Sometimes people say that water is removed from clothes in a spin1j.n tnydzqp3dj 3t ,no .9qz, dryer by centrin jtp..3nz,dd1 q,qj 3 zony9tfugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroundcql p +:joon:s0s i*-m a sharp curve at +qsm o0-o: pn :licj*sa constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly 9n o oym+ 8cizdr0x7/froad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hillcf9i7xzym/8 drn o o0+, (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 aa n9 bx17vbnzbb*f./q merry-go-round. Which of 1nnbzqf/a. 7bxb bv *9these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spill ou 7yar b9t8iqljxpy 1/.h-.wing out, even at 7. uq-/ja orlyyi1w8 h b9pxt.the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? qkqbxc.s3dv*:f 1ai *There are at least three controls in the car which can be used to cause the car to accelerate. xqi c*b1:dqs . vk3*afWhat are they? What accelerations do they produce?

A child on a sled comes flying over theb9jvf.j//e0t c ;my7yhqo uiiiw q6ionw )8* . crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but..ub /f 89)qqemi6o07jyiivy;o*j / wchntw i 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 round;fxl( i1tsp0 e4hgl184 qserming a curve at high speed?

Why do airplanes bank when they turn? How would you compute thekzy q-ex+c/l yf t,43i banking angle given its speed and radius of tyt-y z qc+/x4l 3k,feihe turn?

A girl is whirling a ball on a string around her head in a horizontal plane.ln x yih*jd71xqi1p,9 She wants to let go at precisely the right time so that the ball will hit a target on*1jdnx1p i7lqxhiy,9 the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how l n .hyhufa;x5aiqe1x6 5 ieqnc 36,fs7arge a force? Consider anayehs6, 5a7.e61hcfx5 ;qi3qf ni uxn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double /k,bn ksa 70wx4aik 8nwhat it is, in what ways would the Moon’s orbit be differe nx 0a7k4s bak8/iw,nknt?

Which pulls harder gravitationally, tvcni+p5tk oo;2)j; dphe Earth on the Moon, or the Moon on the Earth? Wovk;oc2p;5+)pji tn d hich accelerates more?

The Sun's gravitational pull on the Earth is much larger t+ itwsqly;c m a+ 7q.;-kw:gdqt+6nqwhan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from ; tmq+ qak-+iqw67lqn+cy:wsg.wt;done side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects a9,vrsrx:bdb)v37 ocrre at work? Do they oppose each other?9r 3r7dcovvb :,)sr xb

The gravitational force on the Moon due to the Earth is only about half thedj/lbre r49 6.x ep2 kd4rrc.s force on the Moon due to the Sun. Why isn’t the Moon pulled away fr449r.cledb /d krsjxrp26r. e om the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun.s, 4 y pe/xl4g0uexwm larger or smaller than the centrip/,e p wg4xxmlu.e 0s4yetal acceleration of the Earth?

Would it require less speed to launch a sateljlscnc,tfe6 cwar9a9t;,9u,/g3w ptlite (a) toward the east or (b) toward the west? Consider the Earth’s ro,9c c,jp tsg3ew9fcn l,r w9a/tau;6t tation direction.

When will your apparent weight be the greatestrv80l vtia q0 :25+pdv.cnmr u, as measured by a scale in a moving elevator: when the elevator (a) :0pv25qluv+tna8dmcrrvi0. 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 are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ;3jvkeh:.rja j3u mbb0jh 6o8outer 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 j06ao;uehr jjvb8 .mj3kb h3 :force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betw8ib)j6qdskg(m* 4v5q je2tt ieen steps 6kdme8)j gi2jtq v(s 4*qtb5i.

The Earth moves faster in its orbit around the Sun in z ey,0hada1aiklk /v 4t) db;*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 axis relative to the plai/,y0a k4 kth1*d;adza l)vebne of its orbit.]

The mass of Pluto was not known until it was discovered toh,g x ijx,myrbp o+17) have a moon. Explain how this discovery enabled an estimate of Pluto’s massmjix o+ghy7 b,1x )rp,.

