Sometimes people say that water is removed from clothes in a spin dryer by c1s zx)l.1f*wtv3)+ u 7g zgqcecozv6g22 dhefentrifugal force throwing the water outward. What is w.* 7fc u2e z)1c zqsf1glt6g3xvoh2e+ wdgv z)rong with this statement?

Will the acceleration of a car be the same when the car travels around a sh jq99xf pl/clh l,5+yoarp curve at acyqx 9+ollfjlp, 95h / constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves atjzkyg:;j 5crx-w j:9o constant speed along a hilly road. Where does the car exert the greatest and least wg; 5 k:9jj- cj:yzorxforces 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 merry-go-roun3tido rns4s/ 6d. Which of these forces provides the cen6issor/3t nd4 tripetal acceleration of the child?

A bucket of water ca8 p* n85o8,ducku1f jsy 3yyntn be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucyd88cu*18fyt3 n ,j k 5puyosnket is upside down. Explain.

How many “accelerators” do you have in your car? There * oc8jo5t3vd65vm qnu are at least three controls in the car which can be used to cause the car to accelerate. What are they? W6853 jotmvonv5d qcu*hat accelerations do they produce?

A child on a sled comes flying over the crest of a small hit6iqu ),idzr)u; bq3 10ifamp ll, 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 chet urz qiqa01pbi ;f3im))d, u6st 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 at high sn4rl+f:o1j4 ;j jz,,tuxkld epeed?

Why do airplanes bank when they turn? How would you compute the banking ked2xygn/a5 ls o/cd9708 rrx angle given its speed and radiu 0yx/da kn rcxd7 8r2o5g/sel9s of the turn?

A girl is whirling a ball on a string around her pw h:gelpt ejr01:- (chead 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 t1jee h:0 :(-plgtwrpc he yard. When should she let go of the string?

Does an apple exert a gravitational force oii6wb-)vyoy ud5q)f2 n the Earth? If so, how large a force? Consider an apidqv)fuw-yyo 2)i6b 5ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s or5c:qe: ps hu,wbit be diffw hesp:5q :,ucerent?

Which pulls harder grave.gggl3,if)qw : bqm .itationally, the Earth on the Moon, or the Moon on the Earth? Which acceg..lge3)bqq :,g imwflerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yep t4 o3y8rekj 9eue:k1t the Moon's is mainly responsibler8e1k49y3u ep tk:oje 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 acefo 7rr5v-l lc(xn: 5t the poles? What two effects are at work? Do they oppose eacr5xn 7fl-:re5 ccv( loh other?

The gravitational force on the Moon due to the Earth is only about half the for.7kpuzq t50vp wx/ (ogce on the Moon due to the Sun. Why isn’t the zw/ u07vpq(k po5xt.gMoon pulled away from the Earth?

Is the centripetal a0bm7n s8:7gcsta s 0xb5bao n0cceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceler7b5xsn0 atag8 bss:n0m7cb o0ation of the Earth?

Would it require less speed to launch a sa/pif7icrs.1kbu (hf1)mus0t tellite (a) toward the east or (b) toward the west? Consider the Ep ikm1b1.c ft(ihu)fsu r/s70arth’s rotation direction.

When will your apparent weight be the greatems6l-wq g 5l6tst, as measured by a scale in a moving elevator: when the elevator (sg 5 wl6t-ql6ma) accelerates 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 fyz;u1l, 5q;ov9xdq xweightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the in5vz 1oqydf,; qx ux;l9side 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 fy1 /fx wqn5 e/9fvndf7m+gaz+all” or “apparent weightlessness” between steps. awzxfe 9y +m71+vf5nn// qgdf

The Earth moves faster in its orbit a+cnw : 5vn-vuro grn5-round 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 factcnro+v-5 v nwn-g5r: uor 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 until it was discgw3)cgupw5qvy+av -0 tzf yf pk(8(3covered to have a moon. Explain how this discovery e-vgft+p8pwg(zuw)k3y0f3qc a5 v y( cnabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mo5a5e)gyb yyk) a e4h5mon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differencea5hb5yy k5ay 4ee))gm in gravitational pull from one side of the Earth to the 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 :awox:f oxmz4+l4aq21980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 itsj*r ;kbnw 8radl0(6e lqk6k4j orbit around the Sun, and the net force exerted on the Earth. What exerts this force on theq kl(ran86bjk*kle4r; wj d 60 Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-,rixhmp1hw. 3*y ror) ) e8sb ,yinz8jkg discus as it rotates uniformly in a horizontal circle (axiyrhpmh3. *os8w )r1eb r ynzj8, ,i)t arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfa m 0ck :cxe)9e9s5iaxfce, and circles the Earth efa0i 9s9:cexx5kcm)about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck .u ,jdem/9i;3by vwsfkc .;+ vm0 luvyof clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cmcy v9;dykvwvj3m+ 0e.f,iu; /s b.lu m?   

