Sometimes people say that water is removed f4r wz(,x2a/w anu/(sf3pcesai4+ q4p l xt5i mrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemt,p5elzx/f aw/c3m 4a4( 2ui4xi r wsna (pq+sent?

Will the acceleration of a car be the same when the car travels rlnxnzzo;rhd(m32p zga6y 6hj 83i,4 around a sharp cx ,(r2hgl r zj;ya6 pd4h3znn 8miz6o3urve at a 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 roaqzbnz toz*k46 q. 0ga:d. Where does the car exert.q 6: az*nqzg0ot kbz4 the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on*)wsc9 rqqgy2 a child riding a horse on a merry-go-round. Which of these forces provides the centripetal ry*s)2qqgwc9acceleration of the child?

A bucket of water can be uqlq-wt s5 o o(usp:*1whirled in a vertical circle without the water spilling out, evsu q :1u(s5-oo lptw*qen at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have izw;7p-3i euj63ks+1 om rioz:rqgd /zk +3nunn your car? There are at least three controls in the car which can be used to cao -p iudu7+kw+zz16j 3qrimeko3r 3s:gz/ nn;use the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smalvxz(3cn wxg+bh/2 mn 0qr)v 3al 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 as he go q gvz(0cr+vn3mb2/w3)xxn a hes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speenpvnj3pgw ezf sfz62116/w3 bd?

Why do airplanes bank when they turf g,+r4s oa3qi;+hhhouj/h 7xn? How would you compute the banking angle given its speed and radius offsg4xa ;qj7h/io h h++3hu r,o the turn?

A girl is whirling a ball on a string around her hea0smv 3 (l : oh9icgjg*lc8war8d in a horizontal plane. She wants to let go at precisely the right ta 0g 3ohl8wl:(8 cjgvc*mi sr9ime 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 Ev2/p95ewd-nf 1r hwq5 dxyuk,0wk v 4xarth? If so, how large a force? Consider an apwhvf/2dr4nv x55q kp k1u ,x w9dy-0weple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what io0fr;vea+0uap/y6b f *wbb) 20vjkuzt is, in what ways would the Moon’s orbit be dw +u fuv/p0 60r;kboa) j0avfyz2*e bbifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Ep wj*;*umx sp*arth? Wp j*x;*mw*s puhich accelerates more?

The Sun's gravitational pull ecp8zbgzg,j ).a8leb3p (z9p on the Earth is much larger than the Moon's. Yet the Moon's is mainly resppzz9bgb)p ,3p z je.8(ceg8la onsible 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 the3rvmgg))h.m7-oklbv equator or at the poles? What two effects are at work? Do they oppose e) 3mkvvhg-g )l robm.7ach other?

The gravitational forc9 0n, dgbzmafadk(p8 *e on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon p8dzbnk0mg( 9,a*f adpulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lahr y9iwou2t2x,4sml1p;w 4 iurger or smaller than the centripu uoi944ilpw2rt1mh, s2 ;wxyetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the ea 8,:eq*pmg 7k szup : s6t8rnoio:/whqst or (b) toward the west? Consider the Earth’s rotation7po6*khgw/::p tm88zssqqri:u, e n o direction.

When will your apparent weight be the greatest, as measured by a sca(d ue)**twcl t(wf3uq35srkt le in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upw)3cst5u 3 *dwq(etwr ( l*tukfard 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 al uw; h/to hj*0g2y4exffected by weightlessness. One way to simulatexl;h h2/t4uy gjow0 e* gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessn3y camm.++o,rko 8z ipi bm7g)ess” between mm g )oz3+8mbkrp,. +coy7aii steps.

The Earth moves faster in its oa1 p*(iio2u6iz: ymaorbit 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 muo:(*yp6a1i oiimaz 2 uch 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 to have9dv 6x0 . j8:lerewydp a moon. Explain how this discovery enabled an estimate of Pluto’s m xdery8:0 9pdw6velj. ass.

