Sometimes people say that water is removed from clothes in a spin dryfrjm72. .vis 6tu :;ilhfukbs 9+b) mver by centrifugal force throwing the ;)+mu lt2f iim 9v6vbsj7.bh .kusf:rwater outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sh (6g*y4 icajhd 7kx0bsarp curve at a constant 60 km/h as when it travel0agicdsb 76khyxj( * 4s around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car wt3*sl1r3w1lo2n r2br)q iyv exert the greatest and least forces on the road: (a) i) olslv1rtbwqy321r * nw2r3 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 chi3dh;zm 6 qtv/+sew*4yf rbpe 5ld riding a horse on a merry-go-round. Whitd5p*eh/wq4; rz6 embv3 s+yf ch of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled inxx)3 a hg-)ogv a vertical circle without the water spilling out, evg gohvx)-)x a3en at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your * snk8j*aqj;l)u4) gs8uu yh ecar? There are at least three controls in the car which can be used to cause the car to accelerate. What aqh a gjej8s)n4*;kus)8ulu*y re they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shnve iy9 *wm(h7own in Fig. 5–31. His sled does not leave the gry7h9wmin e*v(ound (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 inward when rounding a curve at high speedm-:jh6 s/*dk rdn 0hhj:-gful?

Why do airplanes bank when they turn? How would you commy2c,fwcfm2, evyat kk s ).(,pute the banking angle given its spe2wkf ,k) eym,s a(vyct,c2f.m ed and radius of the turn?

A girl is whirling a ballp0 o(.gdq)ly r on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on t0y. qo)(rdpgl he other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth9* ajba95m 6cy.irl+f-coxj6 /nv0uo+sd bln? If so, how large a force? Consider an -x aic0+lv9j .yucsrafdjlo6*5 b+n9 n/m6 boapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were um5 txcq72c*w y-bco/ double what it is, in what ways would the Moon’s orbit be different? bccm-cu * xt752/yqwo

Which pulls harder gravitationall f5dm/xtokz.5y, the Earth on the Moon, or the Moon on the Earth? Whi5x. mfzo5t k/dch accelerates more?

The Sun's gravitational pull on the Earth is much largersy,*k 6qmuj1;f 1ikfd 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 qf;jk,1iy1fuk *s 6 mdthe Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effecxq 4tgde;(ow( ts are at work? Do they oppose each xgqwe;(4 (dot other?

The gravitational force on the Moon due to the Earth is only about half tg.obid -np-u;z4qh3nhe force qpd;n.gi ob- z4-u3hnon the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accele1 (m*ixg-zkq;d-gfsn,rm g ;kration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleratzkmd,rqi-x-1 gmskg;n ;*f(g ion of the Earth?

Would it require less speed to launch a satel9wfer e2d fv50*j 7hmm pmt1.,yaqh4jlite (a) toward the east or (b) tow1j24 tm 0e7,pe5jh m qmah.rdf*w9fvy ard the west? Consider the Earth’s rotation direction.

When will your apparent weight be tha:ijb p2 yrgm1lrw,6 /e greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) mrw ljy/ bmrgp:a2 ,61ioves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected byz:p)fk ml:l3 vo.4/ lpab xz,y 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 fek)o/my: : 3,zvbl . zxflppl4ael on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences 1v rsn2-bwmc51(o u no“free fall” or “apparent weightlessness” between m1-b os1u2orncwn(v 5 steps.

The Earth moves faster inox/ht k rrz jk3+34s7d+to)ly its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a krs/3j zo kdo+yh4 3rl7)tx+tfactor 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.(jj)89r jbuj 0m,brhwb*lh l5 Explain how this discovery enabled an estimatlj juw9bbm 0h5 jlj)8br( r*h,e of Pluto’s mass.

  The Sun's gravitationalg h +u*ys0nd*3j. s1i l*.xd7 6le+iaunhmdjb pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravit*dxu0elh *n6 1g imj.+b7l3d j*dus i has.n+yational 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-u(ie/:;:1 afpbebr dd cvpj- $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Suna- . q0picuh,2lsf(k w, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of2p0ha.,fu- wk lqcs(i radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0gs*0 1ldtuhdtq8 :2fr-kg discus as it rotates uniformly in a horizontal c08rd t2*hdl:uq gstf1 ircle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ear*ro*q s 4auc dbtl.:55.ihbx wth's surface, and circles the Earth about once every 90 minutes. Find the centripetal abdic 5o.sw4 hq*:.b 5xu*tarlcceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clau53b n0wbslj: y on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 3ljuw3:0bn5s b 2 cm?   

