Sometimes people say that water is removed from clothes in a spin dryer byx cs,e*om;*jran/xy9 centrifugal force throwx,s*or 9/; jceynmxa*ing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tr)m1 2hpv,agbd-h ,clr avels around a sharp curve at a constant 60 km/h asv-1 ,gc2l bma h)rpd,h when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hi/97hdonzkg4 gi9mdw 2lly road. Where does the car exert the greatest and least forces on the road: (a) at the top of ag2i7 zd4moh/d g n9kw9 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 merry-go-ro k zd9ugw2eh1s3q)qu3 und. Which of these forces provides the centripetal 2)3kuq1wq z egs9duh3acceleration of the child?

A bucket of water can be whirled in a vertical circle without thenngtrrb(i+k ,,6m* psi/r.t m water spilling out, even at the top of the circle when the bucket is upside down. E*gmikmp6/( tnbts,+,nr rir . xplain.

How many “accelerators” do you have in your car? There are atv.6mm7k-hnjvx5 y ml9 m (qnm, least three controls in the car which can be used to cause the car to accelerate. What are th,kjh(my95mq l n-7 mmxvnm6v. ey? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in(;o ekodi3em/ Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal forceo(e/edi m ok;3 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 rounding a curve at hig n t4us)fiy:p,) ymb/os/)myfh speed?

Why do airplanes bank :+t6uw6x8imkgahp)xzipk 74k 7hxv1 when they turn? How would you compute the banking angle given its speed and radius of the 7w)i: u+ kv4h 16k6hzxp8tgxm kixa p7turn?

A girl is whirling a ball on a stf4 :j s78n7enuus:u*nxi )pel ring around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball ses87i:*xe:u )lpu n 74njnfuwill 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 o6ht vz ))ac 44mxnacyfi.j2t;n the Earth? If so, how large a force? Considerif2 c.j4tzx4vmn a;)y6tah )c an apple
(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 ock5 3f eaz:0;qqaps lc2)n4fgvd-w/krbit be / wde a)szc45lq ;npqacgk-v03 2fkf :different?

Which pulls harder gravitationally, +5w yucxnjz dd fn,*(/the Earth on the Moon, or the Moon on the Eandn zuxj wfdc/5+y* (,rth? Which accelerates more?

The Sun's gravitational pull on the Earth is mg 2o 3o*i0dc9gm l,han4d(nvl uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitati (4 al2,ngoc*odnm0 dg3lh9ivonal pull from one side of the Earth to the other.]

Will an object weigh more at the equa+fp wxa6r (qtb),45-fytm,zfs ba v (ctor or at the poles? What two effects are at f (qycfw6a, bt-b4 tfzr)+m, spv (x5awork? Do they oppose each other?

The gravitational force on the Mosr +ii/;/xb uxenq0l;on due to the Earth is only about half the force on ths/x+; /i0 luq;xe rnibe Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the2h2iu;* f+h 34y ldqgl0zojge Sun larger or sm zldigq*j2o eh hl0 y+3;f4gu2aller than the centripetal acceleration of the Earth?

Would it require less spx10mcoft lx26eed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation 60 mx2 cloxt1fdirection.

When will your apparent weight be the p g(iogxqrkoz;y( gtg391)-p greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerapxpit( gq19)3ggzo gy r(k;- otes upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adverselfs.m *ij1onc +y affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindi 1fs*.+jmon crical 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 other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent+ qapfy14ip hbsez3s4u zd929 weightlessness” between step12zh94s ez3b9qa si+du4p pyfs.

