Sometimes people sayttwy1j:yqqde374b v.ea) dlj eu . e3. that water is removed from clothes in a spin dryer by centrifuge y yl3)td3tde:wa vbqe.jq ej7u.4 .1al force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the x :qj,i b4opsyvaml8,p l:x1ade+)/ f car travels around a sharp curve at a constant 60 km/h as when it travels around a :pplfqe:s m bix,v,)oj14xayd/ 8la+gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does t t;ekm4a9s:s( 4 zmpjwhe car exert the greatest and least forces on z e4sta(;k9sw:m4mp j 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 a horse on an v84to+/ rpd))de:aw w 0dhrk merry-go-round. Whicpknw8w td)v4da/r h0edr+ o) :h of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spilliny3n yey;j 2q ofbt6ndi/+;6ho g out, even at the top of the circle when the bucket is upside do yjoby6dyhn;6/+ ie; onf2qt3wn. Explain.

How many “accelerators” do you have in your car? There are at least thremu g bnz w6(-vrd1t9k:e controls in the car which can be used to cause the car to accelerate. What are they? What accelerations dbm9(w6d:z-kv u grn 1to they produce?

A child on a sled comes flying over the y;elk146t7ktlirr7 r lp n0y7 crest of a small hill, as shown in Fig. 5–31. His sled does not leave the7y elr;i10y 46k 7 kltt7prlrn ground (he does not 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 rounding a curve at exk2oo 82pmr4 high speed?

Why do airplanes bank when they turn? How would you compute the banking an c5bz-arb. tb.gle given its speed and ta.b 5z. b-rcbradius of the turn?

A girl is whirling a yw,pli/cc n2s.ut*g5s ,2qsd ball 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 si.uc w,gy/*tl 2ss5 idqnp2c,sde of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? Ifcw7 4z usgp:7e so, how large a force? Consider an p7gw :u7z4secapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it w 4lf0 )a1hprmq 7ye57wyb dc(is, in what ways would the Moon’s orbit p ye)wdbw (0f5747ra1mlqhycbe different?

Which pulls harder gravitla/26nhqd7 63r; uc m7njakfqationally, the Earth on the Moon, or the Moon on the Earth? Wq;unf ka/7ljm cdnh63 q7r62a hich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Mv 8ck;:sd rr ujq5f9 01gc2deuoon's. Yet the Moon's is mainly responsible for the tides. Explain.kr8d2e; qujr5 dc: 19vcsf u0g [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator( 84ak 6fmoa qlsglr*g.3yq 37u(tddo or at the poles? What two effects are at work? Doadqqgl 8 km3goas.fd7o *(u6t43r(l y they oppose each other?

The gravitational force on t bua: h.qchhqh-85:e dhe Moon due to the Earth is only about half the force on the Moon due to the Sun.8 . hha-hq5 q::ehcdub Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars /p7gz(jhc qi4in its orbit around the Sun larger or smaller thazcih(qg 7j p4/n the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) 9n 2zh ebbw aao;r59 emtvs66q3+)uf otoward the west? Consider the Earth’s rotation dir 6a9bam )ozboh u2 3tf;6+s59 qrvwneeection.

When will your apparent weight beo ) xsc:iyxo,zx3rll g(:),cl the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? Iy)cx,3i lorxll)(xsc zg :, :on 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 q2l-t, kjn 5rcspace 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. Consnrkjl5q tc -2,ider (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 expew( cslx8(gmyhqpu0 2 ee+.s 7-;p kskuriences “free fall” or “apparent weightlessness” between stes(kel x8s.cep;7u(+g mwk-pyq2 0 hsups.

The Earth moves faster in its orbit around the Sun in Januaryevpj(yneui :(x mi tx3m:e/1 , than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much oy( p3,enet (i/xx:im:um jv1 ef 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 untilopw 9d/5ld8:wb3 ;kf tny*lne it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto5d 9dyf:o;pln w ewk* l8b3nt/’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'ef6+ny 2swutmsr f060g 1lhp .s. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side ofyhe s6fspn0m+1l w 0.g26tfru the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 e,n(xdb ma;iby3k +s2$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accele+ kj1gp,wg8y3ma:zinn*97zs je vs, hration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit ky +nsseza31 *z9mg 7pjhgv8:,n,jwi 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 discus as it rot/du;aq(nwh54+ kuqqnates uniformly in a horizontal circle (at arm’s length) oadq5q+ (n/ 4k;nhw uuqf radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thqwlo:5 bec6n.hlg mz x /v78d)e Earth's surface, and circles the Earth about once evv. eq: g7m nb6lzhclxwdo8)5 /ery 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 Earth's surface. $\approx$    g

