Sometimes people say that water isv c+oo7em6r b 6)x,xkh removed from clothes in a spin dryer by centrifugal force throwing6c vom7 e6ohkb)rx,+x the water outward. What is wrong with this statement?

Will the acceleration of a c zdf0x 4n;z7y4mn3y kgar be the same when the car travels around a sharp curve at a consta4y;gz 0fzd3mny4kx7 n nt 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alo0qna /jzc:auts2o -)png 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 hiq/:a0ozp js-autc 2)nlls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merrip*:fgz*j w k2y-go-round. Which of these forces provides the centripet: wj*zg *kif2pal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wateg5cgtyrkm5h w617 +zsr spilling out, evencw1g6tkr z5s y5+7 ghm at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Thddjy ffe38iu+0- ks+here are at least three controls in the car which can be used to cause the car t3-d euyhd08ifj +sf +ko accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as sh;2 zl bw(l.14pujzs dqown 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 decrease1w(dzzjl lsp;2u b. q4 as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hihz,b1 -bn 7r ao ;agpj 5ts4u5/a:rwjzgh speed?

Why do airplanes bank when they turn? How would you compz9mx 38j3vxbz 4vlf9r ute the banking angle given its speed and radirv4 jz9mfz8l9 3v xbx3us of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. f q yd pvch3oq:hg7r1(; t;jrpt4s*f8 She wants to let go at precisely the right time so that the ball will hit a target on the other sp; 1hg*dtc:jhr;v84rpf(s7qqt f3oy ide of the yard. When should she let go of the string?

Does an apple exert a gravitational force4plcb k6z8myt 25b bvr *,p k;p/dyc1i on the Earth? If so, how large a force? Consider an apple vck rz 8ytlk5*/ b16,42mpbcpdyb; ip
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wf x/ng367+jdj.)vtg ghy(pn )7 bfngchat ways would the Moon’s orbit be differefxcnpg hj/j (7)7tg)3y b6+ dgvn n.gfnt?

Which pulls harder gravitati0 4mtsf+n7j3cqyctma)cm-j 4a fvt/dd;).dp onally, the Earth on the Moon, or the Moon on the Earmq)mv f7 cm tj4/0tyntd f).cas -4c3d+d; pjath? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'q:otyp+ 5db3ss. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenc5bt +s :pd3oyqe in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pozkxq0 k wvzy,u89g* l,les? What two effects are at work? Do wzuyxz0q8,vl* k9, kgthey oppose each other?

The gravitational foryp-j e6os*o 0bce on the Moon due to the Earth is only about half the force on the Moon6e y*0obp o-sj 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 osp.n6lhy7a5w5qk n15c+h 6e,axfb yb r smaller thanhf6x71bcp y. yaq n+5h5wekb5snl6 a, the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east tt))y9hzru ta+jpl894(pi , no(hzgnor (b) toward the west? Consider the Earth’s rotation 8yi n) t9) p(tz(a,pr9h tjgzh4l+nuodirection.

When will your apparent weight be zx*rz lal j7gnqf8)15j/ lmird)g jb50pk44 ethe greatest, as measured by a scale in a moving elevator: when 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 itig g1/exa84njm zk0zl4r5))d7r l *pq5jf ljb 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 adverse0 k,e(g osx3( zj3nfe5)z fwvbqfh0*s95 sxeply 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 force30)sh jw ge9( *q05vksenszf3xpf xf,eb(5oz 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 weightlessneug.0b voiu+ :m 6 5vqo6k t,+phgd7dxfss” between steps.ud o.p7u5fqt6:kv0 x6oh++g vb ,imdg

The Earth moves faster in its c 1ylm9dkwn)n/9 e8 xnorbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a )nc8nyd9wexk /m 9n1lfactor 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 discf ,4 d/six8tvcdf3 /sgovered to have a moon. Explain how ti,x/ tfssdd /48gv3cfhis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational ia+qw1v(r1v b pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull f1(q w+rvb1ai vrom 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 bq z*q3zh 6,py 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 a)bdfd6p;t;j9o +gs ebround the Sun, and the net force exerted on the Earth.b d;;ogfjs6 )e9t dp+b 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 Nyfh rz*z 8d.1r is exerted on a 2.0-kg discus as it rotates uniformly in a hyr*.dz h18r fzorizontal 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 cirf ),cyegaq w 5n+nz8(gp( vuuu4;oa7mcles the Earth about once every 90 minutes. Find the guqu7gf5; (ca,az4 8eon+w nv() mpuycentripetal 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 acceleration of a sqkb. w,t)t4qm 9ql6pxpeck of clay on the edge of a potter’s bltq q,m k pt6q4.9x)wwheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a qp/xkmh2 z4x-string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.2zk p q-4mhx/x00 $\mathrm{~m} / \mathrm{s}$ 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 ccaxdj 5u8jx4 2ar can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of ta4u85xj dcx2jhe car?   

