Sometimes people say that water is removed )vnsnt n5dg48 from clothes in a spin dryer by centrifugal )dstn5nn8v4g force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the sawwr2- 2sk8rd vme when the car travels around a sharp curve at a con2w8v2sk rw -rdstant 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 j (tz*nlag:-w does the car exert the greatest and lawtg -*n(zj:l east 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 riding1 zz+p1m :roa0) qmrvm a horse on a merry-go-round. Which of these forces provides the centripetal acv) +azmz:r0m orp1q m1celeration of the child?

A bucket of water can be whirled in a vertical circle without the water spillin ezn2v:7 j.iuqg out, en.j2iq ue: 7zvven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Tda5: kxq)uxjy13d4fx here are at least three controls in the car whicdju )4q d k:yxfxx315ah can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as sho4 -qhknvp:7 hkwn in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain thi7p qvnhk:h4-k s decrease using Newton’s second law.

Why do bicycle riders lean inwar(f);,d)fp mu42u7b dzm kxfv buf5 k vwfs.x43d when rounding a curve at high speed?

Why do airplanes bank xfadl y46yyff5 0vem6xh)q *lal, wp,e3,j -wwhen they turn? How would you compute the banking angle given its speed and radius of-j34, wyl*am50p ,eyxa v)66qhl edx,ffly fw the turn?

A girl is whirling a ball on a string a sq3 n:s zcprkob2ld3q a*yi .nm*w815round her head in a horizontal plane. She wants to let go at precisely the right time so that the 2 3yamzop* db*n8i3 qq:l nss k5.wrc1ball 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, how3zinp010 tl+er6c oyx large a force? Consider axnyoe006 1+t3i r plzcn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moonfwymt tt )6+ n ifq.iq, 9e2kp-t*eua9’s orbit be differenem)ft a2pu 9ti*+6 yit.t ,nfqkq9-wet?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Ea0yh9q/1: uairha5d ) ada6zz zr:ahqzzrda/u5 9z a yh1ai) d06th? Which accelerates more?

The Sun's gravitational w :)pr k.)m1faxv9ith pull 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 gravitati p9thf.w )) :avx1rkmional pull from one side of the Earth to the other.]

Will an object weigh u36s2hb7goj4 ) rj gxcuh,s,*ofw7vx more at the equator or at the poles? What two effects are at work? Do they oppose each xj 4s uuh3o sx 2w*jhb)6g,r,7govcf7other?

The gravitational force on the Moon due to the Earth is only about half the yh1nvuvz7.2 8-zavgq force on the Moon due to the Sz1vv. vq2zugha-n7 y8 un. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around bsbs2s:l dyr3 h4n .l;the Sun larger or smaller than the centripetal acs rn2blh:4y;sbs. d3lceleration of the Earth?

Would it require less speed to la4oqic kgmyd ;89w -;j f1roy3ounch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direc8ikq;fm doyj;c 3woy91-og4r tion.

When will your apparent weight cmu5xu ll/dum o*:b*g8 t vp+0be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acceleroud/8 m*:mg5x*lb pvc0 uu+ ltates 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 hm5zq3 hxv4-k in outer space 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 on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we 5 vh mhq3zx4-kfeel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weikit.lfpai:8*u3-aat 2 zn 9otghtlessness” between step -kap:f8tzi*2ai n9. a3ulotts.

The Earth moves faster in its orbit around the Sun in J8bdbr*gct4ps 5sxq z y.rt()5 anuary than in July. Is the 5 rzs5 xrg8(t*.ybb )4pqctds 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 orbit.]

The mass of Pluto was not known until it was discovered to haw9c19ixrk*xpic 4is 4g(r ww6ve a moon. Explain how this disc*cr xsiw(4wg 1r 9k4 6piixc9wovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger thq f:oltkq-o9xu)3cz2a/ ,ilv an 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 the oth 9lz-vuoa2lo)q k :x,ti3 /cqfer.]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 v:1(d k m*ocma 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around th-jhkg8 .i b/vk8hqc3 fe Sun, and the net force exerted on the Earthcb8q8 jhk3v- gh/kif.. 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 nxcqus2.t- 5nrss ,da*4fft4a 2.0-kg discus as it rotates uniformly in a horizontal cirs 4-24,dnnct .a q5uxtfsr fs*cle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orcdxp6ox zp i9)zwr q3t*q-r kz-f5 ,)rbit 400 km from the Earth's surface, and circlecd3q)r- ro -t9zzxz 5kpf rxqw,i6p*)s the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a p-)*eezouww)g otter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter i-*zg w)ee)ouw s 32 cm?   

