Sometimes people say that water is removed from cl 1ust.ec6+dyoothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with thec d6su t1.o+yis statement?

Will the acceleration of a car be the same when the car tl:m a w.xfs;.)oyrwi9mglejrx. b63 :asb71fravels around a sharp curve at :.ga 1y9oe.;lwsmbi wfrf3)l 7baxjr 6s xm:.a constant 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 hilly road. Whez 3 )c(5gwydusre 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 strez53gds(cw ) uytch near the bottom of a hill?

Describe all the forces acting on a childspcdk*ng8xm /e65 ur9 riding a horse on a merry-go-round. Which of these forces providc5 drs/6u*p k9ex 8ngmes the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circlx:g cnmwnk *: *hmm4o1e without the water spilling out, even at the top of the kmgom*:n*1 cn:x4hm wcircle when the bucket is upside down. Explain.

How many “accelerators” do you hg+h4 8t dahk(2udhk6n ave in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelh4gh268nddu+k kta (herations do they produce?

A child on a sled comes flying over the crest6mfx807l nr7 h )ocd+0 ; eqtykdjgwe3 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 normalnx0rocg)7ewqlk6ym;0 7j3 f+ th8e dd 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 whlj87ibc) 3j 7z h,ggiien rounding a curve at high speed?

Why do airplanes bank when 2z0cc b7 bo +k.vlkl,u 3kc3ditk)r )athey turn? How would you compute the banking angle given its speed and radius of the t+)k.2d0b7vi lb3lcktoca ,k u )czr3kurn?

A girl is whirling a ball on a string around her head in a horizontal ph adm-v;k2l v: lu11ahlane. She wants to let go at precisely the right time so that the ball will hit lh1- ha1v 2 dmu:valk;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 tff1 oepntm/+o 1 fu/br0bt 43the Earth? If so, how large a force? Cntr 4 f// ob3tf+t11eou m0pfbonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tpd pgw-tv8(1ahe Moon’s orbit be diffp(ad-1pwvt g8 erent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mx;j47/jccbhm.g vx j7qtjq b*z i1q8-oon on the Earth? Which accelera q7c ;1b qjh 47qjcjmb*ij -z.xv8xt/gtes more?

The Sun's gravitational pull oa2w0 *,tz qmya,g0f2r qk3 h2d;pzgixn the Earth is much larger than the Moon's. Yet the Moon's isa2h;rmp xf ,yd* 32g0za0,2kqzwqgti mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatorqi ni m 4 rlc375xt0rh-rl4(cx or at the poles? What two effects are at work? Do they oppose ea qhr(4m l74ix 0l ntrr-i3cxc5ch other?

The gravitational force on the Moon due to the Eage;g5 vpmkb/5-qyl .rrth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Ekpbygg5l .r5-mev; /q arth?

Is the centripetal acceleratiyz(fpd g2ay 2s3 d7q2ion of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration o gqy73a2 izdf ds(y2p2f the Earth?

Would it require less speed to launch a satellite (a) tosf 7uts;k g3 8rb0fzl/ward the east or (b) toward the west? fzrl tku3/;8 g 7sbfs0Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in qc)(r drk6on8 k9*ntta moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In wh)*(td68t nk kcror9qn ich 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 adversxe( 6zuldq 4(oely 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. Couoq(zd4lx6 e (nsider (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 “acv sisol-is2gk;ld7q;i;(7 t t*b c;jpparent weightlessness” between st 7;2s co;c7 ;q* vd-g(ibijltltski;s eps.

The Earth moves faster in its orbit around ths0p-gpv9u svq/ 4n0hg4;twuo e Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the t09 t/gons ;sgvu44v-w0pqphu ilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expl elipnvql ;xi0:nyr.2zav307c+ yr;d ain how thiprz;2iyc.:0xn 0ey lqad3nr v7+v;i ls discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Ye uch6wl4rxq0o rn2 -c:t the Moon's is mainly responsible for the tides. Ehw:- xo u ncrcq0r426lxplain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with 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 travelingry0;l i9vcrtye i72d1 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth x ofrc7s31z wd1),j 8l xpfh - e7q;hh3zfusx(in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume th-;)8fr3zd 3q,h h fx1zxux7s1wpc o 7hjfls(eat 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 eki8;8(bacx*dst cayk.pyf u-z9)( wnxerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the d(yu xpa9czk*kb-san)c(8 .ti dfw8 y;iscus.   