  How large must the coefficient of static friction be between the tires and 7 f9r qcz.sc9ih2(mz2e9w x jp:hu9f ithe road if a car is to round a level curve of radius 85 m at a speed of 95km/h hhxuzfirjz2qf.c729:pi9we9 9 sc (m ?   

  A device for training astronauts and jet fighter pilots is desigsn oh9c7w6 ;3q j*b* kwmcljs)ned to rotate a trainee in a horizontal circle of radius 12.0 m . If t6sjk jsw h3 wmb7;9c* cn)olq*he 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 ronopo5gq;j ubu +i +pew; hvwe(m89( v4tating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient o;juwme g;vbo9( 4oipev qh+8(wn u5p +f static friction between the coin and the turntable?   

  At what minimum speed must a q4:x no6pezn5roller coaster be traveling when upside down at the6pxn5zne: 4qo top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including 1 l;xt3 ihf*xfthe driver) crosses the rounded top of a hill (radiu3lff 1 ;hxxit*s =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 or +:fck2l(( yi0a-ce)y q vfewould a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmoq0li:oef rk2(vc )+e fy(c -ayst point?    rpm

  A bucket of mass 2.00 kg5 5fp heaht3kd0p6cu 6 is whirled in a vertical circle of radius 1.10 m. At the6thc p0u5f56 3phke da lowest point of its motion 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 r:n 2g4/us qyn/;rg9nf8 hk:v*g aqfbbv - az6motate if a particle 9.00 cm from the axis of rotation/guggf q84 vn/yn69 vmsb: a-2*ka; bnhfqz :r is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated inp-omrech 3xa.2r u30u a cylindrically walled "room u3erc.mr - p3o2uxha0." (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 r c;0xbb,dtz-n otated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord co;tb-d z b,0xncnnected 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 6nzkoz4p j9 0f(at7hmmed;8 6+yxhy rignoring the weight of the ball which revolves on a st (+h;ydp hm6 nk0x84fzy67jerotm a9zring 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 755mx4vlqv64 i x $\mathrm{~km} / \mathrm{h}$ , 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 oxf3(y:nkybz+ g.+vhz sn 1,z$ 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 verticallme9h 89fueq+adidb4(x aa +i5y 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 exertedp6hsp x b9sy23 on the car (by the grp hb6s2 y9xs3pound) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapoxxavu: 4qetpu) qa ;9;lis 500 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. Iau e4;uxqa9 :ptq)vx;f 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 horizontav )9 w2j.1v5b ;urh5exqwdtvpl circle of radius 2.90 m . At a particular instant, i j9)d2t1u hwxb.;r vv5ewvq5p ts acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 kmc 7; 1ydr0epv7 vw ,q6j8laypg (2 Earth radii) above the Earth’s w yr;e8djpav v,1gp7067l qcy surface if its mass is 1350 kg.   

  At the surface of a certain planet, x51ep7pbk xfwy2h5c,fd t :cq40tbg6the gravitational acceleration g has a magnitude,fd x:0h 126eb7fwcqyttk4 cgbpx5 p5 of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. Theugd- qhy bme6wyg(4+ ( Moon's radius is 1.74umhg ygq( 4+dy-(6w eb $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 dv x0 wlo. s7qu93fms(hs8eqom4 :am7times that of Earth, but has the same mass. What is the acceleration due to gravitw4(7q lm79v xh m0qmuo f3.saoeds:8sy near its surface?   

  A hypothetical planet has a p)btw-ez k2z *mass 1.66 times that of Earth, but the same radius. What is g p -2)*kbe ztzwnear its surface?   