The Earth moves faster in its orbit around the Sun iq1 ho ybp 0.qe(sy:5tln January than in July. Is the Earth closer to the Sun in January, or in July.o(l yheqs5: 1b0tqpy? 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 known untilbspo(0 otd(fpa40b+v it was discovered to have a moon. Explain how thispa sbtf 4p+ov (b0(d0o discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational0jiuybznz4ej l1*mby8 b )1 y3 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 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 ab 1)ynj4 b18z*il0bj y myez3u 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 19f x-p,e-pk t*w80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbitnf- y(zc8uao)np .gg2 k)z4 qq around the Sun, and the net force exerted on the Earth. What exerts u)okq 4) 8p-(fzq.gz 2angync 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 exerted on a 2.0-kg discu.t: po9 scus;bs as it rotates uniformly in a horizontal circle (at arm’s length) of radiusc9b;tpu :.sos 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfac r0z p.ds3ero/(fwb4k6n+ 6ni uy3rqee, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration kz. r/p3nf6nb+ er(q4e6iuo y s30dwr at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of5x+d kk(yn l879hsg4 nlan9,snfhhd 6 4sbgq6 clay on the edge of a potter’s wheel turning at 45 rpqg7l fs nhh9 g5y ,kls6n 6 k8(b4s9nx+dhd4anm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of euo8ga at 6* u5bxp6k-a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33.8u*6 ux5eogbp k6-ata 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 ps0qbsfy+n um:omp+9/ ryj .: speed with 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 is 0.80? Is this re0.mo b+rs+j: mqpfny9uyp /s:sult independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires a (rqg9f t6dwfl.(s l1mnd the road if a car is to round a level cu( t r(qdsgf6lf1mw l9.rve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts l5ke5np ;p q sd8/nov.and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is s8p5 pnld5vo en;/s k.qhe 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 rv x(g72uw. 8vju-wfxeotating turntable of variable speed. When the speed of the turntable is slowlj8eufu -vv(x x2g 7ww.y 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 travelirj10 .uyajm 5nrf1qo)ng when upside down at the tonu.of1y1 q0j ) 5jarmrp 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 m.0tkc.-vn lleqkdl,5 h bo 1qb vre101ass 950 kg (including the driver) crosses the rounded top of a hill (radius oeevq , k1.c-qbt0.d0lrlkv1 5h l1bn=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 minut0m t1tkqvd)/ke would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmostkm/1)k0td qt v point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertic :a/ zysqgrk9*al circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucs 9yg*z:qk/arket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axh-ye c4l.ff fwl70yt, is of rotation is to experience an acceleratily fc- e7f,y. lhwt0f4on of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnid t:g+ /x9xt:+bdcg0va33x2 zmdpx f pval, people are rotated in a cylindrically walled "room.dv td0zxax3m ++dfx 3c /2g9bg: ptpx:" (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 ctn6l( 9lp 38 fgpq720ry dsyht 37nyubircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling bdl93q u83pyfn2blsy6ngh(p77 tt0rylock (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 ignor 7 6;pxrez yzq6p4d firip/)2veb7 r-zing the weight of the ball which revolves on a p d6rprz/zq;y6 bvr) -ep 47xi27fzeistring 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 trave+ w9/0pzm/6xvl yqtg eling 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 0:ncy1b 32idxa) 6thx qyq,qf lees;. $ 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 vertlwqke1jg0v 0fn l ;8cc*iuf 1mc29j- jically 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 .pj01qta)o.tuopno/ net force exerted on the car (by the ground) in Example 5-8 when its speed i putojqo .tnp/a.0)1 os 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500**q jmmxs2t+ t accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 +2jmtxmts**qm. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient 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 radius 2.90 m . At a particular in secs:n4 4un v;uk (mqvfp;5-wstant, its acceleration is 1 wsu( :fv4s;n 4k uq5-m;pnvce.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 ng jlg/3grn, c i ky0h0u,0 hb*2i5o-jxtoq-y Earth radii) above the Earth’s surface if i cqhoxyi,* 0i-n h 0 oj 3yu20r5glbgjn-gt/k,ts mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration gx+/8n lzlhgzq 0do -c9 has a magnitud08 llqz/z +x-9go chdne 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. The ;gaupq-pan:- 18ukey Moon's radius is 1.74:8a-- au gqny;ke p1up $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a rbethj. 1vcr 1 f)rr)cz -g h)skpp*p19adius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity)rhzr )hs.c 9kvppe rc-bf11p )1jgt * near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earzbki,+g l4 5vt60 awykth, but the same radius. What is g near its surfag lwty5k40vba, 6z+ikce?   

  Two objects attract each other gravitationally 6 :qwl2 fnrgb2with 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 p 1*ytk0kqx 1 dl;hjb1g , the acceleration of gravity, at (a) 3200 m *jthk01 qk;1p1ylbd x    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cent.+*saiw7f v/tkxv gn iz8q7m7 er to a point outside the Earth where thegravitatio a/87sfvi 7.qg*xvi ztn+k7wm nal 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 th9p 0n*namtes *e mass of our Sun packed into a sphere about 10 km in radius. Estimate the sum0 *pea *stn9nrface gravity on this monster.    $\times10^12$

  A typical white-dwarf stasb3*bpo)gvioyf.har3/ *o2sr, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on thi3oosbp/)b 2o.ys 3 h**rg viafs star?    $\times 10^7$

  You are explaining why astronauts urzos-*b,lhaw lv3 5:feel weightless while 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 acceleration of gravity 250 km above the Earth’s surfacewahvrb soz l3,-:l*u5 in terms of g.   

