Sometimes people say that water is removed from clothese cx gh4(cw2bt6+ kbj: in a spin dryer by centrifugal force throwing tbc +:jb24 hktegc6 (wxhe water outward. What is wrong with this statement?

Will the acceleration of a car be the same whr3r3 -dlhv p91izj4m1tl. uefen the car travels around a sharp curve at a constant 60 km/h as 9th fdij.u1r 13-zerl4 3 pvlmwhen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do1,*e1f i+i*z+cnrxhna). kz0qm suties the car exert the greatest as azue)q*t1rm i .n +0* ck,+xinih1fznd least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hmv (*pzp y;3rlorse on a merry-go-round. Which of these forces provides the centripetal a;3prlz*v ( mypcceleration of the child?

A bucket of water can be whirled in a vertical circle withoux 4sejd jp6*z9t the water spilling out, even at the top of the circle when the bucket xe*s49j zd 6jpis upside down. Explain.

How many “accelerators” do you have in your car? mgjz7vcxnp ib1a/y864t 4u+gThere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accel g cum6xazi4pgv +yj1748n/bterations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig.ub . kaqbo180sotfrp,q-(f q- 5–31. His sled does not leave the groqsr1okp 0 .q b(f-uqf8a t,ob-und (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 law.

Why do bicycle riderfya.iz 95q)8edu3aeg s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How )xyg.bao3b ,1v )qi wbwould you compute the banking angle given its speed and bb3b)a,yvq x1.wo) giradius of the turn?

A girl is whirling a ball on a stria x0:/p2ycvhyxjy i3 buv ;;y(ng around her head in a horizontal plane. She wants to let go at precisely the right time so ty2 3y pvyvh:/c;biyxj;x(0u ahat 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? Ifc 6bjpw7*o)4glczznn os6 u:* so, how large a force? Consider an apple:np ozwg*nc6l6c*zsub7j 4) o
(a) attached to a tree, and (b) falling.

If the Earth’s mass were vh5.75ktbjp(uu z /apdouble what it is, in what ways would the Moon’s orbit p5(/uuth5k7 pbzvj a.be different?

Which pulls harder gravitationally, the i sw:,hle rh8.Earth on the Moon, or the Moon on the Earth? Which ac wihlr:8s, .ehcelerates more?

The Sun's gravitational pull on the Earth is much larger thana (i a)h2h2hmi z1,s5 abyl:uh the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the othem: i 2ihzh(h52 )alhs1uy,a bar.]

Will an object weigh more at the equator or at the poles?x)x58ed an:vd What two effects are at work? Do they oppose each other?n dx8d:xave)5

The gravitational force on the Moon due to the Ear /ya+7uqx57sdg ginm/ lw:1nf th is only about half the force on the xyma 1lqs +g/nw:ui7dg7/ n5f Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or s z,-dzh+z- xxvmaller than the centripetal acceleration of the Earth dhv-,+x-x zzz?

Would it require less speed to launch a satellite (a) thdz; (puf6i q7oward the east or (b) toward the west? Consider the Earthi(7fp6zq udh;’s rotation direction.

When will your apparent weight be the grea0m-bz:vy t ,p+bvf4bitest, as measured by a scale in a moving elevator: when m+zbvf p4 0vibyt,: b-the elevator (a) accelerates 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 outer space could be adversely affectedm4, j a 324+ggrzjodrq 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 o2+j ao, 3q4mg jd4rgrzbjects 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 favep:w45c./k5bn( pi -rqvmw s ll” or “apparent weightlessness” between stepr(5i5we:cpbps./ mv v4kn -q ws.

