Sometimes people say that water is removed from clothes iyf49 j - nd48+qaj ejsjvbv;5wn a spin dryer by centrifugal force throwing the water outward. What is wrong with this stat-yfj8+bq 9s4ejadw 5jv;vn 4jement?

Will the acceleration of a car be the same wheni: 0xcsh+b rm:ex vm.) the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentlixbmr :sv.0h:)c+ xme e curve at the same speed? Explain.

Suppose a car moves at consta:jj0 xngqi1/ ikjcg 5.nt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on:g jxngckj/ 5.qii j01 a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wst1i m,crll zs-kb7mio(*72l sug:v +hich of these forces provides the centripetal accele+ zl gkr cim7blsmsli:tv1*72 s(-o ,uration of the child?

A bucket of water can be whirled in a vertical circle withoutoy2 vzjf,lh a m73j1 af1xxy12 the water spilling out, even at the top of the circle when the buc1jl2xo13a1vxyyhz a j7f ,f2mket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least-nv (mml; da/z three controls in the car which can be used to cause the car to accelerate. What are they? What acc;ln( /z-a vmdmelerations do they produce?

A child on a sled comes flying over the cresoimo;..xets a32,c c+fc6mr nt 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 sletrm6cacmo2oxs. f .3ne i;+,cd decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders let2 mdv1eso tz7;hz-2q7v 58 sqch/wgsan inward when rounding a curve at high speed?

Why do airplanes bank when they ta18.vw3;km i b3o5, oqwakcesurn? How would you compute the banking angle gie sq5,b3c iwao. 1w38va;mokk ven its speed and radius of the turn?

A girl is whirling a ball on a string around her ho n.8:xuj.cilead in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the ot uoxn.:ci. jl8her side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forc(m6-*jxe0m gt q6vcjbsgoa( ,e? Consider an apple -xbg(*6oqvm mcg0 ajtej(s 6,
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit xcnn6a yo,c:et 21c1jbe diffe,1 :ocnnj atc612yxe crent?

Which pulls harder gravitationallidx wu 9p0-x2ky, the Earth on the Moon, or the Moon on the Earth? Whidpxukw9 0i-2 xch accelerates more?

The Sun's gravitational pull on the Earth is much larger than thaq+2ff-w+ r qle Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pulfrlq w+ qf-2+al from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects2eza *-ll*v7v5kzz y l are at work? Do they oppose eak*zzel7all25 v- *yvzch other?

The gravitational force on the Moon due to the Earth is only about hi6 dj;xf .vi w(2qg)owalf the force on the Moon due to the Sun. Why isn’t w2d ifxwv ;j. (6g)iqothe Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger opf vr r k0ycwm56k:ncx-.1t,kr smaller than the c.:tvk1p50yfn ckwck- rx r,6mentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) txwplae bvg / fu*31:a)oward the west? Consider the Egexpv:u/w)31l ba f *aarth’s rotation direction.

When will your apparent weight be trfr9 k() (vivehe greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acev( )r9k(ifr vcelerates 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 i o 99f)uv6v,lpf+jtjcould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any otjt9, iufpf)9vvlj6+ oher aspects of gravity you can think of.

Explain how a runner experiences wfu8-zn0hjs.vtl q3; “free fall” or “apparent weightlessness” betweenwvj q lz.3hs0nu-t8;f steps.

