Sometimes people say that wate*j gc/hy2 91ylx8/r qjfvw uk5r is removed from clothes in a spin dryer by centrifugal force throwing thjjf 5 gkr/* h/y8vwq2xuc19l ye water outward. What is wrong with this statement?

Will the acceleration of a car be the same wx xb2 rj)gbz. (-nlh;/wy rku-hen the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at k) ;nrz./bw2by ( xgr hx-jul-the same speed? Explain.

Suppose a car moves at constant speed along a hilly roackw/(e; cl.yw ks4f43 hig97ne cu)gyd. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, c 9.h)4nylifyk(g4/e geu7;3wcc kws (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 chil-emza( zx 3k;3dg abq/d riding a horse on a merry-go-round. Which of these fo3az3x-zmkbd( /ag ; eqrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wate3l/z8 ya )v 57y7n1tm fkrvamtpe*z -or spilling ozye*5fpvvyt mm 1/ nza37o a8-rt7)klut, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There k5he6t:zh,-j6ctp x h0m;t 2lb o.5 pztko x7vare at least three controls in the car which can be used to cause the car to accelerate. Whaxpt ho706h5tpe5 k c;6zxthzkt,.ov j 2lbm :-t are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. dozje 2hx 5dor ank)9l(h8k*85–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sledx *5kko2z89(8deh drljoa nh) decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rouqygl )ez/9 dyu 3w4i5qh1- m*9yzujsv nding a curve at high speed?

Why do airplanes bank when they turn? How would os;o53:xngg9 v4opm k you compute the banking angle given its speed an3gskxo5v4: o npmog;9 d radius of the turn?

A girl is whirling a ball on a string around hwt.)n;j7/ aq)k rnio ker head in a horizontal plane. 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 let go of the stq )rkjn7iw;/k) nt.ao ring?

Does an apple exert a gravitational forw0 ,uv7vg0sqsb1t .77 sxvzhsce on the Earth? If so, how large a force? Consider h7s 1.7tvq0 s7z ss w,0gvxubvan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it i(ienl;+ 3osome1r. uls, in what ways would the Moon’s orbit be +.lio e(o;l 3ur1m snedifferent?

Which pulls harder gravitationtqve n 5i(vclcno 70,2ally, the Earth on the Moon, or the Moon on the Earth? Which accnci05tv(l q,c v on72eelerates more?

The Sun's gravitational pull on the Earth is much larger than uqi*v/ le-c/: 6vq.sss0 mz2r +idkr othe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenrq+zsk oqis/v*6m2d/ 0iuesv l-.c r: ce in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at f,wqc h 7psjyygz51j;;gh;a qu3 slm9 2:zf6xthe equator or at the poles? What two effects are at woxas;fqyzpgh;j67123gj,mf :c yqw zh95 slu;rk? Do they oppose each other?

The gravitational forcbjhgg** s/ sg0e on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earg/j*0s* hgb sgth?

Is the centripetal acceleration of (g7 j6zij+olx Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eartjoi +j6zg (l7xh?

Would it require less speed to launch y2u;qx gw)b n6 lu.m4ta satellite (a) toward the east or (b) toward the we.gm n;t6uwql4yb) x2ust? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as m k)hep 0l+,b*ayxm:kg easured by a scale in a moving ex 0gk)p+le,ak* bm:yh levator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long w*+az,nkp j u(periods 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 feel on our feet, and (c) any other aspects of gravit(+wp j*,an ukzy you can think of.

Explain how a runner ex h3oj5aorev.7 periences “free fall” or “apparent weightlessness” betweeno3eah 5.7orv j steps.

The Earth moves faster in its orbit around the S.8hs8d +)kqfknfp (y zun in January than in July. Is the Earth closer to the Sun in Jaqzy k8f8d ()hn .ps+kfnuary, 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 a mo o(au hqf )bz g*o2p2fp (8dh6d(mw,xmon. Explain how this discovery enabled hd (2obo(mhq wmp28(f) g*zpa fu6,dx an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mooneejk u.d6-1ec)cg v y,'s. Yet the Moon's is mainly responsible for the tcegvu-e .key,c j6d)1 ides. 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 travelintkyr2(r v2fp6-cnzu * g 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 acceleratik dmr.:up0 5xeon of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of rxp .rem0u:5 kdadius 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 discu( ;m5uyn 9ybmas as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcul;( y9ymmnuab5 ate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, ai g*-xe( 8kpkpvw /ampc p64: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 grav k/ w4c ea*m:i8ppax-k6gv p(pitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of ar yu/npfi:+h. potter’s wheel turning at 45 rpm ( + :.ihpu/ryfnrevolutions 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 wbcg+n,lbz i494ko ,t vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed l4 o, ztg9+kwibcn4b,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-kgkufkk;bz2j*n7 qap9 6;.wia 0a ird 5z car can round a turn of radius 77 m on a flat road if the coefficient of static friction between t9ra a w fbj2p.z6a;n0qkd ui ;5*i7kkzires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of sa7ranraoh 0w/(n 5 /pdtatic friction be between the tires and the road if a car is to round a level curve of /5 onwra/07a hdnp(arradius 85 m at a speed of 95km/h ?   