The Earth moves faster in its orbit around the Sun in January than in v;)v k5qa cagr8-cy4qJuly. Is the Earth closer to the Sun in January, or in July? Expl48kqcy5qvra -g cav ;)ain. [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. E51e1i2tpg:y ac+/t aq zebdo9xplain how this discovery enabl opdag iq ze5t1y9b/ :+ea1c2ted an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than tha8h.smaci3t-c:hg lf+omtf ,4 :e:y qe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consii ly.a, fg oh:a-438ce:cm:ts+f mhqtder 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 (n .dvozrn oac; f,z9( 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 around thd*1mk2 x m nl(wx;1x ipj5ebev.8hq8ce Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Ear8xn m 1 lx2e 81kdxeb*hcjwp;.i5vqm(th'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 disc;1a ; 5buvujcrus as it rotates uniformly in a ho rba;cvu15uj ;rizontal circle (at arm’s 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 surface, and ci lji v7e-b92une0ch, jrcles the Earth about once every 90 minutes. Find ecli-9u7 , 2ebhj 0nvjthe centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acc-;u x/1w*qlb ei kfw;ueleration of a speck of clay on the edge of a potter’s wheel turning at 45 1bl;u fewuiw- x *;kq/rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a 7kqo( /cixyc4xzjrm35exh- bz(t 6l4 vertical circle of radius 72.0 cm , as sh-x c4 z5hl4/by(xx kzmerqo7t 3(6cijown 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 which a 1050-kg car can round a turn of radius f ) d i5fwev3uvxbo5m),8x+mt77 m on a flat road if the coefficient of static friction between tires and road is 0.o85)xixdfv,5+mbwvf )u m et380? Is this result independent of the mass of the car?   

  How large must the coefficient of stox61cohdhva,i ;tj49atic friction be between the tires and the road if a car is to rac;i ohjd1t 64vh9,o xound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figt+j d5ybe,kz9u+p2 vd hter 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 back is 7.85 times her +2k5j zd, +bdepvy tu9own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntabak+.06 dj qqxf 6(t6 a2chkqecle 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 icadhf(0qkkt e6qj2cx+ q6 a6 .s 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 traveling when upside d;t d1) w9nyvupown at the top of a cirnt) p9v1w;yducle
(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) crossese 1jm hb8e2s pnx2/gf, the rounded top of a hillpjh 1,nmgb/2efxs2e 8 (radius =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 wouldy -e-zp, xmi+ v4syxa1 a 15-m-diameter Ferris wheel need to make for the passengers to f-v+xisz1 yyxe-pm4 ,aeel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whircz(*ovxr y (.lz(3prvs 6ws f:led in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting(zl* o(p.:s6w r(3 ryvfzxvc s the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axisaj*rq/9;m8kh(jzyzvrn q+ : f of rotrjhvq9/;m8fy : (+ qzk*nazj ration is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pe 3(hvfwgo0r9e+eo.v b9:m5zd8wjou h ople are rotated in a cylindrically walled "room." (See Fig9oovw (bj3fh o:v9ergu.08h5dz + ewm. 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 circl n-)2nhkr ta1 9+fkla;wkmpy6e on a frictionless air-hockey tabletop,61al fan9rywt k ;hkm)kpn2+- and is held in this 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 ignoring the weight of;on7z lg6zu. d the ball which revolves on a string 0.60 ;ldu6z.o gn7z0 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car tra 5kqzjnt lpo16c8t 29rveling 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 massesi8nu6ypt7mug h0n 2b dv4.7 zz-u qk.r $ 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 evasiveytzi/jfm0/ mv668pgp9uoe ( c 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 tangential and centripetal components of the net force exerk;-t6yf 2e: ihc;t zcfted on the car (by the ground) in Example 5itc;y2c6 ff: e;h-z tk-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 50aoi za pukl7o w.a+nzz14w43x*98) n zo-bmnu0 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient o-z9nb1*44az k+ xiozw nl )opm7u8 3nzw.auoa f 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 horizontnbb e 7((hjptio;ur(bz -2.xv2 dpv9eal circle of radius 2.90 m . At a particular instant, its aobnp2b(j(u h(z v;ir t-dvxee2pb9 7. cceleration 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 rad*3m /bt;.:5g a8 rgoevowwyjwii) above the Earth’s surface if its mass is 1350 kg8wr: ey/g.bj mo5wg awv;*ot3.   

  At the surface of a certain planet,zpiyn ofy: -,9 1o-rqs the gravitational acceleration g has a magnitude oo:-q,iry9 1f ynp-szof 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radiuq3skc70wxfc5 b;feq 1s is 1.74 scf7c fkq0e31w5;q xb$\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 hasao o4d6ki:kb5 v*q j/o the same mass. What is the acceleration du6vao:do* kb45 qojki/e to gravity near its surface?   

  A hypothetical planet has a mass 1z(.x,b-wlkpdm3;:-0e slfb kyto:bl .66 times that of Earth, but the same radius. What i0mftk b.;s( bdl:wyzbkx ,p-- ole:l3s g near its surface?   

