Sometimes people say that water is removed from cloth5;pyagls+h+ lq:acszay.6) hmb 5 5 vpes in a spin dryer by centrifugal force throwing the wa 5aymlbhgq;6zplv+c ) ysha+:s5.a5 pter outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tram./p0) drc5(n wl kltcvels around a sharp curve at a constant 60 km/h as when it tm.) rdl0ccltp(n/ 5kw ravels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wio agm*xz8x(y zjz7f 2gd5 c,g 1f5yc4here does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on ag5,*(m7 fz4z gccd2io1 5jx8ay xfyg z level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round w0ol kvhq235-a 8lcmeuo ;c8n. Which of these forces provides the centripetal accele85al ml-o83w v; q2ok c0cenhuration of the child?

A bucket of water can be whirled in a vertical cimn a4v sv,vl+k4+u b:z1 6oksmrcle without the water spilling out, even at the top of the circle when the bucket is upside lsm+4v kza 4 1km:+n,sobvv6u down. Explain.

How many “accelerators” do you have in your car? There are m h4qm/prx22yat least three controls in the car whm4m2ph/ xyqr2ich 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 ofmrhj;2s *.lgh a small hill, as shown 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 this2lrj h; gsm.h* decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high sp(bd3l)yz ta 5teed?

Why do airplanes bank when they turn? How would you compute the banow5.gjn 1t ov:king angle given its speentv1 oo :5.gjwd and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pla 4 w0rm sp:87h )-dkmiflcjx7rne. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she lerid 8k:w jpml 7m)-rx0f 7chs4t go of the string?

Does an apple exert a gravitational force on the Earth?t9 ;wh 19 5wmb+0u3 w9mhb ji:tchi jjggj:u6s If so, how large a force? Consider an appughigj ijswwt:1 m9;h5ht : bcum9bw3j90 +6jle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wha;vcg lcz+,4y gt ways would the Moon’s orbit be differ4 +lczyv,;gcgent?

Which pulls harder gravitationall i z3 w+i)g/o+8eeufumy, the Earth on the Moon, or the Moon on the Earth? Whi3if8 m guzuiee+)+/ woch accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Mood(06yxejwv9te8-p.xz+ is:b vlz j 1 pn's. Yet the Moon's iz :vsi px6 j.(lp1veyejbtw-980z x+ds mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two fo5z +lyr lv+u/6osr/ effects are at work? Do they fsz + oly5rl/uro6v+/ oppose each other?

The gravitational force on the Moon due to mqq156m8 mmjuing 8b2 the Earth is only about half the force on the Moon due to the qm 5688bmgj2i1m n qmuSun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acz 220r+kj(wlrg4yc.n ehw2k7 d 1fbqgceleration of Mars in its orbit around the Sun larger or smaller than the centrr4 jdrw2(lc b1g0fky+qnez .wh27gk 2ipetal acceleration of the Earth?

Would it require less spe sttx)n zs3cjjx- 0ph)(h/ l u.54nloved to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dxvt-)j5l40 j thnz3 uhsl /on )cxsp(.irection.

When will your apparent weight be the greatest, as measured by a scale i0z siuq ))c.jjn a moving elevator: when thej) zq) s.i0jcu elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it 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 affy z11hi pd cn(v1b7gf7ga,9)xvx+qvtected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical +fvv(71bgpd gx hy ,t) 1i1aq9v7ncxz shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bejowjm d+n)9e:tween sneo:+mj ) j9dwteps.

The Earth moves faster in its orbit around the Sun in January than in J il;b9t/ef-yh;n*c 3ufzlz*tuly. Is t;n yu* ;l3h b9el/ tzt*-fizcfhe 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 have aomyt,mtp:; uij w o;m5tdz8;) moon. Explain how this discovery enabled an estimate of Pluto’s mjmmi,wot;5: ;o8zup d;tt)ym ass.

