Sometimes people say that wap+ fq.b0.kgw bter is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong w gqfp+.0w kbb.ith this statement?

Will the acceleration of a car be the same when the car travels arounbsin s g 11qv/7mv9 2+gd2vtold a sharp curve at a constant 60 km/h as when it traveosqt d s/g9+vbvi gv 271n21mlls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alon b; :rrs-ssh6yg 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 ley- ss6;rbsh :rvel stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. 7 re d zgom74q - mzh q2hu2*d5nzzd74dib(pc/Wh7bdhnoz42cqqzdmd/ 2(g7ei dz5*7m p-z4h ruich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without 40gg4)0tft8h0nh h2z 0ms llt oecz t/the water spilling tglt8sfctleh/o )z42t0 0h40gzhm0 nout, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerator-w8p howj28ipfvz 51 js” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate82 z jvwhwpfo85-1ji p. What are they? What accelerations do they produce?

A child on a sled comes flying ove ).lsfsio5-vg49w)d ; npiut*6jc s ktc7 yd+gr the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not ac4vouc 6ik t + i*sgcplsj)5 df 9dsn;7-wygt.)hieve “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 law.

Why do bicycle riders lean inward when rounding a curve at high speed?0. + qlikuaqu/

Why do airplanes bank id*ubb4j n 3p*when they turn? How would you compute the banking angle given its speed and ra*d 3bi4 pj*ubndius of the turn?

A girl is whirling a ball on a string arounb/fw 3hjnlq5nf, / (ctd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the stri,jw/f hcbtfnn/( 53lqng?

Does an apple exert a gravitationa,mtn vedm.76s l force on the Earth? If so, how large a force? Consider anvm .,6 tnmesd7 apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, iny.j nk j6a)(km(gc9d k what ways would the Moon’s orbit bdc (6 ny(kjg.kj9m)ake different?

Which pulls harder gravitationally, the Earth on the Mo krha-bks-j6i;fa8 :eon, or the Moon on the Earth? Which accelerat8k:ai;bkr -e jf6h-a ses more?

The Sun's gravitational pull on the Earth is much larger than the g0f7o z.mpu0f3 tjg(2gjgu5 mMoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fg o5z0g23 f7u0gpj ugm(j .mtfrom one side of the Earth to the other.]

Will an object weigh more at the equator or at the frw 1g3ia85e 1bnxl;ypoles? What two effects are at work? Do they rnl1gaebx8wyi351;f oppose each other?

The gravitational force on the Moonwcx 3.9gve-75l: fsjv e6lokbu/zr * k due to the Earth is only about half the force on the Moon due to th7rv.cee/- fl*ok63v:wj 5b gzu9slxk e Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in it,/r cfi1go igo4/du2u s orbit around the Sun larger or smaller than the centripetof4g/ do 1 gci/,2uirual acceleration of the Earth?

Would it require less speed to launch a satellite (a) tk m9q/j3kw1r ao :tg6foward the east or (b) toward the west? Consider the Earth’s rotation direction.o j:rkmk 6gfw 19qt/3a

When will your apparent weight be the greatest, as measured bybkgurpm ,:e d(yz-4- f a scale in a moving elevator: when the elevator (a) acceleratesbz,-r -ue kpyg( :dm4f downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in m7lio*y u9 rt ;lnxd 6d0a*4ftouter space could be adversely affected by weightlessness. One way to simulate gravity is to shape thert;*nlomfi4x6tdd7*0a9u ly 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 weikr8;8ld:rptvax0dz3 nj bs-y + k5,ymghtlessness” between step8;dl3 kkr8yj05yr nmpxad-zb+:s ,vts.

The Earth moves faster in its orbit around the Sun in January than in July. Is hwg n/*)o:toc:ow,:k jot9f c9zm at*the Earth closer to )th o9oc:wg /jfk, : **9cotao mw:ztnthe Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explavwj0*t3 (jfi rd jki0) j8tp0ain how thijf(v8 j0w0dr tj0t)k*ai 3ijps discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moondlw2nn-m cnc7v; le,a7lg:ddl( 4 r -r's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider thed7m e-cw ll ,4c lnd(r: rd7-nga2;vln 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 travelinn(d4+ a.xnl jhg 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 thdf.z*i k:w* lee Earth in 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 d*.zlwkie* :f 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-kgu4dy kz13cmi azg wbgi :h, ;+3yb(/hr discus as it rotates uniformly in a horizontal circle (at arm’s lengt4 da rw:iu/chh b(k3g 3zymi 1bzy;,+gh) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km froa(;e5jtdn8l*v w fl)mm the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle( nd 8lmjv ;a5f)tl*ew 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 accelerationo i((ub3wrfs+ 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 is 32 cm3 us+r(foi b(w?   