  Suppose the space shuttle is in orbit 400 km from th5z47u: /+x3axmxy vbr d. n wp8xp:hdfe Earth's surface, and circles the Earth about once every 90 minutes. Fidx8xuz w+a437hdx: p5 x:brnmvp./ yfnd 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 of a speck of clay on the +zh,gezm qdc +-u p32bedge of a potter’s wheel turning at 45 rpm (revolutions per min++- d3ezm pugzbqhc,2ute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a /sbxdb :40x; jrbl(r)rn jzo/5 moon4 uniform rate in a vertical circle of radiub0 mro) zr:4l/x ( ;ojxjnb snbrdo/54s 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with whi(xhcg6ii8, z+f qzm/j ch 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 indepe+ cf mix/qj6,z(ghzi8ndent of the mass of the car?   

  How large must the coefficient of statq sgro09l g0*eic friction be between the tires and the road if a car is to round a level cu el0*sr0g9g oqrve of radius 85 m at a speed of 95km/h ?   

  A device for training astrona0phrmzg 6 c-g.y.tb/e uts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of razgetg .-b/0c hm6pr.ydius 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 8ui6s. ibf /q 0guoc;zspeed. 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 friction between the coin and tf;/icozbug 6 u 0.i8sqhe turntable?   

  At what minimum speed muoi1:ln dnkcdqwy5)) . cmzj80st a roller coaster be traveling when upside down at the top of a ci0y lkm c5ci8wz)nn.)dqd oj1 :rcle
(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 massy 4-kp9jb e6a ;0,mpp 8eqxgus 950 kg (including the driver) crosses the rounded top of a pg b8yqjke,;a9p 0s -ux4pe6mhill (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 whee43asqq6e2zbx +o t(92 clbtkrl need to make for the passengersb2btae +t9( 3qsl46xroz2c qk to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00aefg)( - hglg6 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2g)e6g -hga(lf5.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 t hdkc+i di700qy4,ojcm from the axis oft y d,oi+kj00dch7 q4i rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplea9l(oj4 oei +)m,gxdsneu 07 x are rotated in a cylindrically walled "room." (Se7ox+ougxs4,i0e(ln a9me j d )e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionlegz+1p gl l/1z ;t558ntp8yzo2st givoss air-hockey tabletop, and is held in this orbit by anvo /5git2g tz l ;gtl zzy+o8ps51p81 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 nl 7w gaf-gq03hg:6ax jc 7yj/kot ignoring the weight of the ball which j wajg:hf7gyg37k0xqc6- /l arevolves 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 m is perfectly banked for a car traveling 75f(0u/e0we , 2 cbkic*ndb .qyd $\mathrm{~km} / \mathrm{h}$ , 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 massehbf0ch0p :4 13txzaw*t6 av yjs $ 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 evas5qxz.oniga pby v;n(9 v2/y8 jive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential art9obbt )v61g v5:w sxnd centripetal components of the net force exerted on the car (b vwb:s9btt1x65rog)vy the ground) 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 from the pit area, goy k)a y7j8lae.clp7 8sing 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 between the tires and the road to provide this alyjlky)8 acp8s.7 e7 acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partrahq .q thu( f:jhvrq).;rn0, icular instant, its acceleration is 1.05 .q0ah;q(u tvrh ) r.nqj:frh,$\mathrm{~m} / \mathrm{s}^{2}$ , 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 /z3b( yklc (gakm (2 Earth radii) above the Earth’s surface if(aky zgc/(bl3 its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accele6 fhka1v jy5*8bt6zg0y 2kqktration g has a magnitude of 12y ykhza6 jg 5ft26v1*kq0bk8t 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 grasqk96v b6i*tm vity on the Moon. The Moon's radius is 1.74 qm 6kb*vi6st 9$\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 a bzbf 2h8j(7q.2 1 f9hwxyh20cch mzmEarth, but has the same mass. What is thbw(x 2b 1h 0.7zhz92qhhycaf8m mjcf2e acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of j.c kayn3v /7nEarth, but the same radius. What is gkvj/n. an3c7y near its surface?   

