Sometimes people say that water is removed from clothes in a spin h,j nna6ru(23gxq./ f /wpwg ;aox:in dryer by centrifugal force throwing the water outward. What is xgqohu/jann,gpa6 w ;:( in2wr f.x/ 3wrong with this statement?

Will the acceleration of a carm /i; q-y2k*k 3d+zdef)cahwq be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroum zywe/ f3; a iqc2dd+qh*)k-knd a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where cpnn9r*evcp422 1+cfr (wqrgdoes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hier2vrqf n2cw4 *1cpgpcn(9 r+lls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a c x;uz7jwyc.3y 9q*qud hild riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerayzcw9 quy.7j x3*u d;qtion of the child?

A bucket of water can be whirled in a vertical circlz0cb;3vk( 9wfkop/ jrt bwi-:htjo: 9e without the water spilling out, even at the top of the cirj 3-wbrzi:kvt9o j(b:; wkh f0ctp/9ocle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are p2u/glk,kf a25 a5 kroat least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerf2 oa ,k5/ k5uag2klprations do they produce?

A child on a sled comk6wd15gi x9 mp+x(yides flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the mg1i9+dx dxy6(w5p k iground (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 this decrease using Newton’s second law.

Why do bicycle riders lean inwakh, xzz frar-.,tg14 lh -+ z-)sa-s rgkp*laqrd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you co j( n49pxkglt2mpute the banking angle given its speed and radius of n l(t29gpxj 4kthe turn?

A girl is whirling a ball on a string around her head in a ho,e g-p6 lx,2w/e zpll3cysqf9rizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other sidqgs2el9,6p /fl-w zy pe3x,c le of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hou l -os0wt*tpf2rmh;/ w large a force? Consider an apl*s-r/2u;mo p 0tthfw ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woxvycft7q2 (/a)mh wojna9) 3bp . 8iofuld the Moon’s orbit bav2b )pic)at w9(o /nfm7j qy8oh3f.xe different?

Which pulls harder gravitationr34m 8gp etal7vib 2k:ally, the Earth on the Moon, or the Moon on the Earth? Which acclp78vi3k t2 bargm4 e:elerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's.l :-x2;zcfum r Yet the Moon's is mainly responsible for the tides. E z: -mcurfx2;lxplain. [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 effects 2 c;g:0zzxonb5k 3 ljoare at work? Do they opp;k o n32 bjx5lgc0zzo:ose each other?

The gravitational force on the Moon due to the Earth is ororrauw94-g f*1t24 -bgux 2ni.wz ddnly about half the force on the gg -b frdw- 9x w1a4r*iu.zd2 rt42ounMoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in itsuvg w/ypc skg;e-077s orbit around the Sun larger or smaller than the centripetal accelerys7 /;7 -gpksg0wvuecation of the Earth?

Would it require less speed to lacyo 1-t dol y;iqa6t);unch a satellite (a) toward the east or (b) towd6;t)oqa yi1t ; ol-cyard the west? Consider the Earth’s rotation direction.

When will your apparent weight be the gre su)g .r3cq7wlatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the3 clwgr u7sq.) same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spendx 3pbm:31qzje qth a 54*wh 1,toivx-z long 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 gravxpqh1zt tb eo4v 3m iz:qw5ajx1*3h,-ity you can think of.

Explain how a runner experiences “fre9ye-r(+ )*;wet m;o hpsrnbzre fall” or “apparent weightlessness” between steps.+-ze)*r ; myeot nrb;(w9phsr

The Earth moves faster ij4ff;f;kwxqr, ga0mm /ny7rtf/ f.*2:iatxn n its orbit around the Sun in January than in July. Is the Earth closer to the Sun in Januaryr q 2 gxtam7nfk,wnfft* 4jy.ma/x:r/;0;f if, 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 gyks s9mhy 5cog+ +t,6have a moon. Explain how this discovery enabled an estimate of Pl +syhsk9y,g +mg ot56cuto’s mass.