  The Sun's gravitational pull on the Earth is much larger than;:9ac8(r;oxdbu u 38q+0tp mj xctvfy the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: tr8 3(q9vcxpm8jt ;o+uu0x y:bad;cf 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 1980 3ng- lc.1soew $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 its9xap ovo o 4xyi0kr1* abm)7k+ orbit around the Sun, and the a7p y )+x0mb19i 4vk*ooroaxk net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-lrr7a4ie 1o:u /0 r ei9x5giwzkg discus as it rotates uniformly in a horizontal circle (at arm’swga 7i59/ 1oeelz r0uxrir:i4 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 surff-vc7yo/ g 6 gtbkrc5*ace, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the graviv6-/* o7r5 tkgycgbcftational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerati(,frkk1l 2)q fwcfj; don 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 )r1dq2cfjkf( k, f;wlis 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ver ;b tkx:t.dbr2 z/dgf:tical circle of radius 72.0 cm , as shown in Fig. 5xb:t 2dz;:rd bfkg.t /-33. If 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 wit.w 2tdnwn.xl,1cz.w qhn60wbh which a 1050-kg 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 resu26n h,wd n1znxwl.cq..wwbt0 lt independent of the mass of the car?   

  How large must the cueh7r k 0rm wo(z m61njfc08t07b oz/koefficient of static friction be between the tires and the roadonr6mjwf 0kc 7 ob 7rket 1muz80z/h(0 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 fightey/ ;xjin rk gb()0dri.r pilots is designed to rotate a trainee /r (by)x. djrin gi;k0in 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 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 fr 5*wr j2:zhtjgom the axis of a rotating turntable 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 fh 5tzj:jw2rg*riction between the coin and the turntable?   

  At what minimum speed must a roller coaster be t)d.3by(n;qz u; e fdxzraveling when upside down at the top of a circle d( z d3qn.xfzy ;;)ebu
(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 ro g z8ywf-ho1b6unded top of a hill (radius =8 ho1gb6wf-zy95$ \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 pexs qm3dfclcfsp,z0mpm+hd6( 3 z/e (8r minute would a 15-m-diameter Ferris wheel need to make for the passengers to feelss3+hmcqzxp( 6,ze d8/ 3l ( pfdmfm0c “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 0i iuaoafk h4luo,f8l9-9 3ngm pcxgu :g948lm. At the lowest point of its motion the tension in the rope supportinp48ohuock9u4 0i8,uag9 lln:l xia3 -9ffmg gg 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 0v-0 n+x0 ut(agp;sjjirzxy :/ zhv1u a particle 9.00 cm from the axis of rotation is to expz0 -y t(/prxi10vvzxajn+j0 :;suuh gerience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" atbnu yy xmz6 r*x 5rvx8u7/v1/l9ml/fx a carnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.)9yvfluvm8rr5 x6bm/y *x /xzlxu1n /7
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 ai jn1wi(ij)i5 +3 azcdha+tf p:r-hockey tabletop, and is held in 3i ap ha nj)cwit:(i d+1+fjz5this orbit 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 ignoa;3x)-w nrv0vj- e( alv(mrriring the weight of the ball which revolves on a string 0.600 m long. In particjwv anvr;e xri (a(-0rvm3)- lular, 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 per6jsnxa6xw0 u2 dc obf9m6r. f2fectly 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 za5t, u7(f hl1g2a fs r2nhwv9$ 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 veb ph.n) dsil7m20awm 2rtically 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 centripet nz54bkie8 e:j 3s*6d .wzy7xwmshhd .al components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 1ihmnk*h d zs 8.w64s3 zx.e:57edwybj5$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformlyd(c 35 u nm4jm/ti6clv 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 /mu 45ndm(v6 c3itc jlwould 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 tt0 ;vsi 2tp4hd v33zpa horizontal circle of radius 2.90 m . At a particular instant, its acceleration issd24z tv;03 ppit3t hv 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth r1f); u fln5o pvyfy5/uadii) above the Earth 5fpn/o5u;v)uf y 1lfy’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a m, -v5c 7eru net)gfb+*,p m+shee kf:/*trlpmagnitpfmv+ eb sprtfk+ n 5e*, 7gcu*h l/:tere)m,-ude 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 gravit jo *tdo+8ydh;.cvq )yy on the Moon. The Moon's radius is 1.74vj;)q.+ydyoo hdt*8c $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earthgwjn38 ,nk 3jobty7l*, but has the same mass. What is the acceleration due 8onbtn *,3y wjj3lgk 7to gravity near its surface?   

  A hypothetical planet has a mas), oq59ti ng3u-m aqoss 1.66 times that of Earth, but the same radius. What is g i-mtq )ooug3 9nq ,5asnear its surface?   