  Two objects attract eachj+7xzskaw3s- other gravitationally 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 vae ds :d+(j+5qctovka(8czxmhe9u+2alue of g , the acceleration of gravity, at (a) 3200 mx+qv( d 2s+dco9j58k+c(:u aemat hez    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tyoj tdj( 5i01ao a point outside the Earth where thegya 15o0jjit(dravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five5k)1d/0 aobq h2 7j)d9* kscysdpqkzn times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thid)jnqdb 1z2 5a9qkp)yk0*dh c/7k osss monster.    $\times10^12$

  A typical white-dwarf kf; )fnr 0d/yestar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this starrn ;dk0y)/f fe?    $\times 10^7$

  You are explaining why astronauts feel weightlesrdgqwuoirxqg5 ah .9i 21j0qe00hi 1;s while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Coxi0 09r1qd2r5 hhgo;jq 1.q ga0u iwienvince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of 9jotvy 3 v6.ksside 0.60 m. Calculate the magnitude andj svy69.v3ko t direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Su z.cj e; w.e p u(4r9ovtf-9+r5gqwogdn. Calculate the total force on the .o-5fr+qvtew.o c9reu9z4gg( d jp; wEarth 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 qcfm 7s26ucw03z) ck nis 0.38 of what itnwf7632czuc s mk qc0) is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usi(vnh zu8rw6/wf,k1bv )shw 0dng the known value for the period of the Earth and its distance from the Sun. 8/vn 1kfszd)hbww(uv,wr 60h[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 stableh m*smwy21x xas(: ej- circular orbit about the Es yxemj-sw1:h2a(*m x arth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the E1hekub+2 9kwt r)w* ,saiixk8arth. How fast must the shuttle be moving (relative to Earkwiw sek u* 1a,rxk)2 +t8hbi9th) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experie aa2l8 ldr+ov1p79mr+c qhw6ence simulated gravity of 0.60 g? Assume the spaceship’sw8r 2a9pod eq+7l 6mr1hvca l+ diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circul 5 5wl/wxrlp1var “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on thewl 55rw/1vlp x mass of the satellite?    s ~    min

  At what horizontal velocity rm )r47q)3 bbd mvktapyeq0)3would a satellite have to be launched from the top of)kp rm)e)37qmr3vbqabt4 d0y Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, h q+;wiq,egusdx1:5 q the command module continued to orbit the Moon ewduqq sgi;51x+ qh,:at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice tha3r)6 8(ie ebuwgmqr4j t orbit the planet. The inn3e)4uqrb 8mgiwr6ej( er radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whatd+37bzo/z ; 4 o z4hlp)mhgldgaf2w,t is the ratio of a person’s apparent weight toaob7 2d)+ ol;3h/f hp4l,gm4zgz dwtz her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight ofzue. l 4m;xw5cx-cy4i a 75-kg astronaut 4200 km from the center of the Earth's Moon in aly; .m-5c4 xwiecz4ux space vehicle (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 con4npr45n f(nad sists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7n(5ard4f nnp 4 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 weightbb74f g/i pavc.(3 vnhi6as, u of a 55-kg woman in an elevator that m3i7an v/h,bu bgpsa (v4c if.6oves
(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 suspendedlx-nly :68ce b from the ceiling of an elevator. The cord can withstand a tension of 220 N and brea-ex8n6 c:ll byks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of j7k-h-,xgqwb h6im a8 a planet with period T , the density (mass/volume) of the hh -a68k, mb-wji q7gxplanet 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) /f* n 6cclcb.9yt xa,nto determine the period of an artificial satellite orbiting very near the Earth’s,x*.anc6 nbyc9l c/ ft surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun likiczvx(vv3 9 )r;jmp ,ke the planets.r ;ip)9v jc(, vmz3kxv Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofg a5nf r9 2xg r:8rf2b+f)jztb 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 76uz5k-:kjewrk5r)trp0s5 ev5 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 in Kepler’s third law is half the sum of the nearest r kjs0epr- 555vk)kt 5zu:rewand farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce hkrkv+ vj..:ncg6-bdnter of the 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 largesh*d/q5qg z ii sxpo6);t moons of Jupiter (; i/ogqiqd)5h x6*zs pthose 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 xnmo-n :e* yr)e17g oithe Earth from the known period and distance of the Moon. no *e yo :n7xemi1)r-g   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons kl ,k3acxar-bc:zk. -, using Kepler’s third law. Use the distance of Io and the periods givel- xc cakk.- :,bz3rakn 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 Jupiter consists of many fragments (ku64gbryy4c:2i vq)n which some space scientists b4nvg6 :ku)q 2iyr4y cthink 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 artifi7jobzsb f+l;l)cg j2)cial "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 lfj+jsz)lb 7 b2 go)c;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 arc from a hanging vine (Fig. mb) /r:w 88kdntzxql;5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he c/n) km:z w8;xb8rt lqdan 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 ac8qivdj-y-3vz/ pg u/uceleration of gravity be half what it is on thyu3zu/8dji - vvpq/ -ge surface?    $\times 10^6$

