Sometimes people say that water is removed from clothes in a spin drye+l xhsl6r*h5w* (itzg r by centrifugal force tg xr+lwh*5l*tzi 6(hs hrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharv-9j cssa 95ydoog5 y)p curve at a 95sjcsyo )59gyo-a vd constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly fkoib*i)03w cq+s s0qroad. Where does the car exert the greatest and 0q q* ks)is0bf3iwoc+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 ridg3bvz 7he:kf a1mwuqi9 v67d ;ing a horse on a merry-go-round. Which of these forces provides 3 vaq:79e k;g 6iufw1bz7dm vhthe centripetal acceleration of the child?

A bucket of water can be whirled inuw*ja wr ,,ob* a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain.bur joa *,,w*w

How many “accelerators” do/v4 fk.kf 9o4mopk5tc you have in your car? There are at least three controls in the car which can be used to cause the car to accelerateto4./okv9 c5k fkpfm4. What are they? What accelerations do they produce?

A child on a sled comes flying over the crs6( y)qzs9.6 jbeqkx mw)fpj+est 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 decreas 9(smjwks))qj 6 zfeb6pyx.+qe as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rouvo3mtbp,n 6-: n stp7snding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banku5uupqv n/i,yb +cw /fv7b6h8ing angle given its speed and radius of the t/p c h6unv/,+bwy8i bufvu5q7urn?

A girl is whirling a ball on a string arouh;1,4cc 1lxq, m0e8 oxa *xgudpkw-rrnd her head in a horizontal plane. She wants to letpa0x-rr8d*x1o m1q c xclhugw,;k , e4 go at precisely the right time so that 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 force on the Eajpq)rxi;l0u1x 95n y(fj1 to lrth? If so, how large a force? Considel(o1f1jpuxtq 5;ny)xl 0ij9r r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would9flni t6 +m,an the Moon’s orbit be diffe+ na9tlm,n 6firent?

Which pulls harder gravitationally, the Ear9cz z+ cwj- n-jfvg0y5th on the Moon, or the Moon on the Ea5n zc+vw yjf9 c-j-zg0rth? Which accelerates more?

The Sun's gravitational pull on the Earth is muchl.2fsn hv2x23qy v.zk 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 t f22 z2.xqyv.h3klsv no the other.]

Will an object weigh more at the equator or at the poleaie1. m t)0 ,maz,soardz/1o + ki+xwas? What two effects are at work? Do they oppose each otmtz.,w+10) /a xzo ,aikaad+r m oi1seher?

The gravitational force onvssqe:f+ j;y vjj8y8pj6om+ as *zj(( the Moon due to the Earth is only about half the force on the 8+ jss:*v;mj+ovj 8f qjja( s6yeypz( Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suw b/a+q; rl b0:w/hu3rvz0n stn larger or smaller than the centb r/nh0+/ 3qb;:vswzur0l aw tripetal acceleration of the Earth?

Would it require less speed to sq rchry)3:/vlaunch a satellite (a) toward the east or (b) toward the west? Consider the Ear/ hrs )y3v:rcqth’s rotation direction.

When will your apparent weightak9+pn -b.ytox .pdi8dr6di, be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acceler.iadpo+- xn .r8bk6dtiy, pd9ates 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 c eqz.tw2 gmv.;uc-b6 m+qs2aadversely 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 falm+sw2qzvctq-ec2m . a.g u;6bl, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” 0r6 cah6rcm 3.szt2hvor “apparent weightlessness” between steps.2tc vh6 h36caz.mrs0r

The Earth moves faster in 7p8 b1wwu)( oyia0*l ecujgs/its orbit 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 facwlbjg )u10a osu i 8(7y/*ecpwtor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until.be fxb0fhsf8;t.tm+ it was discovered to have a moon. Explain how th8b;. bmt sx+e ff.0tfhis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muii5x: bk l s3e*f2, sni3zwj5ech larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hbj*fi,kx se2l iiz s53ew3:n5int: Consider the difference 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 1980se43,3 vt;hixwy,zgr ;ae q,m $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ay1fhii i 71lq8cy+n2 qcyu47in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radiusci4y1 ha1nq7287 li iyufy +cq 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-kg discus as it rotates uniformlk ,)mm5wmakt4y in a horizontal circle (at arm’s length) kam ,mmw45kt)of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbithw4jqm p2h oho0p r3*, 400 km from the Earth's surface, and circles the Earth aboo 42p* qhh3m0rh opw,jut 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 spet76hir9 gb7v8x 3nvfsck of clay on the edge of a potter’s wheel turning at 4b67 vhsri 978vxnft3 g5 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate(43h:i.n3uci j 5 uvylselkp0m-rp 2 icak94l in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If0rvcy u j 29- .3nu:5p4kik sli4heail clm3(p its speed 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 iem) w5 * pxujj2vfjj5 j0a4ql9)be6c 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 the mass cqj 05bp e *v wu)je45 2x6lfmj)9jijaof the car?   