  Four 9.5-kg spheres are locatw:1.b g/nx.ntn yhd3f ed at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitationaln bdw gn/1.fyht:x3 n. 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 t t/ xx-v*g3yck0t(ppii 4b /qzmi1 ae0he same side of the Sun. Calculate the total force on tvqp i/z- k y x1/b0pxc*m3(ittiga0e4he 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 Mars isfrnu*vwx n * w:hx)3-s 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mwx:sfr*unx *h- nw3v )ars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the p90wij6* mx-r.br naph) lwpx -eriod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Ex0lx .* 6wmpnw9 rbr)aix-j-phample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cict663z svx8n+k4h k qhrcular orbit about the Earth at a heig48c3s6v6 z tn+hkh qxkht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite intod ac/ 9m hjgog3mc6f; 9q*/zdd a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occur/d z9g;mf*6qo dg /m a9cchd3js?    $\times 10^3$

  At what rate must a cylindrical spac2/o0d oq dty6u4q prk+ 5g8dcxeship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and giv dqd56g4rutq 0yko/po8xd+c2e your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a saq wlbfy *67a(xtellite 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 very7 bf(*qwly x6a small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satel +c61kx.pl6lwycdr y.lite have to be launched from the top of Mt. Everest to be placed in a circulacylkwx. l .c 6+16rypdr orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oj v3ct qd7agk9mobuu y1/ nx4*r 5nx,4rbit the Moon at an altitude of about 100 km. How long dig7tbyk3 nv rudx9a,j54c* qx1 4 /numod it take to go around the Moon once?    s

  The rings of Saturn are compoc,cso 9gb o(4ha6skd. 1,.sh d uhurj+sed of chunks of ice that orbit the planet. The inner radius of the rings +b,1ks4 .( us djhusa hgoc9. ho6,dcris 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). Whw73tkfu9ypa-o h 4d++p /uqq rat is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the 7hfk9 3pw/uqd 4qtyo+-ua +rpbottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from theuv/ h* /wx0kts center of the Earth's Moon in a space vehicle (a) movingk/0wxuh s*/v t 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 consists of two stars of equal mass. 1lemj4e9dlu5s3u ib b tle. .i xp8r-.They are observed to be separated by 360 million km and tr.pt-uldu9si.j.l18 l e bemb i5 3e4xake 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 ths .n pd6i8na8nat moves dnn88 6ina .ps
(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 t +r x)a+5 .hk*wlmzuna cord suspended from the ceiling of an elevator. Th+*nrulzx) 5tahw .+k me cord can withstand 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 orbits very near the surface of a planet with periodtulruj ;fj*e740w3:8rrp c j myo 1xw4 T , the density (mas8 pj4;u1xrt: *orcrj7wl eyf u4j0wm3s/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws andda5 wko d p: igw:e(gj/*lu9g2 the period of the Moon (27.4 d) to determine the period of an artificialoagup:jw2kgw :/ie5( d g*l9d satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acr;jo far m4/k8eoss, orbits the Sun like the plan;aj fmk8eo/4r ets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ( hr7e8, w8zbhvfr7q jof 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes ve63ack7 dxpinol 0 hl3;ry close to th7cx h6ldlkn;03ipo3 ae surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the(vj0 yz+1i osy 4wglg( center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, per pxi3wtk8.qm u;,1ffx ;r ,khxiod, and mean distance for the four largest moons of Jupiter (those8xki; hp,tmfx3;uqrw f,.xk 1 discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and disfzbka wu( 5h.7ie +xq/tance of the Moon. ze.i/x7hkua b5+f q(w   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of J8v t4 6jad.cv5 brhes6upiter’s moons, using Kepler’s third law. Use the distance of Io and the periods g5t8v4cj erv. 6ahsd6b iven in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragme7r86ex;eaatg/2lweji1 e en 2nts (which some space scientists think came from a planet that once orbited the2/6e gjt8rw7ee 2xeaa1e;lin 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 "pla h4 0)hvl,dll g)zcxx)net" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. )x,l)x gh0 c4hdv) zllWhat will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gol9b q:mvi;nv(q+f u5lrge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest poinf;qlm:9(l5q v+ uv inbt 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 8xun0astcg4 rf3qg ;5acceleration of gravity be half what it is on a5ctsx40ggf; q u83 rnthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spinqxt nd 84-adi-a3 4wel in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anothert4nda wq e3x8id4la-- ?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of grav97rke8o(w(jen9 ysp b(gszr 6 ity at the equator is slightly less than it would be if the Earth didn’t 9 8p(njy(geo6rbe9(7z sswkr 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 frj)*4/o* rh-altfs07 gp sqk zwom the Earth to the Moos)w4h* -t 0s kol/p*fqr7jazgn 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 batuk;unh so;ee.sowv(k9 6.g *zhroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direct6(w ss;hz.. ogu9n ek;u* evkoion?     ----待选择----upwartddown 

