Sometimes people say that water is removed g)yi;s 7,sg+vv; z ly5u:a bjtfrom clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stat ; :tv7si;bgla5)+vuyyjszg, ement?

Will the acceleration of a car be the same when the car travels around to dh9fcy 8i+*,ct/iqa sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expla9yqf,t/ti8od icc h+ *in.

Suppose a car moves at constant speed along a hilly road. Where-7bqedu, vekm7r/ a+q*5g m8+ 03pi hnncy kkj does the car exert the greatest and least forces i3+7/,np r7*cmeaqevn8b-k 0m k k+huq gdy 5jon 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 h:5a/sbqzc3p8c: dr q dorse on a merry-go-round. Which of these forces provides the centripetal acceleration of the child:/pcdasqrb 5 qcz3 8:d?

A bucket of water can be whirled in a vertical0g)e fdw9 owsbw ;g lde*3wh(0 circle without the water spilling out, even at the tf0be lw)3*wd9w( gwh; 0sodeg op of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contrhcw/ +(ebr 9e /bbvbm)3 j lohjwtd 36dbw87.nols in the car which can be used to cause the car to accelerate. What are they? What accelerat3oj(.bc8b9 )7ndetj/hwh rlwwm36+bbb ev/dions do they produce?

A child on a sled co37:h ljt01uub sm,wrjmes flying over the crest of a small hill, as shown in Fig. 3jr bjsum lu,w710 h:t5–31. 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 the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward:gcr 3kfd2vr9 when rounding a curve at high speed?

Why do airplanes bank when they tur)xrw5(c()xsuh/ tmog n? How would you compute the banking angle given its speed and radius of the tur csg hx/(t(mowrx u5))n?

A girl is whirling a ball on a stribyr4/gzwkn*q1 p6 y/ir 70htpng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ba6yh4r/7g0k qp y np*b1t/z rwill will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a wpi;i 82i; rsp/oc xtpc d629tgravitational force on the Earth? If so, how large a force? Cio9tdic ;22;prp/6x itp8sc wonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wayflp(k/ , b(cdps would the Moon’s orbit be differ,/(klfbpc (p dent?

Which pulls harder gravitatio)ynh9o,nxa5 q0fvz x:nally, the Earth on the Moon, or the Moon on the Earth? Which accele) no0,hnvzx 5qxya 9f:rates more?

The Sun's gravitational pull on th8i a5yrew.r ai1ec 5 .ujuc9(kjd/o)q e Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: .i1au ) o a 8.55c 9j(kiycweurqdjr/eConsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more ad4fs2 xw7sjs nh)57wat the equator or at the poles? What two effects are at work? Do 4ws72a sdw7hjsn 5 fx)they oppose each other?

The gravitational force fk35nl +0h vz2ffn ewrg;tg)j lo;2s/on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the gel n) h s2;5t/w0 ;fnvr3jl2f zg+fokMoon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroundprrhg4aj1-c fg c8-(/d v/ppo the Sun larger or smaller than the centripetal acceleration of tcj/4(fv r1p a/c8pdgr op h-g-he Earth?

Would it require less speeq(8zz8 jp .i 9c7ihneqd to launch a satellite (a) toward the east or (b) toward the weq 9jhczpz8qei.7i(8n st? Consider the Earth’s rotation direction.

When will your apparent weigc)7dbd 5y/ huzht be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downwardczh 5ybu7)/ dd, (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 outer space could be adversely affecwpf9 l:wuqj q 7tu1e (y8 (cpcjm(;9trug(tq)ted by weightlessness. One way to simulate gguj(; 9p( :ccqyqtqu7t()jt muew f 1w98(rplravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner 3uv)p7pm8q kc experiences “free fall” or “apparent weightlessness” between steps.qkv37)pmup c8

The Earth moves faster in its orbit around the Sun in January than in July. j2c*5bi ffh2;e ylkyrb . u)p3Is the Earth closer to the Sun in January, or in Jhe b*5p lib3u );ykryf.2c2fjuly? 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 plane of its orbit.]

