Sometimes people say that water is removed from clothes inx9r7oqc1zl7vp4 tuy , a spin dryer by centrifugal force throwing the water outward. What is7 tzxly79uq4pvr1,o c wrong with this statement?

Will the acceleration of a car be the same - fl1o*imtrf +when the car travels around a sharp curve at a constant 60 km/h as +fr-f*o imlt1 when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exuzlc65 db7o5 utqq:wviy.s 5pkf9/x1 ert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on aos qcl95zq butywd565 .pu1 kvx:/f7 i level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse osr(e a und6s/*n-y e-u mqpx*;n a merry-go-round. Which of these forces provides the centripetal acceleratio npq m-saueyu*n6x(ds *e;r/-n of the child?

A bucket of water can be whirlh.z.ie,m6a* ous,,j bqj kx1eed in a vertical circle without the water spilling out, even at the top of the circle whenm ab o6.jkih,qs1 eze, x.*,uj the bucket is upside down. Explain.

How many “accelerators” do you have in yolx(bv z ,wr-e-ur car? There are at least three controls in the car which can be used to cause the car to accelerate. What are ,-b-zwv (rx elthey? What accelerations do they produce?

A child on a sled comes flying over the crest of a p: a28x/cdfsx5v cgs( small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the no /xva85xgsc(2dps c:f rmal 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 inwar d-pbca eq9wm)i yl/186:gwlr d when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you come 5wr.xc 4vlu5pute the banking angle given its speed and r.5x4re 5lvwuc adius of the turn?

A girl is whirling a ball +ra. doi90z:8jf 9panzg s(e ;2 bppcnon a string around her head in a horizontal plane. She wants to le(p ;zg2acop . 9+0fisn8ab n jr9epd:zt go at precisely the right 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 grah,ge ru/fl- kv 7c-; +n;wm9me/ewu eyvitational force on the Earth? If so, how large a forceehy kgv -umeewm7u- r;n9,ec;+ lf/w/ ? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wprmp.urj2 7vnnb ac,p z:-ap5wb2(k2hat ways would the Moon’s orbit be diffe7(-j 2rcwrzpmbvb nuk.2 5anp 2p:pa,rent?

Which pulls harder gravitationally, the Earth on th6i-4jsg o,dq*osk+r vkm wo:2e Moon, or the Moon on the Earth? Which:ks,46gdoq-oi k w2moj+ *vsr accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet+lg4*ddq 1rkzgv+ zx 7wf/q r+ the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.+ gwv zf q/+gdrr*xl7z+q1d4k ]

Will an object weigh more at the equator 2v jk46rl joq( ayr-;eq ;.tlqor at the poles? What two effects are at work? Do .lo kry qjel46q;jtrv(-;a 2qthey oppose each other?

The gravitational force on the Moon due topgs g10l gz0;-xr *j3yfw :7gtvi8kgx the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled a*3xrtgp gk8; sy01jw -zil g:xfv 7g0gway from the Earth?

Is the centripetal acceleration of Mars in its orj c rha6.98xckbit around the Sun larger or smaller than the centripetal accelera 8.6 kjhcxarc9tion of the Earth?

Would it require less speed to launch a satellite (a) toward the easlj1oag5hs88 cg)).vcfp 23dcnlj pc/t or (b) toward the west? Consider the Earth’s r. c)f c dnjcg/135)ll8pspgoa82jcvh otation direction.

When will your apparent weight be the greatest, as measured3 vwyffs+z 70a by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates uy0 fwf3 7szva+pward, (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 rw;ysl)ft0r 3 j3pm8abrx-5eby weightlessness. One way to simulate gravity is to shape the spaceship likewxraj;-brm3 t 5p rsyl3 f)80e 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 you can think of.

Explain how a runner experienc(b *o 012qg)pd hrxgvxes “free fall” or “apparent weightlessness” between steps1)xgb0p rov(ghd x2 *q.

The Earth moves faster in its orbit around the Sun in January than in Jul rr6o y9bs9e9py. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not6eb9o rsrp9 y9 much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was npg(km:mz w.+2tv y8yr (z/dohot known until it was discovered to have a moon. Explain how thi/m(k2hwogrp +yty vz (m8.z:d s discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than they // at 0tbbvrmp4f69t Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the cent a /0bprb tv46yft9mt/er 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 yglo82*zie/if eh (gpwz7c(; $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 bwb ;prw1q)-oy 5 nc2sthe Sun, and the net force exerted on the Earth. What exerts this force ow1bs;c qrwn) 2boyp-5n 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 exerted on a 2.0-kg discus ap03 uz3 ucp;4ufxge4ts it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discu;xzpf33 4gp4et0 uucus.   