  The Sun's gravitational pull on the Earth is much larger tharoa r u.tte,9-n 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 other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25e.a,-9r otr tu $\mathrm{~m} / \mathrm{s}$ . 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 yjy9ujk 036 u36jpfetz( x o3m 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 E7o+cq+ts8v lzarth in its orbit around the Sun, and the net force exert+ tzo 8lcsq7v+ed 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 disr z3-wn.d,82b s7mnf jhn xije5.4htgcus as it rotates uniformly in a horizontal circle (at arm’s length)j5m73 jswg.hnx4enn ir-,f.bt h2d8 z of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's s4 :iy.8ga swd4bxiqy0 urface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitat yga4iwq. yx4b0 8i:sdional acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a s)w ac5 (3kfkohpeck of clay on the edge of a potter’s whee ( hao)3ckfwk5l turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratox we4 y*c94l6is8dnu e in a vertical circle of radiusn cw*olies dux69844y 72.0 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 which a 1:6yq4 apmb yg4050-kg car can round a turn of radius 77 m on a flat road iq:4 64pbyygma f the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of s; u/c u217qaoiwzlb(ftatic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed ioz7l/ (u;2aq 1b fuwcof 95km/h ?   

  A device for training astronauts and jet fig7m6:syz+ t sr8o 9bd/p4t fbovhter 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 oy/dt9+rssbf: 7v8mo bpt46zown 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 a )t8(jww1io gaxis of a rotating turntable of variable speed. When the speed of(wg o)8j t1awi 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 turntable?   

  At what minimum speed must a roller coaster be tra60qektz ;mxyo4 js6 ow3,yb 6lveling when upside down at the top oex60o36bw s ok4ml yzt yj6q;,f 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 driver) cros, -uv-m pr(jft8 r;n4 -vidqhsses the rounded top of a hill (radius jfp,;--duqrt4 isrvh(- nv8 m=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 whey4pfhlss)6/) g )srjrel need to make for the passengers to feel “weightless” at) r)s64 spy f)r/lhgsj the topmost point?    rpm

  A bucket of mass 2.00 kg is whi5,h/: : .c6h*pc(l5uaoka jwy deuzjurled in a vertical circle of radius 1.10 m. At the lowest point of its motio:(uj /,u*6 ak :5eudaw.lh hc5zopycj n 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 a 9pkq+xg;kx clr,rg,-centrifuge rotate if a particle 9.00 cm from the axis of rotg,p x;r gr,c9+x-kql kation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotlg, txq n:).kgated in a cylindrically walled "room." (See:qgk g, )n.xtl 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 c /kt,sroiq y,dt0vx6rd,7w/ bircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as sh,6 t7,0x,dbksdw/vq /trroyiown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the b, ycgsjyj p/ jt,,gwvv:4 f*t.all which revolvesjtvfy g : .*s/t v,w,jp4,gcjy on a 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 radius of 88 m is perfectly banked for a car travelj0lq9 15gaqs mqw7a i3ing 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 massesba- 4sa2tep *v $ 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 d 2mihc5;5 1upuz+uq;cbs1 .b 1vgujmsiving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted onyczgo/rk3tlue4),3iyr7 m t7 the car (by the grou 7ro)y7erttu/yl34gck zim,3 nd) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going v hh -z242xexbds05f75dkp czfrom rest to 320km/h in a h 2x5ekhzczd2x 50pvfs4-bd7semicircular 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 circlgd/rw uuxuan *et1*.6 e of radius 2.90 m . At a particular instant, its acceleration is 1u1gd* wt*n.u6 ax/ uer.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 5)6w;um/uwsj2moi sr Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ifw ir2uw5suj6 m;s)/ mo its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratiox dltq0(gn( 2ln g has a magnitud02nl x dgl((tqe 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 accelen/-gzv,* a vcmration due to gravity on the Moon. The Moon's radius is 1.74zg/v*,nm -ac v $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earthak *opauj xa5oy*368 g, but has the same mass. What is the accel a j8ap65*ay 3uoxo*kgeration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thexcfo 9llket:ik6d3(*m wis .) same radius. Wha i9il f6x)mkstoc(k.dl3w *:e t is g near its surface?   

  Two objects attract eacvrla - gicq r5cn/x9m5tt10 n2h other 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 , the acceleration of grsidly7, cwyv yg:)jd+pa, u t/*v fg(8avity, at (a) 3200 m gs p,d av /j uy,li7(tydgvy: fcw*+8)   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wherenvyu4, b+4yyz.2da ju thegravitational acceler4d+u2,bzynjv.yya u4ation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thxuidwj3vb 7z .;4 6tf,d9ndq ve mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfacxfd u.4nvv9,3qw b;i tj6 dzd7e gravity on this monster.    $\times10^12$

