Sometimes people say that water is removed frcb4drw jh0p;u48.u rlrdl7x .om clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wx.ulhuj;c b87dr.r0 dp4r wl4ith this statement?

Will the acceleration of a car be the same when the car travels around a s x jpzck3u*kf:y810e wharp curve at a constant 60 km/h 8fux :0jkezwykc3p1 * as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves fj b -4xr9jg0c099-wxt8kpj98t x kq5dqg dix at constant speed along a 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 the bottom of a h g9tt 0-xjgq x95rxk bfwkj8 4ixpd99dqcj -80ill?

Describe all the forces acting on a child riding a horse on a merry-go-roun: ps93 ,qqsw2m 4k4dvzir6qjjd. Which:9m2vjs6k,4r iq3sq zdwj qp 4 of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled ini eku351 esdd1,q nfk. a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaesk5 qde.i 31dn1 ukf,in.

How many “accelerators” fpih+h r3)q 1 ;nsp(jzdo you have in your car? There are at least three controls in the car which caiqfr h;)(jps3npz +h1n be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying overtp38iw- vbbc,n05 )vgnv tw-q the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled dew-)v0 vv pitb-w q 85nc3tg,bncrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean mf b*23,c+c +qh 3yd lbiw8oqlinward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankihx2rh;. n2rd )d7isoj ng angle given its speed 2.;nso 7j)2 rdxrdhihand radius of the turn?

A girl is whirling a ball on a string arounegdm 46xkr l*qmn8s67 bd.w:pd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit ar w d.sqe*b 7lmp:d 8gkm46nx6 target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how: yfv k:i yu::z*3pxaw large a force? Consider av:y*uk:zy:fi :w pxa 3n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubv-zn;;5 2tusqniqqw4,7 plcvle what it is, in what ways would the Moon’s orbit 4 -wtqu,qqi;vc n;zpvs25ln7be different?

Which pulls harder gravitationally, the Earth on the a s.kx01 ycll,iu/x23qdv,ps0 7 biud Moon, or the Moon on the Earth? Which acces3 ix sx p/k0ubvy ,d0d1,2uiqll.7 aclerates more?

The Sun's gravitational pull on tl emtj*qwt6aj g*s( ,g,-9acrhe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gr,sm (gawj ral q-96,tge*jct* avitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are anl8:0 9+. wcfu)dw v0(r9axuvw b ncuft work? Do they v) c nu +rxwu db:(vn9fa0uw.8 w9cfl0oppose each other?

The gravitational force on the Moon due to the Earth is only about half oi0hn 6bu bpxi- gdrjy)7o/1a)sj /,ythe force on the Moon due to the Sun. Why ii/y)/jxo) oyu1absij7 nd0rb gh-, 6 psn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around thx* rmb0cmmiig qj(8 8*e Sun larger or smaller than the centri8i gmijc *8rx0mqbm(* petal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east ohk 7 cjf/pi.uy8;v 54el *-z6igjwfqyr (b) toward the wesf; jqi5yfkhjpv.g-6e87wi4 zcy *ul /t? Consider the Earth’s rotation direction.

When will your apparent weight be th,b c5g- wief)ae greatest, as measured by a scale in a moving elevator: when the elevator (a) accaeb)g5 , wc-ifelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected by ; t(vay .y ctu3b*,amcebn y02gr:5*oatj 9gfweightlessness. 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 a t; a*af euocyyb325jg9tbyc:g vnat*m0.,(r spects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent wev8/0e b ,lp .ctzt( cgk;xilz0zd1r/eightlessness” between steps tz1zlez 0 ./vbx08cget/rc;,ikd(pl .

The Earth moves faster in its orbit around the Sun in January than in July. Ig c* vp0fvbp8*p e1y8ks the Earth closer to the Sun in January, or in July? Explain. [Notefpcv 1b0e*gk8v *pp 8y: This is not much of a factor in producing the seasons — 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 un06 m5tniwmp ;dtil it was discovered to have a moon. Explain how this discovery enabled an50pmm 6nw; idt estimate of Pluto’s mass.