  Two objects attract each other gravitationally with a force of yy nttto jo23k6-auk4lfz0 7, 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 jzle2k;za,z8x*jqu 7 of g , the acceleration of gravity, at (a) 3200 m *ukqzlj2e7;z z,8a jx    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poin( qkakv.x*1pms rl1 /mb;f8qlt outside the Earth where th mxpk .rqla8f(1/ s*vq mbk;l1egravitational 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 maw 06dijb(3 go,mu6g n9rz*xmqss of our Sun packed into a sphere about 10 km in radius. Estimate the zuxd, mm69 * bj(0igog wrn6q3surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like oy.6gw / hss5nbur Sun but is now in the last stage of its evolution, is the s/y snh6gb5 .wsize 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 weightlp(10 glco-dk.t hgpz)t ks) 5yess while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by cz)sop()hk1g p . gd5tyl0 t-kcalculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.0k, hq mvo57:2k*c8t(sdxk jomglc;q 60 m. Calculate the magnitude and direction of the total gravitational force exerted od72(t, q ocx*jkh 5vogql0k8mcs km; :n 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 hy)2 c9d(fc(x of d/*,wzg4gbhxkjr7l- 4fof the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a ,oxh(k2 fcjh9)y7 zflcx4 -rgdb4*of( gdf/wline (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)f ; tg:/fd3kfz9mdpj 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of )kddfzt/m;f:f j 9pg3 Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known va;wawwr 55 . )pn9y1txw/x.quuvusy 4p lue for the period of the Earth and its distance from the Sun. [Note: Compare your answep54pu.x r yn9 w/qxuw5wsu v)wt;y1. ar to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelli45 0y ufympc-+d dtojv75iby+ te moving in a stable circular orbit about the Earthi740fmv ydcbu 5ypj++-dy t 5o at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the qv t)j8hg:ej d);sd*k 3nn wn2Earth. How fast must the shuttle be moving (r:8)eth ns wdvdq)j*3k gjn2n; elative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ j*4hd2vqt2k hupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revol2q42h h jtk*vdution. (See Question 21, Fig 5–32.)   

  Determine the time it t0xsg51mw a mo/akes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which i os0w1a /mx5mgs 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 satellitkt( etz q(,o2se have to be launched from the top of Mt. Everest to be placed in a circular orbit around(z ts tqk(o2,e the Earth?   

  During an Apollo lunar landing 1ozo /tma g ze4ivk(1;mission, the command module continued to orbit the Moon at an altitude 1ie /(zo gvm;tzo4k1aof about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plan.cz,eg7(x8rfex3badv aj , :cet. The inner b3fcdar.jev x7(z xca e,:g8,radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter 2 + wtga.d0udtrotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weigu+t 0dwa.dt 2ght (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a v+ k( 0cuoclmtp m 8tsu(yyo5n3 6d;x)75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constan+u6x)50c lyv;3cd y(o sm8(m kuttonpt 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 skp 6;xnzlw. ,nystem consists of 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 midwa,zlnn;6 .xpkwy between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55)vcjlsonows*0t -/.1zud:o h; gdqw . -kg woman in an elevator that/o-.d.0zso1 jq nlc t: u*o gwdh)svw; moves
(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 cor:b .ntdu).lt48gq+ wb 2gse obd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accb. bq2o)gtbl8: tnu+.d4 sew gelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a sately2 jy( o:ydyh ,6ge1zdlite orbits very near the surface of a planet with period T , the density (mass/volume) of the playy( yj ,z ode26d1y:ghnet 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 periodv :i- hu0swja3 of the Moon (27.4 d) to determine the period of an artificial satel0auh:-viw s3jlite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbit) x*8 :qcg) ruikyv(esqjb -hfy+(z3bs the Sun like the planets. Its period is 410 d. What is its mean dist-yqg+er) )u( cyk 83(jb z:xfsbq*ivh ance from the Sun?    $\times 10^{11}$

  Neptune is an average fr7m (,gwm9clty6ik7 distance 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 roughly once every 76 years. It g l)wb2i buee+,-zw.acomes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of ge-,.bibl+eaww) 2z uthe 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 ttm-, 9rr vvp9xhe 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, 8sqobyvj 5)*op5uc 8+ . bunloand mean distance for the four largest moons ovco8o*s 8j5 l .q+nbp5o u)ybuf Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mozmr ihh+q*u go(s )z))on. )gu ()s)ri+ozmq hz*h   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, u8ukql5,v4k ch vn 0 hwxe1;+b: i-vbfksing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the vq+ fh;-4e1 v58bhk:l0iuk xbw,nvk cvalues 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 consist,j u-cyz, d9uks of many fragments (which some spacejkuy -uc9d,,z scientists think came from a planet that once orbited 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 describes dz f l85 b4gvxj-+tbc 7.,ksnfan 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 sug5ltjx4b bfk +ns c,v.z -df87n 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 hanging vine (f5 0e5k wuo/awFig. 5–41). If his arms are capable of exerting a force of 1400 N on the vawok w uf505/eine, 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 a:frc1n rf.u n gx4 sf)-kr+par boh204cceleration of gravity be half what it is on the scpb gkf)a:1r-f n 2+s.nrxh4urr4 f0o urface?    $\times 10^6$

