Sometimes people say that water is reas 6jgv8gp/yw+4 +wnhir,f4y9dgme -moved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrod9 4fijpsggrwn/+ywe4 +m ,a-v6 ygh8ng with this statement?

Will the acceleration of a car be the saq,7d grs94iccb9vf u1 me when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sd9s 7bcv1 9c4riuq, fgpeed? Explain.

Suppose a car moves atf-li2s6i+ g 5shk7 nnfw; rv:q7jz9 yc constant speed along a hilly road. Where does the car exert nf75j+ ri:nyqli; sgs7kw 9 2vhzc-6fthe greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse o1o+f3+ kn*pfdjeu skhea7j zbmj4+ 3.n a merry-go-round. Which of these forces pre7 h+nj43f*++azk mkof1sudj 3.pbejovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical sxegn x + :i6i1ebzj-9circle without the water spilling out, even at the top of the circle wh- gxx1in9 jbe:i6 e+szen the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at l f1r t 6jwxr0h)5amr3ueast three controls in the car which can be used to cause the car to accelerate. What a)1ufwh jm0 xr536r trare they? What accelerations do they produce?

A child on a sled comes flying over the cres*fl2: acge ot6t of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decreaseg*faot l2ce: 6 using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high spl-zki 2zs.n u(eed?

Why do airplanes bank when they turn? How)g(k ul +whbk 4jjb7 rbj+8bj- would you compute the banking angle given its speed and radius of (h8)jb kl-4 ujjbg w+ rb7bj+kthe turn?

A girl is whirling a ball on a string ark7-+6 egbo8 rzd-/tpttu9 apuound 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 tgbud 6pa t /-+pz8ret o97uk-the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earr q v3 b(mlyhyl k19-0+zmaxp5th? If so, how large a force? Consider an apple -r5y0al1mzl9(3hq+ b vkpmy x
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tqlt .q:mca7(q tt -psgru1c8+he Moon’s orbit be-8lqpcs qtu (:.qctm1rta+7g different?

Which pulls harder gravitationally, the Earth on the Moon, or the Mo:2m.q b wke/hd8fxk8l on on the Earth? Whichd.2lhk:8 f e8m/wbxqk accelerates more?

The Sun's gravitational pull on the E: 5r lm z) *,uy0qkpg:b (a9ewbzh4lgex(ts,w arth is much larger than the Moon's. Yet the Moon's is mainly responsible fors,e ( *kxa)yuwlp::rzbb e04gw9ztq,hl ( g5m the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What tb w,+g 6l* :y mtkmk4c9ciwq1two effects are at work? Do thegi4t,k +9wl6y w*1tmkcq mbc:y oppose each other?

The gravitational force on the Moon due to the Earth is only 3p5hr/edlt2o about half the force on the Moon due to the Sun. Why isn’t the Moon pupl5r 2o et/h3dlled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larg+zmfb b 9h w*g m0kfy(,c2p6drer or smaller than the centripetal acceleration of the Ea*(+ d k,0gf6cmf9rhw 2bmpzybrth?

Would it require less speed to launch ai*3 ..ydcrxk yj-+2jvmgz /md satellite (a) toward the east or (b) toward the w v.m3.j+-/idydxym2z c* gkjrest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scaleli0pengt1 1j; in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (eipt;g1ln1 0jc) 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 longr k fjd.,ld:200axuki periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronadk x0i .,ja2:kdlf0ru uts 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 wed0ti+ 1by lr hb 3tjlfj4m475bightlessness” between sthjd4t b57bt3l +jmriy1l4b0 feps.