  A typical white-dwarfyxu ibb pm2vrg73 (u n:)y b2q8h5mzk0 star, which once was an average star like our Sun but is now in the last stage of its ehg02 8u73bv2nzxb q:yip bmm 5(u r)ykvolution, 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 weie1:xx+0 5o0 jf iutpw)*pxbktghtless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration p+ powfbx10*)5jx :tix0 utkeof gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a + knenjxy*aclh0;5, 5 cjz;nv square of side 0.60 m. Calculate the magnitude50;hyn+ck5j; *cea n njl,vz x 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 yearewspx4:)r i+k s most of the planets line up on the same side of the Sun. Calculate the total fori:swekpx r4)+ce 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 wu3n 1suk,n.j zhat it is on Earth, and that Mars’ radius is 3400 km, det .nn3,zjsuu1 kermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ea3upfpoh jxo3z*l8)/ .w(pqzlr g 62 sirth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampleiqow r2hll 3g(6 *ppf3p/zz.juxs8) o 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abo8btm6pn8 rr g5di )-vq+el6 ytut the Earth at a height of 3600 km. 6gbrrv-5i+)6y tnte l pq88 md   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovebmgm *t *b uh*k*ve7z07jyah- the Earth. How fast must the shuttle be moving (relative to Earth) when the reljmyktemh0u- g*7v* azb** b7h ease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ 9 0-gw ko;.gztwjfg(x fbk+-wupants 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 forfg9.t g(k;-wwf-bkgj0+w zx o one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orn: mhcvco) qo.oo7 73mbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass )7c3hoo cnv . qm7mo:oof the satellite?    s ~    min

  At what horizontal velocity would a satelli) pw )9+-li3qudnusr+/y gtinte have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? /)+ gi+tn-uu w dplsr9) qyi3n  

  During an Apollo lunar landing mission,x; 4psw12h j/v- i/vlx onp5cn the command module continued to orbit the Moon at an altitude of abo-x5nw n sjvc/v/hl4 x p1po2i;ut 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn arekt8, nn6a7 fmr composed of chunks of ice that orbit the planet. The inner radiuskrfnatm6 ,n87 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 8jh/gmn o6bc:. 5–9). What is the ratio of a person’s apparent weight to h:6b/gm on8 hcjer real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 o7(;jzaur,asf8wv k gg ye ,.3km from the center of the Ear(w,e .,ayfaj gsv 3u 8;k7rgozth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars yyz5 ;x/srp:ck(jg,vof equal mass. They are observe,g; (ysr 5:k/ vpzycxjd 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 for the weight of a 55-kg wou6wyd+qx*z:bgxt,l i*3vxjtq;o s 7. man in an elevator that bx3 ld w6 uzx,yq7.qtsv: j*+goi;*xt 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 suspended from the ceiwsy*9 bqi n5:p6vx 9taling of an elevator. The cord can withstand a tension ovw :5ipb nay6q9*s 9txf 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the csgfv 5zh ulm-+ q7u617cspq9 surface of a planet with period T ,cv7q p6uh+g 9sm5fz lcs- q1u7 the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to u1wlwuarq* 0o.4q. o:wm9 cszdetermine the period of an artificiuwworu 1mqs:l4oq.cw0 9z.*a al satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only adu,zfn 19a,g-x+fp0qiiuo3 y d(59irz3ve db few hundred meters across, orbits the Sun like the planets. Its period is 4y93pde(ffdz vo9 3r1,z, auiuxq-inb+gi05 d 10 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance oxyx p*. 4nfv9g4fz zcoj4d6 z p9,vic(f 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 e775rz1oe sst2ln :sp every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The r1sn5p2el7 t z7os s:emean 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 tz mwnwy) x+jj-7e a6;nv,ejl;he 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, p+ljd0 +d8 u.sjx1zp rjeriod, and mean distance for the four largest moons of Jupiter (those discovered by Galileod z.ljj0duxr+j8 1 p+s 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 thj ,rj akjc*f1ng -emt1in3 7l2e known period and distance of the Moon. jje1ra2jkcnf7 * tml,gin31-   $\times 10^{24}$

