Sometimes people say that watxk8cv7ve3 x/mw6ip v p037eraer is removed from clothes in a spin dryer by centrifugal force throwing the water outward. 6wa exvvvpi/33erpck 7 8x7m0What is wrong with this statement?

Will the acceleration of a car be the same when -t b.3- zx.ozot8qzun5ua *zvthe car travels around a sharp curve at a constant 60 k bn x5z8t zt.z-.v3ou-z*ouaqm/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does o8gc*;q)knm k the car exert the greatest and least forces oqk8* om;g)cnk n the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding amyk d69 /ezog* horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the c 69koydz*e/mg hild?

A bucket of water can be whirled in a vertical circle without the wpf/f *vtzve),ker.6r+qj/ 08wz8 y gbt4zng fater spilling out, even ajzt tg8 /4p0 ,zwe n/yb .ferf+gzqv)kvr8f6*t the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cge0 kuqj:u26kontrols in the car which can be used to cause the c2:kkg ju u0q6ear to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyingxr-f 1 +a* fmy7nfsdr) over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal f)mr+f7nfr 1f x*-dysaorce 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 curv-bhlq- d u n;b1ku+1wye at high speed?

Why do airplanes bank when they turn? How would you compute the bank)35mxnmksv1 8 cu.3cm z fue8eyl1s*ging angle given its speed and rad 1*.3u f z5cyl)gu1sn 8em8mc3 vmxskeius of the turn?

A girl is whirling a bax;+ 9z9 ecy.shq)io--hf sckyll on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. Whenzsc -y.cq)+isyhef oh-9x9 k; should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how0x(5j l x .siikc08kmb8di:mr large a force? Con(80 :cli mk5mj0k8 s.xrxid ibsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways +6a+8 egp,yqrr xex+ pwould the Moon’s orbit bag8+pxr,xq6p re++ eye different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the n q9lsei erw6(n2(5vb Earth? n bvw(e 2nsl ir6(q5e9Which accelerates more?

The Sun's gravitational pull t7c xz;0as7( ffbn d9kon 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 thexckf79ft ;d znsb(0a7 Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects a) w7snp3s8e ymre at worewnpm ss3)7y 8k? Do they oppose each other?

The gravitational force on the Moon due to the Earth is3w4t1tp zxl(cm el/u1 only about half the force on the Moon due to the Sun. Why isn’t the Moon pul1xw3/t ucp lem41l(tz led away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lab3rtahkx9 bf4os8-r d9gs9coc y:1h)rger or smaller than the centripetal accele8os)-gh91d cbo:94 rrh 9tax3f c ksybration of the Earth?

Would it require less speed to launch a satellite (a) tow5/ih qe/ xxqhryd ;s)1ard the east or (b) toward the west? Consi/r1e5x xyh/h;s )diqqder the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale irkjyu1x no4fy g2 /92vn a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c1 u2fgyrnj92o / xvyk4) 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 adversely affected by 4 62op5g: dmdemq5pagweightlessness. 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 sim4: pmq5og6pg5ma 2ed dulates 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 weightlessner,f xgo)b53 fiss” between ste,fbf o rx)i5g3ps.

The Earth moves faster in its orbit arou4lyucg al6b5wc:-yf iw52 vt.nd the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: T-gibw6cyll t5uw c5: ayvf2. 4his 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 until it wasop 3kkkx :1e6 rf6j xp,:t8 kj.8gfyzo discovered to have a moon. Explain how this discovery enabled an estimate 6ro kejj,8k:y8pofkkp1 xzgf3x6t. : of Pluto’s mass.

  The Sun's gravitational pull on t)/ ,w :-xcwvanhcew+che 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-) c,-h :c+ xv/ceawwnwround 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 1lqc,tx7rj;4sslv)z ze a0qii /-1 tv 0980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 t97u*nklo,ar: g9e rjround the Sun, and the net for7,rn*k: 9urogjt 9l aece exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 x2w /kn5r g/zpN is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0./2/nzxg 5kw rp90 m. Calculate the speed of the discus.   

