw-hby weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on ou4qy y:r:wa+hn e)1k-2mihh w ur feet, and (c) any other aspects of gravity you can think of.

Explain how a runner exl*olp d:s ,(8f5qjl mdvq0w +iperiences “free fall” or “apparent weightlessness” between steplj+5d fio 0wl* 8lqvs,:pdqm (s.

The Earth moves faster in its orbit arodsddj) b7j v00und 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 producids0d b7 )vjdj0ng 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 wt2sxn7 cxxx-/np6 7hjas discovered to have a moon. Explain how this discovery enabled an est6nnjsxpx-xh7 7/ x2c timate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tx*wa v:v.k9kche Moon's is mainly responsible for the tideswkc* x:vk v9.a. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 198(twr ; 3rkctkp 05ic3o0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 2hhu4- +opc -yff*wai Earth in its orbit around the Sun, and the net forcep c*whi-fuo4f2+ay h- exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniu/a:c3b4b,dc dl,mj bformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discusj, bbddc/luc,3 ma4b :.   

  Suppose the space shuttle is in orbit 4mtg 4/gjb**/y3i y ipe00 km from the Earth's surface, and circles the Earth ab* 4iy/pi*jgm b 3e/ygtout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of asiezmy5kh3s/* qu2kt6 r us l9)5zby4 speck of clay on the edge of a potter’s wheel turning at 45 rpmts ukr5sy4/qybm*e5hs u69l z3)i2 k z (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circle6 ct8qfxx2z1w2;x 7 :wluap np of radius 72.0 cm , as shown in Fig. 5-33. If itfw8c 167n w xap2z:; lpqxt2uxs 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+lltx7nknqu6zdk44 * car can round a turn of radius 77 m on a flat road if the coefficient of static fricti kql +d 46znk*n47lutxon between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between thf)u n9wgkd;r0e tires and the road if a ca gr;)0undf9 wkr is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts andy0ei4ypq352x vc4gi r6pt9.tzxs y6i jet 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 weight, how fast isvty s4gix5rp2pze 9i0ty . c ix663q4y 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 f 47w.qyau m72. hj/g -dooxsqyrom the axis of a rotating 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 oq7.2ohuy7 -jwg/d . os4yamqx f static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be trrvbm w8 *b5yg5/dk4e javeling when upside down at the top of a 8ved4jr5g*my/bw5 b kcircle
(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 driver) crosses the rounded to1o co+x(kp7rmw.z gz8p of ao o.x8mz+7kp r c(gz1w 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 woul, :lv,oe6fcc8 c yeceil8et k7hb0 77go4fy w7d a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” e ,707cy8 b,6 o7yf: wvk7 lh oc4li8fgcceeetat the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cv6gil1as 0cd;9i( cgxnm2r.s ns3 6isircle of radius 1.10 m. At the lowest point of its motion the tension in thel9sr.0m1a3ivxn 6i (ssc2 6gngs ; cdi 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 centrifuge rotate if a particle 9.00 cm from theey. 1/;iut xzz axis of rotation is to experien ;1 .uxziz/ytece an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wallerj x6)7la6 npc)nr+r dd "room." (See x)) rdrpcnlr67j+ 6n aFig. 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 rp ny army7x;)5 hf b.sg15*eru2 u8ytsotated in a circle on a frictionless air-hockey tabletop, and is held in this orbitguat5rys;y 7b*ns.5p rx1 )fye8mu2h by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the we:kams5og7zd 0 ight of the ball which revolves on a 5m : 7sdoa0gzkstring 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 radiut1. o1zgw8mijs 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 masse zr0 (ky2)hqsls $ 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 v-ov5dnjozo: ;)pz ,ibertically 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 exerted onh3zsc (20gurv4 ua 2j fnygws4g*m9)n the car (by the ground) in Example 5-8 wh0uu) 3rgyc2z( v244w9mssh*j g afgn nen its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from*jm5o+41 l/k+rqx zke g cn697cuhqk v the pit area, going fromrqh4nu+l*6 1kc qxe/7 kk9o5jmcg v+z 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 with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radx+ a*,tido:ebnz cqsxl p 8i./ .xgx76ius 2.90 m . At a particular insta n/ x*e gztb8.iqa l6x7+,c dx.sioxp:nt, its acceleration 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 12,80;vx 7rckizb1 : +5fgbp0 km (2 Earth radii) above the Eart cbgv1: 5bz7;xrp+fik h’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mcni e rkm b)ok:q.a.*6.;rsckagnitude of 12r) e* qrckkomb6 .is..n:a;ck m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is ksrv kvok1pssa 65;5 z;.wd t19*st;pzq isp51.74tsp6.krzsv;v55psa;s*q kt pk1i9zw 5 s1 d; o $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tims/ ioz0,w btstapf6.d*.e m5wes that of Earth, but has the same mass. What is the acceleration due to gravt5o.pww a,i zfs*m0.dt bs6e/ity near its surface?   

