Sometimes people say that water is removed from clothes in a spin dryer by cef3evyurt.1b rx- 6phe8k6wo c,1lv : gntrifugal force throwing the water outward. What is wrong with this sta16hbv6wrg.,:fx1ocuv rle -pte8yk3 tement?

Will the acceleration rvec, o2nl )1tb*myku9 ir0x5of a car be the same 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 speed? n2*oexrkic r9m) 5yl buvt 10,Explain.

Suppose a car moves at constant speed along a hilly roacr l 3tvt:v z9wrp)(74z 8sgxed. Where does the car exert the greatest and least forces on the road: (a) at the top of tc9:xlt8gzr( zse)3 pvvrw 74a 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 on a me3j ) kevu;7odc ,30dsn ja.zozrry-go-round. Whoa;sc k.z3) 7j, ouddnj30vzeich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without i6cylm81 nq3qasm,m4 the water spilling out, even at the top of the circle when the bucket is ups m mls4a831yc6qqn mi,ide down. Explain.

How many “accelerators” do *f15+h9t /c:n*i -wj ub3unmnvhaes ayou have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleratn9btuvc s ahm*nan:+ujfw e 31*-5ih/ions do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. r jg8sn*lb-an. nh(1b5–31. His sled does not leave the ground (he does n81s (n lbn*bh jgnar.-ot achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when vm m :zyds8o9juz1wz 6(i-cvn i(v8 fw/jm )y3rounding a curve at high speed?

Why do airplanes bank when they turn?3:ca l8g+lcc : *zlin7m8 afkp How would you compute the banking angle given its speed and 83:c:ncafg* lllck7 z+am ip8radius of the turn?

A girl is whirling a balrt,+ g9zqjva/4t-tv g l on a string around her head in a horizontal plane. She wants z4 gg-tra,v/v + ttq9jto let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on tzeqf rf;* ,koodkge,* 1tst77 he Earth? If so, how large a force? Considetzke;s7*k f f*g ,trod17, eqor an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doub*-edvcut+ a5 u+fs:ztr.q (enu6k g8 wle what it is, in what ways would the Moon’s orbit be e :nak (u- qszcwrgud+tt+*568 .fe vudifferent?

Which pulls harder gravitatl*gj: rg)m1.;-qqkyj y7 xemsionally, the Earth on the Moon, or the Moon on the Eaq;)7 xkjyeg l1mrjm.:-s g*qyrth? Which accelerates more?

The Sun's gravitatio+9r0eg l v9galf ,gt1rnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. lg r0lvge9t,91+frag [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at wf h4w0t 1k.jd;rh,skvxe77q the equator or at the poles? What two effects are at work? Do they oppose each otwv0 xe j1k h7k7h,dwqt;4f. srher?

The gravitational force on the Moon due to the Earth is only about ha zy.v37 ko681uopo5guvo9jo n (fgyc7lf the force on the Moon due to fv yyc7 juz9o g.o og5k1o8op7uv6(n3the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su1 mont/p.3csf n larger or smaller than the centripetal acceleratitofpmsc n1./3 on of the Earth?

Would it require less speed to l+2qkjo/ uwxb3 aunch a satellite (a) toward the east or (b) toward the west? Consider t3+ wbou j/qkx2he Earth’s rotation direction.

When will your apparent weight be the greatest, as measur 7ptuc(tr80 w3o:xblued 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 it be the same as when you are on thec:xwru7ubo0 tt (p8l3 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer srz e1op; 7vt)vpace could 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. oz tvr)71;pevConsider (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 “appj t(q3j rl0mb5/*kz loarent weightlessness” between storm5 qt *( kljz0/b3jleps.