The Earth moves faster in its orbit around the Sun in Januan80g,xet7nf6 l +mq sbry than in July. Is the Earth closer to the Sun in Jansl8 6n7m+nxebq,0f gt uary, 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 know 9wjb,slvun2w.r 4zkr :1+gtm n until it was discovered to have a moon. Explain how this discovery enabled anz 9,g s1uj brtrwmkwv 24+.l:n estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Menrqedv5ra2-cg 0t6 9oon's. Yet the Moon's is mainly resporq t9a06v-gerd5 e n2cnsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19-n 5slmd3r0* m v(druj80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eartpq*s 3lmx6 ze3h in its orbit around the Sun, and the net forcep36q* zmxsl 3e exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exw)(f-x o jisk+dn)l 3 fmov7-uerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90nok3 o(-jf -d slw)ux)i+vfm 7 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ciuck(r 3wj5a olg(+ 2u28c targrcles the Earth about once every 90 minutes. Find the centripetal accelera8c2lwotrgka c 5((3ur2jag+u tion 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 acceleration of a speck of clazl4i t9 ufvayw z6;--fy on the edge of a potter’s wheel turning at 45 rpm (revolu;vi-ya tlwz9u 46f-zftions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a,zgw i 3yy,m xn3vid8e+;7 bwj uniform rate in a vertical circle of radius 72. 3m8gi,i zn3;wxyveby+,j7 w d0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed withilb p m*p xbl/ x*x8.h)cl,75xpq-oho which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road i,lx)lxbh-x78bp.xhpq 5 * omlio*p / cs 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between :):7z gei-jytv jqq l;the tires and the road if a car is to round a lev tjv 7)e:;lgqi- qj:zyel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fightervze0 ir/l))lgaclg,y e -(bd2v(cr r8d i* xd7 pilots is designed to rotate a trainee in a hoz )e licr/,2abgr*0 (gvv cy()7rdld-lid8exrizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotatitgj. vw-ko:u8tr mdn ,42yk3qng turntable of variable speed. When the speed of the tu k ujgvkytmnq d8w:-r,o3t4. 2rntable 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 traveling when u .a 17qlsrhuzhp)5.rq9ht.cgpside down at the top o.tpug .h 5r.zs)a9rlqhq7 1hc f a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the dri,g hqm2fbr m(.)z;bbq ver) crosses the rounded top of a hill (b)bz2,mmq( bhfgq;. rradius =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-diamr daavr aq u;3 2dfq2k6lc;.t5eter Ferris wheel need to make for the passengers to feeldavf 2ru l2c ;6a35dqq;artk. “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticalyks b/xy.yj.ecw-e3 va2e8: n circle of radius 1.10 m. At the lowest point of its motion c xe3b2syneajky8.w. v: y/e-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 9.00 cm fromxfd7t7tqn e( 056fpxc8yek d0 the axis of rotation is to experience an acceleraex8(d7k5n0ct y6e7 f0tpdx fqtion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricallytfi)h5i6ape dqae 580 walled "room05eiadai t)5f ph6e q8." (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 circda*)4ktgy1rshw h .g*f+j6 g2jpe el*le on a frictionless air-hockey tabletop, and is held in this or) 62ysrgge k fw*ht1d *+j4jahg.pel*bit 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 thmtbip ;mc(6j *e ball which revolves on a string 0.600 m long. In particular, find the magm*t i(jc6b;mp nitude 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 8o9)m vic ggb:,d9yyusv3g8 s58 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 massesv6eflk )d/pp7 $ 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 evasiv/njp mcqsz d. thj*5c2b6/p(ve 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 centrip ro/rlo(ku/7;f; h 3kqw,rvvr etal components of the net force exerted on the car (by the ground) in Example 5-8krl oqr;(v/u7;k hrv wof,3/ r when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going fragmy6 ;ny(l,z,w uca3om 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 halfwa6,u;n l(ya,cg a3yzwmy 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 circle of radihf c/fh,c0(xq us 2.90 m . At a particular instant, its acceh xcf,(ch q0f/leration 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 radk 8h8bzfax wlfo* /g(3ii) above the Earth’s surfac8b l *oh8f3zfgk(xa w/e if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleraqr/c ikojg+v5g66q y(:frei 0tion g has a magnitude of cyqjqgrv+6egro( 5/0ik:i f612 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 fgna:3 sq9l6u pzq 7eu)y.xi2due to gravity on the Moon. The Moon's radius is 1.74py7 : e2g3zql q xau6un.if9s) $\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 the same makk*7o b q.x7wunfi g*5ss. What is the acceleration dueq nw*k*.xbkui 5f7go 7 to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, oo wo7gy kq6a/h(x8 ko 1ek,f5but the same radius. What is gk y(q8x1ow5of/oo6 7ag,kk he near its surface?   

