Sometimes people say that water is remo1faxzhg3z*/ qlc* 7fuved from clothes in a spin dryer by centrifugal force throwing the water outwg*z7 h 3fl 1z/cfxuaq*ard. What is wrong with this statement?

Will the acceleration of auf )) 6pf va7lq8e m s4kh;-m2ouyv5hn car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle cuq) ); uheml vh48pfskuo-manv65f7y2rve at the same speed? Explain.

Suppose a car moves at constant speed along a rm5e95h)c dae hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill,5r dhmc 59a)ee (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-rmmb 1 ,jheq .8s5ykr2go-round. Which of these forces provides the centrip ,2 smjrrye.85khq1b metal acceleration of the child?

A bucket of water can be whirled in a vertical circle without tu/7x90zkj 1*1s4bf6 en sikihwr.bonhe water spilling out, even at the top of the circle when the buckete0k k ns1xws rn*/4bfoz6i h1b 7.9jui is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cont 3epmhck8id/ wp61ddd q3: :(l 0rtpsarols in the car which can3d03spqrlh(: 1edmt6 p iaw:p 8kc/dd be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comesr obdvfk; v(+, flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between hirb,;( v+dof kvs 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 adi) /)mh sqgvqx *1nk cx,r(8st high speed?

Why do airplanes bank when they tu/15 ;dzkwe+ ym67un g7ukasayrn? How would you compute the banking angle given iagy/s 1u5y 7;m dauek6+wzn 7kts speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.wz/5 lj gpkl;o 49x.ug She wants to let go at precisely the right time so thatx/z l;pjulw. o 4g5k9g the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how lm/djyuj 27w,ehf) +x8whe0y5m ds;vkarge a force? Consider an ap28f; uj7wxdhkh)5vmsjyyd w e+0me,/ ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wako*t-shg. :c jys would the Moon’s orbit be differe:t* kj.gshc-ont?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E*f vh)zdz jh) - lre93h-*hipxarth? Which accelerates9lz3 f-eh*v)hph *r -) hxzidj more?

The Sun's gravitational pull on the Eart)w o u5b u0gp w/;9ef/xjiqty3h is much larger than the Moon's. Yet the Moon's is mainly responsjpft g;/i30uywe w)u/q o bx95ible for the tides. Explain. [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 e meoy:iwg4s u -sufxq3 .j4(r.ffects are at work? Do they oppoum ygjqf:w4 ri. 4xesou .3(-sse each other?

The gravitational force on the Moon due to the Earot:ky )0xis kwo c *csjd j3n+mv.6f4x81l+ qith is only about half the force on the Moon due to the 0m xo14nq.) i 8+sfjcxycd*l: sj + 6ktio3vkwSun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arounyx3i wi6j5648t kk itdd the Sun larger or smaller thant5dxw8iit3 6y6i 4j kk the centripetal acceleration of the Earth?

Would it require less speed to launchx7h lv/8yri/cl:8 aez a satellite (a) toward the east or (b) toward thelchz8y/r i:7vxal e/8 west? Consider the Earth’s rotation direction.

When will your apparent weightws z8;k;qz/x d be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is is/wdq 8;x;zk zn free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected0of* ai +euc19u4 gg1 x(vv ufgkdxs-1 by weightlessness. One way to 1g19 ogc1+uek( ix u svu4g-*v0fxadfsimulate 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 gravity you can think of.

Explain how a runner expef642xo tf j:w0v3ifzn riences “free fall” or “apparent weightlessness” between stept46wj 2fv30f nfiz xo:s.

The Earth moves faster in its orbit around the Sun in January than in J s 8zf7ycz0yby, 4qlc8l9 mf xo()ao;muly. 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 — the main factor is tylfy ;,8z lsy7fxcqmmo zb49ca0 (o)8he tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was3pzjq,h /fdb /3:bvs j discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s masbz q3db j/3vsp/hj :,fs.

  The Sun's gravitational pull on the Eartjpz9ir 2 ;d.mah is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]jd 2im. rapz;9A 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 travelingjdtz7cl/f09c5 .p;,myiu s s d 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 ac om, lt9m-a.wcceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this cmwa-,9o.mtl 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 ru,d 1 nokfj,)on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the spen1jo uf)k ,dr,ed of the discus.   

