Sometimes people say that watet.8m8l6bv jsfb.)n9x9o hdu b2xsyd vdn-; f 4r is removed from clothes in a spin dryer by centrifugal force throwing the water outward. W )v. txb-8fh ov6d.n b4bn2;s9xlfdjuy8mds9hat is wrong with this statement?

Will the acceleration of a car be the same when the car trav,zmg)oj8c kwo inq2 63y c6tm9els around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at theq2m )o8giwk9 ymncc3 ,o6t6jz same speed? Explain.

Suppose a car moves at constant spe06cpajg/6gzek v 4yz*ed along a hilly road. Where does the car exert the greatest and leac/gg64azj60 kyez pv*st 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 child riding a lec-u 8vcii.x d23fgy*dt4l )horse on a merry-go-round. Which ofc vge3i)lu*y lxf42c 8.t-did these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in au(pgn qi)a1*r vertical circle without the water spilling out, even at thga qpr*i1(n u)e top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Thzbs 0srt(o0u3llr: i 6ere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?306rbs lulsr: z0( toi

A child on a sled comes flying over the crest of a small hill, as shown in Fit4i.2d5h s b92h*0pgck10 odz scwoci g. 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 b2 z5 odig.1dc0ihhsts4owcpk*9c 20 the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when round6di cf0m3jm.0xmzir8ing a curve at high speed?

Why do airplanes bank when they turn? How would you cz;fc 7 c:uv8ejm.q *8b7ludxyompute the banking angle given its speed and radim 7cblujv.8;*7 e y:f8cu xzqdus of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shl .l;; ;r*wqb iarry;b9;kexs e wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should xqbe a*rs ;k;rl;rb9y .l;;wishe let go of the string?

Does an apple exert a gravitational forceo akq6p)k.,zi on the Earth? If so, how large a force? Conskz)pi,q oa6k. ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wm1c,1w8qcun+ pnxa1 0z r*zoyays would the Moon’s orbit be zc1p +quc 80n1yw1rn, *azomxdifferent?

Which pulls harder gravitationally, the Earth on the Moon, or h + ap*x/0lhbnthe Moon on the Earth? Which accl0ph/ x+nh b*aelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t 8h3tbsg0wy/t d9/zu fhe Mohtstdf3bw9zu0 /g/ y 8on'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 equa;vok v8fhf f8 ,0n,s ( i*sajhsqs5lb)hjp:t/tor or at the poles? What two effects are at wojv p,ta8iffshhq;h s0so( * 5/fjb:,ksnv8)lrk? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only abmcbjoaiz437e;n z2 2oout half the force on the Moon due t3 n4zoz2obc7ai2j; meo the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar e0wst muu 3;alc4 :l6mfdemxg(ji1c.g:1d s-ger or smaller than the centripetal acceleratif 601x-gm g: .a(me ldc:djsmlw1 iucsue4t3 ;on of the Earth?

Would it require less speed to launch a satellite (a) toward the east or )v ;x s-ipcy5p *x/hc6.alrdvu6ux r ,(b) toward the west? Consider the Earth’ y5,v6 dxrv *;xc6auu -hxl.i ppsrc)/s rotation direction.

When will your apparent weight be the greatest, as meas uo*jc mafx g 91-k;l+kt1fao3ured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelela1f-;uok mg jk1caf* 9t+o3xrates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected a n :;+ xpethj*ct3;yoa 00mxmby 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 gravitaontx0ajmcp3x *:hm + 0 ;tye;y. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner expe i2ycaec4f8)ogd p2j8 riences “free fall” or “apparent weightlessness” between steps.42p eaj8)y 8o2cgcfd i

The Earth moves faster in its orbit around the Sun in January than in July.po1l1wu: m *0gue ,l +5akj.,ux zkmhg 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 a1m1*wz kx,,ampugjlu+.:o lgh 5uk0e xis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to havel(.u 2pv(gkut a moon. Explain how this discovery enabled an estimate of Plp2 uvlu .(g(tkuto’s mass.