The Earth moves faster in its orbit around the Sun in Jan y+v(/lqlpq kjf, j,a*;a.-f7 nwkqnquary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This isk*k l-yq,a/(anl;.fnjf7 jpq qq+,wv 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 disc*5) cowqoq:8:fiy:vk u2r eq hovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass.ef qi:qq 2):oku r8hwovc5y *:

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet td bp/l u d :2/tbcvyrl(8y+/bihe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sidyv2dpl/bu 8/di :b/+ cb r(ltye 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 1 .xdbmmb1;;jtx 38 qjz5+fyj u980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aroun 5l+pa q7e/l+fapwcs609zxlad the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? A 0llxs79e5w +c+6 af/zaplaqpssume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exeriz h:.*l-xk7ptnmmp 0 ted on a 2.0-kg discus as it rotates uniformly xpi0m-l.7k hnz:m*tpin a horizontal 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 wfz ;/8atq+ie c24sw(o /hs gaaj5n1f 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 gravitational accel25aafown(wq4 +//ife gsjhzcas8 1 ;teration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay ozzlm77: w;t* )c x3col,bqnpr n the edge of a potter’s wheel turning at 45 rpm (revolutions prnol3cq:x, w;7c)lp 7*t b zzmer minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a st43: e d/6wonqx-thiaz ring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fixae3q:/-dn6h 4i twzo g. 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 c+r4.vxhj bh5 jar can round a turn of radius 77 m on a fj h.5+hvj rb4xlat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the uqjh by6 k;*hc8 ,xvu)roa ucyu x,h v*8hj6qk;b)d if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts g:lpu0nfr6wzq 26 57m9lirdzand jet fighter 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 own weight, how fast is she rotati06pl7:wgfq9n5r il r dzm 2z6ung?    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 ax6teig*l kzqa*ggo*ms t )s +(*is of a rotating turntable of variable speed. When the speed of the turntable is slowgzs *g**oe+ am)l(gtq6t ksi*ly 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 traveling when upside down atj/qg.a9.rxt 8besh:d the top of a circle j:q.x8e hb/tdg r9 a.s
(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) cro*x.w3v8c bucb sses the rounded top of a hillwv xb8 u*bcc.3 (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 woulci;m69 n3ka;z( x xw.yaq0 zaop4/hskd a 15-m-diameter Ferris wheel need to make for the6o4q0kahc xza/(;sknx.zpw9 i 3a;my passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wh37 7*5hcmlnwd gq sby*irled in a vertical circle of radius 1.10 m. At the lowest point of its mohq5d7 gb3cnm*lw7 s*ytion the tension in the rope supporting 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.m jyoth 4w8v22n9x-qz00 cm from the axis of rotation is to exvtnh z2w- 8 qoj92y4xmperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in9 l+t:auot6dnc5cak- a cylindrically walled "room." (See Finu6 a-a9kl+5cotdtc: g. 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( /qs+z8duw w hx:1idh in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to adz u8(h/1 dwx wh:+iqs 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 timk;f,*x7878smc2y d xdh cwzjge, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partihx7w 7z*x8fkm,g jcyds8 ;dc2cular, 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 radiusd6vm7xq dix70b4i :tb of 88 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 masses ps2 8q av9v2z(kgb0 ks$ 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 re+2oc6 4 rjhn310 $\mathrm{~m} / \mathrm{s}$ . 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 coyf0vpo3w- 4ay mponents of the net force exerted on the car (by the ground) in Example 5-8 when it w04y -vopa3yfs speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelera: jqn)p mlsc29b k8w:3sq; g wejn4bq;tes 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 thsnm:j2 c9el;3kb;)b8qq jgww s 4:qnp rough 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-i pjq15ra vbxy5;fb; a horizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.aqvxr y1bpb; f5-5 i;j05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 Ec g /5,kq(ertlarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Eart5gk /,qrtle(ch’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationalo -jzwoy3- :hs acceleration g has a magnitude of 1ow- hz-y3 o:sj2 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 r1g;20y ztzc pgravity on the Moon. The Moon's radius is 1.7;zp y1tcr 20gz4 $\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 has t0qf +wc.qma2xg*b9) fs q:baahe same mass. What is the f.aq+x:f q)agwbm29*s0ac bq acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tim 4)(yvc5 w2dskh/lmts es that of Earth, but the same radius. What isky/v4 (m2w5dst h)c ls g near its surface?   