  A projected space station consists(d e/xzq r5q;k of a circular 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 the rotation speed (revolutions per day) if an effect equal to gravity at5(rqde; qzx/ k the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–*ty 4a5d4j vav43).
(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 lggjqf9g 3 8p*7n;wq 4xtre. vplanet in terms of its radius r, the acceleration due to gravity at its xe7; gw8n f*trpv4l9q.g3qjgsurface and the gravitational constant G.

A plumb bob (a mass m hanging on a svx kzgyto.i+v (1e-2odc*d,vv fd p6 dd i9.m)tring) is deflected from the vertical by an angleid6xv c. vtem,9d o*fpo.gv 2iyv-1+(kddz)d $\theta$ 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 mo 0n ze(zosa -11i8hzv 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 safely handle the -svzza 1h80z1ooen (i curve?

  How long would a day be if the Earth were rotaeq kq;deql6 :8ting so fast that objects at the equator were apparently weightlesq8: edqqe6l ;ks?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apa6 ophsb nnb/lydvc-.ts o (-86rt 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 roundy3zh/ nrqovb 4b7:d* ys a curve of radius 235 m. A lamp suspended from the ceiling swings ob*4ynrv3hyq do z/b: 7ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as m sohb bum+;x7 ,h+t9qv8yhe.l:mzvl/assive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on hm:l7s9t,ebmv+8hyz o+u; q .vbhl/x a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced t/4wlm rf 9(jz( u3xoyshe presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting th(mlf3uojw y/z(49 r xse core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shb2c q02 o ,ips6eai6civwg6n,own in Fig. 5–45. Both the hill and vali2gc6sc,vni oia,q62b ep0 6wley 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 fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS)r:b, m(: +mldsbpx mt4 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 4:t,m p br:sdmlb m+(xsatellite 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 traveling 2.1 billion km, ((8w5gre pfeb 8b;cauaib)t :is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly aut8r;beb5caew)pg:(i8 b f( 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 shuttlemh wvpoino97m )- q,s93;n fq 6ychv7q pursuing a satellite in need of repair. y7n7p-womc i9vnh3 hm sq9fqv6o;,q)You are in a circular 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 per.z 8sq i plen(3dr2n:hiod of 3000 years. (a) What is its mean distance froeh:lind s3r q.(zn8 p2m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could act55h p7s)fhbptg4pvi :ually "feel" yourself gravitationally attracted to someone near you. Make reasonable avihb5h4 7tgpsp)fp 5: ssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gala lz/etzd/7o, tf5jtc7 xy (Fig. 5-46) at a distance of atzo 5c7ltf,/ ezjd7t/ bout 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 09-zsqzvc/qs 2qb:h zuc; 0b-g.50 m on each side. Find the magnitude and -bc: zcuhqqbz2 g 90/s;qvsz- direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits1cd loq 1a/a- ree0jw( the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swee4(3 uuy19ajghjhz yw(p second ah9ywz1u j(3 u4yjhg( hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing aq: 0fy7wbz;- vsm wui: sinker weight around in a circle below you on a 0.25-m piew- v:q;yuiwmz sb70: fce of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so tha(pa7 n5ut.5nykrp d/ dt a car travelin ( /p7ad udytpn5rn.k5g 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, the Acela, utilizes tilt of the cars when negotiaxwwr1q2m5 p)9dkrx(ym2 fau0 ting 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 radid2a15rkxwym()p urqxf 20w9mus 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.$\approx$    $\times 10^2$