  The Sun's gravitational pull on the Earth is much larger thaw1d5niihkbv d*0 c ;c3n the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. wbdi15*c ;ckvinh 0d3 [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 6m1saz2 dl,m3z ddi-l$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 theyr75 ; ujn k,ruq)poh/pp i)fn+j;r,.cep zr5 Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit izj ryp/+n c oreu q)f;5j7;nph ,.p ku5,pr)ris a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifohm-hb/kw2gypj(,xq) a+1nki rmly inbj , g +2qh1kw/)m(ihanykx -p a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is 5hcq ./ gkvj)+rdcp x q9o e+.l+ec8oyin orbit 400 km from the Earth's surface, and 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 the8qp./cg keyoec +qlhc5xjd +)vo.r9 + Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck o 4i d9b8ebnbw2jkw3/ zf clay on the edge of a potter’s whe bd23/nz8w jbwb9k ie4el 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 in a verti-ctdpc v8 mh81 irc(k 43 5(tclhwb+g ./tiigvcal circle of radius 72.0 cm , as shown in Fig. 5-33. If its sith wvi g. gmliccv(1rc c4 htb-t8d83(/5p k+peed 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 6lm3i futl8 i/y -m27q)mykcz1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static frictioq38ym m y)-ikc l7lfz/m6u t2in between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffim akk2t,x+n +wcient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed x +mkt2wa, k+nof 95km/h ?   

  A device for training astronauts and jet fighter pilots is dylvy18 y3kr xy3wi( :kesigned to rotate a trainee in a horizontal ciriyx kr31:( 8ly yv3ykwcle 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 turntable of variable s rc1peg0 d qx90 dgr5gkhpd743rp (*lrpeed. 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 statp3hd 9g( xeg grr0d4qdcl pp*r0r571k ic friction between the coin and the turntable?   

  At what minimum speed must a rollzzg 3ssy i(morq5/lea7w zx9n) (:n u*er coaster be traveling when upside down at the :/yszg7) si (*3xnzurme o5qal zw(n 9top 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 the roundevd cgh c+fwz)9xr0yu78 2)vond top of a hiloz y x)v7d8u2frwcvng09+)hc l (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15ba.z bs7/zik 0-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at07abks b iz/.z the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertica,4g sx563ep dohoasg6l circle of radius 1.10 m. At the lowest point of its motion the 56oh s,goxa4sg6 e3dptension 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 particle 9.00 cm from1r/tyl if-k4kh 32owd the axis of-kk3oy4d tf/ ilhw1 2r rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated inzwi3(lv:00 a7 orpz sm a cylindrically walled "roo r0ov0 7m:szaiw(3l pzm." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionles -l le:pzc(a*es air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shl *pa:cz(-eleown 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 timekf6 fx6wj 8a2n, by not ignoring the weight of the ball which revolves on a string 0.600 m aw866 fknj2fx 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 ra. t (h:y;),o;yofj1kdkxtkl d dius 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 masse2 m35zoo*pvz*v1glv0yu. a sh s $ 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 maneuvem 4e42xrv4peb r 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 centripetal components of the net force exr,81grcqw8 k jerted on the car (by the ground)c,r88wq1 jkr g in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from zkl:u+.8: f gs;bmncibww(b*the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration +( sw:mkc.bzul;8fb: g inw*b with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular inttsql u x0;w3qw 9xg ,dw,0a7zstant, its atw wlg0t w d, x;7u,xqz0qas93cceleration 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 gravitt4c0o fk r.bhbr;;*f 6w)nx xwy on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfaceb;.r r)o4k;nf wtxx 0*b chf6w if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accew:4xv:le r2 a7 alhn6vleration g has a magnitude of xv7ln6ah:v2w :l 4rae12 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 accelerat17kvl +q.6uokh q vsv0is7w9yion due to gravity on the Moon. The Moon's radius is 1.74 ivqu0sowqklh79 sv7ky.+16v$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ty- z/k sg vtnz3ckh9l u,0m:;eimes that of Earth, but has the same mass. What is the acceleration due to gravity near its surfa vmk9-/eg:z3c nlyt0su hk ;z,ce?   

  A hypothetical planet pklbb3p g*:mi4f* 1pa has a mass 1.66 times that of Earth, but the same radius. Wha1 k: bbp*3galfm*p4ipt is g near its surface?   