The mass of Pluto was not known until it was discovered to ha8 8yjx1c(oty nve a moon. Explain how this diy81y ocx8 jt(nscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mooafa79nt3qgw/qq g+/f, 2an i.uic pd0 n's. Yet the Moon's is mainly responsible for the tides. / quf/7i2,n 3nqt wg0. aafpaigq+d9cExplain. [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 mg v.7od8yadt4. 2 soa 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its 0fg0 t: ku ng59bf*zyrc*sosk +q :c5xorbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a s+rqu:gtk c bc0z5ygof0 5fn* 9kx*s: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 yp,dqu0ow 6 sxesz3h :13nx5 lh7pn,cN is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the5,l,z3pqocu0yn3 pxn 7s e1w:h6sx h d discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, andy 4oqjlk4,:lc circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in iqkl4,c l:4 yojts orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the adh1,fhj pu bv2rso:;. ck+f.occeleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revop 1bh: uocr h2f.df,.s;ojvk+lutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a st*rwlp ic1dx ,z5g5wq(ring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its xgclpz1id5 5*r,wq (wspeed 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 spelbm0t0/tvfa r i030d8n m9baced with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction betl a9 tm0dcmv n btb038ir0/af0ween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction+r:y k;oid(*xldl m(6ffgu ,f**w yof be between the tires and the road if a car is to round a+ ,(ff fyo;*6m* *dflug (xorwi:d kyl level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is de 6v,o 9aklpaur*7d9*x:z an;:s ynj pwic3em3signed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by thepac3 mpl9s wi y7n 6;x :v nu*:*o9za3adr,ekj 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 ;yjk)b:5 treegb0wng/ :*eupaxis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin:ewy5 /jep)*0 ugbn bg:;k ter slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must fozc y 0t9hi/bm* i6eals7j p,2i9n8fa roller coaster be traveling when upside down at the top of a ciry 9n bifpsti/z e 6*0ac ohi9l,j2f8m7cle
(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 kg1pxqlrh u(4+ y (including the driver) crosses the rounded top of a hill p4r y+xlh1q u((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-diametefby /jgsi0 4d7r Ferris wheel need to make for i jb7 g4s/f0dythe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled iiv vgxo, )s+kmb0r+ m6n a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket isks+xv ,o0r6 g+)mvi bm 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 rotatewjp (,n rvpc)5 if a particle 9.00 cm from the axis of rotation is to experience an acceleration of vjw,n(c)5pp r 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ared5ztl54m h4fp tnu 96p rotated in a cylindrically walled "room." (See Fig. 5-35.)4p l n46fu55hdtzm p9t
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 frictionless aiq6 d5 j4d*dyszgnst; )r-hockey tabletop, and is held in thistdsg) *5d4q ;6jzsy nd orbit by a light cord connected 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 timxpwx scc 9j2- ++ickk+e, by not ignoring the weight of the ball which revolves on a string 0.600 mpc ++wxc 9kc-iks2x j+ long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 ld:j:5sykf dp8 xm-7 zm 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 masses1gmq8 0qvgpbk/ j r4z8l+fu8o $ 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 maneuve78 shhu;zk5pe-+u w:iieq w1tr 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 tangentiikujs 92 ou *8n;m7xqzal and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speedzuk7;9o xmqjsu ni8 2* is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accet ceb i 8qx j6js3.3e*ix(z/vblerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assu3 j x iq6txbj3s.ibeec z/(v*8ming 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 . At a parti) *friyh-495zuy,e. esvsda xcular instant, its efzi yehyv 59*as4r,-udx.s) acceleration 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 E/nkh7irmdo l +b- ;an(arth’s gravity on a spacecraft 12,800 km (2 Earth radii) above thek-ao 7d;lnn (+bmih/r Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet,b r/kk /h,.naikyf 1,t the gravitational acceleration g has a magnitude of 12 bkna,k1 f.ry,/ tkh/im/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 oncv wgl/c- c1l6 the Moon. The Moon's radius is 1.7l l- gccw/v6c14 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timel q.;ird4j ub;s that of Earth, but has the same mass. What is the accelerab4;q .ui;drl jtion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the samqj0 1zsml/k8+ aq9s une radius. What is g near z+8a snqsj1k9 m/0uqlits surface?   