  Suppose the space shuttle isq ogq3xd):vtpn./sif3 38bxm in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Findnfxx).g 3/os8qd vb3:tmqip 3 the centripetal acceleration 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 txwrh(g.zb kg68 bi0v3 he acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute)z(xhbirw0g38k g .b v6 if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate inysjm -u- mrk4 om-2hy; a vertical circle of radius 72.0 cm , as shown in sm4ju 2yrm-y- oh-km; 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+bzd8-ot xz30 vl3nt(c02 gr7m ellvi a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires andde lzm3+xto vcb70 3(0zlg2t-8rnilv road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tiresssvccchcwyh(d f*( q/.1 (2hh and the road if a car is to round a level curve of radius 85 m at a speed wqh1y/c (hcs v sd .ch(c*2h(fof 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rot6 o 3g,gs1v fmh;hii2qate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is m hg;vgh1q 32sfo6i,i 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 sfz85l.cz+ 3 fyi6i w otlx(78bndc1fipeed. 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 they5x3(cz8zf +1l6icd7fw n b.l 8itof i coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coasterx6:si/+1 s ufs0rr(:m st4dwg eoq2yr be traveling when upside down at the top of a cifu +drq(x m/ si2:os40rrst :esw16y grcle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roun0dxptr ua.27i8b oya42rmzscs- 8 xv1ded top of a hill (rx xtdpba iv7crzam02ry2.8s-su1 o 48adius =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 m(5i nyar1le -z8mx9geinute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weight591e izr-megn(8 al xyless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circ593hc(f, x:4 zat spocrt dk3cle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportir:hc sazfxoc59 3pk4ct 3,d(tng 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 rotz;2o: 1qecw7g9i2rgqb2f rx n ate if a particle 9.00 cm from the axis of rotation is to experience an acceleration fnwiozcgg1 xrqe9b;2 2 2:q7rof 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically f/vm5xs:cpeao tks .;7scw .h+4k- bz walled "room." (See Fig.sesowhkk a. 5 7vm/sbtxp -4f. cz:c;+ 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless ase,n *lvk meqw(+/ el,ir-hockey tabletop, and is held in this orbit by an+ (qeveew/k s,ll ,m* light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely thisxdyj t54a2 1 p sv6r.g5(agyfi time, by not ignoring the weight of the ball which revolves on a string5dxfi4v(ajrg51yg 6p ts.2ay 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 in0 tv :aygd1.krygk96s 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 masseszd0pnlsw4:d1 s,m07 ih:fuc o $ 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 verte7kmgah ntf/i 9t3 :0v/z *euxically 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 qxj ,-w.bs00/x;foiv7i an h gcentripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its soqha;n0xsif7-bwvji , 0/gx .peed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformze5h tvfo:p)-ur/ nc) ly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and t tuo:5c )z hv-rn)f/ephe road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radiud fejz)0)5s 9e9q0 lkdg: p4n slb6emps 2.90 m . At a particular instant, its accelerat:ble 4 se5s0 9)jqdgf6mp)9k e zpnld0ion is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth 1piq- 1sv kzt(radii) above the Eartq(z1 tvpi 1k-sh’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accele1mj6p -5 gw,srrdn dm,ration g has a magnitude of 12 mngd dj,r -6,sm5mr1pw/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 the Moon. The Moon's radius pc 1r 7h46zrskm-85(mykuxqi is 1.74 c- 1kk5yihsmrq8m6xu 4 (zr7p$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a 2 9po 91g jtd9l p,ppb.d:ajjqradius 1.5 times that of Earth, but has the same mass. What is the acceleraj 9 .o2pgbd99q1dl,t:p jajpption due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bb :sb2f5u d(ud8s 9kswut the same radius. What isu s8s5 u:kbb2dd fw(9s g near its surface?   