  A ball on the end of a string is revolved at a un 2tk rd;,lr: g)7nev95acqvcpiform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If iqnv)epvl ;d ga cc7tr 9:k,r25ts 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 can round a turn of radiushfcli ox-88tn zwns(- ml4p8 9 77 m on a flat road if the coefficient of9p8 in8o(-l- ncmwsxlft4z8 h static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffici 6s9d7nbd *diqent of static friction be between the tires and the road if a car is to round a lev sid76qdb*n9del curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet filx*6,.8y ; jng b go-gerlw,jlq:t6tsghter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her ba- jtx8org b; ejl6q6gg:.,tnw,lls*yck 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 k-u /z iimu22aj6wug; cm from the axis of a rotating turntable of variable speed. When the swau mu6i; ui g-/22jzkpeed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelini3 g(3oqg(n9 +mdthsog when upside down at the top of a cihiqsd+(g( mon39to3 grcle
(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 (includiux wxfyt-2 iz:9 lou+ r :xya pmd2uj:y.62,crng the driver) crosses the rounded top of a hill (radius x: y d.2i xr:lazry +92,up6yjwcux-:ou 2mft =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diavp crrq4 57t/gmeter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poi4 5rvtr 7/cgpqnt?    rpm

  A bucket of mass 2.00 kg is whirlk q6hsfob7da:-m zpw3l0- r8sed in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting th07dzblk8 hp-:3 s qm-fosr6awe 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 ochcii) a2r2 3i 2bh+uepq++ yrotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000p ar2uhc++ichei + oy 2)b32iq $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrica1s xd4rnq;qj 9lly walled "room4q9n;d srqj 1x." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a ciax,m*.d xz;a trcle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole ax t*,d.a xza;ms 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 wv6t,ocjpf)1 xd3 j3m* t(t ucneight of the ball which revolves on a string 0.600 m long. In particuljvpf* 6t3 j()cdt,o xn3um1c tar, 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 perfectf:*u70sof lb 8t7igr lly 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 massesa7 we/hgv;p te9i9h1 ( hztay5 $ 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 evas)fo mj6cn17stna1/as ive maneuver by diving vertically 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 tangencin- tef.1.h9 dige6htial and centripetal components of the net force exerted on the car (by the ground) ieh6ti -e9 c.hfd gn.1in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelervkj4qpw;n 9**e ia0;m h ,;nv fm9zutfates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 22ajntm ;me**v9; z; vku9 p0f4f,niqwh0 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 ciwn- gm yxlzmr3g54::3 9r xmewrcle of radius 2.90 m . At a particular instantmlg5g 3:rw m9w:xry x z-43enm, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth ,c.z13xp w1 mtk yu8pyradii) above the Ear8, .ytxcpp uz3kwy11 mth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magni6t2e:2ag/hm6xxnjj6a/.dpi q o.x u btudetx6ij2j/aeu 6d:b xnhm.xp2 6.g/aqo of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. Txaix gm m yyoe-.8r o2x7/e+zg+u e4p3he Moon's radius is 1.74gm 7 . +ooxxr3yixe 82-4gm+pezaue y/ $\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 Earth, but ha 0g ;rwk: 0ie1f)o y8akz9a5g7gjylnas the same mass. What is the acceleration due to gravity near i89 zgaa ):k0a5w fryekg ;01 goiynl7jts surface?   

  A hypothetical planet has / g0xp8vr1jzmrm1p ig )0kwg( a mass 1.66 times that of Earth, but the same radius. What is g near jg81 xprmz i0/ ) wpr0kmv(1ggits surface?   