  Two objects attract each other gravitationally with a force of 2.5hz(y(dd1 dx,t h0ovqmz g / jrw++(or1$ \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 valuedrmhxwynav*d)1yl+ :(1r3x o-v 9tv h of g , the acceleration of gravity, at (a) 3200 m v:at91n rr l+v*o y1mxdh x v(yd-3hw)   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from b0a dke4s4t+t(/ypyc the Earth’s center to a point outside the Earth where thegravitatibak( ys4 ctpe 04t/+ydonal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron staek1ceorj) idnruxo9*,83l 5 sr has five times the mass of our Sun packed into a sphere abour jclk) rxn u*s,85ie3do91 eot 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf s+x/,.ne k,1tgrk yxm/4ll f aetar, 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 ha lkegk1/r. ytxx4ne fl, m+a/,s the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbc64e q95 z-(h kpzxsgeiting in the space shuttle. Your friends respond 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 25 95-qekh zpg6sxzc( 4e0 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corne0(.8ve(pv* s/d +iybiyik djrrs of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted 0ei. *p iyb +v(kv ydd/8(ijrson 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 s q6,tiij upu,8mh8w*of the Sun. Calculate the totalh,mi8wu it6 s*qju 8,p 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 theo5 lmikg)+h;8m8acd zm8ig4g surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.g8 dhkmlm8oai;4cg8i g)z+5m    $\times 10^{23}$

  Determine the mass of the Sun using the known5oisib86tl w v5ac8;f value for the period of the Earth and its distance from the S l5s6w5v8f;ito8ai bcun. [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 about the Erg53gy,pvyq. arth at a height of 3600 km. v3rq.g5p ygy ,   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650r 8jla.y.x(sc km above the Earth. How fast must the shuttle be moving (relative to Eacs(y..r jax8l rth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencevsppm,3- avaav;3 k9k simulate akap9pk3v;3 a m,v-svd 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.)   

  Determine the time it takes for a sateffz ut-e):517 nmgm/r.uik6 hsjucp: llite 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 small cjguk)zc5fpe. 1 u :sru:7h-fi6tmn/mompared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal vzo.h9wl(t2 ai elocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circu.a(9w 2li ohztlar orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orb4swux 9brqi4/pfc 9 n1qfifa:p on/ ;7it the Moon at an altitude of about 100 km. How long did it take to gw9qp:px/aif9irfscu f 4 /1o7bn4n;qo around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbyod ttb* a1,/e. js.skit the planet. The inner radius of tdat1t /bskyjo ,se* ..he 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 1 igshvp m0u1fmho)p3 n f3l23in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to heluvm3i)s2h3 p1m p03 h nf1ofgr real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cente gk*ylr wd2m6;r of the Earth's Moon in a space vehicleg*lk;mw rd 2y6 (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 consi xjl;m-5r4iuw6 ev5sj5h g ht-/w1qgjsts of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yesv;i5jr4gmh q1 lhte5gj-w6x -5j/w uars to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fo5w/ +-f6pdmzado s 2w,9 dxnbnr the weight of a 55-kg woman in an elevator that moves ddz,x9-dof6w+n5 /wbpm sn2 a
(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 ce8q7k; s ez pwcnm8c0bhn2.-we (df.veiling of an elevator. The cord can withstand- cm qwcv0e;e.z.bdf 2n 88eh7psnkw( a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite o n/ kg243)x 2k yhairnb3mzq)prbits very near the surface of a planet with period T , the density (mass/volume) of the p2hnm )q/rx)pg3in b4yza2k3 klanet 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 andou2fj.-m p shz(vn/2x the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very nearof. 2 z(-pv/umnhsj2x the Earth’s surface.    s

  The asteroid Icarus, thq 0(fdav.o0bqlh* r6q ough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its m.f 0bqqr60*qvahl ( doean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4 bt5zh rihr9)/6pjir6 .5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It l;)lw2iq a*t8 shkwmsv,2i .tcomes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatm8s ;i2t*, 2wallwq) t hiskv.est 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 and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about t4y swbd 6 f(o:swnjg evcew45:;-rx;e he 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 ma.i;a;m qim.i c7lwr .tss, period, and mean distance for the four largest moons of Jupiter (those discovered by Galili; i .w.;cm.tqirl7maeo 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 distance of thepva0d1 z7xw/qcx3 aw 5 Moon. wv1x5wacax0/ z3qdp7    $\times 10^{24}$