  How large must the coefficient of static friction be between the tires and the r*ohi ztq h+::.sjnvpp 7lh2tt is1h0,oad if a car is to round a level curve of radius 85 m at a, t:h7:nh. s*hovp0i 1ijhl st2tpqz + speed of 95km/h ?   

  A device for training astronauts and jet fighter pi nn7x mk,g +ung0w+)ailots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the for0 wn+ngmg +) uk7ina,xce felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variabl naf2(/)vh pive 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 v/vpi(ah2f n)coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsid vxr4 snp:u7b+y11o /evx6w+w t4urce e down at thet+vrsewx:yx v6u+w 7oe4b4 np1 cr/ u1 top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundy7flxoi123,x m 0kmo oed top of a hill (ra7m 10xfo2 ,okyx3oimldius =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 1at,jc .yqvx:it p+b ,65-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost:ij vb.y6paxt tq,c,+ point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circ-ezn: zb(59 1/l9a0hqvpvzv aqp3p qele of radius 1.10 m. At the lowest point of its motion the tension in the rope suppov h(p/vba lzp9qqqp0e9ze a:v-5 1z3nrting 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 9l/)uprzds0k7k2c9uw,yzm f : .00 cm from the axis of rotation is to experience an acceleration of 115,,z l/0z9krwfp) ky7u2cdu :sm 000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ar am anfk4gjl*e:3:-vje rotated in a cylindrically walled "room." (Seej:l- f: vn*j3ag4a kem 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 frict pfdg537 :0co155q dxzhhfytpionless air-hockey tabletop, and is held in this dfhgqzt pdxyf:30oh5 5 51 7pcorbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight o 7rjb2 4vdavq8f the ball which revolves bra 2d7vq48v jon a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 7 byfxun*47:uhya-; uu9 : b0m2bom zrp5 $\mathrm{~km} / \mathrm{h}$ , 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 ,b /yj7tqexz ; /.k-l urrxzu2$ 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 v m.yx4fsg3 s99de z-ccertically 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 ne 89s8pagyjh c0t force exerted on the car (by the ground) in Example 5-8 when its speed is0jsp8ah9 g8 yc 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniforyo4rxr z o;(8nm+ s/pt3y ypm*mly from the pit area, going from rest to 320km/h in a semicirculsm8oyr 3+tz ypor y/4 n(*;mxpar arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At 7d2 qve(hxp +pa particular instant, its acceleration is7 d +ppexhq2v( 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 k:)s9gg fsvh 2vf8zj*ae9 k;y spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass )fgkfs;*g9a8 : 2s hjvzke 9yvis 1350 kg.   

  At the surface of a 6/ ruzt9njv l7g23f ywcertain planet, the gravitational acceleration g has a magnitud6ywz/vnt3jl rfu72 9ge 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 r;rs-o hd5 b6ngravity on the Moon. The Moon's radius is 1.74 ; bs5hr- 6ndro$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hp w.bij)2 rs.aas a radius 1.5 times that of Earth, but has the same mass. What is thsb ij.r). 2apwe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rad)i vkuby2j za07:a *ecius. What ia7ak0ej :z2cv)*y buis g near its surface?   

