Sometimes people say that water is yaji(3)noa56m; p lo dremoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wii3oao )6yl ;a5pjdmn (th this statement?

Will the acceleration of a car be the same when the car travels around a sh6gr k;3 j1udnzrfo/nua r0sy j;;q p7 rk9k7r:arp curve at a ;j : k7/snpnqr0r;k ajfry91g73krzd;ru ou6constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly9jjw0,e/bwd 2amr;a j kgs)we9-5qg o road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch 5kbsmd)r9aa; w2e o wgj,9egw/qj-0 j near the bottom of a hill?

Describe all the forces v (:jmb xj+,.4aac3b5hy a akeacting on a child riding a horse on a merry-go-round. Which of these forces provides the5+ aj(m3 jeyhb a:4 a.xb,ckva centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spil2,vo6etgf xb1us3k5z ling out, even at the top of the circle when the bucket is v6 2 zs5btkfx1g,e u3oupside down. Explain.

How many “accelerators” do you have in y.n*7qq55f q.f)p3cz kil dmr4kweyq +our car? There are at least three controls in the car.y wq4iqn 5d+) pfm 5rkqf*lqk3ez.c 7 which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. uplz*.j k pt((5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.ul(t. p*kp jz(

Why do bicycle riders lean inward when rounding a curve at high speed ewgg/4fi++v4z/ a au(uvazn-?

Why do airplanes bank when theyzhhh5fr uf 9(rt .;*zp turn? How would you compute the banking angle gifr.9u r*zzf5hpht ;(h ven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Sh*sd;obbsz 7kj3 : 0fwcfbp 9isr+9s ;je wants to let go a;jb9w jksc3p* db r7+z s o;bf0sf9s:it precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, 6d w6tpj.iy,chow large a force? Conjpc6,itwd6y .sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass ulo/ p,l:hj5 ywere double what it is, in what ways would the Moon’s orbit be dif 5yu/,lolpj h:ferent?

Which pulls harder gravitationally, the Eamkj+)z8oe1 ij )s(edbrth on the Moon, or the Moon on the Earth? Whe + z o()s)bied81kjmjich accelerates more?

The Sun's gravitational pull on the Earth is muc1*btwqr96 j+f0ynl ejh larger than the Moon's. Yet the Moon's is mainly responsible for the tides. tqb9r1e +yw j6nl* 0jfExplain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatk6 y o6d7g96 uqi2jnvfor or at the poles? What two effects are at work? Do tho fvjki d7ygqnu66 692ey oppose each other?

The gravitational force on the Moon due to the Earth is only ab6 cd)0bo:sf j-qfq ,i 6ecliq5out half the force on th)5f6qoq ji esd-:lib, fcq0c6 e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroune,-q7zcoh( ub lzs*2a d the Sun larger or smaller than the centripetaba cl o husz7e*2-q,z(l acceleration of the Earth?

Would it require less speed to launch a satellite (a) towappj2a6i1ys + crd the east or (b) toward the west? 26pj+ p i1acsyConsider the Earth’s rotation direction.

When will your apparent weigh 7zb c0-hg:yp..6t.kvf zycy at be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acceler. 0 hp y :ackgf.zy.bz6y7t-cvates 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 s ./o m3jwk/q )wwhvol:pace 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). Explawqh:kwj)3/ wol/v om. in 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 w.m+6qx 5ww8c aavn;lp eightlessness” between s+6;.m pval8 xw5qcw nateps.

The Earth moves faster in its orbit around the Sun in January than in xl * o1nd:;.vzxu4wboJuly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis zd:bxuvl;4* x1 oow. nrelative to the plane of its orbit.]