  A ball on the end of a string is revolved at a uniform raxe ae 4spjvk3u) ay24mre1 ,l3r op 3j;w/gw4ute in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3e)kyew ; lex4wv3u24grm4/ 3uj1srj3a ,p oap3. 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 wh ysux :pccr.0 :4lsg ltv44gs 36v+fwr20ks iuich 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?6vic rkp4ss0ts 4srugvc3 :y 2fxgul0l.+w4: Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires anok b* ,52 b(ht4xggyupd the road if a car is to round a level curve ofogguh, 52b4(*tpxk by radius 85 m at a speed of 95km/h ?   

  A device for training astrou/tbe zprua++5 ;eb3 inauts and 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 bt /zepruub3++i5e;a b ack 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 l/wnxsw 8a4ldh n6f(8 axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fwnx(/nl8dh6 fw 8la4s ixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster bettjs3mc w ;z4/ traveling when upside down at the top of a circlez ts3mjct w;/4
(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 drivpl26/oxjy2 hmgnn ;/ker) crosses the rounded top of a hill (radius nyl g opx /m/6kn22;hj=95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to make t2(+7 gq6eb p:xf3hrcb )*gtbl;yxw dn +mh0ufor the passengc bg lxfbuyg+x32tq6*bh0 (h )tp+7;n:rwd em ers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical agjr7s(t9i zym w 8,.icircle of radius 1.10 m. At the lowest point of ay,g9mi iwz(7.8s rjt its motion the tension in the 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/eg9d,n 4nao j a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to expd 4 ,jgo9nea/nerience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are syuo(l m-y .*nrotated in a cylindrically walled "room." (Seo *.myulns( -ye 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 frictionless air-hoc:gg qikj)z id s+5hp-- *g5bahkey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throug:s-i *gggk5 zdb5hq+p jh) -iah a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight o olr wd /d-w62bnqvh)cnbs,;hh0n o51f the ball which revolves on a string 0.600 m long. In particdoh hwc2bhq/nd bl nrn-,s vw5o6)0; 1ular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is 4vi v l -aoh:ybkp 1p:7 aargq*7wz+t0perfectly 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 masse2y3s wy l zar1sw(zuxo8eq9 9*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 maneuver by di+5*ld+gzem qu)x /t wjl-cfgv4s b;1mving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compona-:*d9s8 *- jbry,dofkq swrcents of the net force exerted on the car (by the ground) in Example 5-8 -jso-fb89a,d d *qcrsk :w*ry 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 accelerates uniform siei0)7g 2zp*isb: ttly 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 o*t2gi0s tei ibs)7:zpf 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)x:b d7n p x8 jw64xbbi 82jk3cmk+alp a horizontal circle of radius 2.90 m . At a particular instant,8nkpj8 px2bk6i:d+wl x) 37abcxb4mj 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 12,800 km (2 Earth)kdy7-c (s vxw iy8q/f radii) above the Earth’s surface if its mass is 1350 kgik7y ydcf( )v/x8wsq-.   

  At the surface of a certain planet, the gravitational acceleratpym m)t38vi-aion g has a magnitude a83 -i) ymvtmpof 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. d62sj(qbp 9pjlr ; sjfolj wsyf ue1(8,0zl3-The Moon's radius is 1.7p0rjebyodjl;s1lfp s(lu89 j-j2,zfw 3s 6q( 4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1h1- w j9mgshq;kwap(5.5 times that of Earth, but has the same mass. What is the acceleration due to gr-h h5(aw ;pmqg 9jkw1savity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E +guq8w.t4sy dcf1re3 arth, but the same radius. What is g near its 8rstf1uce3wq y +d 4g.surface?   

