Sometimes people say that water is removed from clothes in a spin dreoc /f05(md vryer by centrifugal force throwing the water outward. Whe( m0r/f dvc5oat is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sa vil x 0w9q9zi1av6t;bt+dh* harp curve at a constant 60 km/h as when it travels around a gentle curve at tiz9adqv9b vha*iw x;1+60tt l he same speed? Explain.

Suppose a car moves at constant4n290zlq;)c 6ibm dklp 2ptvl speed along a hilly road. Where does the car exert the greatest and least nmpcvkd zlb ;liq0l)22p 9t64forces on 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 hom4c* -qhy/ h( oew ao/5;gokayrse on a merry-go-round. Which of t yo/ hm(hkacew;a/-go5qy*4ohese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in ago/bm5bmx.bg(rv b)) vertical circle without the water spilling o)xb/o mgbv5r.(m gb )but, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you hav kv:+b;niu8 fsy: ;1 hc wjochuh..m1we 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? W.uhb1h:iy8ukv.:w wcmf ; j os+1; chnhat accelerations do they produce?

A child on a sled comes flying over the crest of a small hil t7p1itumyour4j 7zwg4yu1 e1 5; :vpgl, as shown in Fig. 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 lawmip w7ytu4 111tgo:up5vj ze ry;47ug.

Why do bicycle riders lean inward when rounding a curve at high spes4( e0z 1bl uvj 934se: uv5hgvrjcr* xamxm1/ed?

Why do airplanes bank when they turn? How would you compute the ba 3)emcl;m8 5 z.xpaaqenking angle givm qe; 3a)5.pexl8m cazen its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal 9/n,(;bdqkgrf o)5azifwq, uplane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the)u,qfk,/az gi5r( o bfn9 w;qd yard. When should she let go of the string?

Does an apple exert a gravitational force on the Eap ylqj*gx5 f2;d ;x c1q)ln2nzrth? If so, how large a force? Considerd; jxnyfllp2q nxg5*)2cq;z1 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what itk.v:0wp uudy2 is, in what ways would the Moon’s orbit be differ.0 u d2wuk:pvyent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon ontqp3.ve5 nomt(o i3o qs3,c p/ the Earth? Which accelerates mt sm,pqpnq /33oic3 .toove (5ore?

The Sun's gravitational pull on the Earth is much larger than the Moo8/y1i74/hus f vmatp kn's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenup8i tvsma41 h/kf/ 7yce in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the v9bpx-e7qz.k)kub b 4 q /6acbequator or at the poles? What two effects are at work? D 4x9qb.vbzpkc )bu/-b76akeqo they oppose each other?

The gravitational force on the Moon due to the Earth is only 3v2.jxlh udk7j5,(3bifrpmg,2 edps about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eaplgv, u,3e22h spbif rkd(jx.57m3 j drth?

Is the centripetal acceleration of Mars in its orbit around the Sunga,rm d3 yf(rd xs q,gx6*f)c8 larger or smalf3s) ,r dxgd (8 x*acq,mr6fygler than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the easts3(zn7 de: k- z)oxhhc+g.ldfuma 9q ) or (b) toward the west? Consider the Earth’s rotation direcs 9 hkzeocnzmhxq3 ).dg7:-(fdul )a +tion.

When will your apparent weight be the greatest, as measured by a scale in*j vpbph5nqtd i ir.n.3c3,7a a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would ia5h rbj.pn73. i tq c3n*,vdpit be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectedjuk4z.a. yd6ijv 4vft9 0 8cut 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. Consider (a) how objects fall, (b) the force wu.za46j8 vtv0 yiju49kf.dc te feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent l,l hb ho a8k-llgd6)nrho+c 4+csi;9 weightlessness” between steps-lil8do 9l l,)h ;crac+ s4hgbnh6ko+.

The Earth moves faster in its orbit around tx4 5k er0x7i64iimo+aoi.l l ihe Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Ex 4ii l5al i.e0xmroi4xiok 6+7plain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was nq 90 f w,8pg3e;jzzmwwpag7r /ot known until it was discovered to have a moon. Explain how this discovery enabled an estimate of fw qgzea9pr wp w7mzj/g0,83;Pluto’s mass.

