Sometimes people say that water is removed from clothes iny4x 3 vr-jyr;l .bm yuxta5.1l a spin dryer by centrifugal force throwing the water outward. ;jl4 5xyxb. myu 1yrv.3lta -rWhat is wrong with this statement?

Will the acceleration of a car be the same when the ca89wm ue;z4mgfk-x e0ivlb o(-i aa 0*er travels around a sharp curve at a constant 60v40 wg i;ome 8e*zx-b0e ukaa9-f(ilm km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hillai3lth(qct;z/lh7k+i1t 5/-r etgd jy road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a d +lgat/ ;3qh7j(tci zlthi/t -kde 51rip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horsel-w nw7y7,ngkpko; 7 oacl)g. on a merry-go-round. Which of these forces provides the centripetal -n7kowyal)p c g;7 on7 w,l.gkacceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sp ;i,n, r cixben v2,q3fcwi1;zilling out, even at the top of the circle when the buc,3n;niiz qx ci ;2fe,,1rwbvcket is upside down. Explain.

How many “accelerators” do you have in your d d:rhkiat k,e;q ,yse/w .a.ld5ad2.r 4ipl0car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations dol /.whdeadr. d0sik ,a2q py.ek,5dtr il;a :4 they produce?

A child on a sled come. ej/6uvp+2 rbkw :oefs flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decreasejfbko2:upv/ew 6 r.e+ using Newton’s second law.

Why do bicycle riders lean inward when rounding v(,abh0r/az ya curve at high speed?

Why do airplanes bank when they turn? How would you compute thz nno6: 69l.pocu1 j xqaeg70ue banking angle given its speed and radiu e:ncqg 9 oa0pln oj761z.x6uus of the turn?

A girl is whirling a ball on a string aroune(p)yr nqyy( /tx+0jod her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she n) yx /rpq+(( tje0yoylet go of the string?

Does an apple exert a gravitational force on the Earth? If so, h/ r7zlb di557j85kd mcyfej4 uow large a force? Consider anfje/5lzk id5m74 u85rcy d 7jb apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double +24 y9r1+rqcpr 4lzsfe0 oslac(ktn ;what it is, in what ways would the Moon’s orbit be +n;pa+ll41zo f2rtc r9e(kc ss4yrq0 different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moonhn 78k uiww di4390he.ehrh7q on the Earth? Which accele id8euh3hhqh4 79 . kwnrew07irates more?

The Sun's gravitational u;( qg3-vtxrhi/o2poz ,9tqrq2 *cdrpull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hi pv hzq ur2q-3c ;ri(grd92to ,to*x/qnt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wh7sut.;r- v h,yguui6 bvck6p)at two effects are at work? Do they oppose each oth.c 7b- k6pi,suhgr6u;vvt) uyer?

The gravitational force on 8 9qdf( e9pm p/)bljo.di-klm the Moon due to the Earth is only about half the force on the Moon due to tml)kbi.9el-qpmdjo 9/f dp (8he Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleq y6: + zwq,lig(bbo(mration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleratbm l6qoiyb z,:gw( q(+ion of the Earth?

Would it require less sc60tjf(d a9qm peed to launch a satellite (a) toward the east or (b) toward the west? Cm dcqj 0f6a(9tonsider the Earth’s rotation direction.

When will your apparent weight be the greatest, sc3qve62wd y3 as measured by a scale in a moving eceq3vysw 362dlevator: when the elevator (a) 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 outer space could be adversely affected by rj5sguffa4e )rwi c*8r2r0v5gv2ng c y.6vb-weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts wal2j4egsg 8vgbr 6fu2vv*fr5ywr .) r0ca5c- inking 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 experiences “free fall” or “apparent web6n*clrkv / nw0ug;a5te/f fzb0 g /l*ightlessness” between st0* e;5 0/l*/ugfnt blag/c k zn6wvrfbeps.