  Suppose the space shuj l8+bxajxx,ka,v0 .ddspvs) , 0 mcb0ttle 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 shuttle in its orbit. Express your answer in terms o8xc, vjbxx+v0kdjabslms d0a. ,) ,p0 f g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of ck ud(+c .z8mwglay on the edge of a potter’s wheel turnindwm8z(+ kuc.gg 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 vertical c ef3df*z*5 xacircle of radius 72.0 cm , as shown in Fig. 5fa5dxfc3e **z-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can roundj 9 j g (aewb8sh0n/lueqr18bw;,epl9 a turn of radius 77 m on a flat 09e9( bjbrq1ape;lh88 ,s gjwen/l wuroad if the coefficient 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 frictioq( hy4t/x d6vkg2 v9o-dkx1csn be between the tires and the road if a car is to round a level curve of radius 85 m at-h46kv9g/oq 1cs(kxvx dt 2dy a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots 73gc9o6wr cwhzak :1 sis designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 time3rwc cas9 7:kwgoh 1z6s 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 tbp0aqf ,4vorr h4/f,jhe axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coij,4f0b,prqr h a fvo/4n 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 and the turntable?   

  At what minimum speed must a roller coaster be traveling when up hkgln ( 149*m9 rx/ysmz.xyf(mccqg/side down at the tofq*mzygmk 9(m9x l1 . ych( xsc/4/grnp 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 roun0 jcen:4t84biofrd 8 67qmvfl ded top ofl7:fdq 8 e64r0im fnvb4tcj o8 a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to 2ux5y fza*kr7make for the passenge*2 yfxzr5k 7aurs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kq11s.eg x7 aki9s dvs3) f:luwg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its moq ixdv)1w . gesak u791:ssf3ltion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a c ca3s*j3 j4qk-r9,aa2ati qlaentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an j*3a ta9aqral,jq 42 c3i-k saacceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people w,:q ap+f)lop are rotated in a cylindrically walled "room." (See Fig. 5-35.)l p aw)p,fo+:q
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 rotaifl(x/n m ;6(kzk/ucrhd 11yu ted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connectikc1z d6lmy //uk fr;ux(1h n(ed 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 timekfh(3 jgynb.i1o 1 ey+, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In jn(yg iy.eoh +1bk31fparticular, 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 of 88 m is perfectly banked for a car traveling 75 -p v)ku7: b emew98:(srkp nfw$\mathrm{~km} / \mathrm{h}$ , 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 : hvlmy3 w5dj8$ 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 d:7lsi 9g6qa -c). dlyss gnd8living 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( re(;k h 9mg*ayapsy9 exerted on the car (by t y agk9a;phm((res9*yhe ground) 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 frl2kgpu(ftv6 . om 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 with no slipping or skiddin lktfg2v.(6u pg? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 me+fh+t eq8dop ;ca41b . At a particular instant, its acceleradec 1pbh ateqf;4o8++ 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 gravity on a spaczz fgoy4 iv9 mmo116u2ecraft 12,800 km (2 Earth radii) above the Earth’s surface i 1m4zou6 g9yvf 21ozmif its mass is 1350 kg.   

  At the surface of a certain p- 0-znzv nk3(lt fm(wdlanet, the gravitational acceleration g has a magnitudm -fv0 (zd3wz n-t(klne 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 on the Moon. The Moon'sv2aa1(5uc/qgat8 15dwc slc x radius is 1.74 s 8ccaw( u25d1q a vg1axcl5t/$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hasepf00s sela ygbx 4t4ih 6,7a0 a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to glst7 0e f6s hg,iae4b0y4pax0 ravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but n;n8sm/c+o mq iah2(am ygu;8the same radius. What is g near its(qui;oachym gma28;s/m+ n n 8 surface?   