  The Sun's gravitational pull on the Earth is doc4.gog ,(s ysar 3d:much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-roo:ag(og r3 sd4s .,ydcund 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 jqt8 ipedbha3 a.;e c*93uyz 81980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sun, 8c-)3hxuvze o and the net force exerted on the Earth. What exerehu)o z8x3v -cts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is z14a q39bqspl9 *w *qs5pe hkgwt8td7exerted 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 disbte8qzlt*p sq awq59 p3k19ds *g h47wcus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, andyw fqbc6lt h.1 ik4 l6l,2df3 n;plt:i circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surnbh3lpft6i:c.6ll f dwq 2y ltk,i1;4face. $\approx$    g

  What is the magnitude of9;u(o ;nfeypc,gref93 z*udo*g t 4kn the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolut,unutkce ;yro*3p;zod9ne*g(4g9ff ions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string xd.h +unc1v(w4zd:nsp qr5:his revolved at a uniform rate in a vertical circle of radiuhq w:x. (v5npc +4 zuh1rdn:sds 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 which a 1050-k/ phus q9iu+zbk5q4hvp7h3jw/w7 j: hg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires andips/9w bhh7uj u q/+wh:h5v 7jzk 34pq road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tidu c, x 7e+e04hspu4cyres and the road if a cy0cse +u 4h u7x4epd,car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilg dp6y9da(au6 z3ymf5 ots is designed to rotate a trainee in a horizontad65d6uy3 ygm 9afp(az l circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is 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 rou(+ 1nc/4rv oj yppft:tating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable pft/pr (j+uyv1 n:o4cuntil a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelingxs 6 nj;4 r0q4gwv+dsp:r;q vl when upside down at the top of a ci g ;06vx4+nd;lsrs4vjw :qqrprcle
(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 th :5 l.6kggjxade driver) crosses the rounded top ofgg la.:j6d5xk a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would /bq44ub t:q wynig9 /ta 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmos/qt9y44/ :g wb iutqbnt point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.4n s0 w ra;unyo6a(vzmxo3:g810 m. At the lowest point of its motion8n(mn a0a 6w ourz;yg s:xv34o 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 a centrifuge rotate if a particl ukj0o62mym0 cvjy,yqn y49i3 e 9.00 cm from the axis of roti0vuy 2oy3, nm90my k yj46qcjation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cf-zyl4y;b zurr ph:5 7arnival, people are rotated in a cylindrically walled "room." (Su;lpr 5:b7fzyh-4 r yzee 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 rot0tk4xuc+./ucm i 8nftated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected t/ucn 0f+miut4 kx8.cto 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 ignoring the weiglv;6.xx q)t e3ospo4ght of the ball which revolves on a string 0.600 m long. In particular, find the magnitude o;togesx. 4q6xpl)3o vf $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 traveliyk0mv21um l ,6tcoh0eng 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; j0;cx ixct) $ 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 lf /ndjf 0cwpp+km8cr45:z/r 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and uank a768qt c5centripetal components of the net force exerted on the car (by the ground) in Exampl567 kq8c atanue 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 Indianapo ftbzt(8 wo;l,lis 500 accelerates 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;t( o8lwfz t,b 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 horizglp26rwd)6 3ks650lp l cpy txontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05p kw0crlgsx6d5 y6p32pll6t ) $\mathrm{~m} / \mathrm{s}^{2}$ , 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.+-gwlo:1z hg0wy(cw fu c5 uh spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its masswgchy wo 0zf:-lu.(1 5h uc+gw is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g r)nu1.isjqi2 has a magnitude oiuj i.q1sr2 n)f 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius imr.r;k;g)n f * il4nues 1.744g)l;un nr*e .k;frm i $\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 Earthmnp b9s 2hv 0 g1wis,m,+e3uuh, but has the same mass. What is the acceleratm v,s39hb0sh 1ug,u2ine+mp wion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tim r hg- )c;gkaj8y+7rcfes that of Earth, but the same radius. What is g near its surface?g c kga7+hrfj8);-ycr   