  Suppose the space sh d3q 1*scojnysri u 2f/s)tk.fw2 :7zouttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Eartt2 *3q.7c znouds2o/ifyr ksjw f1):sh's surface. $\approx$    g

  What is the magnitude of the acceleration of a ;bzay::tq fh- speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per min:bt -;:yzaqf hute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is re12ll2qaw5c--d)f x0te z nie yeg0/qpvolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speedeq0 25 20d)c/pgf zynwilq1xt--elae 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 round a turn of radius9+ 3:o b.xnlgr8lifav g 5es1r 77 m on a flat road if the coefficient of static frfar+nv .s59 g 3elg:rx1il8boiction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between tybu fgag-z95*+ hh84uqsmy6iu :l, q che tires and the raug6mch*bufz54u g+ qls8q-i9 :y,hy oad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fioj kcv+ +t.9heghter 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 o.evhkoc 9+j +twn 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 fromc,cgly o9y.+c1c q mied;4w)j yr8q7r the axis of a rotating 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 of static fricti1 rrjcqicdc, ol7 yy4m9c.gqe8 +;y w)on between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down au :,/ z+cul7vl,w9hp 4 flojzmt the top mz cw4u,p:o/ 9 l+u7zhljlf,v 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 the driver) crosser) 4k/3kwdsue/; ss4 go+yjqts the rounded top egkoy+;4)r4t 3j /sdusw/sk qof a hill (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 minz prfl-zax 8 70q*k5okute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topk7f8 kq zz- 0aopr*5lxmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ra70g.a x:iq bsuoq3ft .dius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buf 0.qutiq.sg oa:3 x7bcket 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,juys o b dy,xr/xii:pffz 152( 7-zdd a particle 9.00 cm from the axis of rotation is to experieif2box-dyxpu , (71zzji 5s /fy:r,ddnce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are r-7bj2 mb x5pldf sk10jotated in a cylindrically walled "room." (See Fig. 5-3k1djb j0-p5lfs7m2 bx 5.)
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 circlluk+e)s;x: n 69oev 4nmnrj/q e on a frictionless air-hockey tabletop, and is held in this orbit byej+ok vsnu) /:qn6; 9e n4xrlm a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by8 6b5+thq-or my4)dhem ld. ar not ignoring the weight of the ball which 4m 8+h morbdyt daqh-l.5r6e)revolves on a string 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 ma6c) s1sag,a gya.ri3tcc-4v is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesl9-pqo45 bmz;m5 girtk, c os* $ 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 v l;z (ghbkdlm,4o98g eflu2y 15z x(bsertically 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 centripef nww:r4ym )f+( ul0vjc(2xrltal components of the net force exerted on the car (by the growfc)jx2mr0 l+yf(u l4(r nw v:und) 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 Indianapolis 500 accelerates uniformly fb ofw enu1/ro06/hm2hrom the pit area, going from rest to 320km/h in a semicircular arc with a radius of 2b0 oone6/f/uw1hhr2 m20 m. 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 cb1w;dj gbr29s +rx i4zircle of radius 2.90 m . At a particular instant, s w dbg+ibz249xj1rr; its 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 km (2fhq k) u2qe2 oaq98ae(mxbod*; bc.y) Earth radii) above the Earth’s suc2qa(qd8 ;bqh2 abofou*9ke e. )xmy)rface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accele1sgz5a 9l/z xgo 5rrr,ration g has a magnituder/s1z o9lza 5 5rx,grg 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:v7*jq1mlq*6ar visk ko b;r) due to gravity on the Moon. The Moon's radius is 1.7l7m b;rqq*)v 1k*j:r skovi6a4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but hjq0 zs:yd6* hsas the same mass. What is the acceleration due to gravity near its ss:6zd*q jhy s0urface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but uk2oo+)ea +h ki8i6g3im+j va the same radius. What is g near its sueia2uak3i ++ +8) gvojimoh6krface?   

  Two objects attract each other gravitationally with a force i.fghx.8qfuq 07c8hu of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a(ze nb.npyvk* dk, u4w dzl+6-) 3200 m6u+ de.zp,z4*kn(-dy vnblwk    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center t:jp(pea79l: pv py1 oio a point outside the Earth where thegravitatio japov9e:p( :1yp7p ilnal 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 ma8e3d 8r 8.suef/zl n st+ivw/2 85o e,xifhjuxss of our Sun packed into a sphere about 10 km in rad8eu2w 8i,n .ulje doh8z/es8 f t/rx3x5+isfvius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lik bmwkqy8lt )hv;eltxj9- ud86*c t ;*i(l cyf+e our Sun but is now in the last stage of its ebcl6ewmji8+ -*xq ;* l) y9tlv; t8(dftyhkucvolution, is the size 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 weightless while ora/cpt*6jmv( ykc sek7mw9z/ 2biting 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 surfac m c/tyc9m7p (za/*skvw2k6je e in terms of g.   

