Sometimes people say that water is removed from clothes in a spin dryer bim1 (bc 6acl 4civgy,7y centrifugal force throwing g6b 7i a, 1mcvycc4li(the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels 25cxh x p 7wvz33qlbgu r9v997xst 7ljaround a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the shl t7 cguwz27 rpxl39j9s bv53qv97x xame speed? Explain.

Suppose a car moves at constant spee0 )u0vti lg*o+6v9zjk chi9p.g.an yvd along a hilly road. Where does the car exert the greatest and least h6v9cg+ y9vinlgup o. ). ji0kz*a0 tvforces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a muej;ng-2e7m-bdz 6 ynerry-go-round. Which of these forces provides the centripetal acceleratdeb -6jyu-mn7z2neg; ion of the child?

A bucket of water can be whirled in a vertical circle without the water spil ee .gitge*orsh:f950 wui.e;ling out, even at the top of the circle when the buckeuft5g:*0eoe. r seh egiw; .9it is upside down. Explain.

How many “accelerators” do you have in your car? There are at least 7u; wcfbs-up4 m5ku m1three controls in the car which can be used to cause the car to accelerate. Whmw;4 s 5-mu7bpuf1ck uat are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown ikpjk w2 i;g,(yn 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. Exp2 k jkwpy,(ig;lain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high spec4e i6qrrd:h .ed?

Why do airplanes bank g hylk;0:cfaaf zl2j.6o)g0gwhen they turn? How would you compute the banking angle given its s0a6oglg0;fc.2)jzah lf ky: gpeed and radius of the turn?

A girl is whirling a ball on a string around her head in a ho)l;do)ebgqp0 ny3 cq 6ialu34rizontal plane. She wants to let go at precisely the right tq3)q;nlybia g0pl 4odu e)63c ime so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, howg gww*k6ud xc1p*u 0,k large a force? C, cwugk*gud6* kwp01x onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whatax j7s/g;qr6k it is, in what ways would the Moon’s orbit be diffk7a/q;x gr6s jerent?

Which pulls harder gravitationally, the Eva*o)+mjd)8 jlke*f barth on the Moon, or the Moon on the Earthbjefo mjld8))+** akv? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than th v5ohdb8xwm 5*e Moon's. Yet the Moon's is mainly responsible for the tides. Explai o5wh8dbv *5xmn. [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 tyrac;f.oh i7/ l6w5m/q yag:hwo effects are at work?a5/rg6flq ;h7 /ym:haw yoc i. Do they oppose each other?

The gravitational force on the Moon due to the Earth a7 q-9w. tozqcis only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earthq c.oa qz97w-t?

Is the centripetal acceleration of Mars in its orq90:p,(c jm g4f6 kc oijzu(vbbit around the Sun larger or smaller than the centripetal jq:(z0( f96 gimkvpo,ubc4cjacceleration of the Earth?

Would it require lessj*x ;zto2l0w7y ke+obf-k a*d speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotatioa2obej ;dzlkf ** +x0ytk7w o-n direction.

When will your apparent weqng7 ( /qm8kpwight be the greatest, as measured by a scale in a moving ele(7pnmgqw/ q 8kvator: 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 periods i.aotp31ef g: zo1/1xg +ow;m v, mb fqw5cwr6on 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 walking1go:6q/ z a .egbw woocfm5wxftr;1vo1,+m3p 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 “fre 0xc93qpe,op5rfi do;(w-y(9d hmpb ee fall” or “apparent weightlessness” between stepspq do cf,( xw-mb 3d(p05eroyp9;e9 hi.

The Earth moves faster in its orbit around the Sun in January thanlq hplo* ,r0+h in July. Is thl+lh pq,rh o0*e 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 a moon.7wty c)v j;n;+v d(qew Explain how this discovery enabled an estimate of Pluto’s my+dcv tnev; w7()j ;qwass.

