Sometimes people say that water is rm6e,b0 kubwg1 uh3*us :wqj6hemoved from clothes in a spin dryer by centrifugal force t w usq,6 b3uhgkh m6u0b:j*1ewhrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be theex7 jwv(.4zqqh6h0 xx same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curvh xjxvew.z4qq xh706( e at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does (s,f7extrn) b d+cz0,2 kuzajthe car exert the greatest and least forces on the road: (a) at the top of a 2fus 7nt cjx+ez),zrb( k0 da,hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. W6tl9ee bscw8w4 4a go*hich of these forces provides thet6saewgo 8 l4c *be4w9 centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wasl3-po d s 0jkt;,je3cter spilling out, even at the top of pel;0 -3,tcs dksjj o3the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leasttxnp ygm; uq)p+)t 79m three controls in the car whicqy7)gu +n)ppxt;m tm 9h 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 smxb ct( w:+z/o 7z3vvhir0v8 nlall hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not ac80z :blv(3 tzwv7/+cvx rnhi ohieve “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 hic c/uh csfz 6d8(0r0rl(q fr+zgh speed?

Why do airplanes bank when they turn? How would you compute the banking oxpxft-2 + ui+ijpgyw-95p n.angle given its speed andpyxnwog-uxi + +j2 p5if tp9.- radius of the turn?

A girl is whirling a ball on a s68fxh9h jcdvg)o3md 4r;6cg s tring around her head in a horizontal plane. She wants to let go at precisely the rig ;rvch4j8of6scgdg6h3m9xd )ht time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? I p pt169xmfc7bm2dh7bf so, how large a force? Consider amx 91df2p 6 mh7p7bbctn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass we8g9fce (av;ym.n46m u,j sfhvk8 tb/pre double what it is, in what ways would the Moon’s orbit be diffes,8fbm9kh(uf m v/68;ag y.j4vcpte nrent?

Which pulls harder gravitationally, the Earth on the Moon, or thed/,7e k twaw*omm(hu* Moon on the Earth? Which d hkwa*,mw*(uo7 mt/e accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t;r1apq lz )8okjmo /; ov-fg6ch; o olzmpgvc;a 1rq/k j6f8)o-e 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 more at the equator or at toers(o.ns.n q5skb7)+vo jm d w ad5j+-9xu z)he poles? What two effects are at work? d .vsuk+9 qaj7b(moo)xso5 nj+)5.s-nrwedz Do they oppose each other?

The gravitational force on the Moon due to thl7rqf2hz *bv sb y+(u(e Earth is only about half the force on the Moon due to the Sun. Why isn’t qzu+s(bh l72br* fv y(the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arl1qkw r;bbxu*0x2 b06qgzmo-ound the Sun larger or smaller than the centripetal acceleration ou w x61q2;gbkmbb00 xz l-*roqf the Earth?

Would it require less speed to launchc(gx5a6 -iv nc.c xll6 a satellite (a) toward the east or (b) toward the west? Consider thnaxl6c c li(6 .-gxv5ce Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a svocaxj6c*xwnk .. 8y(cale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) movek.v*oa j 8 .nxwcc(yx6s upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in odopfgt1;*b7 zuter 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, and (c) any other aspects of gravity p*tbgf; 1od7 zyou can think of.

Explain how a runner experiences “free fall” ornmd yx3y:b ;hly2mb26 “apparent weightlessness” between step; dx ylhnmybb:3 y2m26s.

The Earth moves faster yd1r qz+rngz;y 0wt,tpi m(c-p3i ;/oin its orbit around the 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 tilt of the Earth’s axizicwn d,po(;g+tp31zr- 0y; iy t /mqrs relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovepw*; j-gpin(ps ,n3 1: nqhxjored to have a moon. Explain how this discovery enabled an estimate of Pluto’s maq, jx-3s1*hngo inwp pj(np;:ss.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.e mwi *al2v,h*rlc eomj ;57 /*peldx5 Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the mejepol*awce*,2i57rd x5v;/ll * hm 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 travelin: l g9j;rk98nwe *q ozvd(ga +o-8tofmg 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 in its orbit around thn b/6*ntjisz) e Sun, andj*iz 6 )bsnt/n the net force exerted on the Earth. What exerts 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 exert:l.,5rkizd(arz*xvout*.90*o zgt qe- jrwk ed 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 ofoz ir.5e*jtrz 0olk*d(v:.ar-wqx k* t9u g,z the discus.   