The Earth moves faster in its orbit around the Sun in January tht5gm -imfi)k(. g::ooz zg; 6b7v qovlan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the maio;bg m6o7 tvo: :zzfkigmvgi.l) -(5q n 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 discover6 .mv) *fmdr(cla omq-.5s9pg:z hlwoed to have a moon. Explain how this discovem6q (vog: 5mm cp..)fld*-ol9zrhwsary enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than t w5+2txa0m91zml hlw36zadbn* 0h yhxhe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the ot3 *xwma0axtny0hblwh z61l52h z9m+d her.]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 travelinf.h l.zc1) tch/e 5/df bhl3uc3-o ghbg 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sunu efad8cryqaeyy 2+q m::0i6.7 uq5xz, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circa8q.ay5ycei 7q 0z2d emuu+y6r :qx:fle 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 exer:+5zrghm5 /tboy7e lited on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cat/hy5g be :loir m+z75lculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfkf 3f*na*7u hgic t;.dace, 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 grd7khn i**;f .ua cg3tfavitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acc,b+(k bcr1 6k3wlzr cqrt ng**9rcs0neleration of a speck of clay on the edge of a potter’s wheel turning at 4k3 sncbg*rkln,*(z rr9c +t q61c0wrb5 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vert)i-wiqhw cr0h: h2hq: ical circle of radius )2qiriw c h-hq:hh:w0 72.0 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 with which a 1050-kg car can rou qm)9( pwowxx(p(cpp )nd 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 opmo ) ((x()wq wpp9xpcf the mass of the car?   

  How large must the coefficient of static friction be between the tires and tskq51s pzqc872 w v:9vlrt6bv he road if a cavrvctzw7k6s8bqs2 1q 95pv: l r is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotfe 0c)0 dxp9o(gcg)gw ate 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 hgfggc ecp ))w0od9( x0er 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 rotating tur:q+cz e1 r jy8v2kqa:cntable of variable speed. When the speed of the turntabl 2cveyk 8:1+q :aqjzcre 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 upside down)bc( 6rbx 0qgx at the top of a circle rb6 cx)x( 0bqg
(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 (in/gewdb6os *f ;cluding the driver) crosses the rounded top of a hill fsd/6*;oeb wg (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 would a 15-y-wo fif ;-a4 okqscz8; c6x5zm-diameter Ferris wheel need to make for the passenge4y8ok;axf q;5i s-cfz -z6wocrs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m,pz0ws a2hy/ k. At the lowest point of its motion the tension in the rops2ykh p ,a0w/ze 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 if6 q3-ffyev2 5u apqcva + 8hg/*tsvt+j a particle 9.00 cm from the axis of rotapqa++aefcvvt /yf5 - 3qj6s2ugh*v8 ttion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are r9 jsrj4je773useau7w otated in a cylindrically walled "room." (See Fig. 5-j9 rj3ae7 ujssw 7eu4735.)
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 i r,yxj*8(xoo mq7 qb,ehfq nku:g/7-ln a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass :jykx7qomq (, b8n 7 xq /hgr*uof-l,em ) 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 0)pn9,db9no7vmyr s1+rr tgt this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnit01gbs 7d9pnmty nr)o,rrv 9+tude 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 q l7qwpg8,i c5banked 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 zk oia+c3s;e wxq ,.e*$ 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 maneuver6f5 4 wfjazof,q380xmf9a3 p0qbodd p by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components ofvuck9 +in):lv* bd*qg the net force exerted on the car (by the ground) in Example 5-8 when its speed islb vdqu*gvi*c+ 9 :kn) 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 area2sts0ddwc -lakb5 )5k, 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,)c5l - 5twsk2bddk0a s 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 cir knt(rz68q6vk )smk 9dcle of radius 2.90 m . At a particular instant, its acceleration is 1.ktkz sr6kqn m vd6)(8905 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacecr81 zwl6mf 3wdwaft 12,800 km (2 Earth radii) above the Earthwfd6w8l z1 m3w’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratioeslt ;gj+6n 1hn g has a magnitude ofst ;61g l+jhen 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 c9bez kx(*:jm1 hq2nsthe Moon. The Moon's radius is 1.72 :hbe(sq zm1nk*x j9c4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radixnz)8 nsc- 0ulus 1.5 times that of Earth, but has the same mass. What is the acceleration due to g0 u)czln8n-xs ravity near its surface?   

  A hypothetical planet has a mass 1.66 times thau(7ret51 ej2ccn+ r/xxxpih : t of Earth, but the same radius. What is g cj5+:n7hr e/xuxr1 ti2pex(c near its surface?   

