Sometimes people say that water is removed from clothes inw7spabe0z(f0znn3u. 6 pe8jx a spin dryer by centrifugal force throwing the water outward. What is wrong with this (pzea38npzb 0.7f wj 0s6xue nstatement?

Will the acceleration of a car be the same whzday *0gxi9w, en the car travels around a sharp curve at a constant 60 km/ dia9ygw*, z0xh as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves z8j 05 ovo :xuf0u1vzuat constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at th :jou8fou0zv zv5x u01e top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry0fv. ahg i9 g6g6zbfv.7r 5fu5xrza+e-go-round. Which of these forces provides the centripetal a6zrxgv0bug+v 9ff75 56gefrhz. .ia acceleration of the child?

A bucket of water canlcw.eo 6leq 4, be whirled in a vertical circle without the water spilling out, even at the top of the circlceol 6we ,ql4.e when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lea4bvgy b-rl , h:c/,jzqst three controls in the car whic,h jcrbz:q-gl ,/y b4vh 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 cyq 6s;devlh;*rest of a small hill, as shown in Fig. 5–31. His sled does not leave the ;;h q6yes* dlvground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve a o 8z7fp0 cc)3gp fczq o.+d5mfgn.4kpt high speed?

Why do airplanes bankm q /uuh6+pkun/ lf(vd32lon/ when they turn? How would you compute the banking angle given its speed and dn (luf3/2 /qhkuvp/mun l6+ oradius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.ony+*s 9rzf -kz6ej ynq/j( q4 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. Whe*y-yezj jknf + ( /szr946nqoqn should she let go of the string?

Does an apple exert a gravitational force on the Earth? Ik qfdo:x.g(;mw6a .yj f so, how large a force? Consider anm g(:fwqyk6ax .;jo. d apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is,bfah( bwdw vm8c kc+)k z(fv450jp9h 9 in what ways would the Moon’s orbit be differentd9w(w c8 b c)9 hjfv4pafhk zb(v50+km?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the 3pi1kdwzic+g.c1* q.y eya j.Earth? Which accelerates morei dyc. eacyq 1gwpz*k1j+i..3 ?

The Sun's gravitational pull on the Earth is much larger thao v:ga1vh949 rtm xv8ih, j9ygn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in g 1ivv :o ,g89ha rx9mjvyt4g9hravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whtb o2 yj+,pj8iat two effects are at work? Dj ot ip,yb8j+2o they oppose each other?

The gravitational force on the Moon duqw2mb/h:p7. s1 l jef1c0reej e to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Ea wes1lchj2f bmej :e1r. /7p0qrth?

Is the centripetal acceleration of Mars in its orbit around the Sun- v))f2)1zf6afv8 d m bfoekomh-ny i* larger or smaller than the yko h2fa n 6 v-)*meziod-fffb))m1v8centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the ea*txoap6t n/3: ao3w11ejv+ukyihmu ( st or (b) toward the west? Consider the Earth’s rotation direy+( *ju6xemu :p31thwot1vaon a3/kiction.

When will your apparent weight be the greatj5jgyt5 nm74ly8kst ;* .qdwfest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) iq.*kn fw8 ljy 4 tjmsdg5;7ty5s 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 coobjddb 6afi9; k:jznp:.f 3.g uld 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). jbgj:p9 dnb3.o dzk6i aff;:. 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 experiences “free fall” or “app.04)r *cxtnb 5wi(iay7 tiixtarent weightlessness” between stxiwc (biyxt)i7 0*5.4tin rat eps.

The Earth moves faster in its oa .z6ys0y:ln 1oqdj +jrbit 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 — the main factor is the tilt of thez+ja01 lqon:yjsd .y6 Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expl3 n2v)s bwpyv- zcm9u3ain how this discovezvcnmb w-)9u3s23v yp ry enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much large vevq8mr0 ,5*,srhjk5 j jflv(r 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 tfh(v,e0m vsj*lj5 q5 ,8rvrkjhe other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 vym.a xpw/du(9x +b 9fgr,x5dsy a28m$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in it , *ytsfakox54p:adzo. uqb: 2s orbit around the Sun, and the net force exerted on the Earth. What exerts this force on thx5,a a42osp kybo ftd.z:q*: ue 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 f,5l,cxxopce3 h m+4t d )wfw5on a 2.0-kg discus as it rotates uniformly in a horizontal circle 4h lmfowc ,wx+ct5 pe,5x3)fd(at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutt cll j) v7woe*up*guclw,( 8y,le is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitatio,pcv ,l l) c8g*eyw7luju(o*w nal acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a phiu*8nez 9 z hq9n ;ln2b;7ayootter’s wheel turning at 45 rpm (revolutions per minute) if the wheel;u8n *b9z qo e h29hz7nlina;y’s diameter is 32 cm?   