  A hypothetical planet hag 4aidihx0xq )*q*tw*s a mass 1.66 times that of Earth, but the same radius. What isd )tx**h4 q wxqg*0iia g near its surface?   

  Two objects attract each other gravitatio/68kouz4 4z0fs)foppi oi.elrv sv*, nally 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 gravity, at (a,o84j1kyy/ a+n 6szsnj x t*cp) 3200 m 8s ayxnjn+*1 64cyoztkp/j s,   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ear03xlvoj og+3 a-jdrm: awm2;mth where thegravitational acceleration due to thm max0rw2-aojm +3 vod;lg3j:e Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timesxpk+*q;ml f( h the mass of our Sun packed into a sphere about 10 km in radius. Es; fqplhx*m(k +timate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our S1qxwlh)ek: : mun but is now inxel:q k: 1hmw) the last stage of its evolution, is the 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 wh14e m ke2ka,b(0nakzkloc )w* ile orbiting in the space shuttle. Your friends respond that they thought gravity was just a01a2beaknokm* w )zkelk 4 (,c lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a sxhgrf1+t4 c6 guy g/4fquare of side 0.60 m. Calculate the magnitude and direction of 6crf+yg/ 4ggfhu 1xt4the 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 line up on the *ouwa/aomw+; same side of the Sun. Calculate the total force on the Earth due to Venusm +u/a*wo a;ow, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of grav-r 6luu)5ygt iity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the my-r )itl6u5ug ass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of t 8x/nx ,iaa: /so .:r3w qxb3k;empdrwhe Earth and its 33p:s we n/b/awx: amrk,ix8.odx;r q distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed 0s-, s;wzw)og2ndyezs o4 -mnof a satellite moving in a stable circular orbit about the Earth at a ,mez -n2zs; w0gs oyo) 4-nsdwheight of 3600 km.    $\times 10^3$

  The space shuttle releases a ktuig ,(3ml)s satellite into a circular orbit 650 km above the Earth. How fast must the s(tli )suk3gm, huttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate id +skihy(psx/ (i12m756wm9 z nihsbq f 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 reh6s(i5bw z sqi172i(hys/mkd9+m npxvolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a v 0ez h+;c *lry3zdob6um(7tocircular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Ea eboc(0zur*3t h7mlz;y+vo6 drth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a ssi jzk-(sk*4z atellite have to be launched from the top of Mt. Everest to be placed in a circular orbit ars-sjz(k 4k*ziound the Earth?   

  During an Apollo lunar landing mission, the command module contiht-ybnlga/.) v53bbf nued to orbit the Moon at an altitude of about 100 km. How long did it take to go around t 3hb n-y/fv.l g)ab5bthe Moon once?    s

  The rings of Saturn are composed of chunks of ice that +af z(kz1t;ojar9,a 9anmn d9orbit the planet. The inner radius of theajad 9;9,faron +zmnk (taz19 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 ( bo0i ggn,-d5 80-t4.xhzxejwwc+sexsee Fig. 5–9). What is the snexg- 8ij.z0 oh4x5 dx-g+e,tb 0cwwratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the ce/t)e(b ru) y6ghykn)jnter of the Earth's Moo)y k)gtyur h eb)j/n(6n 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. They ar6fgl(. pyte v;e observed to be separated by 360 million km and tgly.t;e f( 6pvake 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 /(: :-efekb wkdwc ps5the weight of a 55-kg woman in an elevator that moves 5dk:: wp kswb( e-/fce
(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 sus0k74/aipafk a pended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the a pi4a0/kfk7aelevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbitsi))hmwfi+/ w /tcp:oy very near the surface of a planet with period T , the density (mass/volume :i)m+phc/fo w/iy wt)) 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 da v,ir7b:u(l j) to determine the period of an artificial satellite orbiting very 7i vlur(b,aj:near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred+fq2h, /abb5ziz-9x6p aoq s e meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?-h6+5 apxqqez bzos,/b fa92i    $\times 10^{11}$

  Neptune is an average distance of 4.5fi0qrm p) 2l0d $\times 10^{9} \mathrm{~km}$ 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 e 2e71okltn gi/very 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 half the sum of the nearest and farthest distance from the Sun.] n 1koi l2g7t/e    $\times 10^6$