  What is the magnitude of the acceleration bwa,( z w3n. -qkulh;sof a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the (l 3;un,bs.akwqw-zh wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verticipg;;+9b gpf **a jaqual circle of radius 72.0 cm , as shown in Fig. 5-33. If it*bgaua*g ;j9 fpq+p;is 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 4 c3u3 imx1gtespeed 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 result independent of the mass of the carigxm 4tcu e331?   

  How large must the coefficient of static f5ij(2.y az lbfriction be between the tires and the road if a car is to round a level.aby5( 2 jizfl curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter p15+ja ov z13wycje ;pmjr44yh ilots is designed to rotate a trainee in a horizontal circlj+ovz4ma; e4 yp1w 1jhc35ry je of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable speed-4unvj-5-v4 l7 qip7kodbf- w5do rib. 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 statiliuo7-7-v k ibjqwvddp45 5onf4b-r - c friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelinx*xim2l ,r- qtg when upside down at the tol, xi-2* tmqxrp 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 ka1(vq7 vtv t2 .ybsj4o( x(tewg (including the driver) crosses the rounded top of a hi to2a.(xbjvvv (ey7s qw4(1 ttll (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-m-diameter Ferris w (e8wgprfm 2m8bs ;5vsheel need to make for the passengers to feel “weightless” at the topmostmgvprb;w(smf 5e 2s88 point?    rpm

  A bucket of mass 2.00 kg is whirled r pqarek(4 i6m0o3,x ;wc1g u8nqgz-r in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportc 4g6rp-q0, k8w 3(izra1o;qmnuegr xing the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particleao4-4 l jmmvh3 9.00 cm from the axis of rotation is to experience anm-o 4 3a4hjvlm acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplfyd-2w19rsj -,agzm8 5 )okbdqm8ap ae are rotated in a cylindrically walled "room." (See Fig. mq, bjd2y5-ad8 w )sr89zf1ga pkaom-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 rotzwnmz k f3(0ahk07s; zated in a circle on a frictionless air-hockey tablet kwmnzz(3ka 7h0fz0s; op, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not eod nliuub;lzsco7+ ho*2fv-l4;7p :ignoring the weight of the ball which revolves on a string 0z27l vlouic;o:h+ olesb f np4ud*-;7.600 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 c(6hgpnt;ol,w j( dl;qq +c8t k/v iopd8q3a /lar 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 r- a*9q otms 6n5l0bne$ 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 vertically at 310-lq-e 6zzbb ,kv./xs:mj y7fg $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted o.ebu7 t kvcz)+n the car (by the ground) in Example 5-8kc)buevt+7 .z when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pi gl 3mw6qiz* aeop2/t et1ba79t area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of stie / a6ga7 lpqwmtt3 1ze2b9*oatic 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 rad*y4 -2y j2c,hgfo mwsyius 2.90 m . At a particular instant, its ac j-yc4g*2m hsfwo ,2yyceleration 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 g.fog/ v*m+w4l/ 1bnh rsh w4hjravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if gfhwobl/rj w+ s4h */h.v4nm1its mass is 1350 kg.   

  At the surface of a certain planet, the gravitati.q.:i/-vrw 7cgsnkr qonal acceleration g has a magnitude of 12 m/sg7:kr .vsiq- q/wnrc.$^2$ 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 gravio q , pp10k r1tz,qv2r( gwlk;bsz6*czty on the Moon. The Moon's radius is 1.7( z 1kovr6br l1p*zqpgs2;q,0,zctk w4 $\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/k4rr9 tnxm8 r, but has the same mass. What is the acceleration due 8n4 x /9krrmtrto gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thze+*pxx5.m poa2 :zj io)cpamoi* iyf55o1 0l e same radius. What iic5 a5x :m)1pjmo*o 2 yo i x.zeazoifp*50p+ls g near its surface?   