  Two objects attract each other gravitationally with a y-ytlfeou00.(kwi5p h*dyr 9 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 (hrld 8z;0 : ebha76rdja) 3200 mla 0hb6rdde:zr;87jh    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tf4hclg*bqaxw * (uu29 o a point outside the Earth where thegravitational acceleration due to the Earth i4 uax2bc*hu 9l (gq*fws $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has flqm w32t- 8dfzive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravwz8-mdf l2tq3ity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but/kr wr+2iv3u9 uf it(oa1o qa ckuu71l* ov9x7 is now in the last stage of its evolution, is the size of our Moon bo fvuk+3xo u/ai u17 atkvr*9l19 woq(7 i2ucrut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why ast; z +ucz/ayq -bm,7fumronauts feel weightless while orbiting in the space shuttle. Your friends respoq yaczfu/+-u;m,7bzm nd that they thought gravity was just a lot weaker up there. 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 corners py +9m/ d9 kg61gvgtjyu9 nx:m f67pgpof a square of side 0.60 m. Calculate the magnitude p:uv6 +7m/pn96 tygmygg jpg k19 xd9fand 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 the8sc9a eroq+od r,; q/z Sun. Calculate the total force odo/,q;cr r 9 sz+ea8oqn 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 Man * b9ocaz(6xol:gi u/rs is 0.38 of what it is on Earth, and that Ml ucg6/ 9zxono*i(:ab ars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known rmmr o) .dvr+4,i6koavalue for the period of the Earth and its dismv+aim. ko ,r r6)do4rtance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit a b/vjbvm o8zoo8bybap1 c4z56a*da/(bout the Eart y dbvvzo8zaoj486a c/o1b*p a(b 5b/mh at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite icf qep(0 fe)k6nto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs? p6kc)efqfe0 (    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are y 4ebf5p;r1 hqei06 fpto experience simulated gravity of 0.60 h04 qbp e1if5f6erpy;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.)   

  Determine the time it takes for a satellitfph/. knrf lf+h:+rh( e to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orrrl n:ffkh/ ( +p.+hhfbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity w) tv f0mfz6s(jould a satellite have to be launched from the top of Mt. Everest to be placed in a ci zs0fmvj(t)6 frcular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit b, df0ro68:6n3mvkek 2ork ajthe Moon at an alj3om 6 0odbvk2rnfke: r8 ka6,titude 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 that orbit a; anugbz8/qd,:k o3 :yxu i*bthe planet. The inner iq/kau a8uoy;x zgn,d3*b: :bradius 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 0lk78c:skkyp,x8qq y (see Fig. 5–9). What is cqqkskx8y, k8 yl 7p0:the 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 ofz)vgh7y)p(ttt k:6kpw+, a- b+lmk ox a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at cooz+t+6)lyk(ah7) v b,xgk m pw :t-ptknstant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. Thee p - /3q cijqrc:;e/pliv5+yzy are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the ma erl :e3ip -yvzc;5qip/+q jc/ss of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wwm xwuxv+u k8kh2w/50oman in an elevator that movhmx v/kw0 wu5wk8x2+u es
(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 ceilinwubhq uu2 u49(g of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelwu4 uuq ubh9(2eration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period w,-)snx 39b+: q zxekvy:tte e T , the densi , tyb-n9 t::zxv3xe+e)qewksty (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 y7/h q vmlf)6-a08az n0 +santm kp0onp0 isd(the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Emz)lsanf is+m00y 6 kt -pn0dhn 7oq8vpa/0(aarth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrosno0r3qj4mcv h;6h +v aiyq9v8s, orbits the Sun like the planet90r+jai86vvhoq 3yv;hm 4qcns. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averageudgu y c.l;1j-f;2t wh distance 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 Smc2udgf0+q w-cnv 6y7un 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 o2nqv0yw-7g+d mccu6frbit 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 thkn:bls; 7w0uy h3 ggl7e center 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 largesf-bs9z(xa u h6t moons of Jupiter (those difuz(9a-xhb6 s scovered 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 period and ewpg*8 fwr:; adistance of the Moon. *:g8e fww;r ap   $\times 10^{24}$