The mass of Pluto was nohze p4imm 89k+f3dj) f8a,fxzt known until it was discovered to have a moon. Explain how this disphef8m)+8 , kmdx j9fz ia3zf4covery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger tumajuo k;v:l2qt ,j) (j g-uy*han 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 centeju:uk* o,qj()lu aj y;vmt-2gr 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 7q) b sji9t9pupvt1.k 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal a *ji9drmq lvcp7:.j1s1s 3(by g-okgtcceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force jygg1-p lobsq7d mkrvs(:t3*cj. 1i9on 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 discuhmik q 3s;2irk9 :d;rud5 9err h;qxx8s as it rotates uniformly in a horizontal circle rmd9ix; h58q re3iqh : kd9s;xkr 2r;u(at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfa //rje)f:spngce, and circles the Earth about once every 90 mingfep)/ j:snr/ utes. 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 al) -fwzxle))acceleration of a speck of clay on the edge of a potter’s wheel turning at 45lx)awze-f ) )l rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a udayr,ld qi2bryk3u bl4gi d67 5 i20,eniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33.2 d2d5a40idg3 lie l6ubb rryykiq7,, If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg5,vj63k :/ lbyha raua car can round a turn of radius 77 m on a flat road if the coefficient of static frictio kar/a6b 3hvy ,j:lua5n between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static f6jpz7tci+xh84b -paw-a 0pjb/cjp+ a riction be between the tires and the road if a car is to t7a4-x+cap6jbj/pwc8 pih +bp0aj - zround a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate ;*b 30q uhsncueh,f-pi2- nbka trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on 0-n,;hc2bb i ek*3fhs-p uqnuher 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 o.ai*2x4u wqo0v n zev r9jm+(bf 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 frictv x4 +u(b 9w i0.qmeo*jaz2rvnion between the coin and the turntable?   

  At what minimum speed must a roller coow+7a z)a qw.caster be traveling when upside down at the top of a +zqowca. 7aw) 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) crosses the roundez)5jc ij5uf(yt /ow1kmgfc -+w*4xp od top of a h)- + f*(oc 4x5pi/w1cy zm5fjkwuogtjill (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 wouzpllf- qos g99ie,;5 hld a 15-m-diameter Ferris wheel need to make for the passengersl95- 9h,f zeqgp; olis to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. b)cs; qkcfnmui,7) h/ At the lowest point of its motiisq)nu/mcf 7 b;c)k,h on the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must vk jgaw9u jfd7n31o:, ch93o3-tkusua centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience wjtf33va 9us9-: k,n71hcdgououj k3 an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a ci qll+ x2h9e/zylindrically walled "room." (See Fig. 2x izellh/+9q 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 circle on a frictionless air-ivvrx;.;,5 mk;,en 8siggmw9 l s azs nu/e83ohockey tabletop, and is held in this orbit by a light cord connec,ssv; mk5agxr8w iuienmg zs,;8 3 . /no9le;vted 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 thq2orde/ ) c6(uptmvr-is time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In otm/-du6vcp2rr (qe) 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 banks ;gtfxio+u /)ed 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 massesm/:w8ygy-wzc 4jr01 wa7r ivd $ 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 verti )s00b/pftly yxh/5mt cally 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 tangens q9: + s5z0jccrit:lwtial and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its sc9tlcs: j+wr:50sqi zpeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelelx 4huu+ dnbt2;+vdp-rates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be ben;l- 4xvupdd +ub+2th tween the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a h7kpo 8 vlezq 5874spb; x4vtbporizontal circle of radius 2.90 m . At a particular instant, its acceleravtoxlp7e bp;5b47qv z8k8 p4stion 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 gravit)s+*d. t gdiai04 o xl5mri9noy on a spacecraft 12,800 km (2 Earth radii) above mn9si0id5l) r*.d otx+4goai the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certp3qlkmxu5 - k2ain planet, the gravitational acceleration g has a magnitude of x25 lpk-m3 uqk12 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 db ad9w7x 64uzt( dc0cMoon. The Moon's radius is 1.74 90dwxcc 64z ba7(utdd$\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 Earthaq+fhc rw, qda(t 0 m34b8xwu9, but has the same mass. What is thehw(mxdc03au 9w ta4 ,q8q+fbr acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66etqqh +t;r4/ : z qu3+36cdjozihq2ke times that of Earth, but the same radius. What is g near itsz /qdh+tje34;i:qq z e oqh36k2ru c+t surface?   