  Two objects attract each other gravitationally win*) ihd yg)7sbth 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 b cc:1(l pcgc0of gravity, at (a) 3200 m ccl:( c1g 0cpb   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsi0h(4ll fzomg2mk6s-,*peqxrgbo 9 1kde the Earth where thegrhkfme4gm-sog* (6o 2r zbkxp 0llq ,19avitational 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 massedhh,o9bim4ht: yt 4rbgz* 76 of our Sun packed into a sphere about 10 km in radius. Eszm:ibbe9to4*4 hhgy6 h,7 trd timate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an ap; xc 2p x8q*u7bf*xyvverage star like our Sun but is now in the last stage of its evolution, isvxc*bxy27;qx* p fp8u 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 in th.: m2yj; -s g*wggn8z nz6yv u0mm+xoke space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourse;y0vskmnmz gm.y:u-* gxz2 g8 oj6nw+lf 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 axobp5jp z0zm4z07t :w square of side 0.60 m. Calculate the magnitude and direction bp 7jo:wztm zz0504xpof the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the g3(+iy np )ayfplanets line up on the same side of the Sun. Calculate the total force on the Earth due to n3 i+gyaf )py(Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of M 26r1jky nqp*xars is 0.38 of what it kryp2q jn61*xis on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Suj.qx b1rh0a4 vn using the known value for the period of the Earth and its distanceh4a j01br v.xq from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboupy n.xcb y* qzqt3;.b1t the Eart1n bxq*qy3.z;t .cbyph at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circu k9sp2y5t t - *f9dji/r2k51ylflz clmlar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rel/2fi 1lyj92 m9zs*5ct - yl5ldrptkkfease occurs?    $\times 10^3$

  At what rate must a cylindricaz .*0pqim7)h:+ .qvsohx ymp ol spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)oov+: .h 0x7zpiq.*pmhmy q)s   

  Determine the time it takes for a satellite to orbit the Ea c-)6ar p)t+wi;wlceorth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is verol) iw-rt +;p6cewac )y 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 launc40zhx 5meej6 o4 mgpea-h,4g rhed from the top of Mt. Everest to be placed in a circular orbrp- g4hh46aj, 0 mex5zgo4mee it around the Earth?   

  During an Apollo lunar land9nstzvy4k xp-6/bk(q8bcr.vu0wv c 8iu59n ying mission, the command module continued to orbit the Moon at an altitude of about 100 km. Howq (knncrb56 ks0/.iv88utu -9yybv9cx4wvzp long did it take to go around the Moon once?    s

  The rings of Saturn aredmweju;z9m 40 composed of chunks of ice that orbit the planet. The inner radiz0dw9e4m ;jum us of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see ;l;u.ts.x n1 aozz1e uFig. 5–9). What is the ratio of a person’s apparent a. onz1x zetl.1 ;su;uweight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of tu; *: .oasr xh:dphnq);tf h.nr1:bt the Earth's Moon in a space veh:1).d.:ou;ph qhr :sa fnhtr* bxt;tnicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They antz;8/ddbzi 97sdcx 4re observed to be separated by 360 million k;4bd/zn dzxdi 8 tcs79m 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 of a 55 zygus zz5:09u-kg woman in an elevator that moves :u05 syzzg9u z
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatob9:fpn.qcp,h) l( hs cr. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and dir blc9.pscnh p,:f) (hqection)? a =   

Show that if a satellite orbits very near the surfaceqa 6k 3:h+c7bkthiv l+ of a planet with period T , the density (mac +hkavq+ 73 6il:tbhkss/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 period of the Moon (27.4 d) to determ fax 3m50sz* ty9l qborj83j*fine the period of an artificial satelli 3tr98jxzl0m yba*3soqf5 f*jte orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundk5jab/)bcu q- red meters across, orbits the Sun like thck/b -5ju)abqe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o/4 k r0v31as+4az ici o(p.qap lqy.etf 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 roughnerlm 2)g+ .jsjfz)nvv/1 f+sgwo3 )n ly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distl g+r2v+1f/ngvfnss3) ojzm jw.)e)n ance 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 theezli 46 ylr(msdedn u g9(0,g, 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 943 ome9,dg,vges6auaqrt im1 ,hp u- 3s9rb nlargest moons of Jupiter (those discovered ,46me,p rvg osg,1ur3qn3d9 i -au9b tamh9es 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 o 6irvi6/*p oj(gjq//muxyjnv+8 y 8r the Earth from the known period and distance of the Moon. x8/ j6+imoq nojyuy6ivr8(// p j gvr*   $\times 10^{24}$

