Sometimes people say t1pl p2tpt4yqwf0bv;zu33 us 8.bpbq )hat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What isqp;8t0 3u3f4syp2 pbwu 1p. vql bbz)t wrong with this statement?

Will the acceleration of a ca+owxclo+9 a1 ar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aa a9oxl++1wcoround a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wbs4)x-u udz 1ug88ekqhere does the car exert the8)48-xq eksubugz1ud 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 hill?

Describe all the forces acting on a child riding a horse on a me wllq3*y b;hx;rry-go-round. Which of these forces provides th3;yqhl;* xbwle centripetal acceleration of the child?

A bucket of water can be whirled in y+ rvb.;svxhyj7pu) / a vertical circle without the water spilling out, ;xv/pyj)r+ vs7uyb h.even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are a07.nub65l9dp; rezb/yqn iy ft least three controls in the car which can be used to cause the car to accelerate.if5ylp0nb6; e7. by/dn qzur 9 What are they? What accelerations do they produce?

A child on a sled com -i(mmi6:hszfes flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest andmmiz -sif6(h: 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 curvgm wfs9, 64n h)ilxgp3e at high speed?

Why do airplanes bank when they turn? How would you compute the banking a6nn,c /b*ss*i uw8i thngle given its speedcntw* i n8u *,ssh6i/b and radius of the turn?

A girl is whirling a ball on a string arounv2n3kq3n 6zhmh-jb3, i v; qr-npj r*ld 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; lq36vrnn2v hp-k,bn 3zji 3hq-rjm*rd. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forcee 7rsrapjw) js0d* xnjqoiw8;/b53 z,? Consider anjew;bon, ra5s wjjqp3r8s*7 )i d0z/ x apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what aq-3(wn4flb42l *kg h bp8p g oh/t3elit is, in what ways would the Moon’s orbit be differ np2bgot-3q/wh4lebhl 3 ag*4 lfp(8k ent?

Which pulls harder g2p9)e n8d;vm i5xxby2 nzfgo2ravitationally, the Earth on the Moon, or the Moon on the Eagpex9n z5 i2 2vy ;fx8b2no)dmrth? Which accelerates more?

The Sun's gravitational pull on the f(e h3 m33:a p4gxncbwEarth is much larger than the Moon's. Yet the Moon's is3hb4 n3x:pe wmc3ag(f mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What tjd xyry;8z*d9 wo effects are at work? Do they opdzr9*yxyj;8d pose each other?

The gravitational force on thtgsw 8:ngbpa 06l mjhp ds128yr4gd:2e Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from rdy:8wtg 1 2lbggp8: mj a42hss0dnp 6the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger onh-t)zbbps nqn 0hw mt(3v9t6s7 , 5rhr smaller than the centwnqs9n5s7t6mhz( pt)0t bbr n3v,h -h ripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) to(cl:ic0-ga b lward the west? Cca(0igc : bll-onsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as 6a+( fotke/;*ncamthmeasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your wem6och/ t+ e;naft a(*kight 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 pkpv58 rkp):l zyu w+u9,cok;weightlessness. One way to simulate gravity isk wc+) kp;y:up5zu rlk8pv, o9 to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free falq4 y,h7d5k byl-f0/1 m(eoll qnstwc )l” or “apparent weightlessness” between ste1 cw ko0h-/lnf7 lm5q(yy),s4b t edlqps.

The Earth moves faster in its ory+ ;e),el fi7 eekdp )mo1je-tbit 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 the Earth’s axis relative to the -f1+ kme)e j,;p)ey7eeotdilplane of its orbit.]

The mass of Pluto was not known until i*mcgvh+jbn h1 uo8u p5,p/8djt was discovered to have a moon. Explain how jn,j5oh*v h/bupu 8 cm1g+d8 pthis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is b l n/aj+c045zf s,5xy)hgpgbmuch 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 l5byj)p bzns405f,/+gg xca h 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 1cwy r v/fh: 9m5. wi8swnp;l)b980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerbps olg ac3 t3(b*0tw8ation of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Ab 3 cg (ltoastb*8w3p0ssume 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 i 1k :migt -fn7x)5jpqks exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s:)kpx i 7mjk1qg-nf t5 length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from tk a1zn2re+64ew/ojvria5 e .qhe 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 gravitationala +vnr4w1ja./eezre k 2ioq65 acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of q.-1u53ct::. bhvp;5drisuo i ugazhclay on the edge of a potter’s whei v35dzt:i:quphsac 1o5-h uu;.b .grel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string37 s zt1ll ez*wlj9.l(mj0kec is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speedljsj 3el we1 zm7tc 0.lz(*l9k 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 7gsu zm/ ,ipvxqwd*0+ turn 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 of t uvx ,si+z7*/wmgp0dq he car?   