  Two objects attract each other gravcxg.br/52ge( i) mn)jhs i .lqitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200g j0t 1aa*rrsfkp/6c a(y /ciyn2,j )s0gsuf) m n(y c u1r0fj0,j*t2fi/sasyasp6a)rggk)c /   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wh4zvm p 9suuhck s23r)e9gnajn z c3,-9ere thegravitational acceleration due c u2em gps99-,cv93su z)jk4h nrn3azto the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of8:q q wzb bkra63cy3v :jel,(z6qk6hs our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monste(zkq8 hzrwqbyl3:qb6e: svk6,j ac36r.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun fz / nuqx3,zozwkasbm3 +: *po.;swy: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 surfac f:ambnpw.:k * +3xw z/zu3qzoy,os s;e gravity on this star?    $\times 10^7$

  You are explaining why rg5y2 0ya*lw fy 1nf0aastronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker y0l2rfwyn*a 1y5af0g 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 cornerx 6kmosd, -+ v::watqgk 6f5xss of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thre:taxd5-sv 6 g wk,6s+xfm: koqe.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yeal jevn)e3-gpyqkgbu ot,.6x((; fj 6r03radjrs most 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). Tegqe-( uypk)gl,abrj .0xjr6vo t n(33 fj;d6he 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 gr)raajvww9 q* -( 7zsolavity at the surface of Mars is 0.38 of what it*(z aaojwl w7v)sq- r9 is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usj- jzv u1gls)xmy6 nkoe7ir.+u 7- 86qoxk-cying the known value for the period of the Earth and its distance from the Sun. [Note7um-y-.)lxzx- jcoqru yok861si +67e gjkvn : Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sat z61pjzpsait r* 0c1s2ellite moving in a stable circular orbit about the Earth at a heightst s0z11azjp r*p6ic2 of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abekhpi 9c12onlh: *pt4jal6 r2ove the Earth. How fast must the shuttle *e: 6jp hcpat9r2iokhnll41 2be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate *iyq;ql/0fr7w c 1mvvif occupants are to experience simulated gravity of 0.60 g? Assume the spacesvl;r1m/qyfq v0 7i* wchip’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sateleeos rum;5 +4;xsc7p dlite 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 very sme;ue d74;os pxs+m5r call compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal veloge3(im41, l20lkjwp* v vdr8 dpesb9a5gsm *xcity would a satellite have to be launched from the top of Mt. Everest to be placed in a cim a8gsv,0x(w4e djp9l3sbirdm*k1 *pe 2g5vlrcular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbgc fmbc l.er5 +r00rezlt)0p1ut/ux3it the Moon at an altitud+fcp0e)l1b.mtlcx rgur005e tu3 r/ z e of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composer+ 34dwj+ neg-srn2 p0zxkd3fd of chunks of ice that orbit the planet. The inne pjgdznxkfsr4n-03 w32 +d+err radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once evez8 2f gyyz:ym:ry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (bz:yyg:m zyf 82) at the bottom?
(a)    (b)   

  What is the apparent weight ofti1u (,lyzjx 0 a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constanuy1 ,0(tjxi zlt 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. The.hmwtk54jsu ch pycl5g.y+;9 y are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway b9h5uspjm+g 5 y.y4lh.;c cwtketween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight osumv(q yu62wv rhs.s2dr v9a1u)bq/)q -i r-cf a 55-kg woman in an elevator that wciya 2ds qb vu-1qhmqrr-u( 2/s)vvu r ).s96moves
(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 corb;23)rk hmz.cjm i j,qd suspended from the ceiling of an elevator. The cord can withstand azm.bimjrkjh2; , 3cq) 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 sur y3pva7*ftx 4yoe0gy+ face of a planet with period T , the density (mass/volume) ogpt yv+4e3 a7fxyy0*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 per.yk4 lbxq*y6 niod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’ q bylyn*x6k.4s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitsa4s z*q0a*-d,0fxfd yvmr7 dn the Sun like the planets. f ymz00* ,f7*-dqvd sa n4xradIts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average y2*yw,. ll5nz:c 2u : q(/mo tvzfvw-nrent3cdistance 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 ev1 7.sirj7n kvxery 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 neares 7kjv.1x 7irsnt 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 thdgz2 gh rjzrkturhy6- )sj,:o0 f356r e 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, period, an0zk0 jbisx4b .i3.n xcd mean distance for the four largest moons of Jupiter (those discovered by Galinkx bi3. ji x40bc0sz.leo 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 fh ;.mvw h/pwi: tf3c/o,dqe; srom the known period and distance of the Moon. /,3ep;.iq shwmfw/vcdh; :t o   $\times 10^{24}$