  Our Sun rotates about thx:78uo,:osjgwjrlazo x v 4 1o-o) z1ue center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mz ts h l72rx+dd10glo3. s9fhiean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609)dx h30s o2l.sfz7 dl9ht+igr1 .
(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 pf6dz pq1 1y2 k lvwt4ie 3avyr:,y(c8neriod and distance of the Moon. r ct(3vn11aq:4eyz8ifyk ld,y2 pv6w   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiac- lbp.ka:.n ng Kepler’s third law. Use the distance of Io and the peri np..k- lcba:aods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (lezly, s/ :77smoqm. gwhich some space scientists think came from a planet that onceeqmy o.glsl,m /s:7z7 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 desf d 1o0ig)ue603mmqx:hhdb, zcribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surfa h0uhdmeo, q0: gdfzb61 xmi)3ce (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 revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from)7h3 *ppb c0cokitqn. a hanging vine (Fig. 5–41). If his arms are capable of exerting c7p.pk i*) 3o0hnqtbca force of 1400 N on the vine, what is the maximum 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 acceleration of grji)2e5a 6phngavity be half what it is on the surface?2pih5gj en a6)    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a muxi p-,)e8*m3ne5wo;3 tp5clgvpsi me tual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses 3o;wp mg55n cvei *8) xls -,petepim3are 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 gravip 4ow)tfqvvf 4fny:*h6 183r g:c 1xqzoqje1dty at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of tcv:*fd :hq118xq )jev o3nyrwfzpog 4614 fq this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trav-x tnsgpz-s/:kydlbc2 * *i /neling directly from the Ea -*2/k/:pzsnl xc* inb-t dygsrth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wt.pqfq6 u 33pwd 6y5riy5 a nck5:s/aahen you stand on a bathroom scale in an elevator, it says your mass is 82 k5d63 55k.auwaqt :6nyqr fpc/3 yap isg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tk/d)2o/iav ,gwi sx4lube 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 spe idwal ,4i)ov2gkx/s /ed (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 aircrbkf m1cngv;27k u 2z4vaft 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 y6 b 0x6m2hef7ehlst7a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitati6 e 6xlyh0e72btfh7m sonal constant G.

A plumb bob (a mass m hanging on a string) isn) i mycw(9of- deflected from the vertical by an af-) c9y( owmningle $\theta$ 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 cu ; ss1 i,tqu;n;a 6jf-z5hl ike/g7ea design speed of If the coefficient of static friction ulenhf g,i;ec16sjz ;i-5/u7 k; qatsis 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day b/jk)vrky 0jruq21jiy )38 d bae if the Earth were rotating so fast that objects at the equatr0)1 k 8k ir/vaqdbyj u)j32jyor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ofosfa/gg02 5mds)8a nwnx )z7j 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lqm2(e fgt2* fyamp suspended from the ceiling swings out to an angle of 17.5tq ef*y22mg f($^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Th jn9af6(h)ac qus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such hq ja9c )6(fnaa 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 Hut5u,dmr-qq aw np82h: bble Space Telescope deduced the presence of an extremely massive core in the distant galax:udnrap28,t 5q m-wq hy 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 valleyx2f a9aa/.cf g 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 rx gafa.a/c92 foad at A?

  The Navstar Global Positioning Syscba +a z hot-m34hot.4tem (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, a+.4oaa oc hzmhtb-t34llowing 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), afbu zi9-*+ vtmdxa+d3w(lcxy 8ter traveling 2.1 billion km, is meant to orbit the asteroiddu v3*dx8bt +il+y9-( xa mwzc Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursmk)j; ouyg5hy740 iid uing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (40i; gym i)do7 h40j5uky0 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 yearsmp;pw,z+y4 km. (a) What is its mean distance from the Sun?w4zp,mkm y +;p   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "ky94.jxyqe bu+lqa/)-x pz k3feel" yourself gravitatx j.y-3kyklz /e) q9 bpax4qu+ionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ofcox4)dko 1qa8j+ ccx6 the Milky Way Galaxy (Fig. 5-46) at a distancak6o +j14q cxcd) 8coxe of about 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 corner v2xeef-q ;f.8j ietv/gc72 pjs of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the -q7vxvej 8 j2.gf /;cepefi 2tbottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500+jtrq(i ulc+ws h:3( lfp:y;q 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 of the 1.5-cm-lntw; b ui6*a,6zdqu y9ong sweep second hand on your wrist watcntw, a*; 66y9uuq dbzih?    $\times 10^{-4}$

  While fishing, you get bored and start to swin.l6w* pb.+f oc l,:c oztffd*ng 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. What is the angle that the fishing line makes with the vertical? [Hint: See Figld ,6fbcpz:*+ncw.o ft. fo*l. 5–10.]    $^{\circ}$

A circular curve of radiu/3y slb- aq1 pe8,nmx yks5z*ys R in a new highway is designed so that a car traveling at spl 3 yyex8q* 1/ nm,byzask-p5seed $ 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 n0nr 372kejk+ac*7x b2fpdh gcars 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 experien eb+jxhp 0r 3n7gn*ak22kd cf7ce 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.$\approx$    $\times 10^2$