  On an ice rink, two skaters of equal massj97nye* n3 udjerukf 2 dv5w-yk5 .:oe grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are eachrnd ne5k9ukouw- ej2v 7 :.*eyjy35fd 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 acceleratid );4rv2j*kovi :t*(a dk;,cudbmk wkon of gravity at the equator is slightly less than it would be if the Earthu**4to2:bw,akk vr mjvddkk;;)cdi( 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 spacecraft traveling directl9w md dkcf9b6:mm;jq7n4j;x jy from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite f 6;kcdw9m : m bn9j4qmd7jx;fjorces?    $\times 10^8$

  You know your mass is 65 kg, bp 3z6d/h,s1l*cqxdj sut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the el3/dsl c,j qdpx 1hz*s6evator, and in which direction?     ----待选择----upwartddown 

  A projected space station**f6 yogxb+h6vnw0liz: om8 p ie ro7- consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a dv+ilwo0po*iexhfr 8 mz-b6:o 67ngy * iameter 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 ky z+0ald4r4 qvertical 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 its radius r, the ac i:zamxssat 2r-lwu69 xtzs df7v *.8*celeration due to gravitytvas z:l w7xz.uts8x dfi-**6 9r s2ma at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the -va(-o*zxs xlvertical by an angsva( -zx *lxo-le $\theta$ 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 momw8wn6 5 /lqxftki .b97cvbs a1(8dfor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds ca 7oaikbfm/w8s1 ln5 v9bt. m86w(qdcxn a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast t2y 75d6h 4jqnukd0n5dm8gvc chat objects at the equator were apparently wg0nh7jvncd4m 8 d 2k5y56c qudeightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o*5 ph,ea2pkmqf 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 radiuslx8ec* d(r6cp1i ,xhj 235 m. A lamp suspended from the ceil *8hxc,e (xr1 pdlij6cing 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, i )n42lwxsju5 (-ecsdb t 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 lbje w-(xu4ns2d5c)s g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presenc ebn*rq+w2bbz*y - u+xe 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 dieuby z*-+bn*x+2wrbqd 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 tr1af uf 6b(i+s0ufn+ zhe 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?) zub(u 6fnf+rf1is+0a 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) utilizes a group of 24 satellite 9.scdg+m9m7y gu( :-rfun jces 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 speed of eaeu-.s:cru +gm7jg n9 fd9y m(cch satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travel pz,vzv9- xg*h y u4cjc1kl;(bing 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rough-4xzlzp bkhv*1(c cy;v, 9jguly 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 thit lw0i) s -fyc-/aii;e space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but iws/l-0at fi) cy;ii- 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. ( ;.b vq)ecko1zt7r3f ya) What is its mean distance from;r3b y1kcqz)f 7tove. the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the val9uvdxiph.8 hq,(3xuw ue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reason9hxvhu8w(.,q3 u p dixable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of thel0k 1rl 7d8brp Milky Way Galaxy (Fig. 5-46) at a distance r7bdrk 8pl0l1 of 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 corners of a square 0.50 m on each sid: u:2mxnpx).rajx v9we. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the2 9:axvmwnpjxx:ru .) bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orq h2, :tfzvg v6gshlo0 /ls6k;bits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by4t8ys+7p ge72upkgxk the tip of the 1.5-cm-long sweep second hand on your wrist watch? y7 ptpes74 x8 k2kg+ug   $\times 10^{-4}$

  While fishing, you get bored lv.ib,p; uqdzbv5 .: fand 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 vertica.puf b:i lq.b 5d,vz;vl? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway i 9-slplbsc *z(+w+qvds designed so that a car travelin ldvss(-p +clqb w9*z+g 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, st ,00u 9nxgp8quuef 7utilizes tilt of the cars when negotiating curves. The angle of tilt isq0fneg9uu0, 8 p xt7us 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.$\approx$    $\times 10^2$