  The Sun's gravitational pull on the Eao4sbxadr/p 8hn / i gw+u:+b(sel3y0i rth is much larger than the Moon's. Yet the Moon's is m:/ph+8r( assgb+o b3 4ud0iynie /xlwainly 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 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 1980 .c ki u-mhenv5 o+l(2v$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ear1( r dr)8rx6lfkg,e epth 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 radius 1.50r1krg8dex ref()6p,l $ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force ogxiqjuf1:w 9t8i:3 sj :ua;nqf 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.xtng:j;iisa13 98qf w uuq :j:90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and 9/l f9 o ytk00ohh fx0xkk9vlf9 k;m0xcircles the Earth about once every 90 minutes. Find the centripetal accelerationfx m;k0h90v x09t9kkyllffh9o0 /o kx of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelew j (/ds zfv;ak u4vash:g,w1n*j qa6:ration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter i,;ksa j u/(wvj sg6:4ad:vh1n* w fqazs 32 cm?   

  A ball on the end of a string is rep;3d;twyy2holg um-m 8 6ate80 u/ua qvolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig.;du6 8mlu8wa2o eqaty-t uh;0pg/ym3 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 1050-kg car can round a turn of radius 77jo2 8y-*,ht-fk 5hftieot9jonhl 4w+ m on a flat road if of9t,hnw8 t-te4ky hfo2h+5 l *ojij-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 static friction be between thgwtp /se6q.p; e tires and the road if a car is to round a level cuwp/p6;te qs .grve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a9 ,brji ln4 qh-;l )r8m/stwhy trainee in a horizontal circle of radius 12.0 m . If the force felt by tb,;-itrn4 ) /ry8w lsjh9lhm qhe 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 axis of a rotating turntable of variable speect /ac:4sij / jlp;)dcd. When the speed of the turntable is slowly increased, the coin remainss a;ltp id)c/4j:j cc/ 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 coa9h vzyatgjpb4;r/f1 o tm i6ca+(d(c. ster be traveling when upside down at the top of a circle 4z6. fgvorb (i/ dahtt +ja1y cpc(9m;
(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 d-r e;ehhr, mb9;hkyp /river) crosses the rounded top of a hill (radius h ,9 r;khpemyh/ebr ;- =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to ma+nm 7grzbnz 5-o jl5o;ke for the passengers to feel “weightg55n b7 m;zjzno+orl- less” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cibp c*603qo b a4he63t 8hjglbtrcle of radius 1.10 m. At the lowest point of its motion the tension in the ropebog6b4p6lhh3t qj0bte *c a38 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 9-89q6sgezpnngrl lqksjb ( o.s;1z )centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accele oqs.nzble;n1g(8)p qj9 g -s6r9 kszlration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated i ua--enq6 fjf,n a cylindrically walled "room. q jnae,6-fuf-" (See 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 ) ;i7wl 7roa du-is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blockal-7 ;u7 rwiod (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 , precn ou3etk8tm( *+,n /arc gr;ibisely this time, by not ignoring the weight of the ball which revol+ae/t8,o;k(m i uc nr*nr gt3bves 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 radir5bu;6ku jxi2us of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masset zz,xw50kzy2 s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver4ouu mev5hocdt, c;l;8 3oqt27wfea - 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 8(jqc5boro35z zk+eynet force exerted on the car (by the ground) in Example 5-8+ cz5eqy oojb83z5(rk 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, go9jp ;5m):yj6 n nxvz(od4 gku/kwssl5ing 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 road to provide this acceleration wit5wl jmn opszs(u6:k/nk9)v5;d yg4 jx h no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular0wzhe s*tk3bs,9v/( we( ns nn instant, its acceleration is 39 0(tnnwnzskv wh,*sbs/e(e 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Eart5/9p kf/ b1rdkt c*zpeop m,i:h radii) above the :r/k o ,mz/kbfpe1 *i9pdptc 5Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceledu +/6kqhgc9w ration g has a magnitude of 1w9uhgdk/ cq6+2 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration d(isb0g,grzqo ri( :dxx, 4h6due to gravity on the Moon. The Moon's radius is 1.76qr ,0(,zi d(dxbxrs ighg4:o 4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hbg )r2 fsgw yt):/vi9jmy q)a4as a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravgjit)2/9yqfsy4 w) g) avb rm:ity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the syzh joe908bz6 ame radius. What is g near its surfz0e89 jzbh6y oace?   