  Four 9.5-kg spheres are l37 sn4l:iow yq (;ozbsocated at the corners of a square of side 0.60 m. Calculate the magnitude and direosbz qy4:(;owil sn 37ction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets l; cjwrm 6e3aj 3:8;p d+esoalcine up on the same side of the Sun. Calculate the total force on the Earth duo j ar 8cm;+slj33 6apcde;:wee 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 ou23acql xr:0nf Mars is 0.38 of what it is on Earl0:c r x3anuq2th, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass ofz6+ tinmli ra,7i)ze6 the Sun using the known value for the period of the Earth and its e+6i l m7airntz,i )z6distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about thee0ioss s/8i dagdn /9i5.ov4n Earth at a heighgod .0/is /d vnsn4i9iea85 ost of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite in cqn7( tl(xom*zcb4+ eto a circular orbit 650 km above the Earth. How fast must b *o (n7m4c tlzcx(q+ethe shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants)ydmqqcu.w xt;r9t83 are to experience simulated gravity of 0.60 g? Assume the spaceshitt.93y qw;m) ucr dxq8p’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit thesw )v: 6vvnlx9 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 yns 6:)vv9lw xvour result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a s4o9 rqpjzx ua/ w2 o.((f/qj9wno ffm5atellite have to be launched from the top of Mt. Everest to be pla j j uqxo9m2w(q.nof9f4fo/rw ap5z /(ced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, tu31- izbl1dshk7 k n1lhe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to g 7bklkn-d11s1uiz3 lh o around the Moon once?    s

  The rings of Saturn are composed -4ld:v(jgksit, ak7(rwis f0 of chunks of ice that orbit the planet. The inner radius of the rings (i:kiw dkv- a(0,7lft srsgj 4is 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 romuaj4 d,-b,*rs:4 rmrggf4 .sub2sh gtates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her re4ub,g*g.frr rh js -4b 42m:,dsugmsaal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a-b,m.;fxxh3sa 1ng tn 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movg;.nhtx1n ,m-bf3 xasing 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 cons*yd835)hch9k ric qufl2c/dd;l 1aaf ists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 ;2flh1ycq3d9id fc5 )d u/kca*h 8lraEarth 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 thzgs d1s z/ri.5e weight of a 55-kg woman in an elevator that m.5zs/z1 risdg oves
(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 suspef3k ir30t 0n bk2xme.jnded from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction xrf0t3k kn0.e2bijm3)? a =   

Show that if a satellite orbits velb 5zs5u.s+jw,rbd g9z wzhpee :6, p:ry near the surface of a planet with period T , the density (mass/volume)pb ,,l: bje6rwzegws+:z9p5 z5.hd su 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 the period of the Moon (27.4 d) to determine ty u,o5fq n4 *q2h/zsjzhe period of an artificial satellite orbiting zq /hnq f2,4j5ouy*z svery near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun/r +x:x.erzk.3wer :l:x.ao;ad zvkz,k i/ pt like the planets. Its period is 410 d. What idr/;re. z/r ,:+x:.3ko:axpwivzkktxlzea.s its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average hpu 1aqh:78(gf rht ;5a7yc lldistance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun r //1vw6 npsvbj3cn5 bvvkf o2nr6k+; poughly once every 76 years. It comes very close to the 62cv nn3 s5wjbn+of ;b vp6 kv1v//rpksurface 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 thekzp gf7t-:d*vv7d9-w comsj/ center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moon 3auqhc;(c 0gis of Jupiter (those discovered by Galilc;hg0cq3u( ai eo 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 4z kl 4yuy:1hnfrom the known period and distance of the Moon. yz: kyu1 4lnh4   $\times 10^{24}$

