Sometimes people say that water is removedpvjmv ux cp, 5(7+2cej from clothes in a spin dryer by centrifugal force throwing the water outward. What is wr5xm2c(pujpvc,7je v + ong with this statement?

Will the acceleration of a v)dyk0l)h tx,hgb6 y2 car be the same when the car travels around a sharp curve at a constant 60 km/yh0bg t6)lv xhy d2)k,h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the besg xxk45):s c dfqlv*79ta;car exert the greatest and least forces on the vk7l) 9te4a:f;b5xsd*s c q xgroad: (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 *u8bv;zh ny+7.:mdw+ fxiaee horse on a merry-go-round. Which of these forces provide.fumeiw+78:a zhd*b nex y+v;s the centripetal acceleration of the child?

A bucket of water can be whirl77( g9fuj xfk9 i:oyjlbnm4*xoda u5 6ed in a vertical circle without the water spilling out, *4xmoyd5fxjb (g:7k jf 6u7luoa9n i 9even at the top of the circle when the bucket is upside down. Explain.

How many “accelerato wct aah7 hxlr4)w.3q8rs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are theyhl7a. wc )t3whrxa 8q4? What accelerations do they produce?

A child on a sled comes flyi;fyrko3g-qskm4/ l t 2ng 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 and the sled decrease a;f y4lr3gkk- qotm2s/s he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean i x7;xtmf5xoup c 19so(nward when rounding a curve at high speed?

Why do airplanes bank jgi( epzcn8)+fxb 9(r when they turn? How would you compute the banking angle given its speed and radius eb r (8gjc9zx)f(i n+pof the turn?

A girl is whirling a ball on a string around her head in a htvn2u qya28u1 aer+z*x. ksam1-0o blorizontal plane. She wants to let go at precisely the right time so that yaz+u *nravauqm28 -ot2s bl.e1 k10x the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational fi lypxu,ztlb2vz428;6zy 6vv orce on the Earth? If so, how large a force? Considezyl p2 uv2t,yz;6b64 z 8xlivvr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is,4kb;lj5 dk+ rk in what ways would the Moon’s orbit be differ4rk5d kklbj+;ent?

Which pulls harder gravitationally, the Eavn. mny(ymal+s6./v wrth on the Moon, or the Moon on the Earth? Which acc m sny.+l6wvynmv/( .aelerates more?

The Sun's gravitational pull on the Ear0 vonteb50dm1th is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Himb d1v 5n0oe0tnt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator ovcd b 5vw,rq j+i8:ee8r at the poles? What two effects are at work? Do they opd 5,eew8q :vbv+i r8cjpose each other?

The gravitational force on the Moon due t pd:vqktv .k2,o the Earth is only about half the force on the Moon due to the v2dvq , t.kk:pSun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or smu; bf9m/h pwiol+ b1;oaller thuo;pilb1;ho b+fwm/ 9an the centripetal acceleration of the Earth?

Would it require lesso c- mov3+mbuf(r+cu) o2yp9a speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directiovo( 3 f+oormyc ub m9+2pac)-un.

When will your apparent weight be the greatest, as measure*.6 (w mgzqx)hp.lk zy)/csbe d 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 co() ycxl*)kh qp/w6 .bsezg.zm nstant 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 perioylpzo 7a;8pmc;8 9xi rds in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, an8r; 7oaz9x pml cpy8i;d (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” be, r:5n)tdepst 2 d:obzq8h v2+q.kphctween std2q2v+ rezsk h do:c p :qttn5h8p)b.,eps.

The Earth moves faster in its orbit arz1b0ho..mh l 9ay*b gjound the Sun in January than in July. Is the Earth closer to the Sun in 0mblahhg9.. y jozb1*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 plane of its orbit.]

The mass of Pluto was not known until it was discovered bbrzw-;/d7l*)dq )fg r xe jo/to have a moon. Explain how this discovery enabled/ rw 7dbq or)b/ld* )jezxg-;f an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than wmk2 o:38 a-pgpfzd (y8 acsd-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 t3kdc(wyg f 8pza2: m-d po8s-ahe 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 198 42 s893rw6lv95rw z gupphlyb;cc(gz 0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 its orbik5-o yb*n :z ss3rrvh,t around the Sun, and the net force exerted on the Earth. What exerts this forco rzr -ss ky3n5vh:,*be on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kn4tz)5o 8h85dwi rmr hg discus as it rotates uniformly in a horizontal circle (at arm’s 4)8mhdr55h8ni zrtowlength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4003lhvp ue r;*sju12xh9 3ei/g l km from the Earth's surface, and circles the Earth about once js1velh 3 hi3pu*r ;ul/xg9e2every 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 magnitud 5w3 waayqc9f.e of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter isy 9wc.3wfaa q5 32 cm?   