  Suppose the space shuttqw.rc3md -u .tle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shutq.w.murd3 t c-tle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitud/z kj/-3anm hpe of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diametj3z nkh m//pa-er is 32 cm?   

  A ball on the end of a string is revolved at a uniform : g;vdnojb(m3w 55ek q:fnu0hrate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speengw 5oh5 kjdf;q3b:m eu:v(0n d 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 roun*2; i 1bxt9*ra o2p tlf*u4zpdpvgc ;od a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is2cv go;bua9toi pf ld;r p1xt*z2*4p* 0.80? Is this result independent of the mass of the car?   

  How large must the coeffic+c5 k ty(xeub(ient of static friction be between the tires and the road if a car is to round a level curve of radius(+uybke (tx5c 85 m at a speed of 95km/h ?   

  A device for training astro0-5nst,aafdmz* y;5 q: c ugpcnauts and jet fighter pilots is designed to rotate a trainee in a horizont *cdg5u scypa5 ,;-zt :qm0nfaal 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 rotating turntablezlg06;()0 lq wip;tmw:w xmkxbq )5m s 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 friction between the coin anbw5:w6p )izm;wk0 ( smxlq)xm q0tgl ;d the turntable?   

  At what minimum speed must a roller coaster be traveling when upsi4trt3 e fqdono*6w1*rde down at the twtnr36ed14 r* oq*ftoop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses z9 x 6jwo1yz-2 oacm6oh4cg1qthe rounded top of a hill (r19yco2a4zhx6 z mq- 6w1cogojadius =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 -x+eg)r auuwr1uz5dy30 y(apl bxn: 515-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poin+1pzb35xyudauunl x -a :5r(rg) ey 0wt?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle oftnrbdu 0jjw4: yem 4 f+dmf80+ radius 1.10 m. At the lowest point of its0d0+4d4 :yef mjru 8wfb+ mntj motion 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) musjnu-.6r6 q0u, uw7 bzpv ybmr4t a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleratio,ryuv0bq.7uzjnw 6 4u r6bm -pn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoa;,w p g2lh6ytple are rotated in a cylindrically walled "room." (Sa lhpg ,ywt2;6ee 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 rotatr9d qp6n9 ivcpsxjn )/8i+s/bed in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connecteji/ +8sv)rbp ci p9nx6d9ns /qd to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the wei5+,wif: eah tzght of the ball which revolvesza :+ewif 5th, 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 otmw eynuw4o:9/eny3gh(:b o jql6 3 p;f 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 massesb scp4 : xa.c/a8tikg* $ 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 evas35 8qi3q hazjeive 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 and centripem+y u;0qxo0i b77:blel8v:w2bdudiy *ys-ah tal components of the net force exerted on the car (by the bh+-uy2ioxwq:el u da 70d:0ybb8*; ly7 misvground) 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 Indianapofc- tvf6se+5*kek )o r pi26yklis 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,-kcki rye5t6 v2)kspfe+*6fo 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 acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radik 4 z6cy)g.-(ddh cvrxus 2.90 m . At a particular instant, its acceleration is .x( cdc)6z 4y-kdhvrg 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 o9ld bou:2ap+slz2hq 5 nrz2y6f Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 13z6ulbz2: 5lqordn2hay s+ 92p 50 kg.   

  At the surface of a certain planet, the grem, gn/4omn s)avitational acceleration g has a magni ng/e ,snmom)4tude of 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 ok8s,l 0olcfeb8al 6r;n the Moon. The Moon's radius is 1.7r,80l cb6fa8 osel;kl 4 $\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 tt/l x ikx)v.(oq +y6/tynd2lb hat of Earth, but has the same mass. What is the acceleration due to gravity nea il( xt/dvn q) /6bxy2lty+o.kr its surface?   

  A hypothetical planet has a mass 1.66 times that . dkq+*p nboy/ne(pf)of Earth, but the same radius. What is g near its surfac*f .o(kn ppenb)d/y q+e?   