  A ball on the end of a string is revolved at a uniform rate in o8ddh9w o)q2ga vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.qd)w2g89 od oh00 $\mathrm{~m} / \mathrm{s}$ 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 ;rvwtu dlb(8i 2-mw3ha turn of radius 77 m on a flat road if the coef vm;3brt2w l -8hiu(dwficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficie6z2hl 2254f nzra1 gqb)ob mza5z(cwlnt of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at (bwz2 21z4znf6a g5mla r5blqc zo2)ha speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed torz*u ncimql+0 u3j;c+ 6wcmr/ 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, how fast is she cuu/3cc;n jrqml6*+ wr+im0zrotating?    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)ekozm q;d,m 9 variable speed. When the speed of the turntablz9ko m)m,q;de e 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 0 24sz* an*rt jsdo21xo60 xr+b+ol pcpj dr.kcoaster be traveling when upside down at the top 0 bdx2rl 1r o6ps4cts0j zpkoorn2x*+ja +d*.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 topu3zv3dl+p xx ,l;hm 3c of a hilv3 xxu+ ,3 c;dp3hlzmll (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 Ferri14i6-l1wq rliyp lrw- s wheel need to make for the passengers to f6l-illq 4- pwr1y1riw eel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whir mno/5g:,cfz,(t1x ng nddeu0led in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting thd 5gxng,(d 0n,: zc ue1/tnmofe bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from v,wndou-g2 e2 urcmgpo glf..o7)4 f4nz m6d7the axis ofn r4vopo7 .dm-4gm 6gfc 2w, n)g.duz2fu7oel rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cjt7*46z d nhfcylindrically walled "room." h6z 74cdnf*jt (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockeyic6 tyb y+gg)1e5fqf1n eg+lpr/4,rt tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cer4f gfqeetrbc1 + g,yl/p+t5)n ig y16ntral 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 thotqr 6 -58og0l1bkn7 a5y pmr vughzw*6+vv i7is time, by not ignoring the weight of the ball which revolves on a string 0.600 mg5invzaorpgqvt667klv 1 -0h78+uyw b 5o m *r 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 perf r2zvc,ni/tx* ectly 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 masses0le 2fleg/2dt $ 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 vertically atejp kp5jj )1jl)uz nr,yr .6-r 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 :bcn wlad+swq-vcb.v2t ) (-k the net force exerted on the car (by the gkc2w avn-(v:.bdstq ) lc-w+bround) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the gb;vf i2zj04 obee;g) 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 iszbibo4vj; f02g ;ge )e halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a/n;nahfr*qo7lp kx/ d-yk8 ke u2)2la particular instant, its accelerati nl 22luxko78qe*/;yfaakp) -/ rknhdon 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 spax9s *wsb-dt,, qmf3pu cecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass 3-fsq, ,b pt*um ds9xwis 1350 kg.   

  At the surface of a certain planet, the gravitational accbjnrgpp i (i- ua :213b7byx-aeleration g has a magni2b3gppb( iji na7--xr yu1ba:tude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on wu2futw f0q( .the Moon. The Moon's radius is 1.74(u.wfq f w2t0u $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radg kak(z80+vw jius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity0kvj(z 8k ag+w near its surface?   

  A hypothetical planet has a mass 1.6jpe: nuu6pb8 6pc1e t/6 times that of Earth, but the same radius. What is g near its surfacbu 6e8 6u1t :/pppnecje?   