The Earth moves faster in its orbit aro6lf* rm2b(o 7tei.fymund the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tiremtm 7y*.lb26f(o iflt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known u0+ , it ir97oyvmce8 n.6nqcghntil it was discovered to have a moon. Explain how this discovery enabled an +0 nqm.eor9cc v hiyin 6tg8,7estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger ngl9 8-- f k36n/wgets7xbe w7ymnyw)than the 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 center of a merry-go-round moves with a speed o we)/ 3kmslx87ywfetgw7nn ny b--g69f 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 n;e)tr4i-sbryq: ld a6 ;pn2f 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the rg1o+zsedjyp j /w77wr7:5/m9aa r smSun, and the net force exerted on the Earth. What exerts this force on wor rd p7s71m:+mj9 /rs/ae ga5yz7wjthe 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 as it rotates y,t5vgd9 xwqx uva 4)s)l:-ujuniformly in a horizontalt,4x)v g5dau:9vulx) sw-q y j circle (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 Earthz4+8k,(ytwe+ mq 5c,erp cyem 's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelek,pz4em,wy5e+q em (yc8r ct+ration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of am1r0u3 jqigaem4i:toi:5 l5 x potter’s wheel turning at 4mi 5rg03ia tolqxeu4 j:1im5 :5 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a /7xc m)ofnt;v string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33c/7 ox;)tmfvn. 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 round a turn of ra,6b4 us8atwzw:w n*8ce ,qqywdius 77 m on a flat road if the coefficient of static friction between tc6,ytu8qwz w8*esaqn:ww 4b ,ires 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 t1t8x) 1wcbujtires and the road if a car is to round a level 1 )txubc t8j1wcurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and je( /9jzqb.lkpq*i ; *xx;dfkxt t fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back isz .jxkkx/ d*9tf q*(q;l ;ixpb 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 9zia* ca)eu l.ijn9r4of 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 reazcaej.uar 4il*)i n 99ched 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 w;4d13ug kbyh)j:f)s ps k cl.be traveling when upside down at the top of a cir4 :wsb;fhk sdcu3k1y)gl)j. pcle
(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 jx7lu11h;y o lcussl0 10nmj/driver) crosses the rounded top of a hill (ra/y7u01hl1jcul0 o; mjn 1slxsdius =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 ,r442+ ytrj m6d1fzxnypn (sa-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmos yyra 41+rdx(2 fp,n4njz6t mst point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi7xd) (herurg p67, wil9l6 yvtus 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucke r6)uxdlhr6v(l g7e,t9ipy7w t 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 centrifutm24ny6ecz 43j gebm; +o+he bge rotate if a particle 9.00 cm from the axis of rotate+c2omt ezbn6;bjme h43g4+yion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "w harx :8rl -udkn:)y17my87)g lfaefroom." (See Fig. 5-35.) u)r x8fl:gn1r8y7d)ma: ehal7wkfy-
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 Mw:e+b6d/mm;tv5j )m i2 za,voecd*y e ) is rotated in 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 v6,e*e:jaw mec/bm)ty5d d2zv+ ; iom central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignorin6qpubkg- 6gp +g the weight of the ball which revolves on a string 0.600 m long. I+ pgg-k qupb66n 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 m is perfectly banked for a car t of.,q :nbk-irraveling 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 masses9*ankyis 62 bw $ 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 evasiv j.)f-u m(bqcwjqcr/.e8 on c3e maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripokr)p8a 7 *ml lk)cn,ietal components of the net force exerted on the car )kr lon7,)ampci k*l8(by the 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 from the pit area, going fr n(e p/lx+:*cd nb q2e;o,jufpom rest to 320km/h in a semi,ql nc+ of p*unj;p ebx/(d2e:circular 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 skidding? $\approx$   

  A particle revolves in a horizontal ur861:y21/ oduaz t qudm4peacircle of radius 2.90 m . At a particular instant, a2dt1o/ 84 uur 1:a6 pqyezumdits 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 Earth’s gravity on a spacecraft 12,800 km (2 Earth radii)z,ldf a(y+vi ,eq/(y9oyyfi* oyb6 g. above the Earth’s suy,glfq ie. ,dyf9(z *y(6 yyaivoo/b+rface if its mass is 1350 kg.   

  At the surface of a certain planet, t,rb n7,il) zsli/d s/u9sbv3rhe gravitational acceleration g has a magnild7//sr) b uzss3ri ,inlvb9 ,tude 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's radius qg(yegd dqpd/.vqe10/ c 3cf/ is 1.74gd/ddfv3c1y qpqeq.0(e g/c/ $\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 mz6mec rs m)t)*97t v7r*u: igm( gncdmass. What is the acceleration due to gravity near its surfi*u97zcrdgc*m ))gr (t m:smnv mte7 6ace?   

  A hypothetical planet6ac7nb o2tq::+y lj zz has a mass 1.66 times that of Earth, but the same radius. What is g 6l t72za:zjyqc bno+: near its surface?   