  A device for training astro(p3ieqdua; +*v m4 edgnauts 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 back is 7.85 times her own weight, how fast ispdav(du* g mie+q;3e4 she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable speedauewa4;b 6(dc */1j xsksyw7s . When the speed of the turntab64 sax*abc/s;u(kwj7s y1edwle 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 mu y,l j1egnl,9sst a roller coaster be traveling when upside down at the top of a cij,le19sy, ng lrcle
(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 roundiehwx aq/u88 ,ed top qx u/iw8 8,eahof a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diamete h-g3/tc 0gghul40 iyar Ferris wheel need to make for the passengers to feel “weightless” agl0cu/ai 4-hgg0 hy3tt the topmost point?    rpm

  A bucket of mass 2.00 kg is)5m7btbd( qsx whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rop s5dt )mxq7bb(e 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 centrifrd a:-u35jui rwscd/ *uge rotate if a particle 9.00 cm from the axis of rotation is to experience an acce:jw5*cra3r d- idsuu/leration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylix0o,;w* dub khb .oi6u;fo0pxndrically walled "room." (See Fig. ,boufi 6dpx o0*;x0bw; khou. 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-hoyzduq:r x9. c2qzs(j(ckey tabletop, and is held in this orbit by a light cordr(uxq:q( . j2dc9zyz s 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 weightsa8/f * bv; 4fyo+jvdl4y)9mbc/3ne) kbstbt of the ball which revolves on a string 0.60b))vbyblsdo;asf/j c 4+8* v/n t9 fy ekb43tm0 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 tr0xt vk :oxk/ g+f l69io58nbihaveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses :nbuke/ ta5; k$ 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 evasiv n uz3bs9m23 2vlucok6e maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted ongqf fd2-1)5ef4pivnx , 7+gp2no s qqe the car (by the ground) i qg+ i-21 7xppfqdvg)n2 n,e5ef4fsqon 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 un0j ue;podw al)kwt +) wgrx)+4iformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the taua)+ljw;kgxtp 4e0o)+w) d wr ngential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particmo,bl8e- 9 ,uryee(zd ular instant, it9 o,8,yeur le -bmezd(s 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 12,8a9sl gkl jz yj74:s-4vyr4wl 200 km (2 Earth radii) above the Earth’s surface if its mass is 1350s4zw4l27:v4gjsyrlj- al y9k kg.   

  At the surface of a certain planet, the gravitational aupe1t o)h63 u)y(ldo0lxj /c:atsp /rcceleration g has a magnitude of 12 m/thsd0p)ot (lo6l: e3c ux y)r1/jpua/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 accelerati , vv*:v ih-klkiji.ra 6jn0u9on due to gravity on the Moon. The Moon's radius is 1.74hk-i9 j:rla6kvv n u,0*iv.ji $\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 tagz .4wpksc/ o v9;t;ig- +u/oyxbhk* hat of Earth, but has the same mass. What is the acceleration gcbpuxk//+*k yv;wa oigh4 zt -o 9s.;due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rjfq-p6j u6,k7 cfj-ob / mxipi5h0s*hadius. What is67j h p,j5icbh ujxms06k-*offi pq/- g near its surface?   