  Two objects attract each other gravitationally with a forc*fxwx.6/hp fvec t8 m-pliv21g w6/hie 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 gravity, at (a) 3 jf d+ /kj,trx9d(v3z-(m vdul200 mtlvdud- +f(d /zr jv9x 3j,km(    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pointw6guhp*n 1 /rt outside the Earth where thegravitational acceleration due to the Earu* hrp/n6tg w1th is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times sz;7 /srw t-j3sz*f rnthe mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface *fz7ztrnsr;sjs3w -/ gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncgt0 vxho(nf 7,e was an average star like our Sun but is now in the last stage of its evolution, ,t7gvf (nh xo0is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting u66nsgpg7ct7 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 calculati6c7s6g ptung7 ng the acceleration 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 0.60 m. Ca ms jo.l6n;mr,lculate the magnitude and direction of the total gravitationam; r6ljs.n, oml force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plc+ x+sr*h jvs pje1*h)anets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn,v*hs +jpsre*x1h c+)j 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 surfair8x2zhc)4z*w n/ jjxi .:i 14rvm omvce of Mars is 0.38 of what it is on Earth, a)wz8*o xc/ 1mv x i.vn 4hiizr2jmr:4jnd that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sunrk)y7a ;xljr: using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using kx lj;:)ayr 7rKepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a gim-fru+ cq-a3xi0a 5)nejb u7zd3 f0satellite moving in a stable circular orbit about the Earth at a height of 3600 km. 0f7gqfbrja 3e-+ duniu- mzx5 30ic)a   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km ame vqb2amr4h;7* g-9al ax)qobove the Earth. How fast must the shuttle be moving (relative to Earto; vem97 ar*hax2) ag-q4blqmh) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to y5xh7 v8sie. sz8igj.gyq : n2experience simulated gravity of 0.60 g? Assume the sp iyq2hsx5:.g88gsyjve n7 z.i aceship’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 take/ ( u-ycmbvnxz(-oi3m 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 comparedzm3oix(n-/u vycb m (- to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal veloc;rd izuy80*gq .i/by8vxzho 6ity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earzih;*q doxui08zvyr / g.b8 y6th?   

  During an Apollo lunar landing mission, the command mo3x,g )aw/ks1i5baynj4 l)igx dule continued to orbit the Moon at an awi3xbsa )jni,/ag1y 4 l)5kx gltitude 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 orb62ai je0u, c bygcv4r-it the planet. The inner radius of the r g6,rj0cvei -yb4cu 2aings 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 everyr zt-w;,. q6vlsnqq,mgyw )fj8 uv0q/ 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the 6w,)uqs;rqy wzm.vvnq0g8q-lt j,f /bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4dmctoi7zg,f8la8mpb 3 w-;c1k* j 8 uc200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, cl13dcap7;o g i 8kb8m8c* ,zj wtuf-m    ----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 tw6e2scprw g*2uwt6 i rz fpi+24 r.sq/yo stars of equal mass. They are o2*yg2 i fq6p6/ctrziw2es 4u. s w+prrbserved 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?    $\times 10^{29}$

  What will a spring scale read for the weight ou l-ras m4g *7ri*q6hef a 55-kg woman in an elevator thag* rq emi-a746shrlu *t moves
(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 al s,/f7l hpb1p cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevafl/h1p7,b lpstor accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period 0p50q( x rpmfq T , mq5pfxpr q0(0 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 perioqs 30z51wdiac d of the Moon (27.4 d) to determine the period of an artificial satellite or3s5 w1qd0ca izbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only 3l-g 4+m b30 ekklotsya few hundred meters across, orbits the Sun like the planets. Its periodmyk +llkosg4-0 t33eb is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis1 ivj98plrxld4uqrpo 9-2rm ; tance 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 once82bterfs -qd1 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 cqedr 2bs t-18fomet 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 centx tke,9j-4(bc vlmuo3 er 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, period, and mean distance for the four largedk0y 59x dd-mist moons of Jupiter (mxk0yd5d - id9those 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 ad 0sy kxkjck9oh.:: 9rnd distance of the Moon. k0 ::hjokkr9yc9d. xs   $\times 10^{24}$