  Two objects attract each other gravitationallycrr -+jbc oj;ief*7, r 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 i)v. l4 .;wh96xroga mzn:a; iwm(osb , the acceleration of gravity, at (a) 3200 m m;gl.9 6vx zrami: ws(4o;wobnh .i)a   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinurp( c)n.7osit outside the Earth where thegra 7c.(o)nsiur pvitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed igl jp5 *z5bb*4xylt oxk.:e2p nto a sphere about 10 km in radius. Estio .2 ptp lb eb:yj54k5*z*lxxgmate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wa 5f1,gwgstl1 i;a,cnl s 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 gravity on wi 1cl5ns,taflg,;1g this star?    $\times 10^7$

  You are explaining why astronauts feel weightless 5jnabyr8 z1v prbdux;5pz j5;v 5 4i.mwhile orbiting in the space shuttle. Your friends respond that they thought gravitydn5va4z1; . 5jm jpbyri;r u8b vz55xp was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 mzq.sm a9uw4+* *3gdpiara4 )lfmhr* b. Calculate the magnitude and direc4rm9 aigfu*)awpa qh**r d+mb3 sl 4.ztion 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 jk020 e iijj s:6vlcszpy++2dsame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming:2sd6yjcvli+0e kpj2i jz +s0 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 surface of Mars is 02pk5 bw( kafcb14ehm -.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass1h(a efpc2kb 4 wm5-bk of Mars.    $\times 10^{23}$

  Determine the mass of the u,;ba8bz ( l7rui x.qvSun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that ouz.q,8r 7xu;bib al(v btained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about th)no6 tqhepd,k 6bvf3k51v; foe Earth at a height of 3600 km pnhvb;,qef35 t)vk1oo kf6d6.    $\times 10^3$

  The space shuttle releases a satellite into a circular j6f :wr :u5ybfln *:cky(c 0iyorbit 650 km above the Earth. How fast must the shuttle be moving (relati6ry:*:5ffi:cunyck y bjl0 (w ve to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ,2qeljyqz 8zm; if/6 cupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time jfqm6lz;q y2z8 / c,eineeded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the E per:-rf9f caa9mwf+ -arth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small comparef9 +rf -camfaer-: 9wpd to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal veqlk9ttr3d b0i, iuky5/vk;z) locity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? 3);0dykulk9k5ivtz/,qbi r t  

  During an Apollo lunar landing missi l-qn5o-w.j 9 8myj4lslt9dwmon, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around t5nmlq -wljy- l 984j9ostm.dwhe Moon once?    s

  The rings of Saturn are composed of chunks of i0d2(,g tm xxes9z5tc js95idt ce that orbit the planet. The inner radius of the rings etx0ssm 5xzd5 9dt9gi(,c2tj 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 u;+ wu i(hg3dxdiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of aduhu(x i;+wg 3 person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cent8+tp ia2n v+hfe-myu,p/) ky ox 5-ahver of the Earth's Moon in a space vehicle (a) moving at const8-a5pvf+eyo/ u hpa-i+kx tymh )nv,2ant 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 consi0u tn42tgfn/m 4scc3vsts 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 /nnu0fttv4gcc 4sm23point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weigkua;(pw: qlrr9t nn .1ht of a 55-kg woman in an elevator that mow;(:1 rka9u.n trln qpves
(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 fronsk99,qka y2ov1i(wrl a/zw,m the ceiling of an elevator. The, ka,oq wrk1w9say iz92 vn/l( cord can withstand a tension 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 orbits very near the surfpiik8 4r 3px-bdm l4kzrdc425ace of a planet with period T , the density (mass/volume) of the plac p-b342 8dxz drlipm 4kkir54net 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 determine the period ofd auf htxn9i62f+ ia3- an artificial satell 9-antah2+ iud6ffx3iite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sunbe if k: .v,-c.;gj7rh/u ycru like the planets. Its period is 410 d. What ifji/:k.h-vbryg;7c . u recu,s its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of d8966z3fwf ko1u z;jszv ) nfw4.5 $\times 10^{9} \mathrm{~km}$ 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 orbit9r 5 fes:3bjgws the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the s3 wfj 9g5rbse:um of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente7yw(:9xn j.epf ywh0wr of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four la+s37wso+ a xskwp y78j8z9kt lrgest moons of Jupiter (those + 8otsxl+7p7 w sz8ysk9k3a wjdiscovered 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 fro7l(ywm7kr 9ll om2fp+m the known period and distance of the Moon. of l7rp2 l+y(9klmm7w   $\times 10^{24}$

  Determine the mean distance from J4dwg.t6a a0fg upiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the perif.6w4gd 0gtaa ods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt bet1:z *bmwpuqcd( wsbgezo)8 o u6d-of:z7 x8 z5ween Mars and Jupiter consists of many fragments (which some space scientists think came from a px1bf6z5 zgdw*ze uzm) s8o7oupo8c :-(qdb:w lanet 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 df ibsm7fo2r/9yp:d l cnn7-.iescribes 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 f p2 lnfd:b .-9soy7r7cnim/iclimate 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 pf,5gc 4 nnr/td,: 0,e 4by jxa bqi4w6abbv4ja gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His maqn/db4byrjvj n6p5,b,bcf04w :gt a44ix,ea ss is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accel/f 4qvjp2dbt myh96148g sbejeration of gravity be half what it is on p mbfd6jh qb8t v 429sj1gey4/the surface?    $\times 10^6$

