Sometimes people say that water is removed from3 xnx0y*p0 e jf()soqewda 0(q clothes in a spin dryer by centrifugal force throwing thq)oja(w0s dq ef*ey 0xn 3p0x(e water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sha;e,de,djumw e0rkz1 3 rp curve at a eew3 dz,u,dm0ej1k;r constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constank jsu(a4wm2 .ulr*p;g t speed along a hilly road. Where does the car exert 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 u (*ljw gkasp42rm;u. a hill?

Describe all the forces acting on a child riding a horse on a merry-g2gqg u-qa20 ly, 9nklko-round. Which of these fon2- k,2k glyqa0g qul9rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spilh-o/ iacoi+p3b y5lrcwp(9 4 xling out, even at the top of the circle when the bucket is upside down. Expl4r/3ipl a9( -ipc+o cw5 yohbxain.

How many “accelerators” do you have in your(0+cytuz6e ovm *a3k . zn-gtd car? There are at least three controls in the car which can be a 6o(zkv+ mg y*dtz 0etc3.un-used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest ohoa6ys )ubf p02-/ 8im cs;mgnf 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 as he goes over the hill. Explain this decrease using Newton’s second iy)pu6 mmh/-s;8csnb fo20ag law.

Why do bicycle riders lean inward when rounding a c6l7q (rvc. vflurve at high speed?

Why do airplanes bank when they turn? How would you compute the banking s:jw83weo*l:vm rbu(yt f2-g83j oc/qf2jk langle given its speed and radius of jk*j3vrojtf(l/b-c 8seq u m2yg2fl 8:wow3:the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Sh 7l7 hb ki(m0x8zty0lde wants to let go at precisely the right8z(i7txml y7 h0bk0 ld 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 Earth? If so,v)9vk 1g*ka vddwen5 7 jd5dn :u(q+c9uzu.kq how large a force? Consider an app5k *e5(v adnu dvd.knj:+vgq9 97u1zqduw c )kle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mo pi4ls pz;js20on’s orbit be differenp;siz 204p jslt?

Which pulls harder gravitationally, the Earth on the Moon, or the Mqogrv.ajygm :5zn:q6a,l - 8f oon on the Earth? Which accelerates mg -qj8mag6n,5q zf: a.lv: yorore?

The Sun's gravitational pull on the Earth is yomh/ 47 tx9hgmuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain.h g4/ho9m7yx t [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the p: un1xh-iikw. w(tig4gi q+b:oles? What two effects are at wor4(t.n1 wx- iihigi:+wgqukb: k? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about hbp tdn 3 5xe7m ogct,0(e-ei5falf the force on the Moon due to the Sun. Why isn’t the Moonex(fm, 7ent5geb 3c-o05 dpti pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun4f6dqjh 6ditueyxyl7zr 154 ( larger or smaller than the cfzh4r4(q di1y6dej5ly xu 7t6entripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towar.jmo +qh5iny 8*5(ghfak14r ih8ply pd the east or (b) toward the west? Consider the Earth’s rotatiypq 8jkl+. n(5gmo i*5a y4rhhhfpi81 on direction.

When will your apparent weight be the ycfe8m+y ukw7.0- wn ogreatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c7 kuf0wy- .n yw8o+mec) 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 ab2ss qw;dxf 4*5 ex6ofdversely 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) t ofd*6 w; 4ss25exxqbfhe 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 weigh4mn 5ly+ -lpazpcti1+9dlqb8)n8ms xg5e-j qtlessness” between 8l 1p9 5 alq)b5 snx--i j4lczqme8pdy++tgnmsteps.

The Earth moves faster in its orbit around the Sun in January than in ;443.dq g yefzhlh d,aJuly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the d.ld fh,agy;e4 h3 q4ztilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was w2zza;aq)n*5s1 s. 7bzj/zd m et6uzcdiscovered to have a moon. Explain how this discovery 5qba/zns;cwjdzz z)1 .u * tm2a6esz 7enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'zn)pd ,iqg)c6rw 09das. Yet the Moon's is mainly responsible for the tides. qpnr06)) gw dzdc,9a iExplain. [Hint: 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 travelingpiiu h(z:5k1+- 8 b cirqw0odr 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbit ar:xcy.u kvezb h )kd4inf ywk(b*7 75b3ound the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that vbcdkyu:en y3(hbxkb4 w.5* ik77) zf 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-kg discus as it rotates unifob2+2 a2/pijc gm v7dlcrmly in a horizontal circle (at arm’s length) of radius mg+db22vi7 jpac/2 cl 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earpoi8iw +hn w*/th's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the go *win/ h+8wipravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a f f9 njg7lv93ospeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wh99fofnv37j gleel’s diameter is 32 cm?   