  The Sun's gravitational puai48m0nu3p c ftb:fb. ll on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational 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 putb3nf 40bm cif 8:a.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 1980hswd o5r/;5 (+i+ dgilmc1pbp $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acce ix hr)to8ode;uou)l d,8-h :ileration of the Earth in its orbit around the Sun, and the nedhoh; )ei :ti )uur,88ooxdl-t force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2xuo5 py i44trhox: q2v9e 1qc5.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radxpuqiv:2o 4 4cxr t1h9o5qy5eius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfav8 at/ti7rb+r ce, and circles the Earth about once every 90 minutes. Find the centripetal accelr vt+b /itr8a7eration 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 ofunuq 5.umlxx0* jsz 2ikf-,t 90a)5 bqj hq-zz the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutubs5n9xx0- h 2aq *kuz j5-0 ujtqz)m fl,iqz.ions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is q71tmkr-q b,kc0yvhxeu * ;q:revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5 *tcq7h,kxu e0- m1 bkrqvyq:;-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 1050-kg car can round a turn of ;0jydb2j rpaimf:*9o radius 77 m on a flat road if the coefficient of staticab9 pf jmo:yr;j20*di friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the wh3vdko4)c3 v33 i 7mep9rqn xtires and the road if a car is to round a level curve of radius 8eq4 rn3v)7 c3wim3 9hd3pvkox5 m at a speed of 95km/h ?   

  A device for training astronauts)kl q y)z8)c ka6d2bz+f3yekn and jet fighter pilots is designed to rotate a kz2 +e 83)6)anckdk)q bylf zytrainee 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 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 q-4dgw /jx9uhaxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixedgu4h -x /qjd9w 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 7r l:phyu1(i3z )ocrf be traveling when upside down at the top of a circle(clriroz3yf1 ph :)u7
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top u2dkjgrdd le l30e+:5sr1 /qjof a h+e2sul0gdj3dqrr d:1j /le5 k ill (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 msk,la sqwb9rt 42kd)3inute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weig92 w st, 3lk)rskq4dbahtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of )(q- uuxu ;pdgradius 1.10 m. At the lowest poi( )qud guxp;u-nt of 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 a centrifuge rotate if a particle 9.00 cm from the axis 7 mjhrf.q*i4nqc,fj+of rotation is to ,ji.7q+nfrc* q fh4jm experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnicxe/x :f5 ui :ig6lfk9val, people are rotated in a cylindrically walled "room." (See Fkx f9 xcigeu::i6fl5/ig. 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 frictionxa9kob4 1g ev7less 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 show9kbxoeag 4 v17n 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 weightf1z5i8 fp/x t* e.z )*amigjwn of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of**fen twam8.gi 1zij/) z5 xpf $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 fs6ld 16n pf:+j.j7 h gvo8sexmor a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse 7sz7rx6, kswgs $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving verticalc( ,l0a dvabswa 411euly 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 m9:bo8v*ghjdj -,* vlfw9tfp of the net force exerted on the car (by the ground) in *vw* mgjjv:d 9,- fophtb8fl9 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 Indiana x yn k. (x i*y+5zpcy:k:0r13c0upyoi;bzlbtpolis 500 accelerates uniformly 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 of static friction have to be between the tires and the ro3l k0:pcr zix(p+nyxobby u. 5kzyc1:y;i*0tad to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius kitltp0np386 h18cf n 2.90 m . At a particular inst6ti3n8cpf p 8kh1nt0lant, 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 smssx-dv4k(q4 pacecraft 12,800 km (2 Earth radii) above th(k-44q msxv dse Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitau7ra *rln +ybmr; f(0ctional acceleration g has a magnitude of 1rcl* bfrr;ynam0u(+72 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 acceleracw;tfg9eji - )yyzilp4** .cn zqi c66tion due to gravity on the Moon. The Moon's radius is 1.74 .w6iy *tqei * czn6;-zy)jil c49cfpg$\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 Earth, but has yx/ zlb 5h3mm5the same mass. What is them5hm 3l5byxz/ acceleration due to gravity near its surface?   

  A hypothetical planet has a mar m7ilm,wem1*2 pv8qidz 89apbw6e0 ass 1.66 times that of Earth, but the same radius. Wd iw7a1qv e mz089pm*l arb,ew2m6i p8hat is g near its surface?   