  Two objects attract each other gravitationally with x fka* t+mwxv;7o1p0o a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, akvjcr,3x j m( 5eo sa*tvf-;zsq/hq4)t (a) 3200 m 3 veqm,h4)cxr( tzjq5svo f*s-jk /a;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fro*s3ychr+5du z q-ysey (i )zs1m the Earth’s center to a point outside the Earth where thegravitational acceleratioeq*dy 5) (y yuh+-scsz iz13srn due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hasd0 2 5ev49dqf,s g4m-j:kclkep(q;)zf usdwt five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate dgf p ezuedmqfd ;4()s :jw ,k9qlvc5stk 02-4the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an av9qy4 inp/ ljw6m :rx6rq;gx k,erage star like our Sun but is now in the last stage of its evolution, is the s4x rr6 :x;il9qgk/wy mqj6n ,pize of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel w7jxe bzp r9f.;eightless while orbiting in the space shuttle. Your friends respond that they thought gravity wa .9ejfbr;xpz 7s 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 of a square of side 0.6j5xw dn,1 t (d(+pqg, 2ipjkmg0 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere bydnj 5dp m 1wq2gpxtg,(i(k,+ j the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on a k6m yw +wg3 0a5j;o9a zgw/9n6bomztthe same side of the Sun. Calculate the total force on t o oz66k9wnjy0a w wgam m+bz9/5a3;gthe 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 Marsdo3y0) ohmifkw)e 8 v)pc*cqt - srx6( is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of i0ymoqtv c6xp)wf3d)- 8 rk (*eos h)cMars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the rukuep 7j:j/2i/losd7-x fw4wu1s1 qEarth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s u :sw ukflow/x4d u-r1 p7ej1s72 /qjilaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit ahfavj.fov-k-w 5h/6g/kz y0jcjw47e bout the Earth at a heigek5ww jjga 7y/h-.-kvh v /4fcfjz6o0ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satelli kkw:mk(m5b9/q dadg 9te into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occur/5m k bg:adk9wk(dqm 9s?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occu xmdsf**-4tty pants are to experience simulated gravi *sy-4fmx* dttty 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 takty 1it at603vtes for a satellite 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 compared to the radius of the Earth. Does youy6at3 i1t0 tvtr result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitlou ntjtmz 96p/jwu; m7:q*x.e have to be launched from the top of Mt. Everest to be placed in a circular orbit around the tp*6txo9jznw l :mu/ uq.7mj;Earth?   

  During an Apollo lunar landing mission, the command module continued to orjl df(3b3 un4nbit the dfjln3 4n3( ubMoon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pl9c3pa3gz+b6ihk7o*f jjzo3 x anet. The innef*+p3kxc7 og9 6 3zio3 hjjzbar radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig.zc ww0mz.w3)z 5–9). What is the ratio of a person’s apparw3w . wzz0zc)ment weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight oi;4yot-dk eqzu c1vpqo 2a. 6:f a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at cz2o1kd.-oc ;q ip va4y6tq:u eonstant 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 r(0 k+s1ltswmsts of two stars of equal mass. They are observed to be separated by 360 million km and lk1 tsm+r0(sw 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 woman in an elevator t3 / fg**dtq*kt:hyzfchat moves/d c**tqhzyg *tff:3 k
(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 fv-wy 0lr5)ot ymvwh8:py8 lowad2(h.rom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eleval 0w yl:(-wa v8t25yd 8mohopyw)vr h.tor’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wjm-1k ohuh /.pith period T , the density (mass/volume) of the p.1j uhph/-omklanet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the oy4m q6q q8q:j(wtye6Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfat 86 q(woj:qyye qqm46ce.    s

  The asteroid Icarus, though only a fem*6i-6y wpg)oz )x:wz8vzny bw hundred meters across, orbits the Sun like the planets. Its periom owv: ))*zp68wyzizgy b6x n-d is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 hhrxyn8q4-p7ar8 : kx ce:n+g$\times 10^{9} \mathrm{~km}$ 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. It2k4bd6l zb hk08lpkw) 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” thh 2)6pb0kzll kb 8dkw4e 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 the center of the Gala igpgjyneph3 7u:1f)5 xy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 q 7(px ej6s*50pyqzr odistance for the four largest moons of Jupiter (those discovered by Galileo in 1609).qx p ( 6rz05pjos7y*qe
(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 the5:b2 *csa;g ycusyk39e jr p0a known period and distance of the Moon. ec jkary bus23:9p50y* ac;gs   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Keke(nip h4;gdrr0p rx )/f 5.bbpler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the0/prrp n)g. 4brk5 b( fiedx;h Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between M0sif5 zx1p00 dzg) i x-zaeww-ars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbitedx0 e wp5-i 1w azgd-0fszzix0) 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 describx v;sken m(hv+9pb 5d4es 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 l9hd(4 v5 xn ksevmp+;bike 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 period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vini 9irii/2lw2./.gd sie l 9wlne (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 toler ng./li wwsi2l2li i9ier9. /date 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 gravity be half wklur +32c/zlo lm.w3zhat it is on the sczmz orl32k .l3+ /wulurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab 7qdj)itd4k+ d z+ kzd7m6)nvi hands and spin in a mutual circle once vt4+) ikz7jnid )+6m qz dkdd7every 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 another?    $\times 10^2$