  The Sun's gravitational pull on7n mz.5 z uqx 6aa,cqpezdd0+9 the Earth is much larger than the Moon's. Yet the Moon's is mainl0u7azmexpcaq9z 6. zdd+, q5ny responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-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 travelinu-4 p4frc geb/g 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 accele2v f) +l2,2 /f ,xym;j b2jdueclo +gcyhuyxa(ration of the Earth in its orbit around the Sun, and the net force ex+g(/f ;l j)22cu y2umcx+2v, dh eaxybjlfo,yerted 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 h2g5gvb4+g5m m*(blq hjsio4 exerted on a 2.0-kg discus as it rotates uniformly in a horizontal cirov i +2ghm4gjsg 5 *qmbbh5(l4cle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cirwsymk,81jy uwl q,:tx2t t*xh 4gyw+6 cles 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 accelsyh*w4gjtk tul, yx2tw yw +m, 6x:81qeration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge vvj*7 8exdhp93vi+rh of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter+ r*phv8iv 7vj93eh xd is 32 cm?   

  A ball on the end of a string is revolver1jrs-o oj*tg. t )/mc4 yrf5bd at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If it /j- cg1rr.jo r5bm)4*stytfo s 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 radius eixj mz .f4 piw+x0,)d)h(sc+ wnnyi; 77 m on a flat road if the coefficient;shix 0n+x,me4fjiy))d.wi c zn(+pw of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and thenr coi6) b,h,v (tobjdj,p5p3 road if a car is to v6bpt3p od )j i5 ,(hjnb,rc,oround a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots iv el;;y ywa 5cj:4-ttws designed to rotate a trainee in a horizontal circle of radius -4t ; lwejyy:cw;a5 tv12.0 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 xi k 85(ftje// tpiz.dturntable 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 pk //td.i(it 85xzjefoff. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must aj:e*oz*2;w b + sr 4l/d2ji b/*iawf v4fgyvrm roller coaster be traveling when upside down at the top of a cirmj yw:+24/flr vb/ v;zw jgi4f2s*io *e*dabrcle
(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)3z (pb4+xzfdt p ip7,p crosses the rounded top of a hi37if4x dtbpz( ,+p pzpll (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel ,hxl8t/ur;j x7wjjd+need to make for the passengers to feel “weightless” at the topmost ,tuj x;w r+ xjjlh7/8dpoint?    rpm

  A bucket of mass 2.00 kg is whirled in ne2+;hwll(.lmmsl x9hmt/o j0l 77 rra vertical circle of radius 1.10 m. At the lowest point of its motion the tension in7/ll;xho+mmh en tsm290 ll 7rrwl.j ( 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 ifk b7c uts4i32fyv 1wi0 a particle 9.00 cm from the axis of rotation is to expertcs2i4yw7u0v1i kf 3bience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled wjnjhp)a)+oo jt.f (-/ jrny+ "room." (See Fig. 5++nwtj p )j.j ho-(yor /fj)an-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 al lvvi,. q+2ssdq2d+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 ) through a cent qa lq2+dvs +v,s.2idlral 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 weight of the bal0f01.nadtu v q+ w9vrfl which revolves on a string 0.600 m long. In particular, find nw tad9ff. 0uvqv+10 rthe magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of b0ptyor qf-,zq)dm-- 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 masses :0)ohyz7 jzqawi xv.8$ 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 vep;sx. n1ap.cq rtically 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 nk x;)n kw .n5v dbhqwpbt;xvmq /i*550et force exerted on the car (by the ground) in Example 5-8 whenk5dwbxqi*nw0p/ b;nx)vk5hq t m; .5v 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 accelp1jq- wl+.-c ri zzgu+iv( p8gerates 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 ha-z jgicp+zv-1q i(p8rl.guw +lfway 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 with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m .fw7rkq q-9xfs.x,fu*ww 4j d9 At a particular instant, its accelera 7d,kwr *s4.xwwxf9uf qj9f-q tion 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 gra5ut+q iibfs;-ylph8yt i 1b )4vity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfac8yb-isihb)t ytl;uipq f145+e if its mass is 1350 kg.   

  At the surface of a certain planetm( (xz9 awmhuf5 t-2dm, the gravitational acceleration g has a magnitude of 12 u mf 2mxwhdm9-tz5( a(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;f 9no9 bk9gmsys ta z4p4- sqx+(e:dq due to gravity on the Moon. The Moon's radius is 1.74gfbt -osz:+pa99(;q qk9m4 ydexs 4sn $\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, but has the same 3 nj.j1w ,vn q1ikee9( 4fmynv2zvmi8mass. What is the acceleration due to 8qeznvnjm9y 2i(n .w341vfk 1m,v ie jgravity near its surface?   