  How large must the coefficie wxojw2vr 905qnt of static friction be between the tires and the road if a car is to round a level curvew j 9x25v0qorw of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desi v2,g;erck (p2cehxvog1t0jl 8*-hn agned to rotate a trainee in a horia ,gc01rpenc;* l evg2ho-t28v x h(jkzontal 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 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 q.3n ij1t, sph: b*twyaxis of a rotating turntable of variable speed. When the speed of the turntabti stq*p1b wyn .:,3jhle 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 coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster u p8nl u5rreky( d xyavk4kh9(4. /5gsbe traveling when upside down at the top /(uny ( 5s49xkkyv4ah85grp er. dkluof 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 kf,svk)j-l aaqoe ls/*n9 3g6i g (including the driver) crosses the rounded top ofs39,agkl6f ioa*-v nlj)e/ q s a hill (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 min 7dn:hw otkr rw7thje2. x*9:sg/v)ofute would a 15-m-diameter Ferris wheel need to make for the passengers 9:w hfn k2rs)wh/xv.:7jo*ttgd7ro eto feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radil qgvjt :te):n39 *o ybrn)kz.us 1.10 m. At the lowest point of its motion the tension in the rope supgqnblt:zne3)* j kyv:9r)o t.porting 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 9.04ac.5 j7 zfspdnc jm54;h01:,aimkt5b fudb v0 cm from the axis of rotation is to experience zs4d5un:mjcav;.bd5pk fm14a 0f t,bhji5c7 an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindril j/p*u9x lz7ucally walled "room.7zlxu/l 9jp* u" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circlebkd-;22fvq buf/k 3sgyxz.l, on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through 32by ubzslfk2f;xvk -/.gd q,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 n.p aeihid ke jss-79f.iv87+m,nv/v, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magi-/nn.ijm 7+v 8v v9 7 ifph.ssa,eekdnitude 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 m7zb sb noe 0vsjq,qha(t3n t50rq8 15i 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 massesg .,flz n)ubfn4a4vi4 $ 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 evasivy5enf 76: dbgge 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 components of the net force exyh/: exe4txw)erted on the car (by the ground) in Example 5-8 when ehtex/x) :4wyits speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acce u1g 2rib8fj;dlerates uniformly 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 t fr8d bgu;2ji1o 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 radidjcmke v09b2hz,e1 2 ius 2.90 m . At a particular instant, its acceleratione, 01mzv cik2e29jhb d 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 spacecraftpb )awijlv 689 12,800 km (2 Earth radii) abovjpli) 8v6baw9e the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, t 4cpsg pc8ci0e ;(gc-8g 9ahw58aqpnfhe gravitational acceleration g has a magnitude ofe s5gwp8 -gg caa4; p ci(9pcnfc088hq 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1up;jtba/jt) n1jbfy g:j .u: 1.74 jg jyuu1:j )tb /.p;na:b1jtf$\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 / wz/i3vpc7qe; qj6 jhthe same mass. What is the acceleration 3civ/;qjj z7p q/h6ewdue to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. zj2l70(szf1y m9tr.e md x,akveh , k0What ,0 j0m k 1kz,2(zrh.t 9ymadle7svefxis g near its surface?   

  Two objects attract each other g* xjlst-ily;xng:6 hlz2 3*v eravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of grafavn5 mn5j uqcou)4:f )98kvs8 /erj avity, at (a) 3200 mj5 fa /kv8rs)f89ao 5enmvuq4 ju)cn:    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centsptjyu n83u cti8n/ojm4+f-2er to a point outside the Earth where thegravitational acceleration 3opf+j m4iuystjn c/ n-828tudue 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 iq1vileq- 03a*qv ej (Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this moni1vqeav(q* lqj -03eister.    $\times10^12$

  A typical white-dwarf star, which once was aec(;k- dw**aduhgo 8bn 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. What is the surface gravity on this star?g c(*- kdwa;ob*du h8e    $\times 10^7$