  Two objects attract each other gravitationally with a forcernv-n8/v +czi 6 chk- ac6sam 39,9g(hr xgftg of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, td- dkvwi9x24(ng9ohat (a) 3200 m9khw 2odi4nt (g xd-9v    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where tu/ce3lkuv, kl -w;h 0thegravitatio k3ul /cl0wt- ve,;khunal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the9zp9gj;h7ch - n;vmcgwv3oj, mass of our Sun packed into a sphere about 10 km in radius. Estimate ;j9h39cg7o -zgp hn,vvj;cwmthe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, w+j 6d7xb wgbw-hich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun gwbj+x76bd-w. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless p v5 -jg6/aziyz cs),iwhile orbiting in the space shuttle. Your friends respond that they thought g/5i)pysv 6,azig -czj ravity 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 wbhsp)q32*mpx;wd2 iat-fc1 of a square of side 0.60 m. Calcula) t p32-h;1qfdmsxiwwa2p b*cte the 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 yearsep/ve .qc. .h if+w+axvwg4-j most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, ww..+.4peqcvvf / h xejgia+-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 accelera1-h c*) r3z9qpn53prmbky,0uzaz adi tion of gravity at the surface of Mars is 0.38 of what it is on Ea q zzchk3 p -prrzd*0), ab5mnia31u9yrth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knowizho hzb*e/oo8z m lp6(3 o*k9n value for the period of the Earth and its distance from the Sun. [Note: Compa oomei*ho /69lhp*(3z kb zo8zre 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 abouy fh0,qm2u l2xt the Earth at a height of 3600 km.,2hl2fuy m 0xq    $\times 10^3$

  The space shuttle releases a satellite into a circu .z zec,dw:/y j7atp0flar orbit 650 km above the Earth. How fast must the shuttle be moving (relativ/y:t0,pz7jfew a czd.e to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if + e(oo(n 9piywz sq2g8occupants are to experience simulated gravitwqn oo8egyi+z(2 s9p( y of 0.60 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 take-,5w9fk nocn4f rl dpm 5em0 sbr.66ozs for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Eo.56o,zknc f b4f- ds 5nmr60lme9wprarth 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 satdp5s:4z ieq(8vodl* dvg rc5 ,ellite have to be launched from the top of Mt. Everest to diovvgp (ce:, zd lq585s*4r dbe placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mi0 mkmz hqdk(s3hc- 2)7ta*urr ssion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take tutr-z(ha rs 3kk7qmhc0m2) *do go around the Moon once?    s

  The rings of Saturn are composed o3bddow f*k6fg*onv i icc+mu-ht*f b-:5 s)d/f chunks of ice that orbit the planet. The inner radiusd*f:)h3+*obfvb6cs m5 di- du- i *w onfg/tck 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 everyfsm;hlb 9t tck enj)q)c*.4 0y/u: obw 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, ambn0. yh 4:9tksqceo/b cljt;*)ufw)nd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-5mv6 -cvv z 7b1h4cw h44cbkjckg astronaut 4200 km from the center of the Earth's Moon in a space vehbk1vj5m 64c zb7 hv-4hccw4vcicle (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 equalg ipj5qi rmnu6/3lf( 4im*(sa mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What isf4q aj/(5u g (l36s*mrinpmii the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in d281k1qz- d yh0bjm7 b:tbffhan elevator thab2bbhkt110dz7:-ydj 8hmq ff t 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 suspjojr j 0-.g3mtn apd7e46cmwxr)d3x 1ended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator -37xpecwjgjmndr ) d 1oma6.xt 430rjaccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits vq.9 osp c2d)osvo8) xl;m nz(x)*f*mxopf5 i gery near the surface of a planet with period T , the density (mass/volume) of the ps* mzo;8o.vxp) o)l9s 2n* (p oxqi)d5m gfcxflanet 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 perio : 5)*jh(wrois9 yyu1tk6w gs 5yrjqg,d of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very stywyjg(y6,riq:1ro5h)u*5j g 9 s k wnear the Earth’s surface.    s

  The asteroid Icarus, thov )zx6t b.wl/ough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its .votz l /wb)x6mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dista(wb/d+t+fhru0 8+b. l cler:qbn9 x qznce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once everyu.j) ,puqe1s4*yu- scnzlkb- 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 sup ,s.y uc-n- 1jb4skuze*q)ltill “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of tcexd;w u0 c)wf*0l.37afwi bfhe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moozlr (t71vld +q9onpcern t1*(ns of Jupiter (those discovered by Galileo e 7+zpl*9tn1(o cnrtdlqvr(1 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 the Mi 3m dtg; d3dwf,r,y62yj9vaw:z oc;hoon. gjyy,6w3m,; ho:9d;zd 3a fdvt2wrc i   $\times 10^{24}$