  A ball on the end of ;+dhetgqtml50:a j* n a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 g:0;q*tjeh5anlt d+ m $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a t;iandco r3cai8l9 v/i,. 4nzaurn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this r co, nialz3.9d i4vcr8 inaa/;esult independent of the mass of the car?   

  How large must the coefficiens9*w a k;sx3s+ ez2tg cy2oci.t of static friction be between the tires and the road if a car is to round a le+ ss22o9*cskzxytig3.;ec aw vel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astr mkv;ej5 6e 1 s6pnbvh0kwltq0 qe5;k2onauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle eb; w;0plteqk 601ehs jk625 vqnvk5mof radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of agy ns0ayn-( zus)b /n/ rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coeffici/)zb0ny( s-/unga y snent of static friction between the coin and the turntable?   

  At what minimum speed must a roller r:l ,;h2mc uiicoaster be traveling when upside down at the top of a cr h2l:uc ;imi,ircle
(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 roup 1oosn nlw,7+nded top of a hill (radius =95ns +l17o,pn ow$ \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-a1wqolxrk 6at +l7b6k )5*qkim-diameter Ferris wheel need to make for the pas wa5l kkalxo66*qiqb t )7+kr1sengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertico- ros +.3cds4xfnd) ral circle of radius 1.10 m. At the lowesss-.3r4oc +)fnord d xt point 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 centrifuge rotate if a particle 9.0i+6))o8 chqoeotfsys3v qr( )0 cm from the axis of rotation is to experience an avso+isq )) 8oy3to6q )ec(r fhcceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rothrlge7uq s61 9wtwhc mj376soz -n 4j(ated in a cylindrically walled "room." - r(wc7ljj3 he sgtw n7mz o1squ64h69(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 pkm 76xc4erc1tf 1ycq).w,tl a circle on a frictionless air-hockey tabletop, and is held in 6tr qfk1ccx e,w4 1l7p.m)yctthis 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 not ignoring the weight of theym99 bkor4g2 cpe cr2fo:8ad: ball which revolves on a string 0.600 m long. In particular, find the magnitudc rdk coe9gr fm :p:2o8a4y29be 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 : xo,gofzb v*fg5a9l4 is 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 masse;p;zi lp13mm c s:j.uks $ 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 div3-bwb 9nhbeqxn qga6 11fgz)0ing 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 on7 w z7:ufptxky.:g qo+ the car (by the ground) in Example 5-8 when its speed is7::pzu fx+gq to.yw7k 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformlyu :1.5xbx.xlx7lct ed/uzu q 4 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 the road to provide this acceleration with no slipuz:4x/. xlb 7.uduc5lxqxte1 ping or skidding? $\approx$   

  A particle revolves in a horizontal circleh tme;x: d4:biyp+ek1 of radius 2.90 m . At a particular instantikp e+t;4:m1xd :yh be, its acceleration 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 ocu6j /b1d n :x3s0( h)pss0ejygoylk 0f Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) a061j sxyhg oyk 0enl0/psbd)c :(s3u jbove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain pj)j rmmyu;rh4e:7 k5 planet, the gravitational acceleration g has a magnitude m;rhj 7:4jey)5r pmukof 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 accelerationj-2i2roc n0zy due to gravity on the Moon. The Moon's radius is 1.7jyr 02 izn2-oc4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth,a r6,k+ :-4ubs xifafpmb9*u a but has the same mass. What is the acceleration due to gravity near bm* ixraa usp+6afk 9:b, 4uf-its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, )hj1fp wtb/w1mx) n* qbut the same radius. What is g q)*bxh1wmnt/j1 p wf)near its surface?   