  You are explaining why ast*i4r k jos)/(sccvmu9jux 4.rronauts 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 acceles m/ (k4ir*jvxcsjru9 .cou 4)ration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60a.eeqzsxx : 8y kr+)j) m. Calculate the magnitude and direction of the total gze8s)x) qy:axrk +. jeravitational 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 prmg2c g,vqqh fsab.)8 3jr8 8up on the same side of the Sun. Calculate the total frf)j s.gq82 m, hgqr8vp8abc 3orce 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 at the surface ,)wqwzov ( 2s js9w.mvjb0w 8dof Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determinejm2vo)j zq ,9d.w8(wvswbw s0 the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period o,;ckie4o9izejehg, b/y 3; nff the Earth and its distance from the Sun. [Note: Compare your answenec ,f,zeibhk4;e 3;9i gj yo/r to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable o , +b(m7ajoiqa hc2+gcircular orbit about the Earth at a heighoj2(mh7ci,+gb q aoa+ t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the dkq ;64 x 2jkjuieinj xy*(g+1Earth. How fast must the shuttle be movinxej1 ii g 4jy6xdq;u2k( k*jn+g (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical sp-oxerb+1)l kgaceship rotate if occupants are to experience simul geo+1b )-lkxrated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it take2pf2zk+zkw6 v s for a satellite 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 compared to the radius of the Eartpvwk 262z+k zfh. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have tj) w 88k0n.mopsuj :dso be launched from the top of Mt. Everest to be placed in a circular or oj0n).pkdw:u8s8j ms bit around the Earth?   

  During an Apollo lunar landing mission, the command moducz47e k:tv g8xle continued to orbit the Moon at an altitude of about 100 km. How long did it take to gcg t:zek4 78xvo around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the p3t2 7zm:z+xrz .rlocrlanet. The inner radi z:cxz3mt lozr+2r 7r.us 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 in diameter rotates once eve gg8*y prbb(f;ry 15.5 s (see Fig. 5–9). Whatb*gf;pyg r8b( is the ratio 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 75-kg astronaut 4200 km from q h(cl8q:.mjg z6.g fcthe center of the Earth's Moonghjq( 6m.zqc gc f.:8l in a space 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-star system consists of two stz4wy-zp a ec;l8 -sxke8pi y065mq8 ydars 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 i-mly6 ;iczwp yx 8-ed5sqp4ea8zy k08 s the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight ofw9lf ahqd4;. ,ul. qmb a 55-kg woman in an elevator that move9f .b;w lqmal.hu,4q ds
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling l1zbvrf . qlke407.br of an elevator. The cokbr47v q0f.brz.el 1 lrd can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface m0/2 mlp yt-t ux(+4c vzx:nflof a planet with period T , the density (mass/volume) ox-c:ntvft0l (4 l+um /p2xmyzf 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 (27n1 z2d6xguu m1.4 d) to determine the period of an artificial satellitu2 mxng1du1 6ze orbiting very near the Earth’s surface.    s

  The asteroid Icarus, ti7m:m68ogyztk;ukw. js (wzk l9f 4u 8hough only a few hundred meters across, orbits the Sun like the pl.y f:8smkug zz;t84k l jo97ikmw(uw6anets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.fa t5w cp:)++pnt;-s hzladw95 $\times 10^{9} \mathrm{~km}$ 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 vx h-mr oqz 4;y 04hmv(97 xvstbeggyv3.(3k vthe Sun roughly once every 76 years. 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 the nearest andy g( 3qv.z(mmhxbv40sv- 43 kyo9 hgvvr7e;xt farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G-osv q4t ns ut20:glb,j 34 xzuq*b6mmr8je 5ealaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moof m0) ;j0g8 1yixlg sz.;qvphuns opz gl;8.ms1;fjhv)u 00yqix gf Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period ankeu0)s()y/2l 2 n yu,jy cutsfd distance of the Moon. ,)uc ( 2jk/u st)lyunyys20fe    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Ke;:- x9hg yk qggh vukr(;nx3+ppler’s third law. Use the distance of Io and the r+ yxvxp :3(uk;hg9g hn;kg-qperiods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whi0mk) adhs16 bwa2bpk4ch some space scientists think came from a planet that once orbited the Sun but was destroy masw)b 4dp1b0 6h2akked).
(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 "planetjj (fi9 w2z( cukklh);" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon)k(hif(zlju c);k29w j. 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 d2 fm 0g1utm,;loua+xin an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the1umud ,lm2+g tfxo; 0a 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 sy0u42f b7g//i 0qwe/xwbcqu )xhd +nthe acceleration of gravity be half what it i)n00/qbhq yiebd / 2sw+7 /x4xuufw gcs on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gr4 labpa6tz*1pi j5cj/ ab hands and spin in a mutual circle once every 2.5 s. If we assumbc6 *pz1ajit5p a4 j/le their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra(7sden6607bcmsx(rzkx di8 c vity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitu(6dc8 zmibk(edr07n 7 xsscx 6de of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly mov:uafd opdoi r01 ))m:ahmp2 c0d,4from the Earth to the Moon experienc do m a1udhaf:p2)pmdo)oimr:0,0v4ce zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bo0rfb hze .mf4g )k0b0ut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wh fbfo kh0z.0)mgbe4r0ich direction?     ----待选择----upwartddown 