  A ball on the end of a sl1 q)*kk;z g//9kgp0fca azjq*dqom/ tring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3* )kgladfq;a/qkc/z*0g1zkj /q omp9 3. 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 cak-iewwu2n d28m/ fhz1n round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road i kh2nfwu21 md/w8-ez is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and thnm 2*w -phjzg.iu2ol+ av-z/je road if a car is +2.z-hzvi- lpamgj2/n wj ou *to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fight-h ixci8 b /st eo+f.o,q8mue5er pilots is designed to rotate a trainee in a horizontal circle 8cq,ifbu e/ t5imeo8+ -.ohsx 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 ch; 7q5yw;ypj4 :gjumx m from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed ony p;7jhq xwgu ;y:m5j4 the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside ej( -qqo*jr9igg, .ho down at the top of a circ9h.e joq,q*i -ogrg(j le
(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 tme+vj)j;zhsr4ho fc -)iyy; av- 14c kg (including the driver) crosses the rounded top 4ci rj yat;1chy)+v;svm fz 4- o)ehj-of 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-diametenmtbx0 q) ,.rer Ferris wheel need to make for the passen0x) nmrteb .,qgers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical d d(6klr5 2wcvcircle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting ther2l wdv6c(k 5d 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 centrifubwt* pr2jy0+ yge rotate if a particle 9.00 cm from the axis of rotatiojyb tw*0p y+r2n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated/1g+pgt9rhh / 4ejk 4,jroim7 d,tjpm in a cylindrically walled "roo+,1 dje4 j/4,htpojmmgkrhr/9ip7 g tm." (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 ) is rotated in a circlvl ,5ur,4vi7-lc x8/2dyrs lkkbxl/le on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blo lix lvky ,2-l5/kl4rv7lx b rs8d,cu/ck (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 vg,noyu b:*4j not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude y jn*o4:, uvgbof $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 fori/(gfgc(ah u5w;cv8 h 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 masses r7y,unwd : 3s4i5 tu/oowk*re.q 6sxp$ 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 vertically aa6tapkt(: 7a11wsggot 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 owmgq 4k 7x zfgpa60/;sn the car (by the ground) in Example 60as f / xkgpgmz;4w7q5-8 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 a9w, / gz o9ostjmue.;xccelerates 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 th/e zt9ojgo ,9s .;wxume 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 ab4m6ca es+s2xs 33k vcpgabr /xs7(*a particular instant, its acceleration s3gksamxvxe(c3cb a b6*a/p4+ss2 r7 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 Eartsi4xlx v3c a,*h’s gravity on a spacecraft 12,800 km (2 Earth radii) above the E4axvix s*,3lc arth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitatikh9nnx f d1w2p ;rk*1. ;gryfhonal acceleration g has a magnitude of 12 m/s rk1fywg. 9h1*h nd;;kp2fn rx$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravgn )4y ae13fkaakgwn )q.aj (4ity on the Moon. The Moon's radius is 1.7n q)f4g3(ay)e gn .4a1akwkaj 4 $\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 the same ma .hh63 v1wj s(hy3lowpswe*( tss. What is the accelshhv .16((w3eph3wswo*j y l teration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E+ncy 46hpz66 klrnyw6 k-8p0h5kwp vaarth, but the same radius. What is g near its s6w6 4hna+ 6v ynrkzhplcpwp8- 0ky 65kurface?   