  Two objects attract each other gravicy.orgd4pl n g8*w.)ntationally 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 vax dt1s,;kc -kmlue of g , the acceleration of gravity, at (a) 3200 m,dk-;1tmx ksc    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centa*t -,fa 6pqlw *dg8laer to a point outside the Earth where thegravitational accelerationl8*dg *qfa lwa,pa6t- due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron sta28 4e ;yy-kvecxr rx;rw:hie;r has five times the mass of our Sun packed into a sphere about 10 km in radius. Estime:vrew- ; ei2;k8yxxhcrr4; yate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like / ul5,6nsck deour Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this starsu de5n6clk,/ ?    $\times 10^7$

  You are explaining why astrona9)(. bxlhwdkk: m dxfu0ty/0 uuts 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 in teu0f k khx(90d/wbxtd :)l.umyrms of g.   

  Four 9.5-kg spheres are loc4lj nm,4 5.e*xyifrpi ated at the corners of a square of side 0.60 m. Calculate the magnit4finme 4 lypr, i5*.jxude and direction of the 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 the same)pwy :qp oi/a8 side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The m :oipyaq8)pw/asses 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 4(srlpf :ziw7 /.vyd/mx 7 heigravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass ofp7le/y w ixfv .sh7(4/id:zrm Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eart*ciuht il9b)t 17:i uh csb-3gh and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]:l9b*- thgcii h1u3bu )is7ct    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about tnv jnn n5+,:clkhh1j 9he Earth at a height of 36 lvjn1+h5, hc nk9nj:n00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above1g 7ia3wsue46x 9npje the Earth. Hp61un j g exs43w9i7eaow fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyozl1jvvs7 c. ) zphy2-lindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the sph2 p.lyzvs j7ovc1-)zaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite tt1ca h 03cs(luzg ej:j71lr. lo orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very sma 1a j1ehzctr(l0l 7ugl.jc: 3sll compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from +o/by (pg5i4l;d4tbfjd a2sqy-3vh k the top of Mt. Everest to be placed in a circular orbit a2olpkyd qgh+ 4;ytb5d4a-v ij3/(s fbround the Earth?   

  During an Apollo lunar landing mission, the command modrf 1k5g :m+a ha7ieqyo0;/pbdule continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once?aqhap mkfg/dey57o:b1i;+ 0r    s

  The rings of Saturn are composed of chunks of ice gg y;deqe;-0mnm 3ub-vei46nthat orbit the planet. The inner radius of thmiye g vg-e 4dm;q;063bnn -eue 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 Figbfs;i1z7 x *f czbsrx0t+ el96. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, a bl79 x +b6f0tczz r*ex;issf1nd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cent /g1fh .aadzp/*p 3bvwer of the Earth's Moon in a space.vd3z*/abg 1pawhp/f vehicle (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-/5ox myc: eh18z.zplsmc;j :tstar system consists of two stars of equal mass. They 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 the mass of each?tezm5 h.mz1 / p;x8lscoj c::y    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in anngbsjpq:3-n 6yvu9; (bnbxn( elevator that mov-6bxnbnsnygq3( j9bn:v( pu ;es
(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 fr5kgq5 1g.ucup0hb7hu om the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elev7u.p05uh ku5hcgg1bqator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planpdoys;)7s zcg1 2xfqw4) m e:tet with period T , d2two4qpfz;x 1 m)c7se:sgy )the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (j(k113pua6fb /cswul 27.4 d) to determine the period of an artifi u3(f1cak6bjl/ psu 1wcial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the f p)r* 66o)ljxo xqh)vSun like the planets. Its period is 410 d.lor p xv6*6))hj)qx fo What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagfy qwfk2;zkh-yr4/ +y e distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close) 87daihuy n sll2o w509hlnb: 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 l5u 0nw7hil98)lybshdn2: ao 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 rrb.1o 7uol;z the center 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, piwsg72 ( cdwg yf.)b)xeriod, and mean distance for the four largest moons of Jupiter (those discovered b by))wf.g7 c 2wdgxsi(y 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 b:*.vb5n j hmpand distance of the Moon. v:jnphbb 5*m.   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of J07r aneq5)uopupiter’s moons, using Kepler’s third lawu5re0)n7oqp a. Use the distance of Io and the periods 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 Jup1 ,d*gcfp o,foj:spm 8iter consists of many fragments (which some space scientists think came from a planet that once orbitedd1m , s:,cjp ffoop8*g 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 descr wod ;,unrbds9nc i..r6rbe)7z b7x;b ibes an artificial "planet" in the form of a band complete busb.ie6z)wbd 7d n;o9,b n. xrrrc7;ly 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 days?   