  A ball on the end of a string is revolved at a unifojrc5z8va85: dg3 my.b3dg-0sj usthgrm rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spas533jgct b:-u8y. r8hmgvj 0gs dd5z eed 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-t 5.y)-gl:u z 0ysdn6lyjw )aekg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of thtg a)l :w .-udzyy)leys60jn5e mass of the car?   

  How large must the coefficient kz; c *q (im.sarwj91+wt+sikof static friction be between the tires and the road r+ 1wjqaiwkm i(s9tscz +k.;*if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate 52 5bygl.api pa trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is byia 5gp.52pl 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating tur4tn+ b3h k)aegntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turnta+g4 t)neb3hka ble?   

  At what minimum speed musp +oywi:dv 8-ut a roller coaster be traveling when upside down at the top of odv8u: +wyi-pa 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 (includingukwtaqv6df/n/g ,c)tv:e2 iupd 2 r8 9 the driver) crosses the rounded top of a hill (radius :adv/r u e p v69w,kd2tcq2tfnug/)i 8=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 155h+u0.x royiev7l*ub -m-diameter Ferris wheel need to make fvi h oyrxlb7.5+uu *0eor the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rq8 fyq 4(c :ft-)fzdr,z5rylradius 1.10 m. At the lowest point of its motion the tension in tfy-fy 5:l 4zf8rzcqq,dr ( t)rhe 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*e*qtakq .+or2g wm:6o9 fs ss centrifuge rotate if a particle 9.00 cm from the axis of rotatio*s:wet ga+.r oo9sfqs *q 2mk6n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyli(loln(e tcv;-u 0-q2 gepmgh1lhz m 70ndrically walled "room." (See Fig.m1c-;0q(-e(hl hlml pg g2 znveo0t7u 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-ho+)up doq )-) vzxkb-s q3)biayckey tabletop, and is held in this orbit by a light cord connected to a dangling block (maxdvy ))- pki)qo-zbbuq sa)+ 3ss m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring ;7x vm e2int47mkbh szfjh(k3*7ma( dthe weight of the ball which revolves7mki b4a 3j2xhkvsthd* ;e( nm7m7f z( 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 perfes h ;aa 8ea,v ,)d.hsprnlfdd */;o+klctly 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 masses rtao5 p( 33sp)iaoo -z$ 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 verticallzw- v,6. gk, +nzmf e5q)mj32pmyfdcey 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 exertetgzma e1 )0ix.d on the car (by the ground) in .e gx1m0iaz)tExample 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 unij48k( a- qakxg:hdm5q formly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slippingq k:qx(h a-k mad8g45j or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pa k,u6p6h( czzarticular instant, its acceleration is 1.0az,pu hz 66kc(5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 kmus qbw895zvk1 7vpr9d (2 Earth radii) above the sb59 kdq7prv1 9w8u zvEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnes4sfwp ;/jow-0kt7: : xzh yhitud -7 :ww4/j:toe 0hzx;hysfspk e 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 the Moon. The Mo9)4qy nr xo7wmon's radius is 1.74 o 4w9mynqrx7) $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiuxg azj:zr btbp) khc2jb27u8c/4 2lg5s 1.5 times that of Earth, but has the same mass. What is the accelerbpxb7 j28cz5k )ug2b 2/:z 4gljtcahration due to gravity near its surface?   

  A hypothetical planet has -qm;,p gfnd a* mrw)9obv)ry klv(9t 4a mass 1.66 times that of Earth, but the same radius. What is g near its surface? v)ymdmb(l ,o g4 ar- 9)nptwqkfv;r* 9  

  Two objects attract each other gravitationally wip+s 8wu c:v5 z.gsxnw2z1z2vsth 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 gravity, at 2ki z+e8 youye+;hby: (a) 3200 m ky+ee +hy y:28z io;ub   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’q jk7dy5q08rdy9eyq/b3 tua uy 4.cm*s center to a point outside the Earth where thegravitationarb t q04e5 cykmdduquyy7y89 j*3.q /al acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun slr.6n cy j+s;eju-mf78 ul 8fpacked into a sphere about 10 km in radius. Estimate the surface gravity on this f6fm uyu+-n8ls8re7;s jcj. lmonster.    $\times10^12$