  Determine the mean distance fromf(06 9heg ztnfi(swp; Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the vi 96zf(0g;t(shfpew n alues in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (wbt62 nwe.9 hsfhich some space scientists think came from a planet that once orbited tt2en h.w6fb9she 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 1 84hc;8gvtdf v.p)wc;jil ifmdw8j-artificial "planet" in the form of a band completely encirclfhpt;wic -i1m88c j l .v4ddj;g)w8vfing 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 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 hano;rli6y/.gu*y 9 fk olging vine (Fig. 5–41). If his arms are capa 9 oi;ory*g6.lukly f/ble of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half wh:*rcjn- ,k l+cseqpl90m axw2,k * 0sk;jtbnjat it is on the-jbpks,jn*nk *0 x+;,wmr0qlctcks2 j lae :9 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handk98wn5(u *0or6dga g7f* yzoitc ppj0s 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 0pn5z t awo7(rp9iycd0k8gfg*u6o*jmasses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates nd/:h qj+q * cf d.nr03,rztw -+mloleonce 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 magncrl.3-hdf tm,zjre+nq +dqw :n/ l0o*itude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly froszo 1lm z+s,4giu(xd6 m the Earth tg1zz6xoum,4s (s+dil o 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,lk bkb k 2h.e1ti.0xr9 but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelera.bekh tkl r9 0kib2.x1tion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tharh6ct//59dmi m 59lep-yt eaw t will rotate about its center (like a tubular bicyclhi ml56wm/5 p-tdc9r yea/9ete tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vef :r+z;6ligc jzmim4d-44 baxrtical 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 acce, ddb-j)ehcv4nb4om -leration due to gravity at its surface and the gravitatidbj-c4)v ,m bedh4-noonal constant G.

A plumb bob (a mass mn 9m+,/f-wvds:v9jr d uxoq2 c hanging on a string) is deflected from the vertical by an f9s-udn9+o q,/2xv: crw j vdmangle $\theta$ 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 fk*s(r hs gu*b-or a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a chguss **k- (brar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects ir 8k/4 (bjd+;, meng2r irhmpat the equator were apparently weightl kmi 8; h2rmrb,ide(nj/4gp+ress?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartnp6f,l j5mc4doj)cs* /h2t zt 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 03)t 3xksafox *-pseuradius 235 m. A lamp suspended from the ceilinut33-*xf pes) s0k aoxg 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 maorc8t 5;(s6ly vn6)ei uos-oji+/txl ssive as the Earth. Thus, it has been claimed that a pers(r6e s; o)ionctsxoj 65+uli/8v-ylt on 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 =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 zef2, gulr8.j Telescope deduced the presence of an extremely massive core in t8gr.zujl f2e, he 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 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 y+kb;xe2f- -o:wz,taq 0jwova)pa9dthe hill and valley shown in Fig. 5–45. Both thao-pwo9)wj, qa-x ta 2yb fd+e;z:k0ve hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a grgdh by6d61ungy twi )g30l4pf./q4x wyw5z d0oup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an agzlw3qxgw/0dyyd i)d05 1 hn twg.6b p4fy6u4ltitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, imz/ , nrpeb:ktz bv-9x6/,wdz 1/tgk3tpv iq0s meant to orbit the astex v-w 9gv0ekpki//63 zzb:t mq bnt/d,rz,1ptroid 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 pursuing a satellite in need of repairr*p* 3 zdqp8u (qe9.w-t4xw(gouri yx. You are in a circular orbit of the same radius as the satellittwgqu3z-4 . r8qxu xd9*r*iw(ppeo(y e (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a)l3l8gmzv0l +uj4bni:3;t ujpyg 4rg . What is its mean distance from t4ng3:48i0ut;jmlubg3ylv.jr p lzg+he 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 would;e(ny m0nl9p9o *goahm(l+irs m 9a)w need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions( 9hyapwml mn9on(*m )9; i+ogealrs0, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around ttsn41(k bu2ad) d ft3khe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fro3 f1( ka42dtnukd sbt)m 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 squapy6)f2hkwjml060di exljwq t;l7 y38.n poi4 re 0.50 m on each side. Find the magnitude and direction of the gravitationaldfwlij ;4 p0 )3 eihmylxwt2oy0l8q7 pkn66.j force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitsrhkgm4.k:wdi bkb cx 7j889om9myt .* the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced b/bi tkq7(* (amgw4ooby the tip of the 1.5-cm-long sweep second hand on o(baq( 7gtb*mw oki/4your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored andlxvxzlv x03,:sdbw 0a *:a +kx start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.] 0 v s0x:dvl3,zxawx kl+ab*:x    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a vhs4x3at9+: mj13zjhk4 fbk dcar traveling at speej 4:kmdk+41hsfjt339 hvzb x ad $ 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 t6+qgojcfb4+fz3 ) w ,4xedtrqhe 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 normal6 wg +xzq,4e )qdorb+ t3c4ffj force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train 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.$\approx$    $\times 10^2$