Sometimes people say that water is remm 9o qlp2y(ykf3. vzw6jez h-vwhu*) 0cy w;u-oved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemeny ly w9p-hv k6u zz 0o2muec3()f*jh;v.q-ywwt?

Will the acceleration of a csy mojbw n83y*/ 9le4-j4:dpqrzjnn .ar be the same when the car travels around a sharp curve at a constant 60 km/h as when ipzel4jmd /y 3jrw.j4nsn9ob:* nq 8y -t travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along aiqpg,9uk 8v y. hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near iu p9gy ,8.vqkthe bottom of a hill?

Describe all the forces acting on a child riding a horse on a merr564g*lt8y uxcdf . ytry-go-round. Which of these forces provides the centripetal acceleration of the chl d6gtr 4t*5fyyuc8.x ild?

A bucket of water can be whirled in a vertical9+wl wd grqx-bv0 hzf*lnf8; , circle without the water spilling out, even a8+fw ;xdgzfqv h* wlrn9, -lb0t the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Thergaw+ ju3 ,i)ore are at least three controls in the car whi )3j+ woargu,ich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in umor;2vh 4 jq;Fig. 5–31. His sled does not leave the ground (he does not achieve “air hvjm q2;r;uo4”), 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 rou d .8 :n1-jwctivk:,p1bnmv tinding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle uj2;fn,9yzau h(ci :grvn +f0given itsa,gj9cziyfuv; 2 +:f(nur h0n speed and radius of the turn?

A girl is whirling a ball on a stvch3pj. h( 5p5s6b6t 7s05,teuqlcbt/ hj wyyring 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 the other side of the yard. When should she let go of the strinq eb,6h5t760chs/vh5 c3tjyptul p 5( bwjys.g?

Does an apple exert a gravitational force on the Earth? If so, how large a forcexwmc* +-agrxno+s *b.? Consider rsn*-mgw+b .*cxx oa+an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it d* 6r1 cks/r7zdj+ sus-d ax/vis, in what ways would the Moon’s orbit +s ss1rukdd/ /7 r- jvxza*cd6be different?

Which pulls harder gravitationally, the Earv9 oodrr y4.t,th on the Moon, or the Moon on the Earo t9drvr. o4y,th? Which accelerates more?

The Sun's gravitational pull on the Earth ;sm1bn7b y -pvis much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational bb7;-v1sm py npull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects/ :-tvl fp*sr y/a-3ki v gpm-h;t3eej are at work? Do t iet-*y-; f:ar-l/e3jvmhkp/ t3spgv hey oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forcg4mhd;oox/ b ,uw b(6he on the Moon due to the Sun. Why isn’t the Moghod;/bx6( mhu w,bo 4on pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit )jn,r 7vdadt : 92iqhnaround the Sun larger or smaller than the centripetal acceleration of the Ea 2aq)dv n:h7r,tnj i9drth?

Would it require less speed to launch a satellite (a) toward the eayi q* mtr f8.5j4tpu7rn* j,kyst or (b) towar rky4jyt8 j i 7p.*nqm5r,f*tud the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a m08 dqlagz e4e*oving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cazae q84led*0 gse 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 periosa:( 9eor)k wf5hempa 4af8,gds in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylina:okfheew,g8 4psfa9 5m() ra drical 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 experie4/xz la*;w7 qzx5rwoxnces “free fall” or “apparent weightlessness” between steps.r;o 5wzq*lzxx/47 w xa

The Earth moves faster in v*j.hivky3p0its 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 factor in producing the seasons — vphv jy 0k3i*.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 ,; ld,qfn5glm juv27 huntil it was discovered to have a moon. Explain v;52 lqn,umgfhl j ,d7how this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t jgf mpjfro (3 ;xwl+7k3iji)u(g i*.,io) yashe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the uxg 3p7i)jr f,jkli* m+figywas ) .3j(io( ;oother.]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 b9t- ow:ml b(v 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 acceleration8p7 r 4baw1fgmn(zn4n of the Earth in its orbit around the Sun, and the net force exerted on the Earz 17(mbw4ann4f 8nrgp th. 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 exerb3;m sfl:q5m lted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lengfmql:l3sb; 5m th) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbitk t0mpm82otv4 mx 9v)f 400 km from the Earth's surface, and circles thet489vmx 2ko)pmm ftv0 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 surface. $\approx$    g

  What is the magnitude of the acmef, +ixi//ucceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wh,ufc/mei/ +ixeel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate (xi /dc,rh3 sp3jx3 .tq:oxhjin a vertical circle of radius 72.0 cm , as shown x/. jp ot3hix,js3 3drqc:(xh 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 spha x8+usp ;t,qeed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coef;a 8,uhxq+t spficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tire warzibj3lk-)zy6o. dk)4al;s and the road if a car is to round a level curve of radius 85 m 6ai).bz3jk ;w kyzdla-o)r4 lat a speed of 95km/h ?   

