Sometimes people say that water is removed from clopdpgua .)-,mv 5d/+gcire q-ythes in a spin dryer by centrifugal force throwing the w d 5yi ecgd-+gupra-p/,.qm)vater outward. What is wrong with this statement?

Will the acceleration of a car be the s :bmwj7cj:j)rr,wcv8 ame when the car travels around a sharp curve at a constant 60 km/h as when it travels around a ge:ccj8 w w,rjv b7)j:rmntle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the v /q+ydq w,5ddcar exert the greatest and least forces on the road: (a) at the top odd/qw5yv q d+,f 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 ri0y*ws;dabbp ti7 k6lbk.o69jding a horse on a merry-go-round. Which of these forces provides the centripet 76t paysb0*bik6j;9bk. w ldoal acceleration of the child?

A bucket of water can be whirled in a hfm b (ouq)a;3hw:;a) -u. tf3v totzbvertical circle without the water spilling out, even at the top of the circle when q)aoz:bfhub mo-(fht.t3vw 3 ;;)utathe bucket is upside down. Explain.

How many “accelerators” do youqwmq5* ax s-af 9h9j.l have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What aa.9 w*jq 9qh5mf-l xasccelerations do they produce?

A child on a sled comes flying over the crest of a small hill0 twky5n;zc k., 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 his chest and the sledczwky 5tn ;0k. 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 al-y,a+ qz13)a uguvnu9 aga8j t high speed?

Why do airplanes bank when they turkanq6d lw w+9slli. .*n? How would you compute the banking angle given its speed and radiusdsl+9lwin*q6l.kw.a of the turn?

A girl is whirling a b- 5t)rsc sd 6ggu.ll3xall on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the ya-)lg r.s cdsl65txg3u rd. When should she let go of the string?

Does an apple exert a gravitational forc6.5bw s0ea gj3jdsk.l e on the Earth? If so, how large a force? Consia j0.d3j5swl6egs.bkder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s oeq b:rg6mrulg4:x74 prbit be qr:e44g6b m7pl: xurg different?

Which pulls harder grav)t i *(k;nav.6ww 0i ctsms3 ,i/1bbdf2tnfinitationally, the Earth on the Moon, or the Moon on the Earth? Whic,wik(a6 n)v cf;2f/.i*0i sib1tsbwtd mntn3h accelerates more?

The Sun's gravitational pull on the Ea*ns6z ifc2da 1qs- 9jcrth is much larger than the Moon's. Yet the Moon's is mainly rdj2scqfs 6caz-1 9i n*esponsible 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 thpbp4 - k1yz/k. -vehige equator or at the poles? What two effects are at work? Do th/hpe 1 zybp-v-g.kik 4ey oppose each other?

The gravitational force on the Moon due tou;bmrd3-scn pqu81x) the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eu)dp;r -nu81xcms3qbarth?

Is the centripetal acceleration of Mars in ig2e tboz(*/ adpz d4z8ts orbit around the Sun larger or smaller than the centripetal acceleration of gd48 e/t*2aodzb(zp zthe Earth?

Would it require les9 oqc.ljw9tzap6 4 j/a hi1/:xrdh*bps speed to launch a satellite (a) toward the east or (b) towzph* wa./ch tpj1/boxq d :69jr4l9a iard the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as 0olkqren;g x3//*1 -c lot /c g-yjzldmeasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward,l0-zeln3 ;l/*-/cy jto1r dogq/ gxkc (c) is in 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 co9pl- j1u jf ,hvewlx16uld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you caelux1wh 9- lj,1v6fpjn think of.

Explain how a runner experiences “free fall” or “apparent weigfk62 mvex7.ohkh. 7xxhtlessness” between stef .7ovx.2k kemhxx 76hps.