  On an ice rink, two skaters of equasmywggd8 smu3l+0x2m c*u .7 nl mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are the.mg7u 2wns+ mulcgmxd* 83y0 sy pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration ofad/ 934:dsbme4ex gqo gravity at the equator is slightlye /3mq4 4ga 9xo:sdedb 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 mg+ur piivr i ;wk8;oj: dv02fs8 n6w5spacecraft traveling directly from the Earthjkrpnwi6 rmg;u+8oi :w 2vvf 50;ds8i to the Moon experience 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 +dia.( km mkri8ct1-(zbk pm*bathroom scale in an elevator, it says your mass is 82 kg. What is the( rmka bktpm1-+d(k8i*cimz . acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists o6 ) 3rt:cszrlk:ae0ox f a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed beslz:r6 c ar)ko:30 txy 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 vertical loop (F mk4- l9g.,fn6yzg kukwb/1uuig. 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 iwus0/r7 vt8 iih ;iex*n terms of its radius r, the acceleration due to gravity at its surface and the gravh7/rsxe 0 t* ivwui;8iitational constant G.

A plumb bob (a mass ber q2y6yy wk25rji** m hanging on a string) is deflected from the vertical by any 2k*6rbe2*5iwqy yj r angle $\theta$ 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 oftih)k )y)y fq)vfx8 j5bwcv2.0z j*hm If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the tbi.zfyv) c 8 v hh*jq)jy)0k2xm5)wfcurve?

  How long would a day /yjo6 xvz);r:zwscf aca6 : o4be if the Earth were rotating so fast that objects at the equator were apparently weig6:/s6o; voacxzac)jw f r:4zy htless?    $\times 10^3$s

  Two equal-mass stars maindb4(ou 6-myca 5gy mx9tain 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 ak0;3r-b qgpxo,7 axey curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle pry -g0xo 3a e7qb;k,xof 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tfj,d8c6ax ny .;mj 2qz/iw +hrimes as massive as the Earth. Thus, it has been claimed that a person w 2i/mwac 6qxhjf.+ ,zdnr 8yj;ould 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 ex t3*qco so4g.xtremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whic x4.3ot*g oqsch 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 and valley 88m/ysep n -tcmq4-tp*- ixul shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel h 4* nt8p-p myxu-qe-im8 tc/sleaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning-92 ue7cp e8rgku2bk t System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals tra8 gb-27ept ukke 9ucr2nsmitted 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 Rendeh7 cfvo o2sd(2/ara p4zvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a2d47opchr(ov2 sf a/ 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 shuttgq2kmwskre8*f-x7+ 1v r ytk4b mh/7kle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as th2ex kst-khrr f+ g7w7vm * /mbky1qk48e 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 h)*c*sgvilv5ss+ ewzw/./a2 yr*ep vperiod of 3000 years. (a) What is its mean distance frosyhci v e+r5*v*zs/*wv )sp/g ela.w2m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel"1ji do2bx/ n5 ahm4yn8gi n(;u yourself gravidn14;/n2x ij( 8ghinyo5 mu batationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of t14 dogu91nw2 gw: gvxzhe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years xgu d19g nwv:21owg 4zfrom 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 squarkr1v-a - u1l6rsjur0 se 0.50 m on each side. Fiussv-u6l 11rar0- kjrnd the 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 s5 lj t5eve k1:v8tkg+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 1.5ag +3,hl;rgy-qlx wmv +xm5 f+-cm-long sweep second hand on your wrist watch?mx hwq al+5gfxy-vm,+; l+r3g    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ars0 :cuivg3)k mound 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 fishinggsc)i: v 3k0um line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a *-m 5ao ez4;sd7t agizcar traveling at sp-ez t 57; a*mazo4isdgeed $ 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 t;k22jcjvb,dw7 pki x1he 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 A2w xb jkd1c7j,2kp; vicela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$