  Two objects attract each other gravitativyy 4 f4ap gla4q7(-nyonally 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 effective value of g , the acceleration of 7x2yzk76mp qhw7uec3gravity, at (a) 3200 mp7 3w2m7yq 7hcx6 kuez    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside theqkl,)2 kj8qoytt8 * 3iwbhfa 3pwe1b3 Earth where thegravitational acceleration due to the Earth is b op f 3hwkqk)8e3bat* ilj1qt,w28y 3$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spnn3ory.. hp(lhere about 10 km in radius. Estimate the surface gravity on this phnolr(3n ..ymonster.    $\times10^12$

  A typical white-dwarf star, whicvx,b*xa5fn 7wil*j 9dh once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface g, b7djxi5n vf* lxa*w9ravity on this star?    $\times 10^7$

  You are explaining why astw)w+lwo )1y ohf jhi,;ronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earti;j)w+)ohof w,1hwly h’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sa *sya9h;f /s3.axf noide 0.60 m. Calculate fny h/;*xosfaa3 as.9the 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 sam-mc)21 pyduv3sd,v fie side of the Sun. Calculate the total force on the Earth d1mdfvs d,)pucv- y3i2ue to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the + tz0c)zlbi( k +sve1nmb1h:isurface of Mars is 0.38 of what it is on k :hzt+0zbiinemv1(s)b 1c l +Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of then 6lx)dik ,wg2bf ze- ;le8f1n Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16w-)nx82e6ng1lle f,d ib ;kfz.]    $\times 10^{30}$

  Calculate the speed of a 7 jvg6w7or9 cksatellite moving in a stable circular orbit about the Earth at a heig7o6kvj 79gc rwht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circbk(s9 vc 6fehp1;c(ba ular orbit 650 km above the Earth. How fast must thc(9b (k1hcpf6 sav; ebe shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa 8z3 y7lo6lajsnts are to experience simulated7 l6zjosa3 ly8 gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “nz5gn zt5 tf9(wear-Earth” orbit. A “near-Earth” orbit is one at a height above the surfz5 tzw5gf9nt (ace of 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 satel o wqa4/)eeb3elite have to be launched from the top of Mt. Eve4a eo)eb/q 3ewrest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oog6d6ul8 i a,rrbit the Moon at an altitude of about 100 km. H iu,r8 66olagdow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. 20 krilbej w:. s,4gty 40y/oo eiywa*The inner radius o2ab li,gw.0 yyt ko/*eoyj4w4 i:r e0sf 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 once every 15.5 s (see Fig. hmfm 470vk /vxg se4zriqk:iw: z 61;j5–9). What is the ratio of a person’s apparent weight to her m76v 1jv:hm/xezqgr4i :i4 0 skf;zkwreal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astron,y : sbb9yy. -.-pkqx qsoxq6zaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veloci,:xo yz.q 9yks6 xs-qqpb- .byty,     ----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 syste ffqmi e(c*et/ + pq-c-tz:x*pm 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 midway between them. What is the mapit/:*f +e qc-efq*ptmcx-z( ss of each?    $\times 10^{29}$

  What will a spring scaleyo k.n.)zhq yb(55 h lv.eism, read for the weight of a 55-kg woman in an elevator that movyvlb .qmks,zh) ho.5en(.y i5 es
(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 eah wjuu0+4gz/qkf*k: ,0msg jg: iix.levator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum ac uigwk +0 i:h,4x.g0sqfugja/j :z mk*celeration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a 68 d;3g/x6xz iyleshmplanet with period T , the gd; yiex 3s6/l6h8zxm density (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 5pj77 +t0aheerns- sm 7mf*tathe period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near sea *s7 h+57tmjmtpn-r7 ea0 fthe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, o lnr1q+t-i w-9 2kvrvruab9g7bmb+ o(rbits the Sun like the planets. Its period is 9u2-v +b7(mtgrwb avl-bk +rqoi n1 9r410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc2bn*kp(jnk 5 iw 9(ch.fp6 lcce 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 76jyxm: xf,5 cgu gp*c67 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 Syst5c6xgxu*j,7 f g :cympem? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga6wba0(g;otz fp/ tzs(xs ,. odn zw8;ulaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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.(rq ps+r- yif, and mean distance for the four largest moons of Jupsy.(fr r+- qpiiter (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 Eart aesozztx/):( h from the known period and distance of the Moon. )t /s:xzze (oa   $\times 10^{24}$