The Earth moves faster in its orbit around the Sun in January than in+q 5,b)xjr+fc, b eil.a9qtn d 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 — the main factor is the tilt of the Earth’s axis relatif),.qlitb br nxd9, q+ae5cj+ve to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expla4iv qyhn b y.-(7q97tp;3gsmr xk0jk hin how this dis s ;4qb ng.prtyhkhk9(3j7 -my7qx i0vcovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much large54 n1( nn0q jybkael;.qjgmf4r 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.]A child si(nnq1bjgkf 05.nj q44 ae lym;tting 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 travelingahro j y+x.r1h l8;rm8 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 ofxzl3bx 10e m9g the Earth in its orbit around the Sun, and the net force exerted on the Earth3 lxmg0x 1zb9e. 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 discus as it rot. v0 tkh+xbwskg8sdddp2 go *;9a 1pc6vn)7xhates uniformly in ddt xhbo g0 wsscn)v*x89 phvd7a16k +p ;.2gka horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km frtp9)7d ydg) wsom the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its )w 9ptsdg 7d)yorbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerati;- bfyyn;.eaem/(,j 0 ksfh poon of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 3 e,s nbo0 -a.jfy fk(epmy;h/;2 cm?   

  A ball on the end of a stri 3tym2svvj;b *ng is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shownvm2s by t;*vj3 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 rou)dgwf-p 8,1sgmf8s m lnd a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this resulgf fss m1 wm)8dg,p8-lt independent of the mass of the car?   

  How large must the coefficient of static friction be betw1g bev;9 n(:ijset7i zeen the tires and the rntv;e1gb7zeii:( j s 9oad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to r0f1mscoy- 3q notate 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 she rot-3q o1fn ysm0cating?    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 turntab aco8jb( 73+eqmnmj,o le 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. Whaoj3qbao(c em+j ,nm87t is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed 8ny56u a6./b/yknknxm u civ9must a roller coaster be traveling when upside down at the topxv /65may.cbunknu9 i8kny6/ of 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 x5az 37/bqgzm mass 950 kg (including the driver) crosses the rounded top of a hill (radius =97gaz5/xzbqm 35$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter hy* /roja:0 epdud 4c8Ferris wheel need to make for the passengers to feel 8yr:ed4dpcou a/jh0* “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vej2ya3 bihfa.m:de,a2 rtical circle of radius 1.10 m. At the lowest poinh,2a:mei .j3b fa2ayd t of its 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 centritmenc -k elhp4t8g;2+ fuge rotate if a particle 9.00 cm from the axis of rot+tc82 leg4hmp-e t ;knation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindri-r:ywi(f pd0kcally walled "room." (See Fig. 5y(f-w i:r0dpk -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 ro,)l1pw jqqp. yl mq0-xquq *c,tated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m )y l,uq* qpxpcqqm -ljq1.0,w) 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 not ignoring o3 nzasp*fi 2bl9 inw,o3 )/s inmg4-wthe weight of the ball which revolve2oma niib9p /)sn3,wg*zs4 3-wo fnlis on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is -mfw;5(c h rbvperfectly 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 massep9v;zfpo0 / fms $ 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 evz /q r / aydru:1sel2k tnk6k-tt4ko4*asive maneuver 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 cohb5b5 2ntyzwmm9;k *omponents of the net force exerted on the car (by the ground) in Example 5 mo5*kbn z h2m;bw9ty5-8 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 uniformly from the pit area, goi- ;ml2qzmeomt;x8(; m,eq rzv ng 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 x2to mm q(-,mee;8;v; lrq zmzof 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 particfocwfbw f7ft**,6tp*0 4gj wr ular instant, its accelwwbt*op,f4* f6wjr 0g*t7cfferation 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 grdji:pfj ye t0,r;+ ru7avity on a spacecraft 12,800 km (2 Earth radii) above the Ear7 ;uej,yj it:d0fp r+rth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitaob;68zs ed g /h5+fap hva:2cetional acceleration g has a magnitude of 12 md/a6achz: v5;gb8efe sp 2h+o/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 gravit wbma, lvx2a37y on the Moon. The Moon's radius is 1.74 3xv2aml w,ba 7$\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:tdrt )ms -j,h Earth, but has the same mass. What is the acceleration due to gravity nea:t-m hj,td)sr r its surface?   

  A hypothetical planet has a mass 1.66 times 3:3yr yxt(uvw that of Earth, but the same radius. What is yytu:rv 3(wx 3g near its surface?   