  Two objects attract each other gravitationally with a force ofjc 8q9yum8iyz(ah e (1 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 gv 05 tm dc)mq1p y9)yngz2u3thravity, at (a) 3200 m3 pm2dthm59n vzg y1yt0)uc)q    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside ,;1fx5iqc 2tzz*v dapthe Earth where thegravitational acceleration due to z512t;qc ipf d v,ax*zthe Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thj-v lb 5dctsru-a h+;7;qbz9 re mass of our Sun packed into a sphere about 10 km in radius. Estimate z7lhbut;+s bj-d95 cvq -rra ;the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oneto(p 8ur xk94ce 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 Sunrp(ox8k9 uet4. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why a85 zs.fn*bew fstronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought 8nweb .fs5*fzgravity 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 surface in terms of g.   

  Four 9.5-kg spheres are located at the corn8/lmh npj **.a nnjs;hs*u x8fers of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the otheunjma* *p8n s n.sjl*f h8;xh/r three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same i.33a ,6oykjw1i 7cdo yc6zbm side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, as3y3kc,j 6cd.m 1zby oaoiw6i7suming 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 grav /gn-.ybcz3*ai qqk2kpgw-. dll x,,mity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of k g/iwp q*m23-c..d-b azq ,ylkg x,lnMars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for tdn1v pe)6zh .orhk/o+he period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtainedp+rd/ o no)vh1e zh6.k using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a zh77,re+pl*am e yp.gwx3na,stable circular orbit about the Eartyh* rgpmaan 7 z,w+,elxe3p7.h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65;;p2 bhf uho8 wch4t-xy b.ke20 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the ut-of h2b2cy wp k4.e8;;hx hbrelease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occb tbtb ct)3yzou7:1o1upants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 u1bz) bbct17 t:tyo3 om, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for al67 *vgkbd )+r4gw7jtdc u9sx satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface u tgxcrj *7bg lk v4w9ds7+d)6of the Earth which is very 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 satellite +hqho*oa oq- 4have to be launched from the top of o +4qq* oh-oahMt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module0m .ok0ey.hsz,t,aif+ljfco , f f: k;9yq*bn continued to orbit the Moon at an altitude of ab ,jk qy9.bi .*,l y:0o,h nafmsfcz; ot+0ffkeout 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 orbf v*qo66vk 6bfit the planet. The inner radius obofv f vk66*q6f 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 f- fqos55n:b m: (hifkonce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at thekfoin5- 5bqff: :ms(h bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaz so;tmo/ds d2 c(84rbut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constan4bz8dod2ct o m(ss;r/t 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 ofbyemd(z) ayb3)6 jp -p two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of z-(ye3)pbmy6)a d bpjeach?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an ele6oni, mi uug26eiv /m4vator that moves men/66oi4, 2ug vuiim
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevbssp3 k:am*i :ator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s mi kbs*s::mpia3 nimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pzfl3kx :m1i04fhgn 7rx4r ni:lanet with period T , the density (mass/volume) of the planet is krm1hni0:4lfrf nxz 4x:3ig7 $\rho=m / V=3 \pi / G T^{2}$ .
(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 pe;9j5 lx)lmab)3-ia efy,u/1 ny6ioud szx+giriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near ,d5y39baugf1-nji u e/x;+)ix6i y aom lz )lsthe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the S2zqpm c4h cdsh2*xk018qayi 98rz;ce un like p8mczz9dae rqh4cx12 08;kiysh *c q2the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis(*9gtt +fddus2yk9*ju hl :8 omjvjz1tance 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 orbit9-uma x0h co7 amvy6h7 v/yd(ss the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig(am7v-/uymy xs9vahd0 6h 7c o. 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 thei)6eym* ,cep0 .ztx al 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, -gl3rcg:*bm3v* ngfiperiod, and mean distance for the four largest moons of Jupiter (those discoverel :m3 gnrg-c3fg v*bi*d 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 knyzz8 15nkg)isown period and distance of the Moon. 1n5y s kg8zz)i   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mod:v fvwh/;wn /ons, using Kepler’s third law. Use the distance ov:vw; / dwfn/hf 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 Mars and Jupiter consists of manye v:cak /ni:dbh.jpo9p . x;j.(n .sbd fragments (which some space scientists think came from a planet that once orbpds./.; i.:d knnj.cv9:b jxpboae ( hited 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 describe,t0ntlljc m0p5+a mb;s 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+lntjm;,0c 0l5patb m 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. 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 hangi eezi0+ar (*wfng vine (Fig. 5–41). If his arms are capable of exerting a ff *0r wa(+eeizorce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what iy3 ;:*-xi -aiw bmkjait is on the surfama*ak;3xji yi :-w i-bce?    $\times 10^6$