  Two objects attract each l vy-.72u m5 pexkq5xnother 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 acce,j:lbplyy:p;go4s 8o leration of gravity, at (a) 3200 mp,ob: gs:yyp8oll4j ;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ouw: 4yt *ttbp;lkuo. 6vtside the Earth where thegravitationalvuk tp:;bwt6t4y. *o l acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the massm 04itjama) -a r9c*zm+1vqyf of our Sun packed into a sphere about 10 km in radius. Estimate the suti-+1vay*j0) qm cmm49a rafzrface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wax91iou5 t5jg7pvft4 pt :tim (s an average star like our Sun but is now in the last stage of its evolution, is t4 7 tvpigo:9tx5jpf5i tm(1u the size of our Moon but 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 orbiting in e 2h2cqn*83q ;bjtbky the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them ;bjktnqeh c b8 *322yqand 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 lot; wb6)4*lkjl y y z6m6lm*bfgcated at the 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 wbmk6yll jgmtf46lzyb*)6* ;three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.7)c7kyqd90oq xuq w4e C 70w9kc7d eq )yxqqou4alculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration o6n+z k6x/;ngwnk/nby f gravity at the surface of Mars is 0.38 of what it is on Earth, and th ;bz/6kg+nnw n/xnk6 yat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usins0yi9eorv . 556ztc nmg the known value for the period of the Earth and its distance from the Sun. [Note: Coeyt6i oc5vz n9s0. m5rmpare 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 orb-(hm sb+wosi:r8hhn/5 til 4d it about the Eart5 trnhd(/-+l8s hswo ihb 4m:ih at a height of 3600 km.    $\times 10^3$

  The space shuttle releases )c* r8ha nlvr8a satellite into a circular orbit 650 km above the Earth. How fasa v)8nl8 hc*rrt must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants aro4eu ;u1m)jx, 9qwiwte 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 re1,)j wm4wet9xuqou i; volution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in + +923jmlt l +90c hcrsnnoqxfa 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 the Earth. Does yqn+t 9n f 30ljcr+s+h x2cl9moour result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hay0 1qc9fiu p4cve to be launched from the top of Mt. Everest to be placed in a cirqcyi10cpf 49 ucular orbit around the Earth?   

  During an Apollo lunar lanlfng4j t 6/pnaxl:*y3 ding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long dl6*p4aln yn3f: jtgx/ id it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i8upojvzb)9n 5 -gv1wo2ihqv- nner radius of tg-h vo b-8n 9vq1v5oziw2)ujp he 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 ino h z6n2eh8-sm diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent h6 8o 2hsm-zenweight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weig6tq*/ agf m,/bex2by1z q5wonht of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (,1n/ x/q5*zeqw6 fby ga2otbm 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 stj * .ii9olto8 d073z9 mrllbduars of equal mass. They are observed to be separated by 360 mib3*t8lj. imz9r7lo9iod0 ldullion 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 for the wei yuvz07(u b+vhdk6rh 6ght of a 55-kg woman in an elevator that my(b7v6 urhuk6z+hv d0oves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatov(vj9, eybp sf.i15 fvr. The ci9fysbj1 f(,epv vv .5ord can withstand 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 of a planet with peri x0ip3lh de)m3g9*y dzod T , the density (mass/volum)9mlx g3i*z0 y deph3de) 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 and04y rfer1cth5ft0j k :s3lnc1 the period of the Moon (27.4 d) to determine the period of an artificial nfk cr1 hf4j3t0 yce0:rl 51tssatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lioyif e:r;styz74 x7e9ke the planets. Its period 7xeze: s74yrify;9 otis 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dq( zm g)*uf byrih (5jy*u01-emf.rpuistance 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. 1te2du tfef4wy *:yl -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: Tfd :4w2yf-yl*ute e t1he 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 ce9 ufm s uu,vmf4kb( 1.*0zegnonter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largestwxq -dn s.s7p, moons of Js-sx7w p,d.nq upiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the knowni*iczdtm6 rxe48-h bh(qt.:7ql9 xpy period and distance of the Moon. qxbl7emhpcxr d86(yit*:49z-i.qh t    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usv7o/kghh.r2 vnig 0e 2ing Kepler’s third law. Use the distance of Io and the g vrk2h.e on 0i7v/h2gperiods 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 m/q:f kbth yq:6xfj u4- v2h6opany fragments (which some space scientists think came from a planet that /ot hfu kqypvh:2q4x6:jf6b- 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 arkxff3- c y p1ib-+r7bhbao.)i.mx2cbtificial "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 enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth rpfbbk ac x-c ihfxo72ibmb. y)3.1-+ days?   