  Two objects attract each other gravitationally ok.,b6x4d omnd c :a;iwith 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-rl it. 1i)qiihbby 62j.fo4 r value of g , the acceleration of gravity, at (a) 3200 m l.b y6.1hoiq i iri42-) rfjtb   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eaeh*nbi(b 2k r80fiam )rth where thegravin are 0kh2if8*i()bbmtational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed i4sg/4 vkf2 jttnto a sphere about 10 km in radius. Estimate the surface gravity on 2jf44 ktgst/v this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but ig6gcw / 31pjoejg; mymfm5)c6j bp;,ns now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surf1jfmpcgj6;, we)m6pn c3; yb/om5j gg ace gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whilw*dx b *b0-hu(-ojw4a; gdosle orbiting 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 a-wu;hdo wx4s*-a( j od*bgbl0cceleration 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 side 0.(f 7h;pvx dxj960 m. Calculate the magnitude and direction of the total gravi jfx(9d v7ph;xtational 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 u5aqmr5l -8 bg-zk,j9two+ty the same side of the Sun. Calculate to +t zt ubmyl5rkqj,w85ag-9-he total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface;(2va, k-m/7x us 1aszzuw rbsi(dd)o of Mars is 0.38 of what it is on Earth, and that Mars’ raa-1wmz sz7( 2s dk ud,; )xbusvoi/ra(dius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for t2v)w388m b*p w9nc x 02hxhpfo fia+hyhe period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s law xa830xhm w hp*nycfphi892fw2)b + ovs, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a gk/ag6a1e gmiaio;, -stable circular orbit about the Earth at a height of 3kogi;ie/,6m1ag - a ag600 km.    $\times 10^3$

  The space shuttle releasesi/ssy3ze6yj x 9p-l 9z4hjmx ( a satellite into a circular orbit 650 km above the Earth. How fast must the shux -y3yx 9z964 hejpj/( silmszttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate ird4ibg92fgg2) vdti*uw-i /if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one ruiwbtgi9/4g d* frigd-v 2i2)evolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ne01qk0t cx.dmu ar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared 0 1kq0umcdx.t to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launc)vcj 7mua;w )si5 n29tfwf dr)hed from the top of Mt. fmwd)725 r t u;a)ij wscv9)fnEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t jh zmb-wxf,;a 4,8tothe Moon at an altitude of af8 zotw,4a- m bt,;jhxbout 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 the planet. The inrai0ww8 a*e zkz;f8w+ner radius of the rinw+ 0zza8warei8; wf*k gs 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). Whati(q3*exl( wpl is the ratio of a person’s apparent weight to her lpxw qei3l((* 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 center odh) ;roxx:)h*ulox( : jug.eca qw0 /of the Earth's Moon in a space vehicle (a) moving at g*xjd oa0xuoh e q:u:o r).;h/x)cw(l 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 apwu0f-k0-0 v2 nybfpsystem consists of two stars of equal mass. They are observed to be separated by 360 million km anp-byfak2 0p0u0 fw- vnd take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woogy ojj z811p7a+gz7 hman in an elevator thatpao zgo 7g1j78z1jyh + moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevatordn.q 8xymm :-sgq;qc 6. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevam.mdqnqc 6:y- g8xs ;qtor’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with 6b7 d gzdqlxd8y9) ngleg1e)* period T , the density (mass/volume)e)b6 8* ldzglg9nd dy7 1xqeg) 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 thf/yx snr l9l30e period of the Moon (27.4 d) to determine the period of an artificial satellite orb3nf0 9rx /yslliting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundrevid *u0hyd253sq9 bpc d meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean diy qh2udi03cvs9d pb*5stance from the Sun?    $\times 10^{11}$

  Neptune is an average distance tba8 y o 0f.2yuz2bk)bof 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 Sq a:d-dd*;hcyun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepled-yh*:d; da qcr’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of thel7e .dfod(*3xfvyi886tyj/6f/cj uvhsse *a 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 largp:6ess el uuik20dlpl:6r;w2y jv90k est moons of Jupiter (those discovered by Galilep:dswu 9 e v2rsek:ll6j ky2p;6i00luo 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 p: :r bmu: 0doq-c/fhbgvzq+7.rae+dfrom the known period and distance of the Moon. pr: zvqrh a /gfbe +qbm:o-d0:+7.dcu    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin2t2(2f sevmlsxwsji5o 9m34m g Kepler’s third law. Use the distance of Io and the periods given insl (wim 2s24t3mjv9ex52of m s 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 m6u l:*rpau,8 shtqki;any fragments (which some space scientists think came from a planpu t;6,lukhr8 ia*:sq et 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 artificial "p;ad /aduz g41zoaw 5l2lanet" 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),lg1z4za a25wo/d ;d au and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5–t1xar+rm 4l;q o50 )sbgb.1vq e0s ob:8ywaqt41). Itx08 0;ag+:4.rlaq swetyqr 5oo1 bm1qv ) bbsf 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 sureonod22v+ hjk a n-6m1face will the acceleration of gravity be half what it is e1vd n-+j2oh kmon6a2on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inps8h -/8pslzo a mutual circle once every 2.5 s. If we 8 ps8p/sozlh- assume their arms are each 0.80 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 z+ wzyi6bg*6jday, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What f zy6zw*+ 6jbigraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth 0.rfd+m qtqht 0 -l-mewill a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon put-.fr 0m0 m-q+dl tqhell with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, jk6 x(sn2: ekudufyc34n (w2w but when you stand on a bathroom scale in an elevator, it says (ekdjy2:nx fsw (6 nuw3c4u2k your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abf ebc0z+bx*au)r:a ksl-;v 7j3v :kpe out 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 ex; preuzbj7 kac)e0fa kvl: sb-v+ *:3ffect 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 vk 47y lk3l:i m*q+ziteertical 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 r *l4 .scr1hldsy8*lpin terms of its radius r, the acceleration due to gravity at its surface and the gravital*rp yrc.lhd*4 8 ss1ltional constant G.