  A ball on the end of a string is z0i.5jjo*awb) a(7 jgm wffq8revolved at a uniform rate in a vertical circle of radius 72.0 cm m7wj *qo 5fj0zaw(abig8)f.j, as shown in Fig. 5-33. 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 with w/ 8wz mk,ihd6e.so/-; lghjc p+g1ielhich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires an./,lseck8hewp gl hgi1/ ;dji+6-zo md road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeff6c chq y:y/dliaa1g( )icient of static friction be between the tires and the road if a car is to round a level cd)c61c:l gyy /haqai(urve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a /iw1bp7x+j jp+ ch3oqtrainee in a horizontal circ q/+p+c1jijx w37obhple of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a ro esy531c4kw w1+g zczstating 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 friction between the coin ywszz1skw15 g4 c+ec3and the turntable?   

  At what minimum speed must a roller coaster be traveling when vq/sc n+ tp.gif- e7,rupside down at the topqr 7 .v -+/tsnf,cpgei 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 theab+ ;q do/x:2jckd3wp driver) crosses the rounded top of a hill (radiusdc b :xa2 +qw/kjpd3;o =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 revolutionsfvhzjo iokv:60/urtz) y +8b6 per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the to bt kh /8:v6jri 0yfzouvoz)6+pmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10+ry: 8uljrm ra v+ei np,;6,hc m. At the lowest point of its motion the tension in the rope supporting the buck,ra6iej crm: +; , nhpvyr+8luet 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) must0smuligrqt) i )y6xj-0cyak1y i4i + : a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelerati +t m6a jk-xl0iu)ysr0q4g:)iyci1i yon of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylin2b1 qy tw4 mowzpz/fr; wh-l43drically walled "room." (Se w-;tzwbmhwr1q4/l o342pzf y e 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 frictionq;3hb:4 0 hhy(fq3u iev:ccvu less air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central holi4h:uh3 :q0h3bcev(y;f uc vqe 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 , preciselxypl ;8v8k9pnz u,oi56 5jvpncji(u3y this time, by not ignoring the weight of the ball which revolves on a stringn z 8(5lii x5jpvc p,ko yun8upv;963j 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 jsh(q;0 e kdoy4i1 ;mu88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesbh 3 )t7ys;s1iza- zka $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310 t*co 1 : y+0m3dqzxhni0h* byl$\mathrm{~m} / \mathrm{s}$ . 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 centripetaltj6e963 nmzabq 0j jtlr18m9 + oue:qk components of the net force exerted on the car (by the ground) in Exazjtntkmo3698 a+rq m :eb906u jle1qjmple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area au7c2 dehdfa/xe e67,, 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 cuxe 6da fdc/72a ,7euherve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i866zy/g,cdhh( am2avkr ,jj xnstant, its acceleration /z(vmr 6j6 xg hd,82,aya chkjis 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 spzt +u cniz *ttn97t*zk -b6 a5(mr+lzhacecraft 12,800 km (2 Earth radii) above the Earth’s s at h zt(rkn+in-zz*uz cl5bm*t+697t urface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acynw y iggmk,+dkpuu:5)by k4 h)h1o (/celeration g has a magnitude of 12 w n5phm ,+)dk(ihk1yoyybg g4ku:)u/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 thjv i56k lo6 /t9pw;bfxe Moon. The Moon's radius is 1.74 kx poj;wb6ft l5iv9/6$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timesgr:a bh6f.v/vrft7r7 that of Earth, but has the same mass. What is the acceleration due to gravity near/7 :f vrgf vr7a6h.btr its surface?   

  A hypothetical planet has a mass 1.661vqjss 6z8sr( cp: *bg times that of Earth, but the same radius. Wha6(b zvssgq:8cp*s1j rt is g near its surface?   