  Two objects attract each other gravitationally with a force of p zvi8i5a 06r8xl; dv5ky jd)m 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 effectivn6 ybn2( 0 knudz7f2sue value of g , the acceleration of gravity, at (a) 3200 m 2bd 7nyf(znkus2u6 0n   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eart+.kpqn5) cjgau: fju- h’s center to a point outside the Earth where thegravitationalf5g.)up+nku:j- q acj acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fil fx:/ ,vl3gkeve times the mass of our Sun packed into a sphere about 10 km in radius. Estimate tlkf3xg, :el /vhe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avo;8uo+hp ) 1symfoc /serage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the 8s yoc msp/h)ouof+1;mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weqs*o(pga 5nd h*w3 su-ightless while orbiting in the space shuttle. Your friends respond that they g *p5-nu*dwsoas 3q( hthought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square ofn.ru mpwg2n*.j da+k )s39rsu side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spherernujwk9 ns r pa)g+*m3.dus2. by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetb6ni1 b7lb l hz8fy7+o0ys/ nn 5,).efqdqcmss line up on the same side of the Sun. Calculate the total force on the Earth denfm0b db1byhl.ss7i+n8nf cqlq y,/ o56 7)zue 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 what * ;oqn,/ai, r8ddpqlhit is hd8/arnqqo,;l id*,pon Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fobep.(xcy de+tyxwy)5 7lw,m 0r the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtateweyw ) 0mly,p yx+. b5c(7dxined using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mov9j(v y *ukp6(0m go2eme zd7mving in a stable circular orbit about the Earth at a height of 3600 km. (z mu6*dgop(9yv j emk720evm   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 659n t o(b85zgso0 km above the Eartt5gzo (ns89boh. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a )rq ) yzy4tt r.l9r-gxm )xo0wcylindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s rt ot)94xy)qwx yz)r0rl .-mgdiameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satel96vt7..c -ceahtz dg8glvk ktb+/y4 alite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is ob ck t.c/.76y vz +t-tevak8gld9hg4ane at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity di pf5 2ktxej 14n:1zzwould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orn jz 1ie pkxz24tfd1:5bit around the Earth?   

  During an Apollo lunar lp.dkd9 .q0pk 6(xpky uanding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long yup 9k6..dp dkpkxq0( did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that a uje +r4t,w2aorbit the planet. The inner radius of the rings is 73,000 4 wua+e j2,rat$\mathrm{~km}$ , 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 15.5irea1 5p)8s0cx:q fqn s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the topf sq8c)qa:0r5ne xp1i , and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the ceqoq w,veryjh r 3qb(+y. )*pq*nter of the Earth's Moon in a space vehi +3eqyqq)(h*,vy obpr*wj.q rcle (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 mas60 tteq6be adk*kf5r*s. They are observed to be separated by 360 million km and take 5.7 Earth yeafkeq rd56kt0* abte*6 rs to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for tvc p)der kji id 9xc02kzbh(t*w)p3/ (he weight of a 55-kg woman in an elevator that moti2c )ed(3b0z/hprxv()ik w *kcdpj9 ves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatb +ns6aert( 5 anue)+zd qf3g.or. The cord can withstand a tension of 220 N and breanaru( sa q3z)+b de5gen+.tf 6ks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a )obal4irkq:2 planet with period T , the density (mass/volume) of the pra4 o2bq:k)il lanet 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)1t.a tjy57np t to determine the period of at p.jy t17nta5n artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only ar.-xpdk+0,ld4sn o oj jy0d-vp)xe w4 few hundred meters across, orbits the Sun like the planets. Its perioxpndwr0d.4koloj,) jdvx y4s e --p0+d is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of eyv6z yd/i 55zb r7 3fpujq;h1 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 on4:o ym(pnap:r ce 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 mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the S:mra4 :(npy opun.]    $\times 10^6$

  Our Sun rotates about the center of thekk ,nx7* 6zgvm17az 8s-2sw3lqavpea 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, fp-u36mjpd yk :c:*c ww: dw,hand mean distance for the four largest moons of Jupiter (hwd- ,k pf yj cmdpu*3c:6::wwthose discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of pvir2bmq fq+9 tlc-;5 the Earth from the known period and distance of the Moon. b+q9lrv2qmp c;tf- 5i   $\times 10^{24}$

  Determine the mean distance from J5k1 jlh-m9h0 yfs cl,nupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periodslk,hj1h- 0mcy9 sf5n l 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 fragmefj/j+w - dsof-95h8rys4 bjkk nts (which some space scientists think came from a planet that onksbj95 j /rs 8f+wf dh-j4o-kyce 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 the form of a b11ioof:gty9a9xi0 tr and completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface y gtxo1 fro90a1ii9:t (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 a hanginx:i- ewzexplvbi d2)o6rw *874a mn v9g 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 cael8nb id-ov 9x)p*7aiw:rx2 z4wemv6n 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 e6 /omkp y))gq)wm9j(dis9,uqjqq,e the acceleration of gravity be half what it is qw)(qi ,mes6/9ok9 ,)j e uqpgyd)qmj on the surface?    $\times 10^6$