  Two objects attract each other gravitatiy/3 4u1nlwab3 crcry 6onally with 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 effectak8w.;hv) bf e6; wckdive value of g , the acceleration of gravity, at (a) 3200 m cfwbvk.a)w;d 8 he; k6   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth nu-g:,ofxer1m.; r jfwhere thegravitational acceleration due to the Eart .mfne-r,1u f;jorgx: h is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphe t-5g61c5k hp/q2rj7kb7ihvm i0 zbczre about 10 km in radius. Estimate the surface gravity on thi q6krm5g1i07 c-bhpjkcv 2/tbh z5z7is monster.    $\times10^12$

  A typical white-dwarf star,xan2g2u up5,l4e1izi which once was an average star like our Sun but is now in the last stage of ,ua1pnzi 2guxl4e 2i5 its evolution, 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 ax8 n7tibk 2(v;xs/hly stronauts feel weightless while orbiting in the space shuttle. i;khvbx/8 lsyn(t2x 7 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 surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of b99nzq pq,(riz/i7y j side 0.60 m. Calculzbpr 97i9 qq(jn/yz,iate the magnitude and direction 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 line up on the sz a,4 ejl5nvm4y im 5cl-/hsz6ame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all /,e myhcizvsla 546njz54ml- 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 is 0hp i4gn- 5-jked7wdlwp,;4-rznb 1zq.38 of what it is on Eard-izl1prz7 kwh- j ed 5p-;4bwgnn 4,qth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usiqqgjnd q5+l+qu 8pww69 cnc96ng the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws,wq 6nw+jcdng q5+98lq cp6qu 9 Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orb a omn;7uv+(eqit about the Earth at a he;q(a7v+ muon eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Eo7 ,3l-ns1p o xz 7-hugfyqxfix4iy .9arth. How fast must the shuox.hi7 ogyfz7,4 u3n x-si-x lq19fpyttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experir/stfj v,66xlence simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time fs 6r jxv6/tl,needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular :fh-e1mf9m;y5xv tob “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is vb;f-59x y1:em o tmhvfery small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity w0sk-wp 0-h3zcvs(,f 1hanygs ould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit arou0kpnvz3ycs,sh f1 s g(-ha0-wnd the Earth?   

  During an Apollo lunar landing mission, the command module contiox ;(9 mxkqgu.lr-al7 nued to orbit the Moon at an altitude of about 100 km. How long did (qxgor.a;- lxl km79u it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The7ko.:32u ctou i/enrc inner radius of the orknu2i. 3oct/c7 e :urings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9 :koc6o ,l(ved). What is the ratio of a perov,:e6 lco(dk son’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-; nkeai;i06h pa)qy:kkg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, ;n0 k:hpai) ky eq6;ai     ----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 ofptbv)o0.a-7z sf )xlk two stars of equal mass. They are observed to b. xo0-ba tk)lpvf zs)7e separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevatofu,q8m*6cx ( lx rkm8yr that mc8xm 8fxq6rmlk u*(y, 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 han(ecbj/ dwqa31m9 gof3gs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 Ng1m(j3wo3be/qd acf9 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 surfaceemlvcf7) n+g1 8ggp 9w z/tex5 of a planet with period T , the density t5 g)vz/8e 7m+ p1cglfewgnx9 (mass/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 and the period of the Moon (q)0 vwpx -immd1l;jp ljok(5(27.4 d) to determine the period of an artificial satellite or m;pwjko)1((j i05dp-xq mllv biting very near the Earth’s surface.    s

  The asteroid Icarus, thoughselqnn(1 a-sqdlyza 5+ 846q y only a few hundred meters across, orbits the Sun like the planets. Its period is 41sd+qn sqy8le-5a4(an 61lqy z0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancf fph--382x4 chyhcxe, yrec,e 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 Sb)u vj 4.r j5;inaxduq5+7 mckun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s ord)xkuq.c5 7 5m;4b+uvjrja in bit 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 h1j;42ejmv p;qcz b0z q74l2 igafb1r 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 km16h w:+aw v) m6/mnef4 wzqjmass, period, and mean distance for the four largest moons of Jupiter (those diwwk6wm )hne v6fm/:41 +q zmjascovered 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 per: zwt4d 4*z9xd(kyvgi iod and distance of the Moon. *x dz4 :dkzwtyg4iv(9   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, uv ot*cx m2tdy,373rxbsing Kepler’s third law. Use the distance of Io and the periods given in Tablvm 73to3cryxxd* 2t,be 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 ;r;ehfnsv1+s.zuf6s hm. *ud Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited themz.hhv.+ed ru; *1sf;6 nsfsu 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 "planet" in therjk :pj,6xrk)t8 )kenxm t 4+d 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. What will r4t)kk6rjm 8 dex+:ptk x)jn, 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 xk .h,x t/ionmh v/ cuhhd)6-b;-,ijfhanging 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 his swing? His mass is 80 kg,ihh ,mh.6vbh;fn/ txkd--j i/xoc )u, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration ofw(9 i2 c(x,ydg7b3do jtdmo*f gravity be half what it is on the surfdiwo2y g(*7do9(tbxj3m d ,cface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circlj.j 29.zpw sjxe once every z9w.2jj.sp xj2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of.f9bxe0c6:a9o eublw2za r r5 gravity at the equator is slightly less than it would be ifxlbeb:cu rez6 .059r afw a2o9 the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a sp , .tq4s i6hslfh:a;ingc;z+ v dg+ej4acecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and a64.d;f sgnis4v+:+ thl ehzcq, ;jigMoon 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 a mo7 ,ckll53 k+c,adzbn elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direc am,,c oll d3bkcz5k7+tion?     ----待选择----upwartddown 