  Two objects attract each ug c x m 7,zvvez8h5a:6kwt6w,other gravitationally 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 vafj29 d aav(xbip6)pcg 49,- (k7d :hr avyvnfglue of g , the acceleration of gravity, at (a) 3200 m npad-yi72bv:4 r, 69vv9 kcjg( ah p fg)da(xf   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poieedv cc topq*8/:3ak1nt outside the Earth where thegravitational acceleration due to the Earth ispoctq* 8k/:dea3ec v1 $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h .pmx 2x-4yymg-i/uztf xj6y ;amdb30as five times the mass of our Sun packed into a sphere about 10 km g3 yp x. fbi02m-xuy-;x z4/amtmdjy6in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whichx y0zi9fp4nm2ut)/ b.pp2x ioy3)wo w once was an average star like our Sun but is now in the last stage of 2bt) up92 pxyii )3oy.pmw0w4xfn zo /its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while o pg p)9 bif(mi)st8h/mrbiting 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 E8hm/ii9 pts(p)gb)fm arth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cornerys q hd+ix35c, ( hl1+eub9mupfs0- ycs of a square of side 0.60 m. Calculate the magnitude and d 3y dx,+mul 5hc-u1cpysbs(0ef +h9 qiirection 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 mo) f,dv2l*ty8 eco ,gayst of the planets 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 masses 2l8c*yg ) eoyv,t,afdare $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 gra 6a roo6ju;*h0c9meizvity at the surface of Mars is 0.38 of what iti*a6ju 6o;z9 er0mcho is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using 3wp f8ji(dkaf2:yi: uthe known value for the period of the Earth and its distance from the Sun. [Note: Compare your answea8i3dp :2wk:y uf(jf ir to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about zs,*x6)-ro ++m fp0 aihuvytr the Earth x)ui+ry m,sp+hv 6zo-0 *t rafat a height of 3600 km.    $\times 10^3$

  The space shuttle reyl ;rt-d),k fee 9pi/bleases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (re,ep b )if;/krd-t le9ylative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyli p317xu *. xhgaknf/oh)r9tnw ndrical 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 Question7*ha k1pxo3wg./)9ntrnfh u x 21, Fig 5–32.)   

  Determine the time it takes for a satellite to o 0plh7o.py-s)xd r m; .w(gkzprbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height szghw p.- x lp(k 0).dpr7;omyabove the surface 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 satellite have to be laupc5oszd+9 * ldnched from the top of Mt. Everest to be placed i o5lddc*+9 zpsn a circular orbit around the Earth?   

  During an Apollo lunar landingaa /mqkgy pw2+b;l:;)hu r+vk mission, the command module continued to orbit the Moon ak uhkbgavm/ qya:;; +)pr +l2wt an altitude of 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 th -j4bql 9vqb ury5m+k6)s+ ngce planet. The inner radius of the ringsnrg)b +vscq +l6 5u4k9j -bymq 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 diame*.0gd88jo cke,vra s jter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thj8jd*aoge 0.v , cks8re top, and (b) at the bottom?
(a)    (b)   

  What is the apparent w4oryr 22*w )6adkrptz eight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) ry r2rzka6dtw *op2)4moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. The9 pgp666 baz*cgt c/ih +ph2hfy are observed to be separated by 360 million km and take 5.7 Eartfb6pp9cic ghh2a+6pz g/*6t h h years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in a v14i-j 6-k4wipdf fghn elevator that mo44p whfjif--16 g vikdves
(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-rdimo ed(v6uz i,f.st( ,s9v from a cord suspended from the ceiling of an elevator. The cord can withstand a tenfi,r(sdu i9.(, vmts6-zod vesion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite fevvmlu+x r7bwhfp. m1; f)f732o rz9orbits very near the surface of a planet with period T+9.xv7fb2pwh fzlvrm r);fu 7fm o e31 , 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 Moon (27.4 d) to j se p/x7a99pasg;u.ydetermine the period of an artificial satellite orbiting very near 7aax ; .pp/esusyj9g9the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, ocxb, wo+f;hi*l e n)x0rbits the Sun like the planets. Its period is 410 d. 0o)e,wn c+f bl;xih*xWhat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance g:a : 8f4nzu- utu-bwdof 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 comes jm9 x28lr4l 8vlsts-nvery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is lr 4nx l-98l2jv8sm tsnearest 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. ja4o4k5fi5t,g gfo c 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, ,ub i7qfarn0 0period, and mean distance for the four largest moons of Jupiter (0in 0afq7 urb,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 Mouj(lf2+:uvy m on. vju(ufly :m2+   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Ket::8weca d9kc) qr 3jtpler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values i8w c:ck3rat9jq:e ) dtn 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 k qac04e pby 0hz-q0kh 0cqm4ze3e8j5 Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was desteck c80 0aq0 3pmy0zz qeb -4k5jq4hheroyed).
(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 fwdf f36 iodk*np7f:by4+l 76mh .dig band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is al wm.gynfi:lpki 6 db o*d7+47dh6fff 3ways 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 of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vu+kv w9p 8osibwjm8y;qh)2a0t/3i coine (Fig. 5–41). If his arms arekou 2m ais9 )/wp3o8c0 j8tq+vhyi ;wb capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whsl-n5bwroil4cx42uzl 4 ,o; p(x:q orat u n olo lzr2(rs:pwlxoi;-xc,4 q 45b4it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal maspgsz e94cxd x+5uu v7d.7s3ye s grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m lzsd9+x74u xgudev.7es 5y3c pong and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity - ) bi+oms+xdix +qls3at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnits3 )++b+mlds-iixoqx ude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the E7qhp.tx(.4j d 7x bxplarth to the Moon experience zero net force because the Earth and Moon pull with equal alj(tx77xp4bx h.d .pqnd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an eokisc o a4td l:y*6- e, oq+tx7sq4a0llevator, it says your mass is 82 kg. What is the accelera0st-kqol4i ocox :a*eq76+d l,y t4sation of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube th)q mv2q3y v*vmg w7v1uat 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 e*uvvmqg71wqmvy )2v 3qual to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). w r73)rlb4uyczxq:: y
(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, tcvij3xd3z8 v e uaa*yh-1;aq n*3ie( che acceleration due to gravity at its surf*q33 i a ;-vejdiecaz38 a* x1(vcnyuhace and the gravitational constant G.

