Sometimes people say that water is removed from clothes in a spin dryer by m5q vu50.k)6ca*rawq* wybai centrifugal force throwing the water outward. What is wroq*kuymw6 aac.q0iv 5b5 rw a)*ng with this statement?

Will the acceleration of a car be the same wheni y00p6kzho,d the car travels around a sharp curve y,0iokhpdz 60 at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where tr n,m6v+dex ,c0j)jq; n mqi8ljif(.does the car exert the greatest and least forces on tq(dn,8l,ijnf+c0 t6mj q; rx)i.jv emhe 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 on1 c584 )dp st3knmdo eg6al7vxqiu 5m, a merry-go-round. Which of these forces provides the centripetal acc4 is73cem6, ndg81qvpd lum)5kt 5xa oeleration of the child?

A bucket of water can be whirled in a vertical circle without the water s.u xmz-e9. v. gkl2gbwpilling out, even at the top of the circle when the bucket is upside xmgb.u9 .vg.2l k- ewzdown. Explain.

How many “accelerators” do you have in your car? There are at leay- zsa*s;ujbl) 0ujc.w0 ptf6st three controls in the car which can be used to cause the car to accelerate. What are they? What acc0yf pu.j06ba l*uj tcz-;w) sselerations do they produce?

A child on a sled comes flying over th* twdb o9c:hnz 5,t kim o49n5jq1u6due crest of a small hill, as shown in Fig. 5–31. His sled does nnc91oh5mk6 id*utbd4z5,wuoj 9 qt :not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward wzkbp0o;vb* d /hen rounding a curve at high speed?

Why do airplanes bank when they tudww q+-h.qv o4rn? How would you compute the banking angle given its speed and radius4.vwh-+ o wdqq of the turn?

A girl is whirling a ball on a string around her head in a horizomo-m n aqk:u:8tk 5hz6,zo5uw ntal plane. She wants to let go at precisely the right time so than5z6o m-z :a:mk 5khuwtqu8o,t 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 gra(ryc9)-hge vz 9g 1kafcv)db +vitational force on the Earth? If so, how large a force? Consider an rh)( a 9kg)b fz+ cdy9gv-e1vcapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it *i8 zw w r*8lmr,alh5hx:ao.tis, in what ways would the Moon’s orbit be 8w oxm*wr5llh8 a*zt, .a :hridifferent?

Which pulls harder gravitationally9ioz7h af *ndbu7 2nl-, the Earth on the Moon, or the Moon on the Earth? Which acd2 bznhnlf i7ua9*-o7celerates more?

The Sun's gravitational pull on the Earth is much larger than the M/bggdye6c( en.3xb3q oon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the ( d 3cbeq/gy6ngbe3 x.Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are 0 rp:et*5ino/f cegn;a;e:5 ingrc *nto0e/ fpt work? Do they oppose each other?

The gravitational force on the Moon xr8 21twm:9ymfdm6 is o*q.uosk1:pw due to the Earth is only about half the force on the Moon due to the Sun. Whx:uw:*fqomrtmp w.61 12o8i s9k sdmyy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or4p uaszn-z73t smaller than the centripetal acceltnp 3zu47zas- eration of the Earth?

Would it require less speed to launch a satellite (a) toward the east : /y8s1gg7 d0 /o exudawajb*por (b) toward the west? Consider the Eg 8a/:p1sa*g w dub/ oxye07jdarth’s rotation direction.

When will your apparent weight be the greatest, as meas hsqsp)8/gs-ivd*ux * ured 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 8vxs*-hu*pg/d) s qsithe same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in out . oyvbzle6,u-er 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 feby ov-.6e, lzuel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent we.,g e-bplii8y si.p.n ightlessness” betweenp lb.ig 8-niei.spy., steps.

The Earth moves faster in its orbit around the Sun in January than in Ju*m6m8b8of9dfol nz,lly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — tho9fof8 dmml,bl6 8z* ne 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 hla:1k+.qb +lwl(e qe kave a moon. Explain how this discovery enabled an estimate ofqel ka+ l:(wq.+e1blk Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than 9cpizb;nu3q0u8bu n u g wsj(2u9p1 o2the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pul9(p jinq2ug0 s18n 2pu c;b zuuu93bowl 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 travelingy3 izqsj5 4a7, q3eccv 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sun,nnjj/qn + /h8xe-hv4 b and the net force exerted on t hq4 nejv+nx/bh/8jn- he Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discusyur7y5 fl)oyco 9c hu-84tvb- as it rotates uniformly in a horizontal circle (at arm’ocy-7rt4-cu59vf olyu) hyb 8s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from therehjdje4 mj4,9w;m /j Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's sjmj w;j 4ejmr,/ 94dehurface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on t3 kh e .eopoj2-sjw**dhe edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter isoj e*pj.2 -dwhok*3es 32 cm?   