  Two objects attract each other gravitationally with a fot r /0pnf+f/-oj m9q i6+gggiorce 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 o)h5rf/;t wr1yo3dej xyi,fq 8f g , the acceleration of gravity, at (a) 3200 m fi8 hyq3dfo51; ejxt )wy,/rr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center p m k:klggkyk-sfl -e;)/f 87bto a point outside the Earth where thegravitational acceleration due to the Earth i)fl:g7 kmygb--p kke/8;sk lfs $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hasyc1pd3 8su l6k4 lc.ym five times the mass of our Sun packed into a sphere about 10 km in radius. Estimatl4 y 6myp8ksdl 31ucc.e the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whic iep,(n3wjsbk- xrgnu*/fp,+ h once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon bufpu (js3,inbrxgw/*k +np-, et has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitino3is y.. a6j9zkt.od bg in the space shuttle. Your friends respond thattbydos6z .j93i o.a. k they thought 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 a7,hv+kgnd gld)*z tk(re located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of th,g) g7d*h +kndzl t(vke total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the k g0 kq2el1x6esame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-2q el6k1 g0kex38). 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 surface5djmn * 1fbjbwmd4pe*7,a8 gq of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3je 1m4*7m j8b pndqwdg,f5a*b400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val;viiacxv)4 1.3re sidrm 1qo ;ue for the period of the Earth and its distance d ;a4v3 rvcire.q)om si1i;x1 from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular oj(al, 6hc. ig 2p2ompvrbit about the Earth at a height of 3602i2 .vp,ch6pa (jolg m0 km.    $\times 10^3$

  The space shuttle release8a-hc)kl6x54ufs g ohs a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth)ho a4 k)l85sghfx6-cu when the release occurs?    $\times 10^3$

  At what rate must a cylindricald67** i 6o7h7bu4rikj pzm vil spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Qdu* r7 izpvo6*i mli47k67 hbjuestion 21, Fig 5–32.)   

  Determine the time it takes for 9mnxdp/jo1 -ia 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 Earth which is very small compared to the radius of tm9xi1d p-noj/ he Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched tf9nd pvk716m gr;1c gao/uz5 from the top of Mt. Everest to cfvoa15g7t nrp/k dmg u916 z;be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the comt lyn9ji ;tz8e+2lci3mand module continued to orbit the Moon at an3z j +ie 9cyt8t;l2iln altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit u2vkw)rbbp7/ the planet. The inner radius of the rings is 73,00ku7r)vw2 pb/b 0 $\mathrm{~km}$ , 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 wr-7e1 2 rxx*u u-espedo* q-aFig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thxqx*e-d eur *epw 7o s1-ar-u2e top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center ofei-p/a n,henq6c u,kcb* y c59 the Earth's Moon in a spacy *,c ia/uchec-knp,9enb56 qe vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. T3ewpalg-h wl,hvy/t6c 72*h3a a xar+ hey are observed to be separated by 36ryce3, * t6laapahw7 -g3/xvh wl2a h+0 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 fss 0de 3j3gj/s kc))pfor the weight of a 55-kg woman in an elevator tha)0/3spcefk) 3jg sdj st 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 cei fp 0y2uofu*g; ge6o,aling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelep2ugyao ;,*o eg0f6 furation (magnitude and direction)? a =   

Show that if a satellite orbit6adx wy.)b:n qfns0h+s very near the surface of a planet with period T ,f:06q +db) nw.hn xsay 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/ 7)x+bi5wg zako,zcn the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface/gac7n)5o+, zkibxz w.    s

  The asteroid Icarus, p 75l .7k fdyvnb8x(qwthough only a few hundred meters across, orbits the Sun like the planets. Its period ikq.fw8y b75d 7l xpnv(s 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5e 9ebdlg azi-v8a6n/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 ttiqn ce tj*3cq1r *sqh - g(:uchpb/b1p.39 cSun roughly once 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 out1e/n9ptqrc. -3cjbsu* chtp q : gib*htq31(c 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 t:z2*kg a+ w;3+ky jgwfm oja1ohe 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, andyyh ;0rz9 j,jry6pr9l mean distance for the four largest moons of Jupiter (those discovered by Galileo in 9j,ry;p60 yl r9hzyjr 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 l32vogjprkg;*hzor rt c6239 -hjee4Earth from the known period and distance of the Moon. r2 9zlch2 g6or o4- gr*vpj e;h33kejt   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, us/ :o cf5k j)6d7clngyad syq*(ing Kepler’s third law. Use the distad*5y6floq/c cg:dnk y()j a 7snce 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 Mars and Jupiter consists of man1i1 61cys2w/gdp rr*rj qgbf7y fragments (which some space scj1w1dis/g r 6rgr * 7p12ycfbqientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the 60cd)imhd, vmnk 6oh+ 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 same as the Earth-Sun distance (to make the climate temperate), and that the ring rotatekn,cmddm+)0o 6i hvh6 s 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 hanging vin vsf/gxo /69cze (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m loz//s 6f gvoc9xng.   