  The Sun's gravitational pull onsaet1 st2d1cw5 py) fd)pm3r n- d5l. nsg-hc6 the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the ctwg6n1h-edrlaps3c5d51cd) ns-t)2 s p m.f yenter 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 1980d cmyd2zj3p3u5 /4eu b $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleration1bnjb,0fo a1p m,ms 1z of the Earth in its orbit around the Sun, and the net force exap11m fb10, nomsbj ,zerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210ka5m h49a5 a0p;biz-i.2hotvz2abl r N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius vr2a9oi. mlzp 4t2; 5zh kbbah5ai-0a0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in nwr. 3t0h vv ug:7/ykkorbit 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 gravitational acceleration at hkvg37/t:w0k uy nv.rthe Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edgyytrh05/ eoqc ljf ;+0e of a potter’s wheel turni0/t;r 5f0lcye+y hoq jng at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratm,d/ r w g//dew;fous(e in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speeum/,;d drfw /gow/s(ed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn:* .guvor-cl d of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass og *u-d.c: vlrof the car?   

  How large must the coeffic xgty5olm)u8)m *f vv)ient of static friction be between the tires and the road if a car is to round a level curve of rau m)) ov5g8y*x flv)mtdius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fig ,z0l,gx d2(bkrwuytww j6+7 thter pilots is designed to rotate 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,, g(uy6t xbr dltw,wwk02+z7 j 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 a rotating turntable of variab uw f,2t3ye ypjkt+5iuzzn/:(v wir5,le 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 thi ve3ty5rw uzwkjf2,:z+nyt( p,i5u /e coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller97rnsv :t,z0l *j0gq bdth4u v coaster be traveling when upside down at theqbur0vttsdnlg,z *4:0v9h7j top 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 mass 950 kg (including the driver) crosses the rounded 17iqr* / tfznzx8e ,wntop of a wxe7*,8 q t/i1znrnzfhill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferridvz,s 92.h oon 1x8qvss wheel need to make for the passengers to feel “weightless 1nodo.2x9z hsv sv8q,” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rhw9wg3:j4m hzotl93:7 ntzgm adius 1.10 m. At the lowest point of its motion thzwm93tgmhl3:j n47 :9w ot ghze 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 cen 0u0w3agqie0w trifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 1100iq 0gew a3wu5,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrical9y v iin9wd6tzw;1 b4gly walled "room." (Sez nw4wi ;61vgtybi d99e 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 ) isd kxx+t)8f 32yc/5osd r:akdw rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit byo3 d dy5:/as) rxw2tfx+dk8ck 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 tiiv h348eiu7ig me, by not ignoring the weight of the ball which r8iieh iv3g4u7 evolves 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 perfectly banked for a car traveling 3x9wdig l.pairos3u.v.zt *675 $\mathrm{~km} / \mathrm{h}$ , 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 j-d2/bvk i;-0m;gsxa f xurj9s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving verticallyq*bd)jr lx/u 6a/mvxet w v+)4 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 c3; 1jumpbvaj) /pog: oentripetal components of the net force exerted on the car (by the ground) in u pbao;/p o3:)j1jvgm 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 uniformly from the pit area, going dn)c99ti 7zez/ er .cafrom rest to n 7/cc9e.9redzai zt) 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 slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Atw . r*td)m*efx a particular instant, its accelerationt)*. ed*frmwx is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 0 bhm9lcg; ,ejn*or5iEarth radii) above the Earth’s surface if its m9 ;5cg j0hrlm,in eob*ass is 1350 kg.   

  At the surface of a certain planet, the gravitat7h 6rdlzx0hf*zw km7k bqz:*+ional acceleration g has a magnitude fzwhdzklb:**mh76rz + q0 7kxof 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 accelerae-fblp(ch j43 i3kq2mtion due to gravity on the Moon. The Moon's radius is 1.74 l3 (q i24mjf-pchebk3 $\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, but has the same mj 3:87 xsyao72sirma7*swux oass. What is the acceleration due iox x77*3su7 s:aarj mws8yo 2to gravity near its surface?   

  A hypothetical planet has a mass 1.66 time/gi;tm yzt )d 4og-u sv*mdysbg,3 /9us that of Earth, but the same radius. What is g near its surfaco9),yvbgm / ys tt g*d4z3u/;dgsmu i-e?   