  Determine the mean dip-o s3q)g do:vve lxtr v3*81mstance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use :l 3*pdevx8o3q-vs)vgr 1o tm the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mar-q oi 20f/u9.c zdgx,ovhq-e0hk p4yds and Jupiter consists of many fragments (which some space scientists think came from a planet thazgq0-k xye dqhdv2h-/o4c,0 foup9.i t 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 describesxk gwu*zyi )/-mde7:a an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the kme7x:)*ywa gi d/z-usame 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 swingingm,l m k)me4gs0 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 tk0ge msml),m 4he 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 gravihq at-w;6: dwxty be half what it is oa-w;:dx tqhw6n the surface?    $\times 10^6$

  On an ice rink, two i;v 1d -4pxmlun nkk);)cadp;skaters of equal mass grab hands 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 pulling on one another?4p)n)imd1k;ncvk l;x ; audp-    $\times 10^2$

  Because the Earth rotates on mf/0y) )fcom5b fjamw,-vr *oce 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 of g ifv my*bcjwomm o) r-)0 f/,5afs this?    $\times 10^{-1}$

  At what distance from the Earth w x+yo6bh)wfg-8 xwk )qill a spacecraft traveling directly from the Earth to the Moon experience zero nex w+wg8k-x ))o 6hqybft 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 7k10ua z 9rg r8ax5hqxstand on a bathroom scale in an elevat0kz 5arx ua1ghqx9r8 7or, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationc0hj+g o942zes i-rsvfv c/p9 consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) irzo94gvv2-iesj/hcfs+ c0 p 9 s to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his ae:bn:wvwd 4;u7a+ sph(3i pebw48m ec ircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planeqtkgqy k9d ll 4v:l5m0y. /9tja5l3snt in terms of its radius r, the acceleration due k0:s5345ydt9jl yqtklg ll / q9vnam. to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected froh0 o,,kr+ al50tlw kuam the vertical by an a5rko hw0l,+u k 0,aaltngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient ozcwj,,bo6)n gf static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle thn6 ,g,j) wcbzoe curve?

  How long would a day kt1eanc3a4g qc,-4(wkm+vjf8 yal o )be if the Earth were rotating so fast that objects at the equator w4+t4wcy3jk ga f 8qao)1mv,n-clk (e aere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constk4+z0vdvij9lo2ub 3yi-r(y so hc6d +ant 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 235 m.6)o8o. k9 vurcjsttqx*p 8+ pz A lamp suspended from the ceiling8q .zc ppr+)6uo9t8j xksv*ot 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 tt6oylae5 t 0c9hsn,n+he Earth. Thus, 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 a planet. Use the following data for Jupiter: mass =e 5at96h+,nsnl 0toy c1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ex: )1g oi bi,ue-r22axikev(l ztremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbitingz- lg1ei,2 (o x)uv:ii2k abre 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 trav9t sz6lkj-6xmv 46oh(vfwo* qi l84iv erses the hill and valley shown in Fig. 5–45. Both the hill and valley ha6iikv 6h ovol v9tfm 4zqwxsj6-(*84 lve a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group 9we2/ / rv2t, dspzy*iz9ryn zof 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigatir2yi * zzy9z edts,np/wr9/2v onal “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 Rendezvab- hj,r+ i8pvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of a8-j+p,rhv iba bout 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 pursuiipquq ue8n:)zd 64s w(ng a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 )su4uzi wq:nep(q8d 6km 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 f(c 7kzsz8-rrc- 1 ufchas a period of 3000 years. (a) What is its mean distance from the Sun1-kzc7 c8(-rsfufz cr?   
(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 btatt 5 . .dkar5o:fgff(wzg0) e if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonkda(agg tzf.ft) wf or:55 t.0able assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gajsw eb5wla8b9zl54afh )lbi-e8w 6 (xlaxy (Fig. 5-46) at a distan8li(x-be5)ll4wae 86fb9s5wa jw bhzce 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 locat.pztuu8 b(opw e8ub8hb(u0j9 ed 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 midpointueuuup89bbw8z8.p j (0ob(h t of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth y7fk)xs8u:m h $ \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( k.9dg0gje/eg c ,jai the tip of the 1.5-cm-long sweep second hand9(je .0jegg,ic /kgad on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing auzv, 5.r:qhe4 4dylcr 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 Fig. 4rd .,5eqzcrv4uy h :l5–10.]    $^{\circ}$

A circular curve of radius R in a new highway p(u-;e vl 9wf/j ua*lzis designed so that a car traveling u el(wpz9uf- *;jav/lat 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 when negot9, v;*e qjxzowiating 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 feelin jewq *;o9x,zvg 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.$\approx$    $\times 10^2$