  A hypothetical planet has a mass 1.66m+ u;: ,7g66yyvvx aft vp+iwn times that of Earth, but the same radius. What is g+vu 76 g;wa f+mxpty6:invv,y near its surface?   

  Two objects attract eacx,:dvz 8 svmr.h 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 value of g , the accmp6gqi i3npvuo:m4x(2uq9w2m1 zn; h eleration of gravity, at (a) 3200 m9:uu2p6wpmhmno4 ;v3ni21 qgmq (zxi    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsgcz43hasu8 :yl) r;gpide the Earth where thegravitational acceleration due to :r8gz ly c g3)4;sphauthe 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 packeyhvp8 up oku /;wp /pa2f;o(+xytg 4o4d into a sphere about 10 km in radit4 wk+ah4pfxpoy 2 y8 u(//vgp;poo;uus. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wl(1ke dlhqu(:as 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 th kul(l( d:e1qhe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel wt/:h m4 9tdqyx,k ht8ueightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Con:tkdhq8x t9mt4, y hu/vince 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 hk x pb02pnb1qc;p6 0na square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onepc2hb0kx0pnbq p61;n sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets linegm h d hb03,t4;v;+lmnv 6htfj up on the same side of the Sun. Calculate the total force on the vgl mh3,bh0th+4jfmt; 6v;ndEarth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 l wv w )nl,..q2p0lq3o)o okzaof what it is on Earth, and that Mars’ radius is 3 lq).3waook0opn) lzvw q., l2400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eartl v2p.dvjr; 3hh and its distance from the Sun. [Note: Compare your answer t 3vp2. dvrlh;jo that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular+p t.dhy-s 2 je7pd9wb orbit about the Earth at petpby h2d+.9- sdw7j a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km 4irq br79p m;nabove the Earth. How fast must thr 7rip4q9 mnb;e shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa)wjx ujy9ow(k6x0ei 6nts are to experience simulated gravity of 0.60 g? Assume the spaceship’s dx eo9i0)6jkww (ju6 yxiameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for 1 bklos( +;+x0 hvlv 3wcrjm8ma satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is ve; w01vl+l xjv8bo+3rmcs(hmk ry small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity11xz6j 1njy lc would a satellite have to be launched from the top of Mtyn1c1z 16jjxl . Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to or7lo. lh j7e7izbit the Moon at an altitude of about 100 km. How loei7llj7ho . z7ng did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that u3l )jjktqy73orbit the planet. The inner radius of the ri3y tq3jlu)7 kjngs 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 diamet, rv* 4)b x2hor*innwqer rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparenhvnr2rq w)4x *n o*ib,t 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 center of tht;sa45u-bv* l6i )fw)gnn ysgvy gs eh0,w(r:e Earth's i)yh( sguw5 feg*t yg a4s ):bvwn0-n,vs;r6lMoon in a space vehicle (a) moving 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 o55:vg1zube-cc ec e k;u:xag3f two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point mc c ze:c5vg u 13eegxu;-ba5k:idway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for ek3 x. rup2m+gthe weight of a 55-kg woman in an elevator tharex mpu .kg23+t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cor dqbk0n*uml tygs cd/zkg v0g6:+f)04d suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates.d:+d0f/y cs)l z kv0uqk gg*nbgm60t4 What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pln zr;p5m. laa.m6tv4kzd y( o7anet with period T , the density (mass/volume) 7v 5. r; maznlyt .po6dmza4k(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 dg djuk w-;m58j) to determine the period of an artificial satellij dw-;8ukg5mj te orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbit/ghen5 e4hyqs:(+e xxlxed8 zna z 235s the Sun like the planets. Its period is 410 d. What is its mean distance from the Sga ehlenxzy(5 zn:/xdh2x8s+ e5q 34e un?    $\times 10^{11}$

  Neptune is an average u9b) vi3m tetb7m7xx-distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 7 e:2e i aud/v1hkb53b zbkc k5;2vegf76 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 sum of the nearest and farthest distance from the Sun.] hv22be gduez5;f5/cb v: 7kkbe31a ki    $\times 10^6$