  Determine the mean distance from Jupiter foul 7co gnwzs4oja;b- ;.:xq +er each of Jupiter’s moons, using Kepler’s thir o-olxw.zcna :eu;gq+7b;4j sd law. Use the distance of Io and the periods 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 between Mars and Jupiter consists of many fragm h wf: n-qge/of:*hfw+ents (which some space scientists thinkh-n eq +hgwfw/fo:* f: came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planetayvgmcc-m- ;m 78rlb8" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity ofc7 mg 8vma-m8crl-y; b 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 swi)kw(bvtq9 j6m,u (5 ja0cp tcxnging 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 mqvxk9 cb )(t(j5,catj0u pw6his 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 what vw8)(o ziqu4g8an y(q8bsa-v eorj5/ it iwonur)i5 v(jaqa4/8(bvqy -88go esz s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gravcsu yr6 pq9*zpo3+(zle 1cn, b hands and spin in a mutual circle once every 2.5 s. If we assumen 93cyrp pv1+q *oulesz6 (,cz their arms 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 +z-*tbpl27hfe (ed 1iv7 uimv per day, the apparent acceleration of gravity at the equator is slightly less than it pzv+e(b2 v-*lt1ei77udfmi h 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+ n1qk:p(l9ibgxb yi4 ( igs8a will a spacecraft traveling directly from the Earth to y npsl+ x:(ibabgi8i91 (4k gqthe Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whz 7uii:p5x 9s+(nlpyt en you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelerat(il+y75zup ns:tp 9xiion of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that.o 1+dosplak7rl:j*5 kcuil- 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 (revolutiop .o:d 1+-ousjki75*rkl callns per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical l-(58heen i95rk7030 exxjk iad pw ebroop (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 planeti.g34u +u -ryp2bzvm z in terms of its radius r, the acceleration due to gravity at its suri+p. 3m u-grbuz v4yz2face and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defleu8 55v5toqo :mzbku77l u;nr acted from the vertical by an angle t uaubvm : rqnk7 55;8z7oou5l$\theta$ 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 coefficiegnab02om,oh 7 :2oe bntkm3k 0nt of static friction is obhomea,og2 t0nb 073 mnkk2:0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectn dm):, f3baybs at the equator web3 afby:),nd mre apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di l/lg;gz c2x,su6huw *stance 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 spe( +l+d2+vj qcbq -takmbn.d+hq7;hr ded rounds a curve of radius 235 m. A lamp suspended from the ceili qnjtcq- +d( v dqh rbd+2+.7bmkhl+;ang swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been clai3 0pqklr-cus)med 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 s r0pc)k-u3qlperson would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extrexqb ujs vw(,+5mely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting thwjxbq(v s,+u5e 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 itumka+xweuu 85 ;6mfv 5 traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. m 68uf mk5uw5;xueav+(c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a v rp*4 :s, yxs+ki( olfmmuj02group 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 navigatioo2i4sm0s:x ,m+k(vj *frly pu nal “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 trjx dmu-62vp7tzk df; .aveling 2.1 billion km, is meant to orbit the astdjp;x- .utz26d7kvfmeroid 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 the space shuttle pul6 teieh8xv-s4 .xfq -rsuing a satellite in need of repair8eqvtxl s-- . 4ixe6fh. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a perio n1ef+1. vif hjmp.7cu8v.bk7ldgu b 2d of 3000 years. (a) What is its mean distance from the Su17n.fpuhb.ei vg l7 mdj 8f+1b.v2kucn?   
(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 o:4d,b mxhzqvtwi;1 zoa :/3 oef G would need to be if you could actually "feel" yourself gravitationally attracted to someone:di4e zoot ,wvzqh;/:x31 mba near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the4v3nm 03n/xr kbgwss2 Milky Way Galaxy (Fig. 5-46) at a distance of about 32n mvbw xkn r3sg/3s040,000 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 corners of a square 0.50 m on sn qe5bfdo (u1 ig45)teach side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg )dnfbqg1ot 4i(55se umass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eo/ ic m1vxm;b)arth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep seco(.o;-myjv9rxk+g y mkqpcgx6e5/ t )mnd han e m-k9xtpgv)6kr cx5mgyjq( y/o;+.md on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to px6(3ma 5wxp01lnrn dgeu, h.swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing lwmr5 ue,ann 0gp.3d6l1x(x hpine makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway 2cgzso ,5+aem is designed so that a car traveling at spee,s e2ga5omcz+ d $ 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 when1t p 3b 7zoj ak8nc:5j tto85.kqew lpv15m7en negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed 78. kzqv5l: 5ott kj 5cpoennatp1bme87w 13j 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.$\approx$    $\times 10^2$