  Because the Earth rotates once per day, the apparot - nq*b:ew1 pqzp*0vent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magn w:eqvq-0 ** tpznop1bitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direct) e 8c;nrgs4,faw r:i6/goeualy from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppositeoewg ,a:ru rin68 f;cage)s4/ forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom qvx b96w:l+wt, n2do sscale in an elevator, it says your mass is 82 kg. What iso2vbqwwd 6l9: n,txs+ the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cir 5dhmvjc j0v ig(.1t,qlnbr5)cular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be ld bm)rh5tngji(5vqj,1v0 .c the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a versx9bs1v 9h0urtical 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 termsxoq9,k/t2 p/a nxka..o-t*mjv na. on of its radius r, the acceleration due to gravity at its surface and the gravitational consk ant/ox9a,ovmp/o.t-j k.n.q* 2 axn tant G.

A plumb bob (a mass m hanging on a stri761bfr7;gs fdphihpy 6q- f 2png) is deflected from the vertical by an r6-p ;7byf1fp psd 26g hihfq7angle $\theta$ 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 de bdwp)2k+v.qasign speed of If the coefficient of static frictioa vw.db2pk+)qn is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the 7 m9s68 jpopy 5i-+pdqmbs*k*hg /bpuequator were apparently weig mib5p qp7/9 j8bgym6udsh-p+*o*k sp htless?    $\times 10^3$s

  Two equal-mass stars n21qzebsxve(lywe i +-)jax6 eagw0 :2/yq4v maintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a consta*0hrr mh5qne7nt speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle orrn*0 7m5eh qhf 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus,ke,keyq l3- w: 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. C 3ekwy:e,l-q kalculate 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 Spac6u t cs.7ct6n 3ya4gneke3d2a e 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 light escapes). They did this by measuring the 36yts aed7 4cegnck6 2una.3t speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hf /i)k kf(*pk+stzw u lo3cl05ill 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? (s) 5kki3loc 0w f/pkztf(* l+uWhich 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 Positionisdf,je 4p :35cg*vb/p osk kz3ng System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the ppob4ez3k k c:vs,*f d/5j 3sgposition of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after trave1 q49c7pfm i:byzu:r it:cad9ling 2.1 billion km, is meant tpidarf 9qc : by t1:iz:uc794mo orbit the asteroid 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 mof:9 b / -hdypmw9l sfws-m.gpi/1:t the space shuttle pursuing a satellite in need of repair. You are in a circup: po-msdw if:bwm.s19gf- 9 htyl/m/ lar orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a pqd(eghdyx. 9;thv- ,h;j+ g1npdxr f5eriod of 3000 years. (a) What is its mean distance from the Suexhr ptxvhg+9;d. jq; ,1d5 f(dgnhy-n?   
(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 va(,+efs3c0 i8mzmui kdih. j7ylue of G would need to be if you could actually "feel" yourself grafe m+,(suiz7i j 8hm3.yc0dikvitationally 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 wbod3 5fq ;ar+Galaxy (Fig. 5-46) at a distance of about 30,000 ligha3fwd o +5r;qbt-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 squ x .l,z8 u+t bt;p +tccidchg:c/4/bfzare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the squa++, ttb dixzbz c/: ucf.clg;pch8/4tre.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbe0 /l1z*ssqkjz)+t r bits 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 epa jsfm3b6 g2+xperienced by the tip of the 1.5-cm-long sweep second han63mfps b2+aj gd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swio .k9k6t+ tvtzng a sinker 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 makes9kttzv6+ ko. t with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designeckl49t hgfj7 4lwiz) :d so that a car traveling at wh k47ftl)clgij4 9:zspeed $ 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(ki2 c sy.vnnq:rj d*/bspz /m /cp8ef);ert, 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 centr/);2c ,cstr ni. n*m(j/rzevy d fsq:bp8e k/pipetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and 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.$\approx$    $\times 10^2$