  On an ice rink, two skaters.1m1 z 3wn0gwkdss3t.9bcz:q s- bnpv of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.83kzs:z pw9nms cb-.n0bw1 . dq3g tsv10 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appam u.d:x)o k6 1ie7/szrmlw(c;alag:krent acceleration of gravity at the equator is slightly less r:z.6ogw / k;:icx7la)m lsdue(ak 1mthan it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from stm/(5w ,le 2 e2ezksr i/sv8jthe Earth to the Moon experience zero net force because the Earth and Moon pull with equal and op8 e(2,jvre /sslze /2 kim5swtposite forces?    $\times 10^8$

  You know your mass is d 5(kncypr/ma uh8jsuj 7i:;:c*hslt*b: u 1 n65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevatn5*l uy:su: 8ukhi 7( m:1jhdpabtr jn/;*cscor, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wi+jfzdb5f0mg dfodscw9y4 031ll rotate about its center (like a tubular bicycle tire) (Fig. 5–42)w3m 19+ s0fobj0gyd5 dfzfd4c . The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hi+ uiq xmb63:-f 0yzaxds aircraft 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 planet in terms of its radius r, the ac * q)y;o 0j5tgj *iwztrg(h-yrceleration due to gravity at its h5zyr0jt-*rqw j;i y* g)g (otsurface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is dy(0a335gqci y 4e5 aptbfiea7;pd2d weflected from the vertical by an ang i cb3p p5y 32 t7fai;(aegqde5wy40dale $\theta$ 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 banptzd v;n4 x/n:5i)e vtked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), a )/pvni:veztd4 n;5xtt what range of speeds can a car safely handle the curve?

  How long would a day be if the Emm zqft.r(anio 99 53oarth were rotating so fast that objects at the equami.ftq9no(az rm95o 3tor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a coco24+iqz 3 hrm 3jdae1nstant 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 constaql71 (.ys3mmc5 25or fzyo count speed rounds a curve of radius 235 m. A lamp suspended fymcu oclf3m 5 y2sq5ooz(.71 rrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been c-io :)r /.cwexbn zi4y.pf:rklaimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people/rzkef4-i. n.w:bco ir)y :px can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extry;dga)ze-s e-vt/mi 5 emely massive core in the distant galaxy M87, so dense that it could be a b i-ee-s/)aym tv zdg;5lack 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 s4yymzucdh*w e/i5he(o :8 us2peed as it traverses the hill and valley 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 ( yhzhee2 u5: dicy uswo*4/m8compare? (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 of 24 satellityb8ai wopl 9a/(+jaz9j9r t3w es 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 navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine(99 y a938t ajiproz/wlja +wb the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendv1/af;8dys n qjn 9+vyolv(h 5ezvous (NEAR), after traveling 2.1 billion km, is meantn ns 8 yh9; 1(fl5d+jqyvvova/ to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle purhngr y,( kk.9lsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km . krnl9gyk,(h 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 300ide6 f4a k)u8yo4cri10 years. (a) What is its mean distance from the Sun? 4 )4or1kad fi6ic8eyu  
(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 jx*5k4wkvwe e 2ho y:(z7y)kdj g;c ,tif you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumxj e7hcg w (y,z5:k)e* jokdt2y 4vwk;ptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mtno4l1a3 o0 tzilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-0at34olzont 1 years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squareb*e,vfc *x2jwgi sm,)hlru *q ea/1j3 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 bottom side of re/aq21xlh**mcv wsf3 ,ij j eg*bu ),the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartv lhzkd(7b/r / .igjb3h $ \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 exzzp1za:69smq8z u q *7p xnaw*perienced by the tip of the 1.5-cm-long sweep second hand on ypam: z6qzqwa8nzz917 *sp* u xour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing 2 nskagjoqp;;l803r aa 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 vertip 38l2r0ja ;ks;naqg ocal? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway i tw;lb/f5r 7jm82q8 ovwv ;oegs designed so that a car traveline 7;; wgrmfw8 vq8b jo5o2lv/tg at 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 ty1)ii0lth ynn.co zq ;+1n) dsilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approxima)dqiyt;nhy 01o.ilz sn 1+)cntely ). (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.$\approx$    $\times 10^2$