  Determine the mean distance n l0(ms73vhzwrx;xn 1from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the disnm7s1n3zrl0h (wx;xvtance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mw.6 qnwm :;.oajf mu-rars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was auw -w6fmo: .rm;jqn.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 " dt y*n/22(ld m )7w)a.ga*rhvehyhruplanet" 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 gravitytlgnm/2 aud2rva yhh (hwd) y.*7*e)r 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 swingin8c;yg9pom ys 6g 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 point of hipoy8csy9g ; 6ms swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acy9 --5h.z24l1md ksmr f tzv fnpcq2+nceleration of gravity be half what it is on thz v29mp 52dkn hqfcrzy1f4s-+mt .n-le surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a qv1*de0bi5tov 1eq,1,/ frc2 upv fgcmutual circle once every 2.5 s. If we assume their arms are each 0.8q2gt /1pbu ffeedqc*51icvrvo ,v,10 0 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 apparent accelerati//qahd sa, k/o) udma.on of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitu hu/,daa /d.k)qosm /ade of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelin:r*er2l mxy. u1q gf)bg directly from the Earth to the Moon experience zero net force because the Earth and Mo)qbgxuy 1e f*.:2lr rmon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an ele f+ 3nvdnyj6d lfo3+8yvator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direc3on3+ld vj y yfd8n6+ftion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate ab bvhe 9 roo5l,/ a.:k8xdbx/iit jvqx54l+-zn 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 effect equal to gravity ajz+o49xxx hqvbneii 5l8 5a d:ltkr/-o. b,v/t the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his a*8xgg o-9 +bigzsi8spircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of(.k,bdhea4 m8.mdc i1 i qly/v its radius r, the acceleration due to gravitya m. k 4emivqdc/yi,l1h.(d b8 at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical 4,wewee 8:ulzid+c s; by an an ,8lwi c zese;dew4:u+gle $\theta$ 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 wo ax*nfy30ji+7 kvt *design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds o 7yf+wt3kx i a*j0*vncan a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast eesm q-v3, tjv*zj 0:c-zmlu,that objects at the equator werjec v *3-qv,s0 zmze,:mjl -tue apparently weightless?    $\times 10^3$s

  Two equal-mass starsg .:g voh 0fyiydz55 o1y7uj:pti6a c5 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 consxug: l ng /qa2q4k3w;5tbuaf ,,1jl fkfbh7,stant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out;la,q/x: ,lfkfj qkg t3h g 1ab4bns7uwf5,u2 to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been cp +k0l;sj.nne b2vn5w laimed that a person would be cr5nnv0p neb;s j.lw +2kushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. 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 l*tk1y6 3mta zz;itl: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 lt:*tizmlyz3k ;1t6a by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed j c 6p(qh;l/ xjeak,*tas 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 heavitx,( 6ah *ejp/;c qkjlest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS;g9y/ c3)mpj ) /vnzgbresez3a 3jvm5) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals tr g;gse/zv9 j)r3nv3 z3pe)mybc/5m jaansmitted 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 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 6ahj w 20(brmgRendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . 0jmg (2hwr6ba 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 pursuikn 86(* polv1y1(1esks yugip ng a satellite in need of repair. You are in a circular orbit of the*s1g1 8uyis lnvo(p ek(k6y p1 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 period of 3000 yearslo; a z.5b,bdadi 7mc9. (a) What is its mean distance from the oab;bm.i5zdd 9 c,la7Sun?   
(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 y cvrqehojn10l;6 tw s(5/o;hp ou could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, le5r/6jhtopsq n w(hl 0o ;;c1vike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46q0o)xzc5j/jz ) at a distance of ab/ oqz czxjj5)0out 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 eachj6nv-p*r3n sg side. Find the magnitude-nvr n sg3p*j6 and 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 orbits the Eaz)p z)cbn9pyzp-5;jd rth $ \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-loe;,-jph -kjw6lys: x . axej6vng sweep second hand on your wrist watcxhlj va.-:,e-ypsj6 6kejx;wh?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weingl17q :ut:l vx:frm0 ght 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 thel: 0uqfv7rg nl:1:mxt fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway.ehke7* fr-e l2r0gy r is designed so that a car traveling at * 7regf 0lhery.-2erk 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 ca* sripl)/86a n 0yxvlers when negotiating curves. The angle of til6s)vpy8 ea*ir/0l lnxt 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 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.$\approx$    $\times 10^2$