  Two objects attract each other gravitationally with a force orre.p xpxp095f 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,jr)d igxcj 3:) 3200 m ,xjr c)3dgj:i    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earj: sin,4ne ,gdth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is s4:,iejd,gn n $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the m*8n*iei)+5vrpo 4xmptnmap(ass of our Sun packed into a sphere abo) *i+e*r(p no5a84pivxntmpm ut 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once czh;l(r k+g2t was an average star like our Sun but is now in the lastkgr zc+(lh; 2t 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 while orbitino3 sy0v ia/3n, hn+htcg in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince themv3 3ico0sn,n /at+ hyh 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 sch bj097:8 n93 enoe/o(ap fjzv suvy)quare of side 0.60 m. Calculate theu(n e9j87 z3c)nos0vo:av9y e j/bfph magnitude 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 line up on the sm p m7 fafw-dx-+,2omqame side of the Sun. Calculate the total forcepawom-,m d x7q2+ ff-m on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whd1yps4stykn3 o*2 t.7c+pmxuat it is on Earth, and that Mars’ radius3s 4c*pst .ntp+k yx7oydm21u is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the k(,*wtlehn e( cnown value for the period of the Earth and its diwt l,ncee(( *hstance 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 moving in a stable circular orbit about the (zwok yl)u 7,p6k1jga Earth zw,6 17 (uapkyj)koglat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit0sxxj dmvr -9yjl7-5lf;iez+ 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the relea+jei s-l50;mxyv9 lr7jx-dfzse occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are tok+xg o1.45o ch z/eysz experience simulated gravity of 0.41 eg/kyho.xs+5zc z o60 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 tak) ffrpgv7 9x3ves for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above 7v9pf vfrg3x)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 satellite have to be launched from the tophg4k) pz ou::d of Mt. Everest to be place4 phzok:du ):gd in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mo4 +on sv6:5ede*xuq, )wandyu1anej8 dule continued to orbit the Moon at an altitude 4n1ed8 :,neq6d* xn)ay j osawve u5+uof about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thr5 oi-56he,sk w6 wu/weoec)cat orbit the planet. The inner radius of tw r cwci5)/66 se5uhe k-ewo,ohe 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 ow5 hir8fl g+p:nce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real wf:p5+gi wr lh8eight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from p+q0uogu(s3u;q 7y,zb2 uzs k the center of the Earth's Moon in a space vehicle (a) moving at constantqg(;yo2+ u3qksz70z, upbusu 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 3xnd,*a9g+dcgjlo5mb.a-cr )* u pu dof equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to or-*.db) orjda,u gc3 cxga*l+ md5nu9pbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator thagfbb a5r4*q 7rt r f5 bgqba*4r7moves
(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 then/wyi bo hkcy 246e.7n ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accel.kh ebw4yi72n yn/6o ceration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface bnctr:40w:+vqi5ajo+ux .0dk2 u ioqof a planet with period T , the density (mass/volume) of the planet is jk:xc4:u irouw +vd+ .o5abn2q0tq 0i $\rho=m / V=3 \pi / G T^{2}$ .
(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 p9d6en9xx4d ot9* cs em nn.i:weriod of an artificial satellite orbitid*.sm9:new96ox 9i dnecxn4tng very near the Earth’s surface.    s

  The asteroid Icarus, tu+vxa 0uce, :daa3q;u ;jnep (hough only a few hundred meters across, orbits the Sun like the planets. 0;(u u3u+vda e;nxe cap,:a jqIts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 pkv h/u:p c6zo:gk55o $\times 10^{9} \mathrm{~km}$ 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 close tn j jkm7p.y4c*cb-5z4my k3,mv +brd uo 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 k-z3j7p c r b4jcmn4*,5.uvymbk +ydm 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 Galaxy 98;ayr7jbl di,*nrg nz b8(c*i+ m.x2unalyp $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fourx/ i82u.5og/ zj15bthk gsht wd( l7ll largest moons of Jupiter (those discovered by Gaijl7 x2t oh5lwls/d b/k(zgh5g 8.ut1lileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of 10c h nkmji6ogfa+u52the Moon. 5u j6f+ano k21mh0cg i   $\times 10^{24}$