A plumb bob (a mass m hanging on a string) imao(.kamf(p *;mr 2tls deflected from the vertical by an a2m(fro t(*am. ;kl pmangle $\theta$ 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 of If the coeff +do9aw6j(w kajbh8.lgc u nw;::fsph 88 .jcaicient of static friction is 0.30 (wet pavementjh .o w+wj:sapw8cbg8j6:n.9c kuf ;8dalah ( ), at what range of speeds can a car safely handle the curve?

  How long would a day aqjz41*txgmbr nr*)c ( c:3o xbe if the Earth were rotating so fast that objects at the equator were appb1q*jx:mrzx(o 3ngcc)*a r t4arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o 6wuvopj:lm; m4t:,..oy aapef 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 curmw:j3 b7bl v3by skm3,ve of radius 235 m. A lamp suspended from the ceiling swings by: m7v ,3sljmwk3 3bbout to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mazdf8 .n:nl 2tuo;lay:pp51 zkssive 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 Jupi1t2yp5: zzop k fnndu ;.la8:lter 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 Telesco0coz-okwz : mym*+*h4;hmqghpe deduced the presence of an extremely machmqomm;hzo+4w*z k*g :h y-0ssive 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 $\mathrm{~km} / \mathrm{s}$ 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 consta3ush crk1o69sei k ;7z60pi crnt speed as it traverses 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? L31ukri7 zc9r 0h s6seipc6k;o ightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 m8 *0h r ksw*wiry,xw2satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satelr2 wy w ki,w0sx*m8h*rlites 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, is 3)lhk(ki9 r jr0 i1htjmeant to orbit the asteroid Eros at a he)j ih301jk ht(kr i9rlight 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 m dls, z2.69pzvgaj) a(hf ah,repair. You are in a circular orbit of the s agfzhsh6z, a9mdlv)j(a2p., ame radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 30m *1 c6d4olibz h-qdm(00 years. (a) What is its mean distance from th1zdcm h(d6*lmqo-i b4e 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" c:x8 ,aid x ds3x3wba) 4,pcbwyourselfic:4xdw,8 axb ap)w3sxdb,c3 gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig9ncg/dz ;8vw:;a;ux yoxkh9g +kgkw+. 5-46) at a distan9x8v+kn:g9wg;ouk;h wa /gkx y+; cz dce of about 30,000 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 square 0.50 m on each side. ,y n3h om2dcjnh:86ml ;q,ftiFind the magnitude and direction of the gravitational focly,qhmdt8 jh2,oin ;m3 fn6: rce on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg hc2ye uu(gs(e;,lzp;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 th2.f8s:lr +u cqatbqr :e 1.5-cm-long sweep second hand on your wrist wr:qu8lq.f: sca r t2+batch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight a6 objc(2t( t4 jyuafdt4y6 0fground in a circle below you on a 0.25-m piece of fishing line. The weight makes a comple(d(c6a tyy2 0f jjf4t6gt4uobte circle every 0.50 s. What is the angle that the fishing 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 car trave qm v0d9+;s4wzs 3wq,tv2hirq fg rgfr) :y.l5ling at sp4g 9 3s:vqr+v0rwqdms)g f5ftzrih2.q; wyl ,eed $ 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 trap4z eai c(v d;,+ y)c*fwoa-u(v led-ain, the 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 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 trluo*ewveaa4 df a-d( pc z,ciyv(;-)+ack 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.$\approx$    $\times 10^2$