  A ball on the end of a string is re7t:fj ke+8,lfgyun0gc w ;sg(volved at a uniform rate in a vertical circle o lge7;cg wf: s0jf+tgy8ukn(,f radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round o8os+ a/e3k9jghj/p y a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road/+pgh k9oo8ys j/eja 3 is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of:c4f0da2 eaibh.oizd 6;/rae static friction be between the tires and the road if a car is to ri :erfa2ei ;o.b z04d/hc aa6dound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed46 r8* mkru u8gpccrr3 to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee onu 83 6crmg*uc krr48pr 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 ), ctv*qh 0rlufrom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the tuuqh) vcrl0,t*rntable?   

  At what minimum speed must a roller coaster be traveling when upside down at w qca2h qb157xg6e+bpthe top of a cig5c7h+we qx6 2pbbq a1rcle
(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 (incl9ekra i+p3 m0cuding the driver) crosses the rounded top of a hill 3acik9rme 0p+ (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-diametl8q)5 ;w10zpku kjm2 j,xg5 5homgyd8zuzsp- er Ferris wheel need to make for the passengers to feel “weighm50 uo w2k;pg,zq 15zj -8 p5ud yj)zhx8gskmltless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle n1cpd) 3dn x 3dw(8ylaof radius 1.10 m. At the lowest point of its xcl3 n 8y3p1n()dawdd 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 r +so.+rzago+f otate if a particle 9.00 cm from the axis of rotation is to experience an acce.+ag zrso+o+ fleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cad.))mwdkqc d:qe9hbh /)u te;rnival, people are rotated in a cylindrically walled "room." (See .)edkqq h: u de) 9/t;dwmh)cbFig. 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 frictionleb a8:iqkjokyrq 6-b2c* gw* y;ss 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 shown 2;c:babg rojyi-*q*8wqk 6y k 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 igno,u4x 1pb6 enxering the weight of the ball which revolves on a str ex14e6bu,xn ping 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is per+jg 152rua3 yzk (yqhcfectly 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 masse uq *elc*p/;qps $ 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 divp2ciio :nm mbc* 10vr+ing 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 ylp 2v-nq*xs,nygw 3zn3,s+b/h 4gar2 xr3thcomponents of the net force exerted on the car (by the ground) in Exampsny+nzgw 2vgxs pt2/hn , *hy3,r3xlbq-43a r le 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 a2wlr;k(: kq d9x 3myahjxs1f5ccelerates 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 bx(r3alds jk;k:f qm1 5x9y2 whe between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizoz juv4g*/2f x0u:mixmmh. pc )ntal circle of radius 2.90 m . At a particular instant, its acceleratzujm0 igx .mm)*4c:up/hv f x2ion 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 Ela5dc0m za+g:9yw .alarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Ezgal: wc9+m . 0ldaa5yarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationab0 hp:nng- tt7f hhkgl z2-w;.d m*tc8l acceleration g has a magnitude of 12 * 8lfwn;b-gcdz :ph-g. mk0h n ttt7h2m/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 due to gravity on thea39b) *hzzk8 hna.snr Moon. The Moon's radius is 1.74b8zrak hz3*9 n hs.)an $\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 0nn kht-)1t( pbq)cve Earth, but has the same mass. What is the acceleration due to ttv)p1(c)eh kb n 0-qngravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sam wc6 69 ;t5bi c5azg1u)wvebgve radius. What is g neaea1wvz vui5 65g; tb)9 cc6wgbr its surface?   