  Two objects attract each other gravitationally with a cf)z oe3h98s 7weyyb,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 og omjrhmjy 0;:s6: r8 -qxybt*f gravity, at (a) 3200 m 6 yob*y8 jsmg xthjr :qr;:0m-   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E: ;b,l xwtji2q(rsev+ zse3e cy*7q 03r wv:yfarth’s center to a point outside the Earth where thegrave bj +r3w;:sc vr,(3etly:*27fsq0z eqv yx wiitational 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 gfua949z)q z9lp 2zup of our Sun packed into a sphere about 10 km in l9azugfp9 zqp42 )9zu radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf sy oa xcmddlb:8*0tpcy 5 yz(*;tar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the m8yc (ctoadb;mzypd: l 50xy**ass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fez.bex)ggrc vw :.. 0mtel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. zxw 0 bvgm..:e)rgt. cConvince them and yourself that it isn’t so by calculating 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 s1-ur8 y5qusf*b* 29 x,pm qfzeczs5ucquare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the oufzc2u s-1 *spcqe*,x5yu r z8q m9f5bther three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sameex6b y tv4rt/(-ps)v x side of the Sun. Calculate the total force on the Earth due to Vee xbv- xspry6)vt/(4t nus, 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 of Ma/i(:t)yfn.y:2qtat s oi da 2ers is 0.38 of what it is on Earth, and that Mars’ radius is 340 yaa22ttds/nqe)(.: ifoiyt :0 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valu oxy78cioq)t /nao80:yw 4ei ae for the period of the Earth and its distance from the Sun. [Note: cn 7t40/ yywoo i:a8ao)qx ei8Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablexac/7y4 f tk1i circular orbit about the Earth at a4k 71ia tcyfx/ height of 3600 km.    $\times 10^3$

  The space shuttle releasesxb stau)py5 8+ a satellite into a circular orbit 650 km above the Earth. Howyxbu a+t) p58s fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylc skh(iq;apk.d2h1o b,)g ju0indrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s .1u0hpocg sihaj ,qk2(bkd; ) diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it0 6x; gb,kqpfa takes 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 Earth. Does your result depend on the mass of thkf6b;p xg0aq ,e satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top oh w8f o1eja57wf Mt. Everest to be pl1 h8jeww75a foaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contibuviq b 08 5q,veob8m6nued to orbit the Moon at an altitude of about 100 km. How long did it take to go aro u6v0bm ,q vbo88ieb5qund the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pza 1(rb7u5 cjnlanet. The inner7z 5craujb(n 1 radius 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 m2uaocyr6 41 ;3vjkets in diameter rotates once every 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 e a6 vk41s tyor2;j3ucthe bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronautnamzlv;76 wl w8:itn7 4200 km from the center of the Earth's Moon in a space vehicle (a) movinvwn i7t: wn; aml8l6z7g 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 stars of7+lo4/55 bucnkxl wsi equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway7/ux lsb4ik cln+w5o5 between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator thc(-)(bo gv+zy ,gogd 3kwg l:kat moveg3co+z:-owg,gv)bg l k (d( yks
(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 cordldv6 86 kcerz/m l.s;v ;fyhb/5t9lyh suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevat6y l.6vl5y/mkrdt ;;h9 elz8cv/ sfbhor accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite oj xmtpkz w7.. b/2ih.arbits very near the surface of a planet with period T , the density (mass/volume) of the p m x.7./.azt2kiwpjhblanet 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 determincrapia3k ;2 tl;h8z6ae the period of an artificial satellite orbi68pz3;ikr2;hac al ta ting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hu6;v+ox 6pmik,j5e s ykndred meters across, orbits the Sun like k6y5k ,m6vjiox+;s pethe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dista c, /lyx9u0kfwnce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very i(af4ni,lg ,xu. bfjpj .j.(yclose 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 “i x,i(j,lp.bjjguin 4yaf( ..fn” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gala +/ksybg k zk0:7qmqs(xy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 massnago crb/)ii 2- 9(idj, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609).ni d/o-b2jra9)gii (c
(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* zv0cjvvcf pp/*m m:4 period and distance of the Moon. *mc cjpv *vpzvf4:m0/    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moo um./* vfm+ y1ynf;zslns, using Kepler’s third law. Use the distance of Io and the periods gfv;y 1*f/+um.l ysnzm iven 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 Maddj)+k0h /uhhrs and Jupiter consists of many fragments (which some space sch/h)+ujdhk0 dientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in tirn o-j.y ;0 *nwu2aajhe form of a band completely a -yn.o;j wr0* najiu2encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge vidm9ob;c u31zo lh86 n84r brby swinging 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 tole 6bvomorn9rz8b1 d 4 h8ic;ul3rate 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;)s9owaz7 h1p ovu 6zc’s surface will the acceleration of gravity be half what it is on the surfa; 971whz6 zop)vsu coace?    $\times 10^6$