  A device for training astronauts and jet61g4 lreto vy8 fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee lg8vt14 re6yo on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis1e/ ide.1 w(ujk tt.71 wkmdap of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin d/(wkuea1 tdemj1tk7 . 1w.ip 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 turntable?   

  At what minimum speed munx +vyo;v-uuy 5rqd0,st a roller coaster be traveling when upside down at the top ofq,nuu0-vy5d ;vyxor + a circle
(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 thr/yy-ozc3ozm r. k(k1e driver) crosses the rounded top of a hill (r/o3my -k.zrzk1 cryo(adius =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-dk f.7k2k j/u1s-ssfecyw l4 b7iameter Ferris wheel need to make for the pafkk jk/.s4ye-lf77u s2 bc1 swssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of -s 5* 2ma+ 2zjyzrdjy 1wo8cdsradius 1.10 m. At the lowest point of its motion the tension in the rope supportingw1 2y sjy*8acjozd-m 2+sd5zr the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm t+c(+b t:n )q,q3assxniqn 6kfrom the axis of rotation is to experience an acceleration of 115,00nbaxs qtkisn6qq3+t)( +, cn :0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a.vg zc h*f z:45l3acvpre rotated in a cylindrically walled "roo*3p:czvfv h g5ac4 l.zm." (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 circle on a frictionless air-hockey uz*s40 jphk7ptabletop, and is held i4z 7 k*0ppsujhn this orbit by a 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 this time, by h2v*uquvb u(co,uw 5*not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, f(oh5*b2v,vu* uq u cwuind 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 perfectly baneb rsx-c-w2j 1ked 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 masses 9 xl+ wqf9 f5yrihrlk+8u81n z$ 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 ma 5w-nv.+1tkluazu(tjneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted on 7df.kwc :b:h pt9;kcd thwd k hp9:b:k7dcft;. ce car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates n3v7s:ne k:ig uniformly from the pit area, going from rest to 320km/h in a semicircular arc with7 s::kv3ie gnn a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particul6w.cbsh;.s6q kadhhn b9. io:ar instant, its acceleb6hw..d.b q9c a6; s hoshnk:iration 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 o iqu))h9wfx 9 :4gw*5ytpbv wxb*jj h;n a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its ma; u5)wg)i49byqt *p bfwh xxj9*hvj:wss is 1350 kg.   

  At the surface of a certz wmabc,gvh86x. 7go9ain planet, the gravitational acceleration g has a magnitu7,6.a9xczw hog v8bmgde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on tv v7- nlvlftj-tb6)m-8 t 3qgmhe Moon. The Moon's radius is 1.74 -n-jvg mlqvtt )tfbvm76 8-3l$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tihe (t: lfu4+1kcvr,c umes that of Earth, but has the same mass. What is the acceleration due to gravity near its surf+vtu,rh :u cf(e1c4klace?   

  A hypothetical planet has a mass 1.66px27cpwn0hs on.:zb ; times that of Earth, but the same radius. What ip c:o0;w72z n.hnpbsx s g near its surface?   

  Two objects attract each other gravitationally with a fo -2dt8d 6ygnsnrce 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 acceleratibbms1 ih0t;kmfn b92av9*j v0on of gravity, at (a) 3200 mbk0h* tn2 j9vi a 10;fm9bbvsm    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pointkw bdt) eg+a 80ujkzj+z/ s4:t outside the Earth where thegravitational accelerat0:uj k)aw t4 +gb8st/z+kejz dion 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 uc od;+hmb .8emtqw 3;of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monstw8ouhmmq+e;c3td b.; er.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun bsd hn3r* b+wv5ut is now in the last stage of its evolutdsw v h5r+n*b3ion, is 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 astro.bq d jy)0,/vxqb0wg k4i hz;jnauts feel weightless while orbiting in the space shuttle. 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 vi/ ky0. qhx)djb,0jzwgq4b;in terms of g.   