  Determine the mean distancwfy wwune2rvaha04w .i*2j/3e from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Usei/w fahwj.rw4 u 2aynev023w* the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists al tfsdl881zuj4 pi:h2c-o *oof many fragments (which some space scientists think came from a planet that once orbited the Sun but h *8pl:zsocjt if-o8la214 d uwas 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 deslb2d rx ;d,n+5w hfj+qjj/-kf cribes 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 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 d xh b+f;+jd ,j nkl5-wqfr/2jperiod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swir/j d: nuif8 httbr.9;90ri ginging 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 lowntrrt;h0.jui/:ri8g9i bdf 9 est point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravit2f(fh3 nxizw(y be half what f (xz win32(hfit is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cir3;mxwd / rkmmwl g9bkbg:*,8 xcle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anomr ;gkb* ,bmgxwdwm 3:8/lxk9ther?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity 6grxwb z-/hp 74cho5bat the equator is slightly less than it would be if the6b 5pc7-w4ghx rzo /hb Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eo0 bl9f4k:ezm zu2 h4h* gpb)tarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppos)bt*9k 2uz4mhhz ebop0fl:g 4 ite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on +uqi*i 9o ch-v4o*oqv a bathroom scale in an elevator, it says your mass is 82 kg. i4qvo+co*v i 9u-qh*o 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 j 1d/bde 7i:+oadk h*9a npyo/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 e+ khaoba:y7pi* 1d/o/dn9j dg) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his air5noq5dgj- ) mb4ng lw-ekk 52rcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r: st pav)w;ot.xis:s fkh- zc r r2n1pgu*9w-/, the acceleration due to gravity at its surface and the grav-2 nost*: ax )/zus91h. wrpkgvt rwpc-:sif;itational constant G.

A plumb bob (a mass m hanging on a string) is dff0sn +y3yt r,eflected from the vertical by an angle fy f,sryn+3 0t $\theta$ 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 desyd:;3-x bvnwxp3z48inss q 9gign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speex3vigb4-s :pnq 8z;y 3wdsnx9ds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that object8ngyq)f ,ppe 3*prjkmj z+(3 bs at the equator were apparent3(jp3k m f)gzby p,+j*e pnr8qly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ob0il9cb6;wg(vos v e 0f 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 constasm-8tp ar u.q4g62dtjnt speed rounds a curve of radius 235 m. A lamp suspended ft46 rmtqadj 8ups 2.g-rom the ceiling 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 h8pnh m u8i(oo3*ska/ 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 g3 ohiaspn8 * hk8m(ou/ '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 4y dje:yv g0ox,)xq t9Telescope 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 measuring the speed of gas clouds orbiting the core to be 780 t4yvod q9, g yej)0xx:$\mathrm{~km} / \mathrm{s}$ 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 0a+* l q 4yosjeo)l9fphill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvatureeosfy)oq4 lja+p9 0*l 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) util1xgr8gwe5y2; ajnq*m izes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to witj2 x;wgr m5ea*yn gq81hin 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 (NEAR), af (m beb:b fc g7rrna)8cfw0m.*ter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is r*rr ew( mcnb.7 g8b0fmaf) :bcoughly 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 purvs c:x-dt oc06suing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abox c0st6dvo :c-ve 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 is its mean distancem*73ib02byre.n2aabtu v *;9 wal.axsqlm u + from the 0+aub3rnl*mel2ya .u;qa sbi b.2t9m*wax7 v 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 ac :njm c* 9qwgth2k) w4lo6s2jbtually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumpt o4:)*9 ghcqjw6 lktsjw2bn2mions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the ceg u+0hyr e* cjv+zc pz39jo0c.nter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,0. u oz+h 3gr*9j+ epc0vzyjcc000 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 squareaji2htyyr3 m85s,0n b 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mas rj3s2hi yya,nt5 8mb0s placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitfq6y1 mvu4gce ( :is9 1hyrp(t 9d-uqvs 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 te+xska x.*q6s he tip of the 1.5-cm-long sweep second hand on your wrist watc s6s .q*+axkxeh?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wei)jecly r ,+fq85m px8cb:uvvz0ix7,ight 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. 5–1,:mqf 8 8u5ybzx0cp+ vcxj, e)rv ii7l0.]    $^{\circ}$

A circular curve of radius R in a new highway is designed c,m un kn6:)2 r*so2-xyzhmqj so that a car traveling at s -y2o6zq )mk2ncjx ru*hm,n:speed $ 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 negotiatinoel ,f0whn. m zl/zw**g 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 experienlwez,n/0f.m* wzo hl*ce less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$