  Two objects attract each other grj1veya- e6k.abtx/y )p.fl r/avitationally 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 acceleration of gravity, at (a) 3200 v7;2a* kaxde pmd2* x pk;7aaev    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ea8 yha 38opjs9frth where thegravitational acceleration due to the Earthpsaj9yo3h 8f8 is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of oqjw7ci.q2 5tr0u 9lwgur Sun packed into a sphere about 10 km in radius. Estir2j .g7 tcq5iwlu0q 9wmate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an 3dzi8p17eu9 n dipy/laverage star like our Sun but is n3 ni98z y7upp eid1l/dow 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 star?    $\times 10^7$

  You are explaining why astronauts feel weightlcznrk e(z7m a62q(/aaess while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up t6 c(zqaa2 en rkz(7am/here. Convince 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 cpq :zv8 0e0mxau;g0--o,k q jd:qbz izo3,o veorners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on: ; eoz0 8i,,-g:0kuo0meqvzao3 pd-vxzbqjq one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plano3;siqp,vcwl (*qd12o q rfy7 ets line up on the same side of the Sun. Calculate the tots r(2 ;oq3cqvql,i1 dp 7*woyfal force on the Earth due to 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 Mars is 0.38 of what ;q /.7lzbmth vit is on Earth, and that Mars’ radius is 3400 km, determine the mass of Marq7;/m vl tzb.hs.    $\times 10^{23}$

  Determine the mass of the Sun using the knogmrsblw i-059 wn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 9ml0 5r gs-ibw5–16.]    $\times 10^{30}$

  Calculate the speed 2ohmo bjvtk86clo(b 3k5c+9 v of a satellite moving in a stable circular orbit about the Earth at a bt6m(o9vh+ coc2vb5 3 kk8ljoheight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a cire gj3w(el 3yz-cular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs lg zw(e3j-ey3?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupmss ezxd)v/fve iz:yxw2n7,, 74;orwants 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.soy7 zz,) e4wismnxe v vwdrf/2 x;7:,)   

  Determine the time it takes for a satellf fypmakiw5 x --09l2wcjhe +7ite 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 smalh7y0cw 2 -el5p-kim xwfa+9 jfl compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would 6 1n9 xfs gwku)mov/k*a satellite have to be launched from the top of Mt. Everest to 9 m*u)ovsk1g/ n6wfxk be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continueerrg0kr*m36b 8g dvp 0d to orbit the Moon at an altitude of about 100 km. How long did it tarrm gk vgd0e6r* pb380ke to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thn( nys5iqs c9at 45o65+ qn9skzwstybn k (1+jat orbit the planet. The inner rakot w 59q4yzts+sn+ b 9s 1nca 5sk((njyiq65ndius 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 injbi6),uz pagt ),i;2ta (mirg diameter rotates once every 15.5 s (see Fig. 5–9). What is the a)rgtzu 6,,ibipi2(g mj)a;t ratio of a person’s apparent weight 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 6u5elfs qlbn- 3rskz k/y(e 4:qr*6pnkm from the center of the Earth's Moon in a space vehicle (a) moving at constant ve/nesl 6-z nrls63yeq:q 4f5r p*kubk(locity,     ----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 eq2z2)m/-f,z er2pssc brpj :ykual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midwam-ez, :j 2r ck/yrps2)fzsp2 by between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wocl.ha g8bxj 0*man in an elevator tha lxcg*. 8jab0ht moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the cj,)tkrl aq-jefh85p. ht6 (yyeiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direcehl f qp-.ta,j8yyhjk( t6r)5tion)? a =   

Show that if a satellite orbits very near the surface of a planet with pere(wf) vy9y1q biod T , the density (mass/vb)v(q19 y ywfeolume) 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 determine the pcvnwl2f (skx edcow04:o 188 reriod of an artificial satellite orbiting very nearcl:d8rsk c08wfewnv o14(xo2 the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,98bkcd :g,w77aoj9ggdh i8z d orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun7z aw8ch7 ,j9dd kd:i8bgog9g ?    $\times 10^{11}$

  Neptune is an average distance lh 9qn/)gm+sy 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 Su:5xdt:: psk fyn roughly 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 distance s i:d fysx:tp5 k:n 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 Galah6qdco - *6ahgcpt82sxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 larges6yhf s.zps(edfby 63 3a uq;s+t moons of Jupiter (those ds.yaf3h+36ez(sud b;p qfy s 6iscovered 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 af( oxxwg0,yg91 m7h0zdyb s;from the known period and distance of the Moon. (as xd9 f og;g7 ,x0hwyzyb01m   $\times 10^{24}$