  Two objects attract each othewx; r0 zju0;40pcuxey r gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 32006ot4/ fmh; 0 menqij:f m4q ;mih0m:f tjeo/ nf6    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outs,(dtjc 09d sdkide the Earth where thegravitational accelerationdd j9,t0s (ckd 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 mass of our Sun ;ymr6c:o6 opqd u82m.h.xx oqpacked into a sphere about 10 km in radius. Estimate the surface gravity on thiqdqxy hpr. 8ox;2om.cu:6o6ms monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likl hf i)0fh qyj- 7leheh;.m79me our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass oe l yh-f;)h m0j7mfi.9hleqh 7f our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel w4 rxzxv:t p7 hw95,atcgna10w eightless while orbiting in the space sh9,7x1: 54n rt wvzpcw gaatx0huttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squa-jsqaek/r*b2fvc9: jr l * u*ure of side 0.60 m. Calculate the magnitude and direction of the total gravitlu j v/:9 -rersa2f*b*kucq *jational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years (*t)5ry1neotn pb j cm(5f u7vmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sj1o( cn(5)ey7 pftbu5t n *vmraturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.3dgw5otchw po0l4) ; 0,dkjcuos/1yt5 8 of what it is on Earth, and that Mars’ radius is 3400 km, determine plyt ;/oouwck0 d tg d wjo51,0)chs54the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using th x89.h/xqttm -zf4o*ixn 5gwqe known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examtxig9 tqm8zoq x/5- *fwxnh4 .ple 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ci 5,kdx wyp,-tsrcular orbit about the Earth at a height of 36 d-5wsxty,k,p 00 km.    $\times 10^3$

  The space shuttle releases a sak2h 0hk9 gdz i(:w*yrutellite into a circular orbit 650 km above the Earth. How fast must the shukzrdg 29 yhu0(h*kiw: ttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindridkm3i olwpaf,c/l5v9zz:+ ,a cal spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give +i pw5caz a zmk,,o/l93dfl :vyour answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular ey ; .fa1)k1hbala b71 ejlpz5“near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very l7a)hz; fbyal 5 e1aep1b1.jksmall 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 satellite have to be launched from the tog +.boadd1tc,o ,q3ou p of Mt. Everest to be pl.,oad3, to c d+qbou1gaced in a circular orbit around the Earth?   

  During an Apollo lunar lf4hxwvd69u i -anding mission, the command module continued to orbit the Moon at an altitude of about 100 km. Ho9fu4v hd-6w xiw long did it take to go around the Moon once?    s

  The rings of Saturn are composed ofa,z8wx-:-cg tj*wbl y chunks of ice that orbit the planet. The inner radius of they gbjla -,-wz*8 xt:cw 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 Figowq(qo76 u 99n8bqdbc1xcgiiy20x + f. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the botto18(uyqc 0+idf no6g xxq 27wbqbic99om?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut8ok-st*,zi0 l -n eaay 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vel*ts0, a8-iakn-y ezolocity,     ----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 stm:wwhr*7w-wu i zqq4 2 s 7))jjs6qnhdars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years t rqhm4u2 q7*njw:)wzji hdws67-)sw qo 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 .1 bjql5gih,o of a 55-kg woman in an elevator that move1b,g.jiq5lho s
(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 olb6r:injw*:a1 .hip ling of an elevator. The cord can wl 1.bro:ii 6hwanp: j*ithstand 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 vefwq6q; dvrh. ;ry near the surface of a planet with period T , the density (mass/v6q df.rqh;;wv olume) 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 v2pgo-; /z;dr,qt 75rwoqp ltof the Moon (27.4 d) to determine the period of an art gq/-wl2od p tt;,5orp;zq 7vrificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a fe:z u9et w eoht i: ;9)sc4,jodza:0pebw hundred meters across, orbits the Sun like the planets. Its period is 4 dj;iep4oze:tbc::u sz, we09 9hta )o10 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.uv3 i ynyug004 l6o(an5 $\times 10^{9} \mathrm{~km}$ 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 rougg1kndffb;+ +ohly 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 out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and fartheko+ gbd;f1n +fst distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga+d.q z/cl zz*dcs0u2o laxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 moons ,wp1v drf 1cguj)zygi(*)0 obof Jupiter (those discovered by Galileow)0y1dg (,rouj pz1 *bcv)fig 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 fsa7ypnbovwi -3bplyh)9w+( x5+ e+fj rom the known period and distance of the Moon. i -sh(3a9b)eovj5y ++pbpw +yl7nfxw    $\times 10^{24}$

  Determine the mean distanrjj3la+ 0uke2yj z.h0 ce from 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 0hujr.y0ake+ j2jlz3 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 bee89 89uzr f4td1twzdutween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited tdt89uzw t zfu1dre489he 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 descm2v 3yd( bk9fns4gb+v ribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotatesd3s v nfb(m+ykvb2g94 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 vykvmh 8vd+0y ,ine (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,0v yh+ ,vydmk8 and the vine is 5.5 m long.   