  Two objects attract eak/0 4h5 vcw;y8;jj29h3)8vt cnykzsf sli nvtch 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 acceleration of go*ldr29xf s c5ravity, at (a) 3200 m 2*rlc95fsod x    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the arztl1*y 6 +nnEarth’s center to a point outside the Earth where thegravitation+1l a*nty6 rznal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fi3v qcn,y- lxx9ef5d+g az(2ysve times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gre vnxzgla+2(c -d, 3q95yf xsyavity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b d1add vtn9 .ltc*o.z1ut is now in the last stage of its ev 1.tln 9*od vtdcd.a1zolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whigz a*c56 ;ylvyle orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that ic;vy5 y6*glz at 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 m. Calcvq:l3y ) 4v6yb f)ktxfulate ttx: y )v43qyk 6)fvlbfhe magnitude and direction 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 q,ivf +vv61 zs)y6d(zpvi 9 xkthe planets line up on the same side of the Sun. Calculate the total force on the Earth dus v6d6p fv9i, qxzv)z+viy(k 1e 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 7:l+qbs wtzz3the surface of Mars is 0.38 of what it is on Earth, and that M sz:7t3zb+ lwqars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knowuuh57kfitxlxzbsp3z 5x 2 n6+6pww+6n value for the period of the Earth and its distance from thh s7x35xpl z2t6wiwn+zb u66pxfu5+ ke Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about)m(v k+ ej( */ctz;6ydpbkynm the Earth at a heighykk(/ep y(cv6bm m;)zdn*+ tj t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circrd z7 h2 7hhpmu,,*qdz-ruo;gw8uu .ee4kee (ular orbit 650 km above the Earth. How fast 7heh-q,uw4pre duez *k,72;umr .gu dhz e(8omust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricf 6(+r(wt );gdduvhwkal spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diamwdg)t( k6uwh (;d rf+veter 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 fo*h(t-d*57.8am(fqx wdr (f ugdtr xy iu5l(lqr a 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 very small compared to *w5d8ga udf(ullt.q(7- i(h5tdy*rq x(m rfxthe radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched un7ggzb752i/:g nm zkyh5v.u from the top of Mt. Everest to be placed in a circular orbit around thek7 72y.gg nbuz/5:hu zvi gmn5 Earth?   

  During an Apollo lunar l3 i mtuq:,+selanding mission, the command module continued to orbit th s+:3l m,etique Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.cfy-.n4w*esi+xlq.91t ru l1 ozd s+i The inner radius of the rings is ss+u.1 o+i.l 9li1zfcy- tx*end4rw q73,000 $\mathrm{~km}$ , 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 diametel f.93ykbz3dg r rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a pblkyd. zf39g 3erson’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 astronaut4*oinm 23emha(gv x,.mc( twb 4200 km from the center of the Eagcm,em . t(w2h mx4nibvao *(3rth's Moon 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 of two stars of equal mass. They are b+ ssus v-g-:kw2 dm f(obl8v5observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between thl+bws(uobvk8vsm-fg- s52: d em. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elev0zrhd9 uq6 9 o yil.h(e2-.pb / :w;ypxnmxvutator that moves0/r;h6w 9izm.9 2xeh(n tob-l vyypx.q du: pu
(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 col7*ya6; ek6t ajq (b+zp:q ssord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N an:aazkt+e(sbjl ;7posqy6q6 *d breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbf ovnoqp02+w+tt; li oq 6*gql6eb 82jits very near the surface of a planet with period T , the density (mat j+opeql2ft i2 ng; 6bvq o*qlw0o86+ss/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period oe b2 i(7n02za:mhpof of the Moon (27.4 d) to determine the period of an artificial satelliob ma7zepf02h: no2(i te orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrossdh d+w-p8rxsa2mb), t, orbits the Sun like td 8+bpd-whxsram2 ) ,the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance n fb.z:ymk; 2m7skhm2kyt88 (1khky yof 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 t,z(1tta- v *pkmtlfjdnj7 6x /he 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 sum of the nearevl tp6t x(t 1kzan,j-/7mfd*jst and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gahsgjaq6b*s: f p(8 -yglaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 th+is m.i:-wybs e four largest moons o:wsbs+miyi . -f Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known1sj;x fpbta1 9mb+.1amb ll 9h period and distance of the Moon. p1xf+ 1blm;mhtsa 9bb1l9 . ja   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiterp 2h+bt;d;1s hrdcb.h;x i1lv’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to h.xrhps1t d;+b 2lcdvh1;b i;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 frag-/q;j+km-r nb z:y*tyxzhtn8ments (which some space scientists think came from a planet that once orbited the Sun but wm *thzkzq/8:+ n xnbyt y;j-r-as 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 "planet4*1 hg7sqdd ew orc9e9" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (whse 4r79hge*d9qo wdc1 ere 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 of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arokq0v+7k40z/f utyjk c 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 s+uv0o7f yk0qk/4 tjz kwing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of granc mknd616 *aqvity be half what it is on th1 *da6kn 6mqnce surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mu iua*b.4b u/pxtkp+z .kpt*7 qtual 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, how hard are they pulling on one qpz xikb. +*t7a*upt .p u/k4banother?    $\times 10^2$