  Determine the mean distance from Jupiter for/. lfd44rvz1 iyw4-6h-xs2boe w skqp each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compares4b6 s. 4fp z1qd i-yo/xwhw2v-rl4 ek 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 d- ) - wn0yqzn1ao8dvvand Jupiter consists of many fragments (which some space scientists think came yq)z -wv1d -0dnonv 8afrom 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 of a bb0kv b q 99clvg;p9+fxe6x0 yxand completely encircling a sun (Fig. 5-v0 fq bxpcgkvl0;ex6y99+bx940). 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 an arc from a ha q2ha+)kf ) ,i3aky gu9.qpvltnging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 th)pvqu3glfa2 )a+ .ky k9qi, kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acce1 eb7za(qwlql-:*9fvz q ub5 nleration of gravity be half what i9-: anbq(bzvzq*1w75l eflq ut is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass g d:hx)akw6qcu *)f7j orab 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 phu 7o) k6qfwd *xca):julling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration oga ,y8ie7qw0ef gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is ty0aiqw e eg,78his?    $\times 10^{-1}$

  At what distance from the Earth will a spacecrdrwl/ t1/ ysm7aft traveling directly from the Earth to the Moon experience w/rtsy/7m1dlzero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elevqq). 3cn; kv/f xdsiac;k ot*:ator, it says your mass is 82 kg. What is the acceleration of th:t *ka3/k ; fxnv)o q.qd;scice elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat cshed+9 1,rmq8.nkmze 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,1em8n sd+ck9hr mq.z rface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fvo-ck6 *crao.c),+)pni hka jig. 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 k-(1fyvgjq lw;. 8pifi 1v9zlng-xy8 of its radius r, the acceleration due to g8;p-iv-ljf (.1yklx gf ig8yzw9v n1qravity at its surface and the gravitational constant G.

A plumb bob (a mass m hangingdv)xw p, 74tzmo9-t pv on a string) is deflected from the vertical by an angl-,dt)oppx 947mvwtzv e $\theta$ 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 coefficieno irjq)41brv9 /wx0 k :)p8fqs;wqvq5 h0mi jft of static 4mi q18:9q)hqxo s/;bjqv5) 0wffrivrwp0kj friction 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 vpb -ed8jdt4 y93(yki. rq w.gEarth were rotating so fast that objects at the equator were gp ky.bd3t v(94 jewqr8 id-y.apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain+h8azs-dukjlx-yd ( + a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp s5mu;:m(sud h2bkk4n*: jysg juspended from the ceiling swings out to an a(sk:hm;d bu:jung5*km4 y2js ngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 time1 s*,m7za d:t f2ihgxks as massive 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 ghxa zgm:s *di2,f1k 7t 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduc6 qe qcv:jd.(p(nsyq:ed the presence of an extremely massive core in the distant galaxy M87, so dense tjvp sn(q e:(cq6 qy.:dhat 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 traf(j,hja(f*:p ygma0 lverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car (ag yljj*ahf0m ,p:f (go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilik+4+/te iaw r ivo39vfzes a group of 24 satellites orbiting the Earth. Using “trianriw +/t+ af3ev49ikvogulation” 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 ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), aftersyftupw ;+nu+j*(5h wg::ty y traveling 2.1 billion km, is meant to orbit thfs(tu5w :+ ; *:yypghywuj tn+e asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in nee:c,5p.1crly e )zrreate1;bb0: cy qi d of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. ce,bl p1tez)i.q bcya 0r: 5r1yrc;:e
(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 perio.i8+d j03 mh4) mfvfjx1z tnxtd of 3000 years. (a) What is its mean distance from the Suvfm +nt8) .jhjftxi3 1 m04xdzn?   
(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 w+n/ etab .a3ygv4.lr dould need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, likglby3v.d.4ta/+e a nr e F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around t wrkq/o*uxs( xo0 (.pahe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ceu/aox*.qw xk pos( 0r(nter $ \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 :b b(w+,l6cky,c;zbnd 4 )kf(rpkecz at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifyzl ;(d k,)kcb4c r6 f+p,(n wc:kebzbth 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 5500 kg orbits the Ea w5wz/leh:qc dglj30:rth $ \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 th-+5eakj13gto:ohgw ) xj h( tye 1.5-cm-long sweep second hand on)a oet wk:-3j o +5hg(jthg1xy your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weigcmte l5 s35m8jve6e 8lht 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 with the vertimee 653mv885ltjel cscal? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwah291ph ntz u8brm- +uby is designed so that a car traveling at sbph hmt-rb29nz8 1u +upeed $ 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:u08kv,u;q0ra sat ht when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela traiau:uq,v ;t8rs0ka0t hn 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.$\approx$    $\times 10^2$