  Determine the mean distance from Jupiteruvr m(*ci -h1b for each of Jupiter’s moons, using Kepler’s ti1h- cu*mrb v(hird law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupbw+w fmi4ikznr1 ++v0 iter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but ik4rw+wnmiv 1 ++fb 0zwas 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 describ- w 6mj91gl3u-spkzuf es an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like fms9-z wguu6lpk13 j-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 byr h ex2x9ch;n4 swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a foc 9h4nh2rexx ;rce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration k+(rnn*2-y5 iu k4 7aryl hgwvof gravity be half what it is on the surface? yrniyl h 7 2wrvn 4*-+(agku5k   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin tm.hwg e;+ x ihceqh9k*2.x0f 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 pul0e2;tmf+ .9.hxh*qck gix ewhling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparenih2e y(v4 p/ dmhb46lkt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of thihe (vilk4 2 dpm/y6bh4s effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling loi jrir+s79k// jny( ey3 pv-directly from the Earth to the Moon experien+ syyn- j73reij(v//io lpr9 kce zero 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 scakd y g51hn)/s*ueach /le in an elevator, it say1haekyuc gs h/ /*d5)ns your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stb 48x qpz+)ca)1pyrnnation consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation sppc)4ny1b8 nx+p a r)zqeed (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 aircraft v8- (c5. rtwpbvl(u,4 y zyrblin a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of i -le sxe *-::loj+jzv*8ljboats radius r, the acceleration due to gravity at its zjos* : b+ -a-8*jjevllxol:esurface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecvh8n9t tlg7 0hted from the vertical by an angltt90lhh8n vg7 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 In, j8v.h0skwmf the coefficient of stvs 8jk.0m ,hwnatic 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 Earth were rotating so fast that objectsagupj7pcfba8gf q0s y .bi+;y-s+;4h at the equator were pua4s +p.gfb gf;q7sby;ac 8hi jy+0-apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distuq1cm( hxoz+ x3ylaj/* -8kl 4ajn6fmance 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 curverxet,w26dl +c of radius 235 m. A lamp suspended from the ceiling swings out t 6cedxrt,l+2 wo an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tius5pt ihy)a;pkv):don ipnb s,,p 2) :mes as massive as the Earth. Thus, it has been claimed that a perstviysp, npndp: )5s iah,;uo)) 2k:bpon would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =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*4xfg-4 2wi v yy8udq)y -;ggmfgvl 6k extremely massive 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 galgkf ;4yv dyw-mf64vx g )* -gqyi82ugs 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 traversesh ox86/si vzwh+fl+n8 the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the norm n68o wzs ++ivhf/l8hxal 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 at A?

  The Navstar Global Positioning System (GPS) yq ,nizw3 25mmw gp)omre8(x1 utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, all2)nmoezqg 58 m mx(pry1w,w3i owing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelinkk o4enghfop *j,h,2 *vhcoz i-)0mz 3g 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40p3f oc-hvznigh hk ,,o 0e o*jm)z*42k $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 satellikk6hf)t e6x b59:q6 9egrug y,efxzh.te in need of repair. You are in ux6kgy:ekt9gbe6h9e 6zh qxfr ,.f) 5 a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a perio:5 yakfjhn d c)zpvj48uh90-dd of 3000 years. (a) What is its mean distance from y)h45du8cjh 9fpkdavj-0nz: 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 sf kd2/ k 7t8rhc ;crqcr13*wbwould need to be if you could actually "feel" yourself gravitationally at1d7rrr/*fcbcs83kthq 2;k wctracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky W:ctmcs50n4 -aoj g pqjc89t(fay Galaxy (Fig. 5-46) at a distance of about 30o89j0 (54-f pmaccts:jqc tgn,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 cornerx3f w2i,x):a a2yyktr s of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth ,w)x: kyafira2 x23ty1.0-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 nss9;:3bdjy z kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5:y/;wmw: -tivs bey/k t4 ifi.-cm-long sweep second hanm- ::eii;w 4.yf /t isvbwyt/kd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arn2ox5wi cxm;i g )vv(n*xy(6dound 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 lig()w ii n(yn65 xxxmdo*vc;2vne makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiykpck(-t3 /2.5wst zmyf w1uuus R in a new highway is designed so that a car traveling at spwsy.25/k3tm(wyuz cf p1k- tu eed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negoti9kz ,gf:w1y.rrlpj( pu. f5l kating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not b.1(yrpg. :jllrf9kw,uzp kf5 anked 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.$\approx$    $\times 10^2$