  How far above the Earthtuw2 x i h l3+zob6*zn- k7v2nxl5eh7h’s surface will the acceleration of gravity be half what it is on hnxx7-25v2*leuz6w +l hh7 zb nto ik3the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spi p5(li3tdyi(rn in a mutual circlepriy3ti d l((5 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?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity mhri *70u) qm8jz ig )ctc.l4bat the equator is slig* cij47c )u8 gbm.0lq)ihtrzmhtly less than 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 travelio8zk:fbd+p); u)y zizng directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal );)bouzk zyz8i :+ fdpand opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but 3zp.),j no xa4kxz, ifwhen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direx ,z xpfjzo4,ak3i.n)ction?     ----待选择----upwartddown 

  A projected space station consi./ i cne-78cs2tl qfp0uwn3x0csfa: ests 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 du:0cec72lnfen8q cp-3 ai0 f/ wxsts.ay) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43).ulwj phv)7c q-sm5; k2
(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 accck 4,3n2)it aovkk,j ;q/si vheleration due to gravity at its surface and the gravitational constant vkk/joc itk 3;)4a,ns,q vh2iG.

A plumb bob (a mass m h*g9 msk ((p.0rqqowb g,rby)kanging on a string) is deflected from the vertical by a ()sr gb p wbogqm(rk*9qy0k,.n angle $\theta$ 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 o5ui;vegy j0+d -ift.;l a .ukzf If the coefficient of static friction is 0.30 (wet pavizv ;.lj-0 gy.de t;a5kifu +uement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at;:*n-5afum+ng qtvg .emnwblb . .q w8 the equatunlqw.t.-n ;*fggm58aevb.m:q +wn b or were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a conp w py f)vf9 u- ru0b*n3y,*ysgi7vxu(stant 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. -tq*i:qgrl :c A lamp suspqc- tgrq ::i*lended from 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 Eazu) flhq2wl*nt 2(b vqwgzuob( 5o1 o1j-*b5 lrth. 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. Usebuo2l h2wu*w- n q5t gb11*( l5b)ozf(qov zlj 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 du s..ecxscl m;;-go; voya7 b3educed the presence of an extremely massive core in the distant galaxy M87, s;c; .s-leyba m7 osuc ox3v;g.o dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley sc9fq 62i* lkwbhown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? 29 6kcwiflbq*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 satellites o yz f9y)9itk.crpad,-rbiting 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 .r yip cdy)- ,9zt9kafsatellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), af.ocahy p4v )tfb3p,s de0b/3xm(j vt)ter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rt(3e0 3jaxpdp4,mhsb)/v b vyo)tcf. oughly 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 nee7 zw0dr+q wd2bd of repair. You are in a c wwd72zq+r db0ircular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance fr nn(5.-3y;di:if9y t emfavkeom the S - idyvie5(a9mnytf:n;3fe k.un?   
(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 n esp64fbwk)(be if you could actually "feel" you4 bp)s6(wfkne rself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the l:k(;mu dvq1pag91g0 i e* dqiMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years uq : di10(;g *g1 eql9kidpvmafrom 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 core4q0: byk c,dm tc(q9hners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on am qhy:c0t(c9k ,d4e bq 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 orbits the Eartk( jn3m i(jwm0h $ \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 experien -xy5:uvvfi )cwugqp)33 j4qa; aek2lced by the tip of the 1.5-cm-long sweep second hand on your wr )up-:3i)flqye3 5k qg2 ;xc4vu aajwvist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to s3/0b jbz bgvn15b4sxkwing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes /gvz bb nb3 0k15b4xjsa complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R intcv oagw. l-f2rz-g qkb (3:,wat h0f1 a new highway is designed so that a car traveling ac-rw kz(f2a31hat wg b,ot0 . :flgqv-t 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, utiliz s-d ti)p(ln2mcru 68n+.k blles tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripept6lm2 (s)+-.rudkl8 ibnnc ltal 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 (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.$\approx$    $\times 10^2$