  Determine the mean distance from Jupiter for e-x(i/ju *t j po(5lrl+v.yefh ach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in rl(5 fpl( te* ui+h .j-/jyxovTable 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 bet0-gxk :4yubvbpgsa+ r7lx 4b0 ween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbitexaklpgvrb g-7 sb404xy b+:u0d 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 artificial "planybidd),lvmz0-vne;- et" 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 d z-y0,i mv ;vd)beln-apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to crosm ;yi7z d,piy-d 78nyjs a gorge by swinging in an arc from a hanging vine (Fig. 5–4; ,dpiyij7md8yz y7n-1). 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 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravi1kuws1;e flb l3 r-(jyty be half what it is on the surface?;w1 (1j yeufbk3r-sll    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin zs( tpapr b9b3gw,s4) in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 4b w psg9)bptraz3s(,m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per do*nvct xvbk.9ut865e,z 9 qfeay, the apparent acceleration of gravity at eb.oke9vquctzx5, fv n 69 *t8the equator is slightly 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 spacecraft traveling directly from thjm9m9d(6pgfm (+lc eq e Eartm dgm+6jcm9(plf9e( qh 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 bathroom scale in an elev-vbz*8jadrr vh.roz8xw 18)go2zq n -ator, it says your mass iswh zgazvqb*8oxo rr2ndz. v81) rj--8 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tfpg 4*scjtybvl4*w* nhp)62y hat 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 n)t2*hv*p 4blg4p6yj*scw fyeffect 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 loo ,ks( nm:9gvh0srjdl3 p (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 apiosik+m0 g:.ap b6s1 planet in terms of its radius r, the acceleration due to gravity at its surf6ms1psik :g + 0api.obace and the gravitational constant G.

A plumb bob (a mass m hanging on a strjc(me)* km5cmx6 8bik ing) is deflected from the vertical by an an5kme )k b86 i(cm*jxmcgle $\theta$ 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 q5rd0g gs46cc is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safeld4cr q 5g06gcsy handle the curve?

  How long would a day bej(vgb(vo*:fl o5 a+yo5 7 dnjh if the Earth were rotating so fast that objects at the equator were apparently weva gyfo d5o5*b(n:v(7hj +jloightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apa-zy;b:/s)lx6wxpp e m 4vp e+j;jv3mgrt 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 o;2c o8:uwjrv pf radius 235 m. A lamp suspen;uow cpr:j 2v8ded from 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 a n6 2:ayjohv at :g.mf;y(sqt0w0n2xss massive as the Earth. Thus, it has 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 's. Calculate the number of g 's a person would experience at the equator of such a planet. Uhyg.s(omf a;qjwt:xtn a00 y 2v2:sn 6se 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;zfii ,6wuug6bmbqb.5b/u s,n * dp6n Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lights m*n f 5 6ugquibbn/wi, p6;uz6.bb,d 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 trav::ko9n*c (w9n:g2+prqapcxv3g d u loerses the hill and valley 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 heaviest? Lightest? Explain. (c) How x(+ 93k2gq*pvdowr p9cnna:uogl ::c fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning( uml(cnt qfpkn7 *1 v2tx50s;nj 8jrj System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, wif j5 r 2n8sjpc1*t;(j7xuk0mlvtq(nnth 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), after traveling 2.1 billion km, m* s8k8;decjois meant to orbit the asteroi k8j;ds*cem8 od Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of rrx; wvmpo/ g-h+o; 1nxepair. You are in a circular orbit of the same radius as the satellite (400 km abov ;+w1g n;r xx/-hpomvoe 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 o01 ij 9x o64o10yto8xaxgtwhof 3000 years. (a) What is its mean distance from ty oix4g wotx0oa1t9o8 16j0x hhe 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 "feeqvwtw:t ri)bw :.mk9 /r 9dkq:l" yourself gravitationally attracted t9dwb/ :.wkwv tr9)qm:iqrk:t o someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around theu 1 +2a:9 bwjrvj8jbzk center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years frob:1 u2b9v+jzj8kaj r wm 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 corn ,)q rk2f*v,t1nycukcers of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass p2v f ,crn*ck1 qt)yuk,laced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thyh1q-jie +,* wisme70en5 9t xmtufq.e Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long hbi hfx5 *fw /bks*4ixjw8hke366 b9wsweep second hand on your wrist watchb* b5iik96h8 e4s xwf*kf jbw/6xw3hh?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinke :,3: h wlob(j6bl. 8w;nrivond/fpstr 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 m hf:ivrtpb.o;l8wno 6 d /,:n ls(b3wjakes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed8i zyk +ehsg5* so that a car travelsk* hz85+ igeying at 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, t(70f (jo-rl axt7n cvqhe Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radcr 7jqf0(-(a vlox7t nius 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.$\approx$    $\times 10^2$