A plumb bob (a mass m hanging on 0lx u,h0- turba string) is deflected from the vertical by an axu lrb,u0h0t -ngle $\theta$ 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 des ( lbhyk,oz 6x8mey,y;ign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car saob(, 6zy e8kxyym,;lh fely handle the curve?

  How long would a day be if the Earth were rotating so fast that obje y:qp;tz z9o u0,o0omacts at the equator were apparently weightleq,o0tpuy z m:o;z0a9oss?    $\times 10^3$s

  Two equal-mass stars maintain a constant dista qww6xoic x+n( +we w2eha fs+)s)5dq/nce 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 radiu4cjy,bzf d 35uhp0h1g s 235 m. A lamp suspended from the ceiling swings out to an angle ph1cy fbgz5hud, 3j40 of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth.0avpmoqx,jgj122u 9 fk jj7t6 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 tjgv790, okja m2 px1fj jq62uthan a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Spald*gmid2w) 8 d0c 5pdbce 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 sp)2 d*dibp8w d mgc5dl0eed 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 tra i7c6a4.j.u9q,*b icu v y;gvr*vjwwv verses 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? Lightes6v.ju 9 *,c.ivqwa r74vw vc ugi*j;ybt? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes n/;-ca/2a 9p n/ mmuarld*u 8z42dcejtk5jgsa group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the ;2un5rp2dg mu*lc/d- c4a8nzaajj esk 9/ /t mspeed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travel86lw9fkvdvq jbkaa 8/2. j+nc8oaa x+ ing 2.1 billion km, is meant to orbit the asteroid2xwnvk8.j qca/av6l8+j9af+kod a 8 b Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in 0 er :uhr5ansswz24y+3tb4ua b).ikmthe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the.ik)3bn ta hms4+y 2sr0 a:re 5ubu4zw satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its)gprfd6e:59tyhgc* k mean distance from tfd: egcpyt 6rg)5h9 *khe 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 be if you could actuaa 6h: 8i9br-tx loemk vi*k;0elly "feel" yourself gravitationally att lb:oa 9vi6 h8xe;k 0*rmeki-tracted 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 * yzfhu nw7( d2k81swyGalaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centers*17zf n8 dyw2k(hywu $ \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 +tx0lpc,x1..v wpf vuof a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the botto1 uxvw clt,p.+px0vf .m side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth js2-su g(*s6 v kpz6hp/1ru bd$ \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 thw5 cvcl9; 3iddu,fyy9u r9/iue tip of the 1.5-cm-long sweep second hand on your 3/cld 9ywi;i,u9 9v5 dfuyrcuwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a ciulp9v* 3w 8u7ttd oe u(wc-rpq;lgl** rcle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the ang** w39drecout-(wlqplt 8 u* ;7 lguvple 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 d b s/q6i:f z:cij2+ubuesigned so that a car travel+b2:fijzui6u/q c b: sing 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, utilizes tilt of the cars when negotiatimcs00di6 tpm9+vw l1p vg wanf 5j747hng 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 does not tilt.wvd i1 m74 tja5g076cfmv+0 9 pnpwlhs $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$