  Because the Earth rotates oncprh:fkcj 2l,6am lt:vmc/+ w 7-ay cb1e per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Ejc lrhb,tc7:aal w2c+k y/mp:-fv16m arth 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 spacecraft traveling a 0zy3pw11vrn directly from the Earth to the Moon experiwn11r z0a p3vyence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bubeg,bt wst7m)8bq 9l3t when you stand on a bathroom scale in an elevator, it says your mass is 82 gm7bte3bwq 9l8, bt s)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 wil ;-7nesft s a5polhi u7*pxj8.l rotate about its center (like a tubular bicycle tire) fjsphs l8*-;. 5txien o7ua7p(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 be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4 fwpz y;r5c72ot,vkt 33).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of itne9zhff71 go. s radius r, the acceleratinef 9o1 z.h7gfon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string)bk r543kmv -06kmg tld is deflected from the vertical by an anglem rdlkg34vkmk06b-t 5 $\theta$ 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 th5mvdc hwdkdxl2;65 1n e coefficient of static friction is 0.30 (wet pavemen v5m1ch; 5d26wkx ddlnt), 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 t g y+ nnh-;za*vc3z.lphat objects at the equator were appaz-lng;c* n+ a.3hy zvprently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0p fuvba;j1+lfe d48x1 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of ra+dtq(+ 6 o1h+fqoehvrdius 235 m. A lamp suspended vf6 oqd(1q+rh+h+ot e from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claime/i9cv)l(4 iu qqhw,sjd 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 such a planet. Use the following datqq,)ci4 vsjhiuw ( 9/la 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 an3v,qzo8xt oa* pu-ud8 u:l7 dp extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed ofd83: -ua 8 ,pxotlqovdzpu7u* 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 hil (evno1 oep7kb42 v)x*anp6 hrl 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?)knpbv4o6 (2ve 1x)nh a r7e*op 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) utilizes a grhvd3)*qok 4f8 0mcvb moup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautic bmcvfd k*mvo3 q8)0h4al ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid R(d hd y6x0uj/*qpu xu6endezvous (NEAR), after traveling 2.1 billion km, is meant tojp* 6(qy0du /xhuux 6d orbit the asteroid 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 pursuing a satellite0(su4r)mg t ,l:nzku ju*ak 5e in need of repair. You are in a circular or) l,kgus*ez:( 0u54nu jtar mkbit 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 period of 3000 years. (a) What is its meannop s4c:h-lt4p (dc.jhm2p2yafx9 + q distance from the Sun (9htcj-s:2f4qp .hd py2xmnpa4l+co?   
(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 "fe+aq.0l /zfuapx+ )klbel" yourself p+l.qa 0a)k/u z+fblxgravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cjs0i5m f5dsw3 enter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centerwmid3 js50 fs5 $ \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 vnb) 8,jds/vc,m 3ih hm on each side. Find the magnitude and direction of the gravitationalds c/ ji8m bv,3v,hhn) force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ear-dv9uv en c7*tzcv bck*(,l7jth $ \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 k4 )w5 f4qjjby-kh v5xtip of the 1.5-cm-long sweep second hand on your wrist w4j- k x4)w5q5vfjy kbhatch?    $\times 10^{-4}$

  While fishing, you ge1yp dzgr 7pcot ,+f:r0t bored and start 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 circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [p +g,yofzp:t0r7 rcd1 Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiusm234 hjzqzzy6 d9s :ik R in a new highway is designed so that a car traveli9m dhq2i3syzz6: k z4jng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of thev2pht: kmc02e f0j 7od 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 no0kojpfdmtce02h v: 2 7rmal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$