Sometimes people say that water is removed frx1; 8zqa8nm3 qzifar/om clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong zfaai83n zmq/xq1;8r with this statement?

Will the acceleration of a car be the same when tha8e6jvdh o+6d e car travels around a sharp curve at a constant 60 km/h as wdo8v had ej6+6hen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constan- ud 9j0( efa0sj);nwg5eqzvgt speed along a hilly road. Where does the car exert the greatest ave)ge9(w ;d qu50jnja s-z0 gfnd least forces 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 ch2vb5uyrnh:5 8n/pzmt,a* x fp ild riding a horse on a merry-go-round. Which of these forces provides the centripxf8hman5 *2,tvp / z: ybrupn5etal acceleration of the child?

A bucket of water can be whirled in a ve;l-jgutoi3( cnu v*y6 rtical circle without the water spilling out, even at the top of the circle when the bucket is upside uy-oc6lg 3t(jvu*i n; down. Explain.

How many “accelerators” do you have in your car? Ther/ bet7ly69y-5vqc/pzg9sl w ae are at least three controls in the c zw q7bg/ lts9y59/6ea y-cvplar 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 show6 yrg1pegm. upg2l4;b .icd9s n in Fig. 5–31. 4g g 16p9.2sdub c ylgpir.m;eHis 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.

Why do bicycle riders lean inward when rounding a curve at high rht:xq ;j(*saspeed?

Why do airplanes bank when they turn? How would you yqykxw t+,p qdtlc7i8a784o,compute the banking angle given itq ytpi 8w8c ,l7tx+a7d,4 qkyos speed and radius of the turn?

A girl is whirling a ball on a string aro 8/q2u5lgbk :sf s r3gdqzd:b,und her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. dbrkgd g25qf:/zl3 qusb:8,sWhen should she let go of the string?

Does an apple exert a gravitational force on the Earth? If s pm wzoq /gq2dr-(39yto, how large a force? Consid -w 39/(2yopmzqtrgdqer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woxunl k55ze21zuld the Moon’s orbit be zul zk5 ne12x5different?

Which pulls harder gravitationally, c93rh1o, xqy/ojcj 6sthe Earth on the Moon, or the Moon on the Earth? Which jc 69,qsoh jxo1cr3/y accelerates more?

The Sun's gravitational pull on the Earth is much larg vt8)7gtowf wa4 ixa),er than the Moon's. Yet thef7a)x)t4t wv o8aig,w 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.]

Will an object weigh(v g0w+ djm,50fw(ro z t6tvoc more at the equator or at the poles? What two effects are at work? Do theyfmcj+(o6zvt0,vw50t g( wrod oppose each other?

The gravitational force on the Moon due to the Ea )4f0epxf pqh p2n1 ;ovrke)a,rth is only about half the force on the Moon due to the Suf;2p4anq 1e0hkv)p,pfo )xre n. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars io jckg9sxy+co 6w5;w)n its orbit around the Sun larger or smaller th ;kygx+c5co wsw)j9 6oan the centripetal acceleration of the Earth?

Would it require less speed to launch a satelliterrdgk7ys,;k3+sb g7 e (a) toward the east or (b) toward the west? Consider the Earth’s rotation direction.s7e+ d3byk;r7kgs ,rg

When will your apparent ,x;ao+a;pnnb )x62 fufshz r7weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you a);af ah szo,f br7nxx6+p n;2ure on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodsvmf/i1 zb 4ol, in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet/v 1, ifblm4zo, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent wd)m1::pukl 3m rf5 qjpeightlessness” between stdl j1rpq35 mk:pm:f) ueps.

The Earth moves faster in its orbit around the Sun in January than in Julya -z8 s41w fivoz9+gx fn0l*yo;9bilu. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This 4aywiz-zu0oof1l99fbi + gl8xv n;s* is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have ;x4m1 l*xi-jjyej0 wta moon. Explain how this discovery enabled an estimate of Plutyj; ml0 4 jixet-w*1xjo’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. p l (cwp5izhw:hq/7d ,Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatiq,wh5ld/pp7:i( chw z onal 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 traveling 1q b9iw.9ik7it q fc)f8980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Su.1 b+ oyl+2qxzyhz7rkdcvs8t l*c oz9r-7j/mn, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a m2zol l.otdscc 1xz-y7*/kb r+ +z87qvh yjr 9circle 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 g vlntc:4f-;e N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate thgtvle-fc4: ; ne speed of the discus.   