  A typical white-dwarf starax36 ks*z y2 ktp)zdwq:8t 7ds, which once was an average star like our Sun but is now in the lastdq6s8 ykt dk:3zzpa*2wts )x7 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?    $\times 10^7$

  You are explaining why stsyk5w. 8dr1vm4u.9(fwhq el/wjomjc)0v * astronauts 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 calculw /rmdu. .)yes k(19s o8jcq0w4v mjfwhv5* ltating 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)arc 9c0 m v/wjsvuwsy ))82uh of side 0.60 m. Calculate the magnitude and dicvs8/uc)))ymuj whrvs0 9w2arection 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 s2e wtgb w)h2b*b ,u4tc1t+zrmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all f, 1h*t2b)csw2zt4bu b+ gertwour 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 sur 4fc1ffpeb q;,rg u+5 ln+4gvkface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine t4qpgefngfk 4v5, cr+1+l;u bfhe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuew 64ees,lt9 oa for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampeotwae, s6 l49le 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable j;ohxq pg m *s8/vamft; ;k3+kcircular orbit about the Earth at a height of 3600 /q;mk;a kg s*j8m+hv3xpfto ;km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km aboa-t mkv(vuy0wv7,vskqcd 0 64 ve the Earth. How fast must the shuttle be moving (relative to Earth) when the release occuq(-0t7,mvkk cau 6vvydsw4 0vrs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experienc6-/a7 otf )uaskxjdf bd+hrv;lz::2f e simulated gravity/v6 ; 2f7-tj:zlr:k )affu+xo d shabd 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 takes for a satellite to orbit the Earth in a ha/: h0u9vq 9rl(iz 5wckf9pocircular “near-Earth” orbit. A “near-Earth” orbit is one at a height f9rkhwli(qa0 ou 5/cz9 hpv9: above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from y anc7,ak:rw 0the top of Mt. Everest to be placed in a circular orbit around the Earth? ,a c7:ayrwk0n  

  During an Apollo lunar landing mission, the command module lxqmz 4v2 )ot8continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? ov )qxzmtl4 28   s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The in(r/ o+c0ihf)d) fna gmner radius of the rings is 73,000 mo dni0af)c+( )f/ghr $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. b(gwfep)/l wd9mkz38 5–9). What is the ratio of a person’s applpb zk w)d9gf/ew 3m(8arent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent w7ax5g s5pkyib4r ,yw8 g np81deight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veldp yg 8175rw8ni45 sabyxpg, kocity,     ----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 htz8mhd40xx0,q xk t3 of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth40q,xtm dh hzx t30kx8 years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read gb-mt e0c;y65pgop-rx g4c-f for the weight of a 55-kg woman in an elevator that c4 6-pyfxeopm;5cr-g- btgg 0 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 xxrlgs s k3;,;6wsz.70hqux jfrom a cord suspended from the ceiling of an elevator. The cord can withsrgqkz ,.lxs0x 7u6s3hj;;ws x tand 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 tw5v,g 6avs 2kihe surface of a planet with period T , the density (mass/volume) ivg 2wk56,svaof the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine txrwv h*x um*/sqw;/srci6.q5 he period of an artificial satellite orbiting very near the Earth’s surfi 6xr*su5c rqhm.*w;q/ws/ vx ace.    s

  The asteroid Icarus, though only a few hundred meters across, or fam1 m8s6)sqobits the Sun like the planets. Its period is 410 d. What is its mean distance from6 masos1mq)8f the Sun?    $\times 10^{11}$

  Neptune is an average distay i8 eg9y nr-b j uuopx7(q1cpqr4:4s6nce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 yeah9 6k ndg(mje9rs. 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 n6h k99(d egmjnearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of thy:7nb hxo4um35hi )lk e 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 largest moo 8e skrt1x;cnsh0 jf*,ns of Jupiter (those discovered by Galiln;xj08ch, *er1ksst f eo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon.40ovyt;cbd jso . v:3z o.3;jz c v0:b4ody stv   $\times 10^{24}$