  Two objects attract each other gravitationalltn-sn p:)b3 y*+h hqowy;6fgfy 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 v)v7zbah )u/ud 5ndqk ,alue of g , the acceleration of gravity, at (a) 3200 m dh)u5d7 uq)n,/ a kvzb   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center totrutju+n)iia, 2 uy622xl27 ;kyfm ip a point outside the Earth where thegravitational acceleration dut+i x6 22i, urtpi;7 na2lj)2umkfuyye 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 Sunpb24 4 bm5k1nwq;dete packed into a sphere about 10 km in radiusdebw5k4tp nq1bm2;4e . Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butioyw.k8dg :n , 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 star d8oy,:ig .kwn?    $\times 10^7$

  You are explaining why as ),m1 -*m(r.8 jfnyswpqtp4vyjocha 4tronauts 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 bjs)q(.ar nmwp1*-o v ,cjh 4ytmfyp48y calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locatmi.gga-b(ay04e ksgr,- m2* qe1w j rqed at the corners of a square of side 0.60 m. Calculate .q*wm,qe-yg gki rm4r 1s0( j-2ge baathe magnitude 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 ) nbsabyi: j5zf0d7u- planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and yj7bai5 0dsu-znbf: )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 gravit5e f+b.(keplr y at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determi.( +e5lefkrb pne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Evcl+vag;(66jxfk9 pa, li5hrr7e dr0arth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawsc6r 5xf,v viljr6(ra9+0l; kh gaed7p, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a )u1u3mc 8cgvhq 9nc (bsatellite moving in a stable circular orbit about the Earth at a height hu uq9vn3cmcc( g 8)1bof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th,h1 hdsgi5sx vel959:14s jhi ch s(nk7zyao(e Earth. How fa1ysvs4djh:,aokz i9 hhssl5(5 xe g(i1h c79nst must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricaldkc cxtn pz k1:9 qta.s+g5-y6 spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume theycx15 :gd6 cqa k n-k.+tp9stz spaceship’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 satellih- lvvxlj*:l p6tci 5)te to 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 small comparedv lpxi65tlhl *j-cv) : 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 t.nn5q +q,aq1jkd7a bfgu2h ::hp m y9 3g9kblphe top of Mt. Ever+ 1ha h:d.qb99j nablq3np5kf7 :q gk2m,gyupest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to-kqhcy2thsp / ;,eq4g orbit the -g/se kqhtc,4hp; y2q 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 orbitl+ , c.rntj5nq the planet. The inner radius of thel rjt,+qnc. 5n 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. mq7kzkj8sac(w66g w+5 s (see Fig. 5–9). What is the ratio(g8sa mcw6kw+zj q6k7 of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75b+k4;vn/+f i ht gr207kkjh gw-kg astronaut 4200 km from the center of the Earth's Moon in a space vehikghgr2k+j +fkibw 4n0 ;t7/hv cle (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 ofppzotwmg m.5 hd+bv4sl7 f4vs+qv ,1 / 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 pmd mzohv .q5lbf4/wp+4v1+ ,svtg7 smidway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator th vrb6..d /;t:tq0.)ug c 0whyuxy wcogat moves g6 0 ogwuv dwc . .q.;)xuy/tbrhc0y:t
(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 fromah -5;i 1ivtxpvko6o) a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eleokx ;a5) ovi6pt-i1vhvator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a-8cca70zr5ne+ f)xzyg1ijpw4 o 1ywa planet with period T , the density (mass/volume) of the plgz4w o15 7i1 xyc0-)cyz8na+r jfwpaeanet 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 pj-y12 )tiww u(27.4 d) to determine the period of an artificial)2 pwiu1t -wyj satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th9eo 8ub qvhu;k9op,(re Sun like the planets. Its period is 410 d. What ,9up (eb o;kr q9uho8vis its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average 1igv+3t+iedz 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 onr0d vjc*) -)p+ fregwoce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39))gr+-rjpvo d f*c0w) e. Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy.vfeco/jy0. ,rtau y5p t*-n d $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,g m js aj:; ov;d28yn3ss2i/qa and mean distance for the four largest moons of Jupiter (those discovered by Ga jga:ysm8 s;aqv 2insj/2od3;lileo 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 i pgp4b(86i nuthe known period and distance of the Moon. i nu68pgipb(4   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using K ds(ld:-st(lnpexd. lj 7+2ob8g0l mwepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare7gx+( o8tdn .m2sbp:dd (l-jewsl0ll to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists oz8yy 5hh7r- t 7qo l4n50nfdr5 xbzp/vf many fragments (which some space sy55y07no hfh74l5x dr pqv-bz/n8t zrcientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form e x bl) yv1csjd+6i)6wof a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotas 6c 1ejl )xv+i6)wdybtes 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 gorgi,6 pyz,4 i5t dmln ur)*rhys,e by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable yd)lzh ri5,t ,6ri p,4*un ysmof 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 surfac 7z-b apv *d:uvj*ok e/qh97zpe will the acceleration of gravity be half what it iskvp7zbq/ h*ejua -: d p*vzo79 on the surface?    $\times 10^6$