  On an ice rink, two skatershdxv 8/elzhj*az5 wo:p ,(v g8 of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg,w zov:g d/,eza8(h* xhv8j5 lp how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent ,*kgp /rrkbair10a2jk dl i,1acceleration of gravity at the equator is slightly less than it w*1g2 db,k/i,pr ara1k 0lri jkould be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecr,lbp;dea 9,q(:t vhrkaft traveling directly from the Earth to the Moon exper9 lqv:kbhdrap(te, , ;ience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, dijzkbg k; *4kl1s2,4pe 3e eubut when you stand on a bathroom scale in an elevator, it says your d3 ei, bgesjl42p k; 4e1kukz*mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboc ua i6u++qi78crh s(iut 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 Earth (1.0 g) is to+6i+ a cu sui(7hr8iqc be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verti/a ygbw1t g+n)5xtow.cal 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 plaxng+e2m(b zp .ms4v1qnet in terms of its radius r, the acceleration due to gravity at its surface and ebn+m2(q 4pz msx.v1gthe gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the v8*u iqq 25qdbva-)ahxertical by an angle *uda ix-bqq2) qv5h8a $\theta$ 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 w-t)j;x5 m3qi 6oid j0fta u8vis banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at t5a mfdv 0u3w ;i6o)8 -jtqixjwhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectsy7 k0gj7/ueq sv 4oar/k7rmz+ at the equator were apparently weiy4rmkerko/ s777/ag u0 q+vzj ghtless?    $\times 10^3$s

  Two equal-mass stars mai1sd ncjzj,,3i7 v u-(t hgi1fcdm8w(gntain a constant distance 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 constanur8qeq 0( )k8jwqp x0;auj; r2er gda4t speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an anglwrqra;2 jx0)p( dejg 0u; kqaq8r84ue e of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tips1 ah1llw x:2oy0*rndh4sitle p2 -7mes as massive as the Earth. 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. Calculate the number of g 's a person would experience at the equator of i0t12e1dnl:7lxwh *-ss oa4 yph2pl r 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 iglwi2d tpot,v22*v05*ymxf presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lifyv*2i 0igw,d t*2mvl otpx52ght 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 traverses the hill and valley shzer) yffv*z 0w,.7dl - z;bqhxown 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 far.ld* z)hqv-yx0f7zbe f wz;,st can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili)k ,x(+ayfror-45yi peg5hj qzes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to r4yrkji fo(+)g ye5,xqp 5ha-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 trafsc +em g/v4n-veling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15-m+cf egv /s4n km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in nee bjqf2mn2f(7y d of repair. You are in a circular orbit of the sameym7fq2b 2jnf ( 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 period of 3000 years. (a) What le0zgh-gq) . kvj ../tk+d;keit nzf7 is its mean distance from the S+fd q7 k.e. ie.)g ttkvgklz0/h;-jznun?   
(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 actually "uut/rz vwvi/eu4yu1,qtg6 -b j,cx*)feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiog,r* wj-x6y t4ciuzv/1,v uu) e/tqbuns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of f3 h( q5.gcwa7vi )3,bsyuukw the Milky Way Galaxy (Fig. 5-46) at a distance of about 3wh)scbg a(5vi q3ukuf7,3 w.y0,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cornersswfj w5wwy:u351 ) mlpms,/ a8kvcf,d of 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 f wswu1 ): wf,3v/d,mck5wy8spla5jm of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500+:dwhz0p;bv.yquy 0kyk x+zd;ny * 6j kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip otoxr+j2c1hq :oka 4d) f the 1.5-cm-long sweep second hanj kr1to4 d+2c)qhxo a:d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a c6poriya0n95fnau 47 9fb-u w zircle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What ia f u0a9on wzi694fby5prnu -7s 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 higvs ) 4vme/uyn. o,0oxbhway is designed so that a car travelingvysmx,on/ ov4ue) . 0b 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, v;lbzr0drs( 5,hugomqqw edk6+d:1 4 the Acela, utilizes tilt 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, thus feeling more comfortable. Consider an Acela train that rounds a c:dq0er(q1rw6 d+okgm;z,ubvsd 5h l4urve 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.$\approx$    $\times 10^2$