  Two objects attract each other gravitatio v3* rzv;zqz6x k5ept ,5ods)onally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accele)ou jgkt k)e+/ration of gravity, at (a) 3200 m eo ut)/jgk +)k   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centjx j 15,md8 -faq5st,4tttbzxc2 yen 3er to a point outside the Earth where thegravitational acce,s18f a3eqy ztb5j -nc52x 4tdtm,jxtleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mw -.ggt0d8vif ass of our Sun packed into a sphere about 10 .8-gfw 0g vitdkm in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avera+v9lc tcg3 h8*ao2fk7avt o9 rge star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mt9 c3t kl+v* ohrf 28o7gaac9vass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whiw(qaols e 5m.lo1 q/8ale orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself 1lwo.qsea5qo(ml8 /a 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 t v3u 1ctec-4md2xod ) ksi2j jn4j*yt*he corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thrknus 4*32cj4 2tedoc*)jiy1m-vtxj d ee.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of u,z(b0fh ztg:l7flu: the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming 7zt0z, uh(::ul bglff 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 surv n/;ppm8hd48xg j(aaface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the ma;djh 8agna4( vm/ pxp8ss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period3jpw6 svu i0e7 of the Earth and its distance from the Sun. [Note:i s7pj6 0wuev3 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 circulqzl q 0 0fus3/f1olfxz( g+:l y82jfcvar orbit about the Earth at a height o+1 oqx0s 28z0l3l ffg (y:vf lzqjcfu/f 3600 km.    $\times 10^3$

  The space shuttle releases a satel;ht-s29 vteik4bobnt8 i):ftlite into a circular orbit 650 km above the Earth. 429 onf)t-itbe;vttsh: i k8b How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a c6k zaeyzq,::p ylindrical 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 Question 21q::6 akzy, pez, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a ci faxl5n.m; jj-of :l*qrb 7 ,*pyg0nfzr+ wj+drcular “near-Earth” orbit. A “near-Earth” orbit isomj5 lr+f:ajxpqb-,nlnj+f g fy7*0d *.r;wz one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity woulqrn-ea/ 4fybz:mf(q c+qb)qi87 pz q(d a satellite have to be launched from the top of Mt. Everest to be placed in z4me(-if / qqf +p8 byb7:qrc(naq)qz a circular orbit around the Earth?   

  During an Apollo lunar landing mission, /ozip4515 x h8c+httmvxmk4 u7rq* ;ta v-m zhthe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around to7uxpxa -vm qz5cmt 8z+/hkr54;4 hv* imhtt1he Moon once?    s

  The rings of Saturn are composed*pt awp5ut/yj ,ollsl,a(y.4 of chunks of ice that orbit the planet. The inner radius of p4 u/yp5, sjl*tal ,ayl.wo(tthe rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fiw,)*rj x3+gaf2v h rx p,dvv2tg. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at t,v,a r+vf*2t x3)jv2xw hdpgr he bottom?
(a)    (b)   

  What is the apparent weight of a 24hakc- m ast075-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at a 4tas2mc-k0 hconstant 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/i 98fjz hj, ths9lu7a system consists of two stars of equal mass. They are observed to be separated by 360 million km9jj,9sh8tf l h ziau7/ and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an eleo r8507iz09zukq s bvzopnr7*f4 p6iyvator that moves q7 fizz i9rnp 08oyb *74rov06szup5k
(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 suspendebyas ucbg4(o vb-)(mq1o2 /hsd from the ceiling of an elevator. The cord can withstandasb/ogb2c4s v(1(bmh-u)o y q a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface oo2t9l;i8tj 3a4l9e ln 5pgw zvf a planet with period T ,8plovwt5a 9 jnilt ;4 e9zg2l3 the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon1 4x x+m0r wpjpgemj0)k vy4;p (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s4pg xjmp4j y;rx 10)wkvme+0p surface.    s

  The asteroid Icarus, though only a fewpb vmp*k7hh6 ; hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean 67v *;bhhppkmdistance from the Sun?    $\times 10^{11}$

  Neptune is an average poo+ m i:fs9xlyf9s1) distance 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 every 76 years. Ivjsw.,po65 rct 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 nevs 6pwjc. ,o5rarest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of wo:xpbx6w6)ckvq2m m)s )jn4the 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 fourck h/fmind1zc ;en78 1 largest moons of Jupiter (those discovered by Galileo inc/mekc1;8 7fdn 1z nih 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 ajvu l xq,0tq;15 bwfb/nd distance of the Moon. b1v qljtx,/5ubw0f; q   $\times 10^{24}$