  On an ice rink, two skaters o:/z64fibafc yg4 mch (f equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual ma ch4 y(bgamz:cf4 6f/isses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatesnnyo ghn4w0priw e79j::h9 o 1 once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didrw0nn:9ygjh:h9e4n ioo 7pw1n’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth w;h1c wuqlx5j.olmwv qm, 79r9 ill a spacecraft traveling directly from the Earth to the Moon experience zero net forcem97 h 5mu;1woq .lwr,xqcl 9vj because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is h s3c8+x- ewri65 kg, but when you stand on a bathroom scale in an elevat38+e hrwi cxs-or, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo9cv)g -n :hmsfmteck;5pr- .a w. 0slo mq/er5ut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tub kmrv-f0me.c9qsgeco)aw ;t 5. 5-: nsrm lh/pe has a diameter of about 1.1 km. What must be 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 vertical loop (Fig. 5–43).0uxnp q 1t7jm;
(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 planex6 wt,r hdg:k;jfq ) uw7t-y;9bvv8ms t in terms of its radius r, the acceleration due to gravity at its surface and thj,kq w;y- ;vtd:b9h t)wsgmx7vf86ru e gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical i w7dy +m2z:etj;f/ h 8v0inciby an angle 2:t 0hmiv7f/dcizi e 8;jwy+n$\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the hx +t2 ra7z1:cvedwd-ed.z q8 coefficient of stadcwe v-8e+ dr.zh 1q7axt:z 2dtic friction 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 Earny:zooo k+s/x w4+ldx4bl(w :th were rotating so fast that objects at the equator were appa/l4x:dwn4 w (+o:ozklosy+bxrently weightless?    $\times 10^3$s

  Two equal-mass stars maintain tg5/mky8 v w,8v+wkgqa 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 coe:l ng 0ph.hlt+fjkg (h47c+ anstant speed rounds a curve of radius 235 m. A lamp suspended t4hgn f a+.:j0ph(7gelchk l+from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Ea9 ybdprt1n yp)h/y1v 2rth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator/r1ty ypdyph9v)2b n1 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 Telesc:vj ;-yp-qwr w ljfz833pdj r*ope 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) q8rpld3jz :v3 yr -f;-*pjjww. They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley sw zw: 5q:rl v+kk::xgyhown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces ack+ yl:k:v:r:w wqxz g5ting 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) utilia7uq9osgm0+s+t vfa na ifp* 0/08npfzes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational /9mn+v p 8+0 *0f70 asiaa gnptqfofus“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 Rendez i)*q9t kgnnu3vous (NEAR), after traveling 2.1 billion km, is meant qinng3 9 uk*)tto 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 the space shuttle pursuing mo; abu9ov3/vsf4f 3l g4 yxz6a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behi x6vmo4b 93g;aouy /vfz4 fsl3nd 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 years. (a) What is t) gti9a;rwq-.b46ddi4tt3 *d a egwz its mean distance from the Sun?ir tzbiwdtt .dq gtew46-dg *4aa 9;3)   
(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-k( 31gmp 5caiyed b1kou could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable mkc3 k(yapi5b g1 1e-dassumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way G2r37 t 0a xe26fzt3oszdj5 vp:mgjx)w alaxy (Fig. 5-46) at a distance of about 30,000 light-years from tor mwgf7dje532 2:30 vaz) xxpjst6zthe 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 eac4vw..5o fdyrj)oxza8 h side. Find the magnitude and direction offa zoojd.)58vwy4. r x 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 52x ;z lhx0b3zalvu23 c500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced byfk.j(-3;zcmkx n-y el the tip of the 1.5-cm-long sweep second hand on your wrise-m3lc- fzy; . (kkxnjt watch?    $\times 10^{-4}$

  While fishing, you g,p*y u;mjjo3 zet bored and start to swing 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 makes with the vertical? [Hint: See Fig. ;ymjuj z*o3,p 5–10.]    $^{\circ}$

A circular curve of radabd )es)8z- qvyha6df, (:gmaius R in a new highway is designed so that a car travelh v z-,dy(mag efd a)sa)6b8q:ing 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,*k4sju vhpxz , m/81ij utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the 8/i4mhzvj1 *x,ku jspfriction 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.$\approx$    $\times 10^2$