  On an ice rink, two skaters of:z7 t- 0rmb-bqk9ur 0sc8dos4 w7bup u 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 pw-zpdmsqc-8 07bb0 ur:u9 r t74uoskbulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent 9l5q2pfzj7w sly5b1 b acceleration of gravity at the equator is slightly less than it would be if the Earth didn’tjlbqbz fw75l1 sy92p 5 rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spaceeqinz5s+3:0skk6z tikq .n 1bcraft traveling directly from the Earth to the Moon experience zero net force because the Eaqzk st siznn5k6b0.iqk1 3+e :rth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on p8qm, k6k.:1bg(clm bqe3 jnza bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dirb e m6lpk3m1.kz ng:jqq8b,(cection?     ----待选择----upwartddown 

  A projected space statifd/raqit/0 b. on consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the su d/ribfa/.0q trface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircr2 / .g*32hvd(ria9eyt tyopaa aft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms-/ t:und+f() pgai.w .edmv;:letecn of its radius r, the acceleration due vt d-.mn(.de;tgp:i:+ )wc eleaf/u nto gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is r3o8ge1rrn0d3 qzau*jy 3kq;deflected from the vertical by an an3*qyaor3rj k0 1uzg8eq3nd r;gle $\theta$ 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 coefficient of spqwrqp iy ooki77 /8tt u5-.-rtatic friction is 0.30 (wet pavement), at what -iy 5.t-k qorrqwop p8t/77ui range of speeds can a car safely handle the curve?

  How long would a day be if t(9wdle xw6 3xbv;sw p 89v7d+vacxc7qhe Earth were rotating so fast that objects at the equator were apparently weightx69 ad9 vc3x( 8 cvb7ldqs+wwvwpx 7;eless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.3a-vz eq+4 znt0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A63qyr vo0* t0y/xksnw lamp suspended from the ceiling swings out to an ay6 swr0no kyxv3 *qt0/ngle 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)m(.re wgos 7bo7u5g +zze nj. 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 equator of j5 bnz7u7gr m (s+ wgoe).e.ozsuch 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 presenceigis:yi8v,0 z of an extremely massive core iyz:i vg,iis80 n the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the h5qgmko 77v;pe 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 5kqog;m7v e7p 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 losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utiliznh/rgjynj )0ww1( trnh t4 r;+es a group of 24 satellites orbiting the Earth. Using “triangulation” and signal+(rhn )rjtnwyrwt j0n;h/1g4s 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 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 bilkrn vure0 ypq)u ss4gt h-;of+ 0;3ml5lion km, is meant to orbit the asteroid Eros at a height of about 13;usr )y+kglpe; mofu-q4 rv tn sh0055 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a,0 lk e+xfj5sn satellite in need of repair. Youf ex,kls50n+j are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distanc4 vh-ai 3jg-re+ 8pmhle from the Sunli+3vaep-rh84hj - gm?   
(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 lunljs9f391y actually "feel" yourself gravitationally attlsn13uf9j9y l racted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cente)bt(h9kt dw4l ne s5 3rstd5y87kfp+t r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ckp 7tt rhd4ssfk(35+e n9)tlbd5t y8w enter $ \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 ofs+8yiax7z 6h+4 r fad8nypi4i a square 0.50 m on each side. Find the magnitude and direction of the gravitational forcenya6ia4si 8 p7zf 8hri4x+dy+ 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 nf6u 9ybi6g. sndqh 5*5500 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-lwz;6ewtet.b kdx( p., ong sweep second han.wbt.6;dexp kt(wze, d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and stap4 i zb t./tb5i;+jhfb u-gt5grt to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cg5f i.gbp jb54 +it/zhb tt-u;ircle 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 dejzieo g l:z9/+aep+ tk/zi2m h6c7o6nsigned so that a car traveling at9ml 62j+opogzztk/i ca hne7zi+6/e: 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 when negotiating;iy .t3h+fgu g 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 friction force needed on a train passenger of mass 75 kg hit.;g gf3y +uif 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.$\approx$    $\times 10^2$