  A projected space station consists b9it 7r lb/yi: :*t.mvuxhcq, 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 effe u/mi9c. btx i*tvy7:lbqrh,:ct 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 aircrarv e7l6j/ygrj03a ll ,ft 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 planetba 6:i-(upep 48f c tqxyc(7rc in terms of its radius r, the acceleration due to gravity at its surface and the gravitational6urf c7p ca8e(c x:y(-qip4b t constant G.

A plumb bob (a mass m hanging on a string) is deflected fro8znl l0dpsj5 6d7-hanxd 5 yakkc07rhr q- f96m the vertical by an ang78sddhqa0 n0jd5-y9 n l h 7ra6ck-kxzlrf5 p6le $\theta$ 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 txbazs 1)g )j(9gs) cmhhe coefficient of static fricti(s j)zx1 h )9gcmagb)son is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast t3hugq d 3oi8: jtb7zg2hat objects at the equator zq8j ud3 :ohig27gbt3were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8- gy* cg7u9mzowcn4f- .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 cokrhqz-eml) 2m a5 m,t1c -bmt:q 7dl.tnstant speed rounds a curve of radius 235 m. A lamp suspended -tmztqrdb mke:, 1qtcm h.75m)l2-al from 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 m0m7z o4qvgwb3 ppr: q-assive as the Earth. Thus, 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 equator of such a planet. Use the following data for Jupiter: mass =34 pmvbopqz0 r7: -wqg1.9 $\times 10^{27} \mathrm{~kg}$ , 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 presence* s9xfi3. tm2nzp iid24hqql/ b24xf i of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did th f i/st4fib*l. 32 42mdn9iip2qxhzxqis 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.cv uiid)z dl v6p,8(i speed as it 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) W zvi,8id 6dic)luv(p .here 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) utilizes a gro/ys 1gpq+2r kmup 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 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 ]. m+2rp/y1 gqk s(a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvousv6b1r.mjnk5. r :hnh h (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly hr bnhr651: hm.kn.jv40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 .lmtv 0ihkbt (le 7 )thb* 4tdbc:)uo)satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 vt.o)thcbt* )b(t u) k74em0l:bh dlikm 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 d tyhr8v5 z m;rz-00j0q)svbpa period of 3000 years. (a) What is its mean distance from the Sun? ythjds0z;pm-rr 5 q v80)b0 vz  
(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 actual3qtpf75kyanc / 8,xskyh-+w0tvh 4cbly "feel" yourself gravitationally attracted to someone nea5x,q8c swyy4 c 0-tkt7/+hnpahk 3vbfr you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around t0;3otll. rs (7jhijo c a8nl0vhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centeri00ohc tlo;ajl.7 l8(r snjv3 $ \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 locate/;cu twa8 ,-nvs(wfrve/sg )u d at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint tv /;c(v ug8,ewa-fu/)nrswsof the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ,.;*bm 1pr 3y6ck nyluaoid+w 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 sweeph owhst2 x9g3lf76zzr9m 09u m second hand on your smz 0f9x t r2h7w39lh go69zumwrist watch?    $\times 10^{-4}$

  While fishing, you get rk6 cfp8f 7w9z:7ledm bored and start 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 circle every 0.50 s. What is the angle that the fishing line makes wi 789reklc6 7wpffd:mzth the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thn:o8fk4iik4z au a(z)at a car traveling at spe u8)az:ik afkz4no(4ied $ 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 agu,3tjb k+)onegotiating 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 ). (k)3 ao+tgbu,ja) 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.$\approx$    $\times 10^2$