  Determine the mean distanc4 ,mgt.yru p5we from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance o4.ym gtpw 5,ruf Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists ofj-+14riivexb3 g c(nw many fragments (which some spabn 3gi xc-e r1iwj(v4+ce scientists think came from a planet that 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 artificial "planet" in(l,hax d)0k9:4yo d d qjcgm(p*r .hjm 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 r4 , 0)pkmy(xqa : hj.dc9dodgj(lh*msame 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 lj1 hb,gwg(52aku c3w a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerat5,2 lajwwbk3 ( chug1ge 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 gravity bih;dz uj,f20q e half what it is on tj; di0f2hzq, uhe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands rq)u2yj: cbw- 7; 7hrhtukn bfh.(i7z and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulli ctznwi(. qhjh b2kf-7bry:77)h;uurng on one another?    $\times 10^2$

  Because the Earth rotates oncevee 8 (vmvwx4x6q0f3i per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction(x 36wf0 imxveq4vv e8 of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveli3gt4 6sjwb4h 8 p;nnkung directly from the Earth w4uhgjtk86snnp34 ;bto the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on as hvpd/)))yjr bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direjh) /dsvy ))rpction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about i,0fwp08p a tsits center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 kmw00p p,a 8sift. 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 y3d*c;poc7ciicqsa lt)a.gt k 88h 59(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 th(:(u(v hm bisdeko/t/e mass of a planet in terms of its radius r, the acceleration due to gravity ah: e m(iku((/bst/ovdt its surface and the gravitational constant G.

A plumb bob (a mass m hanging onvs 01 - iy(c gnhlyuli5-a:bb. a string) is deflected from the vertical by an an05.ils-bg cu:hbv 1l yi(y -nagle $\theta$ 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 spn/o m y 0dnj69i7ikyw-eed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle td im nik -9y7n0o/wj6yhe curve?

  How long would a day be if the Earth were rotating so fast that objecvc x2; :cw ump/(spwqt:1; tqzx *uc1tts at the eq* ts(wux/x:p:ccu ztc;vq;2qt mp1w 1 uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a 3loqk9qq*ak-b r9fovf *2 qp2constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 0qgt)d4+xn js235 m. A lamp suspended from the ceiling swings out to an a)qsn4gt0 d xj+ngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as thwp)9 (dx0jzgwgzzfr8 qxh: tfm4n4e;;x9wr +e Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a 9 0hmgzpq )fwz;(fz4gr4:;tww nxrjx98e +xd 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 r5z6tw -8hqjchojc9 l 6x)v9cdeduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thq9 5xcz- jow th)r6c8j69clv his 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 shownjn28vak7qs 6u 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 nka 8s7q62j uvlargest? 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 :zc4 v hw*da1n(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 Eartv*c1zwh na:d4 h, 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), a2vqe +wk8)4vf ioiwi(fter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Erosq ov2if)w4v i( e8k+wi is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in n,dvibr)u; o 1o9uqn n(eed of repair. You are in a circular orbitr(; i)qonv don,u1u9b of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a pe-,0hb.h)v ali jc /krkriod of 3000 years. (a) What is its mean distance from thei-/kr ajb,ck )lv .hh0 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 woul73l* v5o+ orm:atsvf rd need to be if you could actually "feel" yourself gravito3vf vr +5r*:sa 7mlotationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around thc0u ;4ek8 cchzj 4vvn)e center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center ze;cc 0)uv cvnjkh844$ \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 lo ol dwi w93x6/ooqycdf+3ug8 ,cated at the corners 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 o8ydug +3wf/owc l6oid9qx3 ,of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5emkt1azt).w , 500 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 experienmjp i*s8..bllv/e)x lced by the tip of the 1.5-cm-long sweep second hand on your wrist .b.i *em8ll )/jlpsx vwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a7m v xvjmmom e2x ;3xe;a:xv.89a 2vgb circle below you on a 0.25-m piece of fishing line. The weigh3xmb7:avx;m va 2vxme;ovxem. 9g2 j8t makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in az57;op jgyjl. new highway is designed so that a car traveling at ;.7zg5ljyojp speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars w7nll,r0 we9c yhen 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 llew, y09rn c7less 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.$\approx$    $\times 10^2$