  Two objects attract each other gravitation6i30/hnn qe-*uij0 0i ksue zlally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accef4v 6n8elb bt)leration of gravity, at (a) 3200 m b84le )bv6nf t   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance f7fd)0 -zt0.nqns.rccwo,h -eq vd+ ud rom the Earth’s center to a point outside the Earth where thegravitational acceleration -0d fs, .w+cn-.)dehcq7z qdo vn0 rtudue 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 y; s- t4,qoervof our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on;t er4-qoysv , this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Suntg,:jig b5gs3 but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this st,gjts3g: 5gib ar?    $\times 10^7$

  You are explaining why astronauts feel weifk3f2l 0e4kyq( ce, pxghtless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them andyf3lf24xc( ep ,ekkq 0 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 sn,c5 2+ llqvbuquare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one s+,uvcnl2bl5q phere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pqtf8n b p(4t5llanets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sa58n pt lq4t(fbturn, 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 6db)/my,9ox cj er2a;t toy1l gravity at the surface of Mars is 0.38 of what it is on Earth, and tha, ytcrxy1t9jbe;da/62oo )ml t Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of theo.1z(iylqk9 f0iw0 zg Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examp ykwlf 00og1(z.qi9 izle 5–16.]    $\times 10^{30}$

  Calculate the speed of i. zbxu nzg2 ktg7+wde8087ybe e.: rw)louy,a satellite moving in a stable circular orbit about the Earth at a hee.zuewd ti:0r8b b.x8yw elo,2g y+gn7uz) 7kight of 3600 km.    $\times 10^3$

  The space shuttle release .83vtifsmo ch-ma 93ns a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be mo.mc33t 8f9n ovahm- siving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if /yb vl2kqi97q occupants are to experience simulated gravity of 0.60 g? Assume the spaceshi /q2 qv9blik7yp’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 Eart-tb7l fkl,m 5x0jsyutvp:5d) h 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 debk:5pmdl- t5f jt7,0 u)vxlsypend on the mass of the satellite?    s ~    min

  At what horizontal vhl/.-zm )wzk(4yl:hh lgl1 zw9b-vzc elocity would a satellite have to be launched from the top of Mt. Everest to be placed in h bvcz zz:k hhg)-.1(ll-zlm/y9 w l4wa circular orbit around the Earth?   

  During an Apollo lunar landqr lpt)*- v;jring mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go arjr tqvl-rp); *ound the Moon once?    s

  The rings of Saturn are composed of chu,1ml(loly xu;nks of ice that orbit the planet. The inner radius of the rings ism ull;x1( o,ly 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 -*9w)v4 akd kplh1;9ne: 5bhoqluzy nin 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, 9 n*wqb u lhvo45:9pyezd;a- klk1)nhand (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centi inu7e(..1 kmciih6 rer of the Earth's Moon in a space vehicle (a)rm .i1n6 i e7uihk.(ic 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 const 2j3a;uo*7hpm 3a9l qa zzim+ists of two stars of equal mass. They are observed to be separated by 360 mulm zaiqj2 ;z3* t+hop37aa9million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevatw4zu .mu*uh qto/9c )ior that mo u/q)oc uthi.zmwu9* 4ves
(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 ceqf5 6stlqlz,5hf zsx x ;a71)viling of an elevator. The cord can withstand a tension of 220 N azqvt 5qxl,sf7);5l ax1hfs6 z nd breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits ve,aeng+m9e, fpay g: .kry near the surface of a planet with period T , 9m.a g a pg+ef:,nye,kthe density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the pop(+5i +lmv37t-adex evhbn6 eriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’sb6 evme3+(o-+nh 7 i ta5xdvpl surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits ther+0*kq /hb,zwf meopg ./cda : Sun like the planets. Its period is 410 d. What,.z0mda h :pq wof/k+/brceg* is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of z//yd /c* yh7b9xojagz6wj2 l 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. dc b 7dejap7:u )ammfwb7 76:qIt 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? Whab j )pu:7d6qcbmmdw 7:a 7ae7ft 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 Galjlu0w .h0yf 7m,dso2saxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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)z8:8e cr,rz)od xjnk mean distance for the four largest moons of kxe)c,zrn8 d8:j)o zrJupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known pk gpvz8(ttxfg;j;sx)f 283v c eriod and distance of the Moon. ;8v8s2)fftgpx x;tk3zg cjv (   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinggk (vvn*64g+9mtoi dds :qw.j Kepler’s third law. Use the distance of Io and the periods given in Table 5–wko6gd(gi n4j v :*svmtd +q9.3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter g wd,0,-cos dn evx:x(consists of many fragments (which someg vx,, w -eocnxd:0d(s space scientists 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 a)two tpsv11d/;h3 iprk - y6p.bgy0 alrtificial "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 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 Ea3; dwlkpgv-)/ b 10r.tiaoy1s ppyh6t rth days?   