  Tarzan plans to cross a gorge by swinginjvz lk,(--gmgw0 q/jd g 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 maximj0kg/w -q-,mldvg z( jum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration;h a/ ws8;uzm(c,jz c83kdik0.n knbn of gravity be half what it is on t3 bj/;.8mau ,k cknw nnh8cz s;zk0id(he surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in w u3foc 8,d.zca mutual circle once every 2.5 s. If we assume their arms are each 0.80 zcf do8.cw,3u 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 7lavv8- hc /iuper day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What -a vci 7vhu/l8fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spa jf q(qyb/8v d0f1wk7qcecraft traveling directly from the Earth to thedk0yvj8q q7/fbfq ( 1w Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, *r wv7k x*g2+yxagq+g9 d,mn rbut when you stand on a bathroom scale in an elevator, it sarnr qv ky+*+ x*7gdg 9w2,gxamys your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about;+mdxy dl ke fh5ek4/r+-v61 y+8eiodyt 7bq b 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 to be f81e+efv 6br /-q4dxlh +emd 7yty;k+b kd5iy oelt?$\approx$    $\times 10^3$

  A jet pilot takes his no2raq( qznwb*vf :(p ;xyj4/aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a pztjr4(3oces .lanet in terms of its radius r, the acceleration due to gravity at its surface and the gravitationjz.43o r( etcsal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vernwk pipns eb,-+c,( p,tical by an ang(,spkbnc n,-ipe+ , pwle $\theta$ 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 designf18.0tni dxalg: 8c ug speed of If the coefficient of static friction is 0.30 (wet pavement)18 i a n:tgg.0dufclx8, 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 oblvf;vzd fr6p2jqs9/7p b5bb5jects at the equator were ap6 2 bvr/sp795f5qbd f p;blvzjparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain 5xye3w7xw v1byl/+ x: ;c xdvta constant 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 curvr 0j m6n pa.q biihm((z-ke bu)--o9zle of radius 235 m. A lamp suspended from theqhzl )i9k .ur (bm ozp(-ne-6bimj-a0 ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been l;3d+xt+23qlix w r lqclaimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can ;lw23lxrx+q+ i3qd lt't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space b*5aerp 45egv Telescope deduced the presence of an extremely massiv 4e*5gbvr pea5e core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the plw*iek 9h/mt3r0gu0 hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would th / r0*pki3glmw9u0ethe 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 of9bxzci znn( 8- 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 centimet9 ( xnz8bc-izners. 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 travelclh crmh ta2;1 i(g+b7ing 2.1 billion km, is meant to orbit the asteroid ;lc a2rhh1b+(m7tg icEros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in needmd tn 9egv(.2 1ochm(o of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but g(9d.co2e(m thm1ovn 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)a4.l x 6y)ygpb3(b mf4r8cj rg What is its mean distance frorca) 3p6 m4xjlg8y4 ryf.b(gbm 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 value of G woubu0 cwd3jg c2*gsj 7rb:ep8o :a1mxvg dw5 n17ld need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiobpw7ea g u5dgd2gcr7n 8x*jmw so:0jv1c1b 3:ns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galax +elni+ex 1oyjcx/:r8aly/1 vy (Fig. 5-46) at a distance of about 30,000 light-years anecr/ jexv l: /xy+1yi+o 81lfrom 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 w)c7oz5 zzfv5at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 7zcz)o5vf 5 wz1.0-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 orbits8 sy4j2 xeh qu.9xpex;v :fi*v 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 experiu)updpcctgd +:/-a)aenced by the tip of the 1.5-cm-long sweep second hand on your wraadu) d-ptg+uc/: p )cist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aropk x/)b5)f dd1y-x dkjund in a circle below/d5jdk ybxk 1-f xdp)) you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is7:n rto) ,ziamjklee xa+.k. ) designed so that a car traveling . )ekjmr)+ izax7.te,nok l:aat 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 gd64iidnk(vli - n7*uol;2 pethe cars when negotiating curves. The angle of tilt is adjusted vdi74ku(6ignp n l2e;do-il*so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (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.$\approx$    $\times 10^2$