  How far above the Earth’s surface will u r8eulwykq*btlwh1341 o8e-the acceleration of gravity be half what ityhbe u4 wlu 8l381woekr q1t*- is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grad 3nhar(+0btk( ,z ytgb hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how nbazdr+g,t k( yt30h( hard are they pulling on one another?    $\times 10^2$

  Because the Earth rota,)gul mn-.j+ drrmf w9tes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t mj+f-.r ) drmul,g w9nrotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrw2z/pe,j7b:ulc m(e siav: qon,31ckaft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equalqzm,j v(:e 2iocen/37usk pl,abcw :1 and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in nqf.9bq-ihi 3gim 5wk co;n./an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction;bfcok.9. i i gn5- qm3/iwhqn?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate *e jz05xrd:/nz wwgc ;about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is toczne j /z5;x:0d w*wgr be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–47tj vai-x+z,hpr * i :7nwug5c3).
(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,k-j1h (:vxdwb the acceleration due to gravity at its surface and thevj(dhk -b w:1x gravitational constant G.

A plumb bob (a mass m truax5k90 3ar0r f qa8 hanging on a string) is deflected from the vertical by an angle xkr9a u50at 0fra3r8q $\theta$ 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 banke zla;qhpnzpwa*f02 e: ;z2;w pd for a design speed of If the coefficient of static fricpe;20lzzqa fah; w2:wp; np*ztion 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 Earth were rotating so fast that objkj ell0m7e1x a 9np4:dects at the equate0 4:1m ap7exkl jl9dnor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart2*nra3s20w2 fd sh9i7+mrcc7kaub x b 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 r9 tocqc; tc2 :p5znyb:adius 235 m. A lamp suspended from the ceilingozt:pb tc2n q:9y; 5cc 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 x5x2q7g3x6dk iuf 8rt the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experi3iut5x fkx2d7 6qrgx8 ence 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 Tel9 io a0yhyyny fpr+7/ce44rq cy ,o84rescope 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). Theyarh+pcy 4c8 e09yrniyy o r ,4/qfo74y 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 valley83j/xll bwq22qk.zfg4l)wvee b15ld l)x0 gs shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would th qxflx)0vl54 g)8ldkb12w l2ee g s/3zjlbq .we 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 groupa s ;ym1.i3wpk 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 i p3swm;.k1ay 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 8w7v yh(pa6 jetraveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of ahe 8ajv6( wpy7bout 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 ins g1e6b( qa(g7ihvyy- the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the sam ysqae7(bvgh61y ig-( e 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 / h8tly5 dy6odc:y,qb period of 3000 years. (a) What is its mean distance fro6q5yh,od: c/dtb ly8 ym the 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 valu(2 ujtqe+:k ede of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Makqu:+(k dej2t ee reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a disl3*,h6 *iyq y3kwz+0gd tth vz 1khx7rtance of about 30,0t x3dgtlz7krhz ,6 vyk1hi3+ 0qw**yh00 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each siden)l3x:boo ycm6o)(/e ww6va c. Find the magnitude and direction of the gravitational force on a fave wy:olo w)( ox/ )bc366nmcifth 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 kgqhy)rb v:z y4j /1xvk msa4,k/ 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 the tip of the /e b/,asel0km1.5-cm-long sweep second hand on your wrist wamk eba,/0es l/tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cir; w x*oo7o3p b6nxl2b (. ,xytetenmd1cle below you on a nx 7w pot m;o(o3.x dely*2nexbt,1 6b0.25-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.]    $^{\circ}$

A circular curve of radiustd fkai (l0n8/ R in a new highway is designed so that a car traveling at speed l8fn a/tk i0(d$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatinwkrxs)-9ygz76 dk 9d 05ceo dxg curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a cur7y6o)-w9kkdc9d xes gz x50rdve 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.$\approx$    $\times 10^2$