  Tarzan plans to cross a gorge by swinging hmw:dpp40fuv 2)z4gi 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 tolerate at the lowest point of his swing? His mass is 824v)u40 m ig wpzd:phf0 kg, and the vine is 5.5 m long.   

  How far above the Ear 9xzb1ulq0 xnbh ks+59th’s surface will the acceleration of gravity be half what it51z+uk9xqsxln 09 bbh is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass g ym0 3m0/q(a,(mp suexfe7xr irab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m 0u y (x0mrs,m3q/fma 7 eiep(xlong and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth roxh)hd 82g)y jitates once per day, the apparent acceleration of gravity at the equator is s gdy2hi))8jhx lightly less than it would 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 spaq*bd l9 azrcn1w6epr*-j 1do(cecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal a1 zrb* 9noa1lcd(*p6r e -wqdjnd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom xxo8l 8ik l.-yty4as0iq0bi0scale in an elevatqitxo0 x.8-is0l yk4 ylba0i8or, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about i0y xccrsv,i-:ts center (like a tubular bicycle tire) (Figvc- xcs:iy r0,. 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 aircraft in a v1n0u(d oo:lc 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-6pf0 rqq2g(wce1vxpt13xow i 0cdb* a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitationiw x0f cp1bq-d2*3reg cqpv6xtw (01oal constant G.

A plumb bob (a mass m hanging on a string) is defle6vu.m8tzm e50cxmf l *cted from the vertical by an tuv0mm ze.*f56l8 cmxangle $\theta$ 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 spm:xd u5qa n lovlnpve: a d9;7vz4r,o91dc6x,eed of If the coefficient of static friction is 0.30 o97,5 dxulz,q: 1e nvp4 madr dc9:vnaol xv;6(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 objtb03r 0k sthh(ects at the equator were apparentlthst 30r0k(hby weightless?    $\times 10^3$s

  Two equal-mass stars9opr4axe) q( mdwc1h ) maintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constanp;gd o0 ev 1 uij3,r)/v*dmcgst speed rounds a curve of radius 235 m. A lamp suspended from the ceiling cguv3jgd,/psir e;* m od)0v1 swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claigoqt axt(v(-f b31u9tmed 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 few1 gt-qtutf(o3va 9 (bx 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 ther2u4lwlp5y qsn/y 5d+rkg +g5 Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by+dg rl2q5y45uy5prlkn+/sgw 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 (0v- /exeip ofspeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of cxe eo(ifp 0-/vurvature 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 at A?

  The Navstar Global Positioning System (GPS) utilizes a group of*6 q4ftfn ts ;q6urx bs;iet*u( 7sq1f 24 satellites orbiting the Earth. Using “triangulation” and signals transmitteds;bs qrq6;iu(utseff t* 6ntq7 f* 4x1 by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous .pewiu qic40i/gbbm3,42 dpm (NEAR), after traveling 2.1 billion km, is meant to pmmgiuid /bq.i 3,e2pw4b c04orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuingjor-,afr8)i v f f2yg8fyd (/xr +ud/c a satellite in need of repair. You are in a circu gxycd ,-y rfd r8a+)//( fjiv8rffu2olar 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 period of 3000 years. (a) What zvwc+ia5wwsxyt - 9+. 9zrj+dis its mean distance from the Sun? wwd9rsz -ij5+ac y ++t9xz wv.  
(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 coul0gw6 g3new1wd,+ bmyb d actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions,mbb d0ygww3w neg6+1 , like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of t1( 2gk3andzu3 a nb(eennfi(bl46 q)ghe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,zdl1k( (( n3naqga i)2n b36ug4fnebe000 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 squarbnvkmq9a 0 . +9(o rfedv3kwt0e 0.50 m on each side. Find td 0r(e9af vm.wb0ktknv93q +ohe magnitude and direction of the 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 t8zgd,1bki2o0 :osu c: k:denyhe 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 tqxn-h 5bdgi+,he 1.5-cm-long sweep second hah,xq5 idb- ng+nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker mlw q9t ,nsgihc(e 2:xa,39pzweight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See a92mzc eq:np, (wthl9ix, g3s Fig. 5–10.]    $^{\circ}$

A circular curve of radiue xem 3*bm:tm4s R in a new highway is designed so that a car traveling at 4mtm x e3*:bemspeed $ 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 3 krx:8cnu d6; zwnyw-of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a ;kr nc6 xy-3 dn:8uwwzspeed 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.$\approx$    $\times 10^2$