  Two objects attract each o.e cvv2 awz +ekyeb) e+*)ny:cther 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 effecti(rx4 3, 4n :zsc,ldicblt5lqkve value of g , the acceleration of gravity, at (a) 3200 m 4ti,cl zs,r3q5ckb( 4lx dln :   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from t4 f*t zx/ljqz-he Earth’s center to a point outside the Earth where thegravitational acceleratzlqz/f *jx -t4ion 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 S les h gj+ncz*)8k/c+fun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monc gn/)+sezc*j8 fl+ hkster.    $\times10^12$

  A typical white-dwarf star, whiccg,++bp4 wjb ch once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Whatb ,cp+4wcgbj+ is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space +oq3ll ,3 iszkshuttle. 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 surfacs3q+ iz,lk o3le in terms of g.   

  Four 9.5-kg spheres are located at the corners of a lb 8l8 g0sjtb s3*b2yzsquare of side 0.60 m. Calculate the magnitude and direction of thej2blzst38g0bb 8sl* y total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on 9kveyp 9m8; hvthe same side of the Sun. Calculate tkv mep 9yv9h8;he 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 of gravity acgkzow83w);t +q4 h wl g1ds4 zkapb/),nn-xqt the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thh+c ;q)3xzobqtwglw) -4n nk8k/a1pz 4 ,g dswe mass of Mars.    $\times 10^{23}$

  Determine the mass of thbu ioq+pre .:kd5.ts/ e Sun using the known value for the period of the Earth and its distance fro.bik op5 sr:./+udqtem the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of ascc3*3/elpmnyn( u*l satellite moving in a stable circular orbit about the Earth at a height of 3600 nl u*s l33cpe mn*c(y/km.    $\times 10^3$

  The space shuttle releases a satellitt3m7z-9dlh 4o x d;8rqsm-lzoe into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rela;ooq -zt37msl4x 9zdm-ldr h8tive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotab0-2 +xfrrzd bte 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, Fdb-rz+r bx f02ig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth intx otu pvd25)- a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass oxotp)tv- d52 uf the satellite?    s ~    min

  At what horizontal velocity would a (tghanxn ,,1ls f3f5tsatellite have to be launched from the top of Mt. Everest taf xt 5nftgs 31,,lhn(o be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mul18soq r*3/ ut 9mtymission, the command module continued to orbit thqto8 9t lu*yrmsm 31/ue Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pl709 hzyk, oi bdymcml3ji38 e0anet. The inner radius9ykh3oy ze m3bd 7jlm,i0i80c of the 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 4bl amaf6au 9 gdxqb5;p7-8iv in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to hxagb8audl4p97avi qm6 5f; b-er real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of ahq-yjo*ayiumbrr ..s4 o 47 js9a-t6g 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle4 *m7r. -jsthoa. 6usgyjiq ro9-4bay (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Tha2wkjl,n poz65 h;l,sey are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the52 la,kswjp ,6z ol;nh mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevatfs /86r dzxya4or that /fray zx64d 8smoves
(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 corls je )ylto (+bne.+*3swzpu4d suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. (u 3sb+e+oz.wt s)jlep*4ynl What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface x i(v1e:7g j5 4gqqwxzof a planet with period T , the density (mass/volume) o5(gqxxq 7e1vjwg 4: zif the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to d w-b:plq o3*now+2 e(- a++xk r2qb nzhwwlh7metermine the period of an artificial satellite orbiting very near the Earth’s surfe-b-n awr lh: o3+oln 7khw+mb+qwp22(wzq*xace.    s

  The asteroid Icarus, though only a few hu +w:fsco ch0j*ndred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from :sch+o *j0wcf the Sun?    $\times 10^{11}$

  Neptune is an average distance of)bv+c3 qw;u mka7a m,b 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 yeara .fecg2 3cbx;s. 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 th xfc;2a3.b cgee nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of t: q+y0 oxtr5sshe 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 fourt ykurb+lr;:8sll9xa o* r 1;r largest moons of Jupiter (thosl*x:bs8r r 1;y+;trkur9oal l e 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 known period and distance of the Mb e ,svzqy5g0ef)6ns ( cn9rw,oon. z ,wnfeyc sr05nq9,(gsb6 ) ev   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s h,yiwvp;pzf )u7,f s.moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to,.fis)7 fzhpp, wyuv ; 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 cyxkyh95i zn fmw7q+)-onsists of many fragments (which some space scientists think came from a planet that on9yk7-n yq) +h w5fxmzice 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 jmqo/b/x9 i/i an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitanji/ imbqo/x/ 9ts 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 days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fi aob r6(l(,(1kez yasdifo 24ug. 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 lowesa(ds ubl((ryok 2 z,o4i f6e1at point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earthlj+xycd 18 t:g2iib8c ’s surface will the acceleration of gravity be half what itd8:8 ilxcb1jgi 2c+yt is on the surface?    $\times 10^6$