  Our Sun rotates about + hojo* u sz ou16h.ri)fd:eyv 3ief99the 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, pebt*o1i7grxar:jl1. 4dxd k-z riod, and mean distance for the four largest moons of Jupiter (those discovered4j1grk:.* -bzlxir dax 7dto1 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 Ehrnwpr; z;z38 arth from the known period and distance of the Moon. rw z;;rzh38p n   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mo(bvf2 rhkqb*dd/qvvf37,m 9 j ons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabljqh/3d( v*,kb9dvm qrffbv27 e.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and 3crvku :-k9s un 5k.caJupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but wa3s:v 9ukn cu .-a5ckkrs 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 describee27tj 9lekn:pw dm:j;s an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quicklynk9 jmd :7te;:wp2 lej 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 gt(8zom53tpt x orge 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 mass is 80 kg, and thxtt 58 m(z3tpoe vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of graviagnt 6x6gx 8.zel)9qn /wuhlq q+ a*u8ty be half what it ia*e/h89 wug x t+nqxg6)nz .8lqu6alq s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal ma9a3bnq04yej t ss grab hands and spin in a mutual circle once every 2.5 s. If we assume their ar9yt e3njqa0b4ms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appy-i2qlwq2f r 1arent acceleration of gravity at the equator is slightly less rq iq2w 1l2-yfthan it would 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 wi +,t0dcm;oln tll a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moo+doln;ct 0tm, n pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when 8vfw btayuk :24xm7x4you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of th2av4fu: 48 yxm txb7wke elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboutnmj),d-9f b(h, sn oepn f8/fl 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 equ (ef n ofl )8mdj9-ns,bfn/hp,al 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. 5–4 f,j e*qk/la0 kfc5xxd)n,xl-/;nsuy 3).
(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 iy9ml di+ 9nfo/16ml2hv z5gzin terms of its radius r, the acceleration due to gravity at its surface and the gravitationamolyzl h+d6m/ni9 951 2ifvzgl constant G.

A plumb bob (a mass m hanging qgp*pz4x; ai/fvk7 7don a string) is deflected from the vertical by an angle4xpakv/ ; fz7g*d7pq i $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffic n-wrzphd;;p vpb .0,wient of static friction is 0.30 (wet pavem;bnwdr.pzv,;0w p p- hent), at what range of speeds can a car safely handle the curve?

  How long would a day be if thefixx,)vq *xz 4 Earth were rotating so fast that objects at the equator were fxi q4* )xxz,vapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constac tnp5z1) o-fjnt 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 constantp6fns 32ake g 19n-gwtzfhs55 speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swin2nzspg55f t nafs6 -k31ewgh9gs 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. Thu +7t ci696;pgoylc lx4pw zx+es, 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 expe9 xpe4xy76;pccg wi+zt6+ollrience 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 Telt;k-j 4 zagmelx66a9 , y7nswvescope deduced the presence of an extremely masvg7y4a;s,m9 wn6 6j- xzltakesive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 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 jq 5cw);gub7wxn9wa xb *om9 /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)n w;cg59 w7xoj*buq wx/ mba9 acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilibsf: rl4/jtg.ln5z 2rzes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these tlbrg2 4z5/lrjs: .nfsatellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous fuzquev++dmtn(/ (hvu; jd)0(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 (d td0j uvuvm;q/+ hun z)f+e(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 s 2g*s73gq vpr/ ,nrzoiatellite in need of repair. You are in a circular orbit of the rgr/q p2vz3ni7,gso* 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 period of 3000 years. (a) What is its meank:6a-htk p1c 8dtxb83kiy c /a distance from the S:-kh8c/6akpk3 ta b 8xdcyit1un?   
(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 actuallyfp kzu+12g7sclo)t7 *ot+nun "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptionsc+nf) 1k77touu2gn+p*ls to z , like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fi96 9 w, 32zluhy4gq9wu bc4zjp gj9crcg. 5-46) at a distance of about 30,000 light-yecw94bc c 64jqzu93 ugp9hz,g jyl r92wars 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 a2+p ;dtfxqya ls0 h(2on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bq(l a;syd+0a fpx2h2 tottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eam -cy5b76p xhuy. :5dt tljky2rth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-lo d8mw;ph1 c2dnlblf: 8ng sweep second hand on your wrist wa:w 2 m8dpbclhl8d;f1n tch?    $\times 10^{-4}$

  While fishing, you get bored and 5m)7kuf53njxuv*;.wpq t bk fstart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cirum7vkq;5nj) wf.*tpx u 53bkfcle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that au *sngs5r:*b zmx :e*s:qlzbt)5t. jb car traveling at spe:smxrzn5bgl tb*t z **eju5.qss ::b)ed $ 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 nbnj7h+a lremlg3c s oldjf /:-4x2*), 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 exper-blcjn* 2ma +jlsndx/rel:4o)3gh7fience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$