  Four 9.5-kg spheres are located at the corkswo y; t ba41l28)yfe t/ax5aners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the o)a fx2ty/a18el ko4ta5;yw bsther three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most ofjuz)-9tu e w7k the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venu je)w97uzu t-ks, 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 of gravity at the su (:,m/)l )i7ocfvxgv vs 6yezirface of Mars is 0.38 of what it is on Earth, and:/gif )vzs em(,x cyi )lv7o6v that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value tn9(ps guo,0( it:ms9omqjp*for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtai,gqj p9t0(o9us*(snt:pmo i mned using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cir6) m,mr1 9hi hwb/mrhrcular orbit about the Earth at a height of 3600 km. 1mwrr h rmm,i6/hh) 9b   $\times 10^3$

  The space shuttle releases3u60hq7r6 wt /mi1*ftveg23 jkkrb ua a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occursu71 3h/6btifw tam2gu keqkr03*r6jv?    $\times 10^3$

  At what rate must a cylindrical spacex p :hm5qp/bo7ship 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 21, Fig 5–32.) p/hox mbp:q57   

  Determine the time it takes for a satellite to orbit the Earth in a circula9e1 m)tn.u rrz-ep3 qgr “near-Earth” orbit. A “near-Earth” orzg n9e pe rtm)-3.1uqrbit is 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 would a satellite hyp w.,ew0ima m .3/xsjave to be launched from the top of Mt. Everest to be placed in a circm.m30e/ywswiap. j x,ular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuzz c+g 6tp86r4vjm u(xed to orbit the Moon at an altitudeugjm+x zr 46pcv8(6tz of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are comh6lkedwl +h/+ posed of chunks of ice that orbit the planet. The inner radius of t6hwe+ld+k/h lhe 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 0k 3uc ;+ijdmc.7qyv *.nk wjqFig. 5–9). What is the ratio of a person’s appar3vmjccjy7.q dqk*iw.+ k 0u;nent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaupmm2nxjlik2/fn t 5z.) /6sgrt 4200 km from the center of the Earth's Moon in a space vehicle (a) moving atp) gn2x/i5mksnt /r62 mzjlf. 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 syvxa3uabmzl x96 y.uqh 3m t452stem consists of two stars of equal mass. They are observed to be separated by 36maulquxt mv.9b3y3 z4 h52xa60 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read f3h9 btd,jg ke-or the weight of a 55-kg woman in an elevator that movegk 93eb td-,jhs
(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 elevb ws9bqqp k1b4uu3c:6re-n: nator. The cord 6kwqnn9 4q-su:rb:1ue3 pbbccan 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 t yo7b(zqhi) 8ehe surface of a planet with period T , the density (mass/volume) of the planh7qy bzo(8ei) et 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 Moon (27.4 d) towtx3kgaz3z+;2eglj r )3 m py* determine the period of an artificial satellite orbiting very near the Earte*z j3kg)m3apzl3; xwry+t2g h’s surface.    s