  Tarzan plans to cross a gorge by swinging in asq phz )io+-8ln arc from a hanging vine (Fig. 5–s lihpqz)8- o+41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity/m/lv kzky1w7 be half what it is on vmwzl1k k7/y/ the surface?    $\times 10^6$

  On an ice rink, two skatedm6max 5:)k war4ylvl6 /.inwrs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are e/nm x54r:av d6aykw6mw i ll.)ach 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 accels7l.j9 agc .ereration of gravity at the equator.gaeslcr9 .7 j is slightly less 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 42 y7wzakl2v cspacecraft traveling directly from the Earth to the Moon experience zero net force because the Earthk42wz c2y7av l and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand ovq+1bip /i:o ;wn3p esn a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direct1bv; wsi : 3o/piqp+enion?     ----待选择----upwartddown 

  A projected space station consists of a circu73g-lnf riwt cns2k-8 lar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter ofk8 gnrn7cfw2l-si-3 t 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 airc )x isbc.ksp-9x(l3 idq9 v0odqc j)* qhcaf5-raft 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 ofyqu46 tsob:q4 c62jdg 0al)gx a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational con44uq sj lxdb0g)6q2ga ot:6cy stant G.

A plumb bob (a mass m hanging on a string) is deflected fro( i9lobuej.lx 5,ttk *m the vertical by an b5 ltxeoi9 *ku .tj,l(angle $\theta$ 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 If the cor/uku2ut8cm+ l1*y 37m av ozmefficient of static friction is 0.30 (wet pavement), at wha/a u 1k2t*uo8yrmcm7 vlmzu 3+t range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that object9t65hn 3glqv s)kr:bls at the equator were apparently llknbs6rhq9:)vt3 5gweightless?    $\times 10^3$s

  Two equal-mass stars maintain a consz8r8 ul-5sq0eou r1g ztant 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 sphbgfr6349y 4pignb g8d 8(fly(g2s apeed rounds a curve of radius 235 m. A lamp suspended from the ceil8il y g4d3bg6bps n( af8 gh49gyr2fp(ing 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,(j i k- fbvybm-qh6wx)r* 8jn. it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the eqb*x .rj8h-injk)y(bqv -6m wfuator 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 Telescope deduced the humw9m)r .j hz4 8n+ws,jma8ypresence of an extremely massive core in thej.wnw89ya8m)shm , 4+urz hjm 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 hp: mafsw,l5c zj89c;p ill 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 c;p5,8 fc pas:l 9jwczman the car go without losing contact with the road at A?

  The Navstar Global Positionintrisjd.u *oa b 8/uckk8*imp 5l /2nah 3,cr9tg System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed ev9pa8t3 /jal/m,h obri 5r*ukc*s udn2kt .ic8enly 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 Rendezw f lya)uy19)wvk:0jm vous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros iufyw j 90) w):may1lkvs 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 purf)x u yq3xg-.rsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abo)r-xx3 q .ufygve 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 ha(kky/2 xhja 3flq, x,qs a period of 3000 years. (a) What is its mean distance from the Sufk/ x(jxayk , ,3qh2lqn?   
(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 "feelm6 /wo6zzlql9w3+ d qxwx914 jgohvo-" yourself gravitatvoz/6qmx1l wo o6wl99jh4w +qdzg3 -x ionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of th3 -qycmy/+i ese Milky Way Galaxy (Fig. 5-46) at a distance of-seyqmc + yi/3 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. ovfo zv2vb ,uzin3k 91,4a((m* onwlx50 m on each side. Fi nbu4k,x*z(f vm23w 9lo,z o(v ain1ovnd 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 square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass *szyvq g* dpu2+- n+9a+rj zmf5500 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 the 1.5-cm-long sweep s z 2ayu;ks7ft8fq2se1econd hand on your wri s8s1eu2f ;k fyq72tazst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swinyd,lc hrsa) 4w.xuk 8(g a sinker weight around in a circle below 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 fald ,w rc(xuy.)8hs 4kishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R hges wm(+z5k r1w1vm:in a new highway is designed so that a car traveling a+5w:(mehmwr gzvk1 1s t 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 the cars w /*slox2vg*n37rsqr yhen 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 r7gl2o*y xq/ vss3 *rnmore 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.$\approx$    $\times 10^2$