  Suppose the space shuttle is in orbit 400 km aygzy2ft+ax y1 wojh 2) h33v-from the Earth's surface, and circles the Earth about -g2 ay1o)v23 3fht j+ wzyahxyonce 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 surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge vj7vtbo37b* p jxoj :8xmoe6/ v5ek7xof a potter’s w/ 8 e xo3vjtbj7e7 ox67vk:moj5*b xpvheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate ) q kyps06 s:6rjli (qczi,3jmv2y9qvin a vertical circle of radius 72.0 cm , as shown in Fig. 5-kjv) q6 j:i i ,z9y2( vmql3q06ypcrss33. 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-kg car can round a turn of j(ba*1r pfdpt*k*s i0 fu)n:oradius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is t1r) o:n*pd*bik *u afjpt0s f(his result independent of the mass of the car?   

  How large must the coefficient of static frictioo 9aibqena yto.m*7)0::sa t vn be between the tires and the road if a car is to9nt.i:b7a0 e:ooy*sa q avm)t round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed t+(4vq wrxiwtu d:r;1lo rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her owrwtd1iv r x+wl 4uq;:(n 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 a5g4oq0qae xf/d a+7d kxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static fri4 a kxd qa5o+7qef0gd/ction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when u/ u/ak,t+db q4 5zkgg.bci j yph3 -*rgpd3ii:pside down at the top of a circler dhyc-g3jzu g,iid+5kbb.qi:/ kg* p4t pa/3
(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 (incl1oj .(zgq.qkquding the driver) crosses the rounded top of a hill (ragzqj o k.1q(q.dius =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 rxcb1bw 4f10) rk/(lr v+yjx rwould a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost pf1wrx 0rbc/(vk 1yrb+j lx) r4oint?    rpm

  A bucket of mass 2.00 kg is whirled in a 7 :*j1tba prcp-pa.uh vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 Nprbu.*-t1cj p pah 7:a.
(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 partux ) 2 daht6 432oxr q3+jbagjhd9:)a;bpfoqficle 9.00 cm from the axis of rotation is to experience an acceleration of ; q43)tpoqba : d h+)3j2r2ogf xhbaa6dfjxu9 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated 2+w ktr*y5j cd.nk: pnin a cylindrically walled "room." (See Fig. 5*tkkdwr +c: 5nnj2.py-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 r nxjxhkac9.()x5/ojn otated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) througxcjh x9(n j ao)/5.knxh 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 th:,rtxp :z ;jet yuza*:is time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find t,x ap;ey:t *:zr: uzjthe 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 radiusd .v1rc.0mz +hcoroxv 1i9 ,zs of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesn emkr aaf-v0;9/i ;na $ 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 atf9t0iunwy* 3v 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 centripetal componentpuy8r jw/ 0a:0i(lvsabk(szc c :c ):qs of the net force exerted on the car (by the ground) in Examp(:c :zvw 0a:lqrji(ckb/su)0a8cspyle 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 f1 xsg5 c6 ms-:p4cdwgm8jmn.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 fs :w4mm.j5x 8-61gmgdccsp nacceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizon/ qs kl*7xm 7q39zhwba kel0q;tal circle of radius 2.90 m . At a particular instant, its accelera3b*kwqhsa m7/k zxl;elq q0 97tion is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacei.vaxo)c4yx /craft 12,800 km (2 Earth radii) above the Eart x).c4/oxyaiv h’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerh13n 1yzwk-g bation g has a magnitude of 12 m/1-h y3wnbgk1 zs$^2$ 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 isz2 f8 /zfz5uwrcxg );i 1.74x) /zwu;f2 58rfigzcz $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, a o bv40/nba7wbut has the same mass. What is the acceleration/bbw 70av oan4 due to gravity near its surface?   

  A hypothetical planet has a mass nlia8 lp kvgeo3u; ;ircy55(01.66 times that of Earth, but the same radius. What yc0nv385ai k(pg eur;li5 ;olis g near its surface?   