  Determine the mean distance from Jupiter fo,5z6ut)7dn4cv +.puz avk e tfr each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5 p ev6zntdt va4fuuk,.) +zc75–3. 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 fragments vwm0;rpe9d3q(which some space scientists think came from a planet that once orbited the Sun but was destroyedvpwmd3qr 0e9; ).
(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 ahsv mktzewqqdu0 evjj765.y72;0 x6 h4ecoi) rtificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly en x4h6t7 esk0uhoj)i;cdvv7 qqewj m56.ey2z 0 ough 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 s+g ue36owt: ,u ol+nhcwinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate nluo:u+ t3cw6 geoh ,+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 gravit,63c i4 qp8l vfirh5bay be half what it is on the surfaa5lhci6 f 84qp,bi3vrce?    $\times 10^6$

  On an ice rink, two skaters of equal mas mo:j f1u(7unrs grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual mor 7(:unjufm1asses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparentiov 0(ax8qo sg/(9w+t pef5 ps acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate t+vt(0qisa( o/p9e o fgpsw8x5he magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dizmve-3x x7bl4rectly from the Earth to the Moon experience zero net force because the Earth and Moon xml-3 4xvebz7 pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand onkzijblf:* a :, a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration jbi*f:z,ak l: of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wwnrc *o.n:q:w gpcaa32a0n r t/tqb 11ill rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effec1:g* a1rwtw ccnp oab2 nrn/.q3:aq0tt 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 aircra9.p ,cw3n vregft 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 p h+5 s*v9ob9x pv)cniof its radius r, the acceleration due to gravityio+h5ns pc)vv*9bxp 9 at its surface and the gravitational constant G.

A plumb bob (a mass m)w -5(9ldug ghy9f msb hanging on a string) is deflected from the vertical by an awl-bu 5 fy9gh (dg)9msngle $\theta$ 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 b7vt+x2 dg 4pnbanked for a design speed of If the coefficient of static frictiotv24dpx7b + gnn is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earkiy9z acuumle+2 h (9w ipmh8.bz.8d-th were rotating so fast that objects at the equator were apparently weightless?8 zk8.cp-( im+m hdu 29izl9y heuaw.b    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8. u6-s ke+et:rk0 $\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,-0.vui riopn a curve of radius 235 m. A lamp suspended from tho .-v0ri,inp ue 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. 4hu tstz*1o sk)74o rw4sdvp)l)3ifr Thus, it has been claimed that a person would berot4 71osv4sr) tp hz 3ls )k)dfui4w* 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 th7g(gt0e.y/xk n m;b xwe Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thi(ktbg7 m/x0 ; .nyewxgs 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 thpb ee2ypc/ *m;e hill and valley shown in Fig. 5–45. Both the hill and valley havmpbpye/c*; 2 ee 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 i+u fi1 wu8bx9a,rt v4group of 24 satellites orbiting the Earth. Using “tria,xwa89r 1 t +u4bifviungulation” 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 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,loen4skb yo12gn,a9yhk4 6/e is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 n2hys4 ngea4 9,o1yl/ o6kbke $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 pursuinwzdmt/v*t +5m)ucz o5 g a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km /ov5+ * c uzdwmmttz5)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 perio a 36n*.chhjtld of 3000 years. (a) What is its mean distance from the Sun? c3.a6h j *nthl  
(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 vayzwxuv t9b c/f0g )*b4lue of G would need to be if you could actually "feel" yourself gravitationally attracted to cyv/fgwb* b uxt z)049someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arou:lej 8f :)qqvdb45azca k76 oqnd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yea q e78l :ad:qzfo6a4k 5q)bjcvrs 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 th08ctq0a y bv/k0cgppqi*,ya f (w2kx2e corners of a square 0.50 m on each side. Find the maa0ycg2 vkc0 *x(fiqk 8a0w/p p2 bqyt,gnitude and direction of the gravitational 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 5) pkd1x,y6et1 avg,ru500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by tcoxbk*1z - +dsh-7a ku5 shbdi/t ;ed;he tip of the 1.5-cm-long sweep second hand on youske 1d+k *uzd;;ch st7x/ bo5b--aidhr wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wxmd* 2j2olik -sdt:xg-2 n,oh eight around in a circle below you on a 0.25-slmog:d2j x2,hdnit*-kx2o-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.]    $^{\circ}$

A circular curve of radius R in a new highway cv/-z7q bs 9o67gmzfg is designed so that a car traveliozmc/g q77b- zf6s vg9ng 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 tilt of thn18s+kop: 4qkgfsggv h;(tc5e 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 n+stg5s h q 4(g 8cfpk:v;gko1that 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.$\approx$    $\times 10^2$