  Determine the mean distance from Jupit +aub d87gr20ryr29pnk b44nrh lt 9lf5x*w yler for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.9 k a *+h928n7l4lbrbp5nx0yfr r tudgyrl 24w
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betweenrw*2u d9o 2bty Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once*ytw2ud9o r2 b 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 "plan1h)bfhh4k*u n et" in the form of a band completely encircling a sun (Fig. 5)hfu1 hb 4*nkh-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinxz 7g8 3x;x 4d lxt4vlvi20tqtging in an arc from a hanging 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 toler74tl0lx42 xv3 dtq8i tgxz ;vxate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gnenv 4+s:gk,6 pppoo :ravity be half what it is on the sur p,s6+: onv:pgon e4pkface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mud/ )wuv9 y6dtotual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indiv6)yvodwdt /u9idual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per wi55 a /0lmt t5y.(7 jubnu m-afsfvh*n )4vuoday, the apparent acceleration of gravity at the equator is slightly less than it wah4) vvl0(ab7/wm j5 5n.fm-*ufyntt 5 osiu uould be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fj+u qi0oj8l.z66sz x crom the Earth to the Moon experience zero net force because the Ea6.6c+lzj uoi xsj8 0qzrth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you u8n0 +xaa-vsglnc ;/bstand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleratas c8v;bn/xl-a0ugn + ion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cn* w.mhae w/t,ircular tube that will rotate about its center .hw/*ntw, em a(like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his lt064w5o c +jk-bf bsold73ry8gb4ttaircraft 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 l-2gfooti-q(ct03m -awsl( din terms of its radius r, the acceleration due to gravity at its surface a t2sl( 0caio -f( gomq-3dtwl-nd the gravitational constant G.

A plumb bob (a mass l6nrq *+m js:r m hanging on a string) is deflected from the vertical by an a jq* l6rr+n:smngle $\theta$ 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 baa0; or:fqsrj 6 ejd4w.nked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saf0jrwfdor;qea6j.s:4 ely handle the curve?

  How long would a day be ip/+3 jl4jr zmvf the Earth were rotating so fast that objects at the equator werez3+mjl vp4rj / apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cn(cm1c/7 pw2 ilmz/iponstant 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 roundet.0t l bvq),ms a curve of radius 235 m. A lamp suspended from the ceiling swib,l teq0m. tv)ngs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timev 2)y cchoput/a. ,5(+wqoh sus as massive as the Earth. Thus, it has been claimed that a person would be crushed by the forc auhuv to/ psc,yw2 qo(5c+.)he of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope dedu-kj5q ba3grq3y86pv rced the presence of an extremely massive core in the distant galaxy M87, so dens6k vq-g8br5rajpy3 q3e 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 speq7k1f0yx50 ypj ;b4qi*uqz xxnl,k-m ed 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) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road alx07 yy0 -bnz;x54 qiqpmukk f,x *q1jt A?

  The Navstar Global Positioning System (GPS) utilizes a group ofq*rsrko-*rcx./fe. g b 0x;a o 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these sa s -;*bf.agrrrxq*.ox eo/kc0tellites, 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 Asteroidi )rjgn xp6,ta ;+::nnmtg )wo Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Ero jg+6in:mtg);wxn tp),roan: s 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 pursuinn brt8odgv1s663y rh zjc;8-pg a satellite in need of repair. You are in a circular orsrb 3d6vnh - zyp1 ;jrgc8o68tbit 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 hawu: utsl38xlp00 -( q)ztb*im j(palcs a period of 3000 years. (a) What is its mean distance from-p:tcl 8)*3w(a pitm jlxb0 uq( zusl0 the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could b/q vbdd*4,v0za, ky bactually "feel" yourself gravitationally attracted to someone near you. Make reaavddbbk,4, v*0y zqb/sonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ofq13e2 2xoctqxaz+ow+dmj ( 7r the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 12mtqxo7e+ oqxc(dzw a+3r2jlight-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side. Fqn gx4b +d9 /jr8 rkk3.fytj4yind the magnitude and direction of +f r qykg/ky984dtnbjrx.4 3jthe gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits te:dqr ktgk+--4ak75e2cjwo a aj;t ,z he 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 acceleracp;w t; bq9ltx69 i.i2ouy 7s8oyl+ow tion experienced by the tip of the 1.5-cm-long sweep second hand on youry pt.lu9+89yx 6blqowooi7ct;;2 isw wrist watch?    $\times 10^{-4}$

  While fishing, you get bored an kpky66h,ar4hd 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 k6 k rh4ah6,pycomplete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designedx/ug p(bz a8v0 so that a car traveling at x 8u/pg 0avbz(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, utilize2t3/b1yu) poe8lkka sp3 k2tds tilt of the cars when negotiating curves. The angle of tilt is adj1sotbu8 ey k3k2p/3) ktd p2alusted 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 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.$\approx$    $\times 10^2$