  Two objects attract each other gravitationally with a force of (5;mgnp1qb sy2.5$ \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 gravi;/ e0hl(zgybh+*dv;km nsd 0qty, at (a) 3200 m +0qd;em/zhy;g0bd l ksh*(vn   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frol/amm, f vv 8ikzqep/j7v w - fuvc(idb;,+*k6m the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth imwbi+ i* 6ckmpdeq// vk7 f;j,z8v(,uvavl -fs $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hovmjv a7 66mg;ly r uc5+(zpx(as five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity ; armmux6g7+y(c (vpj 6vzl5oon this monster.    $\times10^12$

  A typical white-dwarf s 75m)2p:d du,ulaqtf dtar, which 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. Whpufa)dl d2 qu:, t7m5dat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbit .b:uujezjv(krlw:( 7 ju3x-7 z sz-vaing in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’(a.vkz3rbwv-xzu7:ju jl j s7e( zu-:s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60.u fm/lxwk tw2g7 86bu m. Calculate the magnitude and direction of the total gravitational force u/m g2l k7x .t8f6wuwbexerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plaf gzd(d 8g*e8vnets line up on 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 line (Fig. 5-38). The gf* g88ze(vdd 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 Maroj1s8 qrvz eo8 wd9;6bc3 s0eys is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine t; rwe 3zjdo1s6 y0oc8 q89ebsvhe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth pbessd4;e wt p5g(pg;je4 c .7and its distan5(b d 4ees7pjwp gpgetc.;s;4 ce from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablepjib4ly;s8t . circular orbit about the Earth bj.i4psy l t8;at a height of 3600 km.    $\times 10^3$

  The space shuttle re tb ;e40p5ftvgleases a satellite into a circular orbit 650 km above the Earth. How fe 5tpvt4;fbg0ast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricawdlb1;+*/x r )qif t8ebvry8zl spaceship rotate if occupants 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 revolution. (See Question 21, Fig 5–32) 8rietz w8;dvbrx+ y*f/1blq.)   

  Determine the time it takes for a satellite to orbit the Earth in a cex 6 gkz72huu xcyp a39/23hmeircular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very smal2exkhaec6u2 hxgm/pz y 79 3u3l compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launp0 -hyy ucn*(*5waz26k pp dwiched from the top of Mt. Everest to be placed in a circular orbit around the Ey60 w 2uak5wzc*pi-(* nydphparth?   

  During an Apollo lunar landing mission, the command mol09h rkj l3gevj9js 30dule continued to orbit the Moon at an altitude of about 100 km e90vj0hlsgj9 j3 3lkr. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed ofme ; 7cv7fwb5i chunks of ice that orbit the planet. The inner radius of the rings 7e7 b vcwi;5fmis 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.8x()uy c+z 5t ywfg+rk 5–9). What is the ratio of a person’s aw r+uyfz (+k8 )tx5ygcpparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km /6 gdi43ga/fqcyodq, from the center of the Earth's Moon in a space vehicle (a) moving at constant velocf6i3q,ogg ac/ q4d/ ydity,     ----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 :5 +q( iv;0m l 2gxu:penzlipvof two stars of equal mass. They are observed to be li vlgv pm2z+uxei:;n q(:05pseparated 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 woman5)nen;ohdn) i in an elevator that mov n edn)o5nih;)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 cord8 vidnzax+8 pf;4dkb qo qu533 suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the eleva453dkbp;x8 q8u3n +faivqd o ztor accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfa60 3mwgc hib*q;yw* tgce of a planet with period T ;i 0y*cw*tbgm h3g6q w, the 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 the period of the Moon3n+ b8xome r1yva5: )wx/trkf (27.4 d) to determine the period of an artificial satellite orbiti bva5kr3x8m+yto e /w: nf)r1xng very near the Earth’s surface.    s