  A projected space station consists of a circul63 bs;gbsxcna w m9 o1),xgr-nar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed bs xn) mgbx,ngw- 6;ao9csr3b 1y 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 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. 5–9, ,66a0: np7cybilbs igkla z43).
(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 its radius r, the acc1nytu :ktm+f4vs 8oxpre4b4(/ pi6d m,xm y /seleration due xmbnm6dutpt ,o8fss4i1y4x4 : (p +/ ekmyv/r to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vefl3jcl. ryp-ld(+a 5lrocn v*7 ,gl-t rtical by anlp ,+ rygco*a lc3 tflvld-7n (l.5j-r angle $\theta$ 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 coefficient of l-5/1agm 8ohttt 6(xg sf*f zpstatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle thg tf5fmpa6-gt o1 h8z*xst(/l e curve?

  How long would a day be if the Earth were rcoyb9r*88xt sc+wndsp c29 :motating so fast that objects at the equasmy2w nc+*88:bcx sd 9pctr9 otor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanco1su; ka4tus3e 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 constant speed rounds a curve of radius 235 m. 3-+ttr ys qrl)o9) pf3 9e2z qs-h dttqpqav;/A lamp suspended fr qav h)q;ot -2)t3tr9-z9spqq+p sryf t le3d/om 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 Earth. Thus, it has been claimed th-fbi;5mw r3 egat a b; 3f m-5greiwperson 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 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 Hubb/y 9:,5xhedl(ckmqpl i xmn*; .+rooble Space 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). Tl hmb lpq,m k 5e xy/di*n.;9orc:+x(ohey 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 valvxizf1 em0 1q;o/) bidley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Ligbv/)1 ;i0e1fdxomizq htest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilize6 8j hhqyujm+ 1 eq7;+djmy5aas 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 “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the+j17 y8qh 6ymujh aa;5+qm edj speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), afteavif: 8;6qde kj 1rv rs1+fp1or traveling 2.1 billion km, is meant to orbit the asteroi+s 6vkei d1;rof1qj:vfrp1 8ad 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 a satellite in neew a )g:+k hi6a*qbga/ld of repair. You are in a circular orbit of the same raalq6 :g+*bhki ) /awgadius 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 years. (a) What w3 t hkz hrz6fs5p)i s:+j6ns c492*ck7aiscjis its mean distance from the S3 ci:shkz6 p* 2sfi7)5czw4ss h+tra6k9 njcjun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the va:3 mje/ qec4srz1 rh+wse)iw7 lue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reseij7s3z+h rcwq)r4ew/ 1e m:asonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga.*nplizfs9 o(d m*m9mzy x5i4:/a xx ilaxy (Fig. 5-46) at a distance of :sim d5( lx4f *9im/pyxzmixa o .zn9*about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corneza28hz h(,nzh,c /x cwrs of a square 0.50 m on each side. Find the magnitude and direction of the gravitationah c/2ca zn 8,wh(zxzh,l 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 wd5t )corm*-k 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 experiencsph z8o9i :5wqj *4urled by the tip of the 1.5-cm-long sweep second hand on your wris*ljuqr ph wozi5489s :t watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkey h+x swn23)zj+;ic1 1 zxuszjr 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. ixw+cz zzsj312h+n) 1uy;x js 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed ss+;m y ylcx)k6o that a car traveling aty;l ck) x6s+ym 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 . 67mc ,scjfzn2afu;mof the cars when negotiating curves. The angle of tilt is adjusted so f7,f.u6mjnc a m;z2sc 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.$\approx$    $\times 10^2$