  The asteroid Icarus, though only a few hundred meters ao;aqq/cs5nu m 78b7yl cross, orbits the Sun like the planets. Its period is 410 d. What is its mean distancesa7/q5yolqbm c7nu;8 from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 gm-(r d)kdp. l$\times 10^{9} \mathrm{~km}$ 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. It comesm -b);h nv/rt(paggnp38j z -nad6rr/ 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 /rgz -ra;np n)gdb -v3 m/hjpr nta(68still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the t6(uwxmej5+ q y15, a5ggrzp tGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, per dkt)fyqxjl5v.k1d,i .d01a1sf; j vtiod, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 16 fky. j,qdtdvjvtsdlakx51)1 i10.;f09).
(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 nxy8i+ qjgz*1da6:1vqiru 5 l5dta,p known period and distance of the Moon. a5n: ia5diyurjpztqg vxdl8*6 +,q11   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo91bseu ) cv4zgns, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values ingbvu14 9 scz)e 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 cons . h .absunw c,zc*3ch.fr.)ubists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was decfrhhb.cc .*.ws).z anub3u, stroyed).
(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 artificia12t 9n.jrlwevk*r*-wv ue7m 1km e g0rl "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, thatel* .* t79v wrknur0me-m gevwk2r11 j the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by sq7 ww g 2-0f:uy+lha evz;aj4mwinging 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 at the lowest point of his swing? His zqajwu: h lfg4yw0+vme-7 2a;mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what dzp:0alsr *)(n. tgac f;g ,wbit is on the surf(, nadfgr.wczal0t ;sgb)*: pace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a+v + ),9lcuub oelpeb; mutual circle once evee+oe p +lbl)ubc,9u v;ry 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity abot/r6lh fb*8b0ujq ) t the equator is slightly lerfbbb8h0/tlj6) uq* oss than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spw.efl iv1.: amg8+/ujc;h pnpacecraft traveling directly from the Earth to the Moon experience zero net force because the Eartuhw+m1vcgl .p; fi:/ 8pen a.jh and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an ;.kq t :1e9v/v *i9enhtdg lgkelevator, it says your mass is 82 kg. What is the acceleration vn*9/:t1hi9e. tged ;qkvlgk of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station cons.:iz+z4 )ej/sdtyxt8akfig9lai ( b 8ists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formedtit)4:8z9/a(+j8g z.d la y iskxeibf by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft ifq2hfyob663k)vs + d dn 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 of its radius r, the a wl,/m-is v 5ynq1c7nxcceleration due to gravity at its surface al-5 yn7xvc/iq1,nm swnd the gravitational constant G.

A plumb bob (a mass m hanging on a string) is dotx400ipp1 h heflected from the vertical by an ant0hipx4 h 10pogle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of h8w l 56bnxn7l If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safel hw8lb65nlnx 7y handle the curve?

  How long would a day be if the Earth wel5fg+rav.qaz j :7qz3re rotating so fast that objects at the equator 537qvjf+lzrazaq. g:were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintainefxpkz n hi+/*7 8xwi+u9iko 2 a 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 curve g2bnh3 jm)lq dwl -k:,of radius 235 m. A lamp suspended from the ceiling swinqb, lhdj 2:mwk -3ln)ggs 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 hv * qhufb5j6z7s7co7glm; u1fas been claimed that a person would be crushed by the force of gravity onb mf1qs hlg75*uo; 7cjz67 uvf a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Scfac pm:. 4wee1;bu(mg 9h, qvpace 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 this by measuring the speed of gas clouds orbiwuge9 mfcpvb1c(e4q :h ,.ma;ting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown in 6 )up r9ciyjh2x x0mwgx r*))yFig. 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 the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without pc x))jy)yh69rxgm*2 0 ir xuwlosing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24hnv.vonygdpo 2m 6*6: 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 distvo. vnyd*:m2h6nogp6 ributed 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, is c 0v7 4(izyt1lmm wm4omeant to orbit the asteroid Eros at a heiym oi1z744wvcmt 0ml(ght 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 shuttl/236 a4gzox.*w zwqg)v/0pa /h card5 srxvmqe pursuing a satellite in need of repair. You are in a circular orbit of the same radzo)4zv5xg *. r hc3ad/xwarwq20 gpva s m/6q/ius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yey 3hx -+7yt- uplaoj,gars. (a) What is its mean distance from the S lj 7gyhxuy-,p 3ota-+un?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if youide1foc7e,a )te q 5z/ could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions,)51,e7 efdeq/ t czoia like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centfiz9uk/nu.fv2 ew9k7: jqtv7 er of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light9w/ ij9fvq7:2 vef u uz.tkkn7-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 6lwk ibj:bkm9pf :( 26fsx3delocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the squareplkib6f62fm3(sw 9dbkj ex ::.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi,pw0jpj +u v+ylk am2/ts 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 12k1n 6g8(gvkqrce) e62liag)o5u s b:sv5jl o.5-cm-long sweep second hand on your wrist wagke)c2r 5av2 su qvlk(b 66si1o)5len :ggo8j tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker941wzj4 ywx wp0j: g/:vmvble weight around in a circle below you on a 0.25-m piece of m yvjwv g4xjlzw4/w0e b1p:9: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 is de e;obo9 t0w(fr5 :lwrnsigned so that a car traveling at sp5 fb9nww rlr ;t0o:eo(eed $ 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 to rd-snj)*net o;n- *milt of the cars when negotiating curve r nj)-sonn oe;**dm-ts. 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 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.$\approx$    $\times 10^2$