  Determine the mean distance from Jupiter for each tgytx 3 vh-s8xg4x:y2 of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values x8vgsxt-x hy:3tg 42 yin the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whjdx 6/iu* f-mujk q;w y6-nsf*ich some space scientists think came frox6wu *ikqm6 j- s nfyj;*fud/-m 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 dee(7wsb z+r lx9scribes 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 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 o7w l(sbr9 xz+ef revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. qm+q9tk 4ysagg*aq)8 3 quey; 5–41). If his arms are capable of eyga uk e;9sqt*+a3 ygmq8 4qq)xerting 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, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be :cse nl6- .xaihalf what it is o6ex :il acs-.nn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handa+9 qb4p lm5ups and spin in a mutual circle once every 2.5 s. If we assume their arms are epu9pbqa5l + 4mach 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 pdt2dzllfei v)4 qb,1.d3xn4pz h o*b7er day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is thn l pv*qdb1,)hlxz4b4d .od 72 zetfi3is?    $\times 10^{-1}$

  At what distance from the E znvy637rycm ; nqg/p)arth will a spacecraft traveling directly from the Earth to the Moon experience 76ynr qc)v3 zg;mnp y/zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale iny85pqy7 oot2 n an elevator, it says your mass is 82 kg. What is the acceleration pn5qoo2t87 y yof the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c(/,tj zgdr wy)onsists of a circular tube that will rotate about its cz,tjd)/(y g rwenter (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft innb6 myxo4 ,jl1 a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, th1azi,ami-fu ):qz i (pe acceleration due to gravity at its surface an:aiqza)1mf piizu(,- d the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertictcp/ k0/uikd qios e1vxr6p8 pq:+ ;a0al by auk0os 6qe/kt :va8p/ pqc;d+pri i1x0n 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 I( pycmrg c.)c,ln.x;4 x/q(kbyt 1zqsf the coefficient of static friction is 0.g(tcy l ,ks; /.)(qxmpnz.1c q cbyx4r30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth w4ynnt *g;q(nld n .aq bhr-3 r(+i(dsnere rotating so fast that objects at the equator were apparentr+(nsn.3qybqtla4(d ;n h-r gd*nin( ly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distan;. ewkbqoa5 9bce 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. A lamp suycc m3l6iq :urn ;((ljspend jl(:icmunc r(;yl6q3 ed 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 Earth. Thus, it has+d ymaf4tv.t 7 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. Ca7vfytm+ .4td alculate 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 ue+aooy4 z4i3 Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780y eoa4u+ z4oi3 $\mathrm{~km} / \mathrm{s}$ 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 tksam)(-k d wf1he hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the nsadmf kw -)k1(ormal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satew)* cxkiedq.q 49us2wllites 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,)xiwd q kcuw92*es.4q allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (Noc(ff7aphg5 oo j3r1 9EAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abouoh7farpf1(j9co o53 g t 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 satg9j670bs4 h0 hbko gob xn2y1qellite 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 be06 bjgo24qk h7y0bo n1x9 ghbshind 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(/wta3a,lx lo period of 3000 years. (a) What is its mean distance fro o,(/ lwaat3lxm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to b *pmhp q 63b1nhl+ua:se if you could actually "feel" yourself gravitationally attractb*3u6pn h ha1pq:m+lsed to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way 0u76o5pwggh8t+o5s gaqlj)o Galaxy (Fig. 5-46) at a distance of about 3oph85 )u o+qtwg57ljoa 6 gg0s0,000 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 b ,))h5mqnzvo the corners of a square 0.50 m on each side. Find the mo )zbnmvq, h)5agnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earjb12x)+vjv3, +sz sgbgvj g s*ell d*-th $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long s,f9dsm d3tusle6 , fj3, vqy8eweep second hand on yofm9 ,t3 ede,su6yv,8q3ls djfur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a s:dgb td16;)5hn1 0d2d*nuwl b eivc voinker weight around in a circle below you on a 0.25-m piev16b 0*ch;eduo1 d5i dg dn vn:wt)bl2ce of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trart0lt 9 raz;,obr- .2uo9akwrveling ,o-zrrw l t90u9bra kr;t .2oaat 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 ti)ygqlu)q1 y8 x.5awri ygbi05lt 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, th )0y.5 iglbyq yaiq 5g1w)xur8us 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.$\approx$    $\times 10^2$