  The asteroid Icarus, though w2 hl sp9t*hu( /i,debonly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. Wha( h,u2ht *dw/pbslie9t is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist olwuv(yvqp1 gl4+ 8ttt -j*1kance 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 f)cf2 4x+xkd5lf l8x;1(wmic cu:8 ymqu qk. cyears. It comes very close to the surface of the Sun on its closest appro+c :x8yq5;x4lmfuq)2c(. ukw1mc k fdf8xcliach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abouq86(s4p ux*1 ezuqcalt the 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,2pwp(,9 1ory ggeoya+wj/ b:* jqd4ea j0gq)x period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1baq*g (e /4 g9j, g yjo:r)2p0+o1y wjwdaxepq609).
(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 disw6fij3lq;n; 4jac1 kv tance of the Moon. i 6qkw1n34 vlj j;a;cf   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupib9lb0em:(c oodi/ g( bter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in 0bodi (lb:e9og m(cb/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 -aeqnxw+ 6t1l1 6ibct Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbtb+1-6nc q wxie ta16lited 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 an artificial "planet" in the form of a bz bq9id)u0p ;yu1, lxiand completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this uu0zb;d9 ,i1 yl)ixq psun 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 vio6qbls* nr6-w9a t8bwne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on 6o8aw b-qtlbnr6w9*s 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 accei03h q5zkb5yjmrp) -qleration of gravity be half what it is on the surb5mq 5q- h0)yr zjkp3iface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and ys*usvmtj,q y 28 s-o6spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long an-s*v ,o sjs2ymyu8t 6qd 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 appare75)hn7jkg e xbnt 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. j 7gxe) 7bnhk5What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directlqj eb,:0j4 +g yt0ptdoy from the Earth to the Moon experience ze+p,jj 0 eto4 ytd:qgb0ro net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bud/+mac,(no4hz q*j l ct when you stand on a bathroom scale in an elevator, it says your mass is 82 ,ao*h + c4 z(jqmdnlc/kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a ciry*u15whn30rs0 uk 9e kgr ylf*,uez;gcular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earu9 *5u *fyr0;n 0kge,heyurzw 3s1lgkth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop p;g3qxs j4 fhm na6s:.(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 ter qmfxke1vaecl)4 c 81zfu85 3gms of its radius r, the acceleration due to gravity at its surfaceec5m)qfgckx8 lu f1az413 8ev and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical byu029opy ozfa6 an ap 0uzoo6a9 f2yngle $\theta$ 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 bankedz3*nxv ydt1z ( for a design speed of If the coefficient of static fricti nvy *zxt3d1(zon is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Ear .gg:kv*splj 4;ki/1q pis.oxth were rotating so fast that objects at the eq4 s.l *;xp gikkpo/1.jisgv: quator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distancebij65tgvu vz*yp22l5vmzr ;pn) 1v, p 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 235tzoa 4czrcpqqe/( -ks.pe,m5/u z: h0 m. A lamp suspended from thz -c:k,psmezo tqahc.p5( /4/ zre0 que 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.p vc79ltyzs r.; 4dxn;k:o 30v vyvi.h Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. ov3k y7l d9z;i4sy0ntv hpcxv:.;vr. 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 presence of anx8 gfj9;*rz ge extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whi8 ;xgrz9f g*jech no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it ty )qerharf --/raverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast a-e -fyr) /qrhcan the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites o)8k is7 -oymof*al oj8rbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Easoojo7mf)-l 8yaki 8*rth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.ih6 e;tu5 o5 dexgbz1:1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Ee5; ui x6e5z gd1to:hbros 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 ir g+vx3i4o;xp q5(rbf n need of repair. Y x+ f5 vor4p(;r3qgixbou are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a periok /a4k :6:j.4ll vo crhcyrij+d of 3000 years. (a) What is its mean distance from the Sun? v46kr/lkc: y+loij a.:j4hrc   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if y*w, wkt/ss0nja o/)ejou could actually "feel" yourself gravitationally attractwj/wsa ste0)k */,joned 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 Galaxy (Fig. 53.;.u a6ufr wyj0ji rw-46) at a distance of about 30,000 light-yearsi3r 60uwa.jrf.u;wj y 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 side. F gpbv- hg/2 *j*rck1*xw oiu-eind the magnitude and direction of the grav c1ou *wg2rhji- bge/-xp*v*kitational 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 Eartz7e wi7zyh-q +h $ \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 tdixoa.o k0x/q:gd 6nq h j-m71he tip of the 1.5-cm-long sweep second hand on your wrist wat 0/:m1a7qo-.dix gxdojq k 6hnch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a c8towz m6 52wk)nan)cns )6i k0lw.fuuircle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angl8.2 nna6)uk )wnw sz0 octkf6 lwi5um)e 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 designe j.g0j.ct9yfi2v xwh8 q1kq.ed so that a car traveling at speedyv .1xek fhc280qw t9igqj ..j $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of thakl3cf 9k(7)2lxr g jme cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train d f2rk73 ()k9lmxgajlc oes 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.$\approx$    $\times 10^2$