  Determine the mean distance3( lad0kx.xsv from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods give( 3.sxlvxk0ad n 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 anoeyfc*qstzu1 9on2nlf//x ./ d Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but/oef /ols9 n/ytcn1.u z2f *qx 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 dejue l3kobkza : e51 wf2p6,rvvo 92g;zscribes 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 our own, that the distance to the band i 16 5r kjg:a e2wz9 vup,2kfleovo;3bzs the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an ar,dfi;hhc3 n3 e+e n.hbc 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 80 hb.ee,in+3nh d3fc h ;kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface wiesbo 7lm/qsh)cuao)xw;q8/8ll the acceleration of gravity be half what it is on thwm; /oq8bs)u) ohelq7a8cx /se surface?    $\times 10^6$

  On an ice rink, two skaters neh8w2 n j89qcof 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 w8en2q h9n8cj masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dm0gvws0c x1g6 k/vf;f ay, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g c g gfxv/fm ;0s1v0kw6is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelins(8 w0wf*d pub qwpozot.- :4wg directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with eqw4*pb8qszw. 0 w:of u(-towpd ual and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in :3gbq nm5lt2vmmfu*n ni00sl -p 1s4f an elevator, it says your masg3m- tfnmmpqsi f2041u5nvb n:0l ls*s is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statiyk-18lk:w* eban4m fq ti1t0:banp /j on 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 speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 :b4e* ya:a0kjlim1-t/8w bt nfp1knq g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a ver(-*8hmu chg3rxmjb1mtical 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 plp 0jxw)f8sm qf/+u9 tlanet in terms of its radius r, the acceleration due to gravity at its surface af8 pq u ft0sjw)x/l9+mnd the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by o,ceb3k6zn5q an angle ,53 kebnzoqc 6$\theta$ 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 bankev k j(1uhs08cqpj 5t-od for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeo( 5qkup 18tjcs-vjh 0ds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fastxl:h.r5z7fj8inkz j. that objects at the equator were apparently weightlen.:jlf.5 7ki8jzzx hr ss?    $\times 10^3$s

  Two equal-mass stars mainta btc ,g8n7pp.min a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m:9)g mgofcvvj/l z2u,l -b6zt. A lamp suspended from the ceiling swings out to u69bgzfmlv :l)ot z2cv,g - j/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 n5asm1t xi :hs:wc2.s 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 a1t:mh5 s:nsc2ws xi. '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 deduces9iy*(60t ugj/uj b s eq(s5nwd the presence of an extremely massive core in the distant galaxy M87, so dense that ittbyj6j0nq u s(weu (*iss9 g/5 could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill anuq)diy.zvo0ct s 2,atgtie,bt51 ;7 td valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces actingz207s .tte); 5cia ub t,v1oidqty t,g 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 grod27l*v d 39 obqb0gzerup 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, allowing continuous navigational “fixes.” The satellites orbit at *rzg2q ed9 d7ob03b lvan 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 Rendezaocq2i0n+pgx,)rqw0 5 tu;r e vous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Er2 io05 xr;r,cuewq+ qnpt)g0a os 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 pursuia drmmbpw:9ku* cqfue;7770jng a satellite in need of repair. 7be97mrqkwm0uapcf *j: du;7 You are in 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 periong h 6, m 3(enn+z)z7dspye8jzd of 3000 years. (a) What is its mean distance from znpz(8j6) m z gn3+7,den hsyethe 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 could7nejk1 q9;flz5 px7vi actually "feel" yourself gravitationally attracted to someone nexlqf5jvi 7z ep;7n19kar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxysk6wy 4 wq+r/ c6843.mkb jwkg b6mvhr (Fig. 5-46) at a distance of about 30,000 light-yearsk4 rky/vm 4 bw+6sk .w68wh6 gcmr3bjq 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 squarem ff(b8;; gzyd 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bf8 yzm;d; f(gbottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ef gumend9iavyoo p;b72y(87,d-a :hyarth $ \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 1bv +q)8*m k:gco jrj/bv5pr:s.5-cm-long sweep second hand on v+) o:jr8mbkqb: c*gr/v5p sj your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkek5pe r.u,5xew8ao(rl r 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 with the vertical? [Hint: See Fig. 5–10.] 8r(,uaoexkp5.w 5lr e    $^{\circ}$

A circular curve of radius R in a new4+ xk3(ialn vf highway is designed so that a car traveling at speed4x kav(in3f+l $ 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 c. -y;wung)t.*ygpsknegotiating 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 banked and t )cw..;yu y* g-sktngphe 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.$\approx$    $\times 10^2$