  On an ice rink, two skapz j7onuyw fr1)zaps/ (f :8zl77an3dters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one aoz 7nf:/yr la8a)unswf(37 zjp7dz1 p nother?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity aryxv a)s:kz c0 2*beo.t the equator is slightly less than it would be if the Earth didn’t rotate. Estimate theb. :azry20*vo k sx)ce magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrafte.1doyl9ih.jx r/6rj traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pul.j.oe 9x/l yih1d rj6rl with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whex (.xyk).5rxluus p,qvv7,t6(mte (ql t;cd gn you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration o; k)t,x x5 .v6 , ed.qsyvg(7prq(tu(cllumxtf the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat.ztn7)s y p.dte about its cent yd.tszn .p7)ter (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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.a,ce9ets h) 6x 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 plane ,j9r0 c jmisqyq)y,g0k2i+rqt in terms of its radius r, the acceleration due to gravity at i)i+ crjy j9yqq qgm 20ski,0r,ts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from thsp5g6 gw 6srd9 l1y 8mp7uu)jae vertical by an angle pu69gjd)1py8sgl ua rm675ws $\theta$ 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 6-c un09fv 1hw zltgjb 7as: do3ltj4;speed of If the coefficient of static friction is 0.30 (wet pavement), at what range ovtsda u4h-: fo1g0c tl l7 ;bjwzj63n9f speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast may.1yg8pa2 op7 sc2dthat objects at the equator were apyca8smp2 27 y1 d.opgaparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8 /65e3*khpv yzp s-nkj.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 r cd-10cmk/76peg /q a 5ebktpof radius 235 m. A lamp suspended frompcpb c/gd5 k-7/tmqaee 1r60k the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been clfrd-n 4px h/ 918dv8v cw)egesaimed that a person would be crushv s9ev d1freh-n)8wd 84gx p/ced by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Te agzit9+6xis-b9e-5i:w z nat lescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black ho-i+6:bz9zte a axwit- 5n g9sile (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 il6 4wt kdy,r1pt traverses the 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 the driver feel heaviest? Lightest? Explain. (c) How fast can the car gpktwld64 ,ry1o without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelli :8zq v0whzwo4tes 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 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 mqw vz :4oz8h0wiles [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 (5 m-lms 5u0uciNEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . 0 li-m55ucms uEros 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 need *f5 tmv fnxhpz-mm+5j*z j)ru5w2t n5of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behwmj 2nfn5- t pv*f)zx+ j5rm m*t5z5huind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance fe- *s;t4q pq:qim )hgj gj/aa0romh-gptj:/g ;sjq q i*aea0q4)m 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 would need to be if you could actually "f z: med.n86xqhsuqnyv * (w37xeel" yourself gravitationally attracted to someone near you. Make reasonable assumptions,s e7: x3nhqdy.8x n m(6vuzw*q like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46sf-w n/rpg8a11 n58(vs einrn) at a distance f1n 5-rpnr1 svie/( agnnws88of about 30,000 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 eaf43p ,+ emxt qmo)f*v*5*c+ mjzcttooch side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sid*fm+fot 4v3co 5mo t ,m)*+qpzejcx*t e of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 559fhz50v zq.huyysp6n y:fe(9 00 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of a;q+ roz0wng, r7k c3uthe 1.5-cm-long sweep second hand on yourrc,+a3zwok;qg07n ur wrist watch?    $\times 10^{-4}$

  While fishing, you get h ;ur3;vhtx5pat 7m.i6qp ,j5s wy 3ambored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. Ta5hxv6; wq r 5p.3pj,i7;tmyutah3mshe 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 ld qo:ecc2i95 highway is designed so that a car traveling at:9lco2de q c5i 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 t-okm b 0lmymvjm n3(*8ilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the frictim( b oj3*yvk -mnl8m0mon 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.$\approx$    $\times 10^2$