  On an ice rink, two skaters 42t2fq7 yx kgmof equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they 2qx gky4m7ft2pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, 8wnh4 ,eec. pzthe apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of t4,wzhcn e8 pe.his effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Enroru.7y8tolc e; -:b arth to the Moon experience zero net force because the Earth and Moon pull with eq :ut8r.ye7nrbc;o - olual and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an e4v etc xqxce:9n:b-s xhj:tq8: l, xa6levator, it says your mass is 82 kg. What is the acceleration of the elqvcxethc jq:9n:bx,:s lx xt86 e -4a:evator, and in which direction?     ----待选择----upwartddown 

  A projected space stati )h wt3x 6uc5.znxd-fgon consists of a circular tube that will rotate about its center (like a tubular bicycle g-5hc d w.t63x )uxznftire) (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 hiet/ mhv5rqgmjx+w 74/9-xyros aircraft 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 i;ri (jdqwc tq2:5 *itqn terms of its radius r, the acceleration due to gravity at its surface and the gr5t jq:irwq2 i;d*c(qtavitational constant G.

A plumb bob (a mass m hanging on a string) iafv s ij-oy(6pk8o 4f*:51pmwrm wk byzn *v/;s deflected from the vertical by an angle 5 f;ap8wvf/4mn :6jrs vyoo ymwbz -(pkk*1*i$\theta$ 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 desig1tgjzwa1 ua .2n speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saz .atg12aj uw1fely handle the curve?

  How long would a day be if the Earth were rotating so fast that objedc vi,mpw./bziog8/,usb; :r cts at the equator were apparently weightlescbi ,v;di//mzwg 8ob: p.ur,ss?    $\times 10^3$s

  Two equal-mass stars maintain a consu k cd1z:y46ooxc99f mtant 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 curhy;mzer :ocuqzti1.395x9 fwee 8n2rve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17 nqe c emft915yzu;rri hw8.3exz2o :9.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timevy, 7uhtq)3p87ohamf nz-* fjs 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 g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following h mf-8v3*zpoqnty7jf) u h,7a data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ex zvoxv/296zql tremely 9/qzvo z6x2 vlmassive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constantbrd dz24+skk2wvp9f -fh ,i7 z 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) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go wzv,k -2h 7bsw pd9f2rd+z4kifithout losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a groud 5*mv si7rrd7a5 pllzg(9 km+p of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determi+ad s7vz*ml5rk d( il 579mgrpned 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 (j4 o;yidgsb.- 8w-liaNEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros isds8;y.ig al-i b4j -wo 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 m ,e1pbdus w+*shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 +1ebwmsu* ,dpkm above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3xs*mqz*wk3/8n7u drs000 years. (a) What is its mean distance fromx*8qd *kwn/ 3umrz 7ss 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 actually "feel" yourcyv jh /j) h-q:8o1sy;*naah rself gravitationally attracted to someone near you. Make reas )8s1;hhh a yjq*no:rja/-yvc onable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of thei g)y9unuywaq* 49f; m Milky Way Galaxy (Fig. 5-46) at a distan*iuwy) fqa49ung; y9 mce of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.504zi r5pg +-yxg m on each side. Find the magnitude and direction of the gravitational force on a xp54z i- g+rgyfifth 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 orbitpe+drs*qc84:ee ex t6s 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 rwk4/yg5tj*0d h(i ru 1.5-cm-long sweep second hand on your wrist h*jrrt g u /w(45ki0dywatch?    $\times 10^{-4}$

  While fishing, you get bored and s;(w 01 vbb1h2bfqb 7jpq g4ajgtart 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 pvbbh;0f gw1ajb(b7qqg21j4 with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hi a(sduz7n 5f nm.w7(vighway is designed so that a car traveling at speed7nv ( s.di f5zmanwu(7 $ 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 o kg-j+ qqo+n8rf the cars when negotiating curves. The angle of tilt is adjusted so that the mqkg8+o -+rnqj ain 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.$\approx$    $\times 10^2$