  Two objects attract each otn8k i47h( lpcnher 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 accelerat3w:omh,bcix 0) / srxk;(t clkion of gravity, at (a) 3200 mc:,x/ cl; i 3st bw0k(okxh)mr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr(7o +ivrai:*// 2ka7po9t jzvkbphatom the Earth’s center to a point outside the Earth where thegravitational acceleration due to abtp*o (rt/7 7zo9ika/ +k :j2pvavihthe Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the ,+ fk65n/f-/m)g tc2r.hp ehzr kic hzmass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravihrk )k.fgec 2pmh/-zn /f ctizh56+,r ty on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likft 7klf 4 :e.a/fjst4trns6k-e our Sun but is now in the last stage of its evolution, is the size of our Moon t6t: nst4l.fjr 7e/-kf4 faksbut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whilqr9jv ra9;zd7w xb70f/ qcz z1e orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface ir70arzqz;bx7z99 vwqj/cd 1fn terms of g.   

  Four 9.5-kg spheres are located at the corners of a squarekn(y w/5*tt-e;xahwk gn t3zhn)2 d8s of side 0.60 m. Calculate the magnitude and direction of the totw;(x8wke3nn25 sy th ga/h kn *d-)tztal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sideepqbk*i7;t. f of the Sun. Calculab;q *ifkep 7.tte the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses 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 o-4p)1v tx a(keubg*ud f what it -x 4uv)kpgbe*a1d(ut is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the ir 7v1;fr0v+(two.rn;10 pnst ticd dEarth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawsrw0nvtc1.s;+f p(iv7ntdr; 0iotdr 1, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mo)tuoye. 6mqy3ntba (s-e3 3 oiving in a stable circular orbit about the Earth at a height of 3600 e ynoeitt y3-.q6 a)o3s3ubm( km.    $\times 10^3$

  The space shuttle releases a satellite into a cir :7c td3w0jou4 zz*dpicular orbit 650 km above the Earth. How fast must the shuttle be moving t 03c*jzd7doi4wzp :u(relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshi .r1f e2zrx1zgp rotate if occupants are to experience simulated gravrf .gx1z 1er2zity of 0.60 g? Assume the spaceship’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 saca0unm0h / 8nu6r )ecyadwq, )tellite 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 the radius of the Earth. Doeny ,6)n)e mac0huac 80qwd/ru s your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellit:n4i(p3jg l.w 3khgt xe have to be launched from the top of Mt. Everest to be placed in a circular orbit aro(htjgg p33k4ilwn .:x und the Earth?   

  During an Apollo lunar landing miss;xp iur-s-6 asion, the command module continued to orbit the Moon at an altitude of about 100 km. How loni-s6r- s;axu pg did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks gu87:mdy3 rt gk(ps9;gd 8p v+olh h;qgj)2quof ice that orbit the planet. The inner radius of the rings is 73,0098jgoyuu 3vt ;k +qghslr2)q:gmpd (dgp; 87 h0 $\mathrm{~km}$ , 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 rothk;*xiglk1 yeybw 4+c;r-,xg ates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the botth;-xr wgkx1yk;+i*e l4, cygb om?
(a)    (b)   

  What is the apparent weight of a 75-kg astr)js gukqvf084q fzlgca, (j+c h97l:i onaut 4200 km from the center of the Earth' c0 is)kh4 g8g :jlf9( ajfluq7vqzc+,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-stascz1 tzq 5zx2 v5*l9nnr system consists of two stars of equal mass. They are obsectvz*xl2qs 5nznz 5 91rved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read 9oyh4t *i bcd17ua 4qffor the weight of a 55-kg woman in an elevator tha7dc abh41qifot*u 4y9t 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 cord suspended from the ceiling of ay748v ur) ks,s9iyeyrn elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’iyy 9) 8e7 kysr,rv4sus minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near te6xb:bksaqw.r/ m ,h w7qh+d;he surface of a planet with period T , the d qahqw h,; 6b.wr7k/s:xbedm +ensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the x8 5)tsc2xanm period of an artifim2nx)t5 a scx8cial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a wb:6bg v+zvy +few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fry b++v:v bwzg6om the Sun?    $\times 10^{11}$

  Neptune is an average d7 kr wc(w fb; --*ldpu);b d5ohwutvn1istance 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 76 years. It comes very clokca586h t9dcbewh/ xs 9pfc1;se to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatesta/wh;ftx8169 kccdb9s 5 hcep 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.]    $\times 10^6$

  Our Sun rotates about vaf4h h: cis+.gt v+k7the 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,t+/3 yqd.m:e8 tth dm khk6bd,vw8mu 2 and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1 .tvht ,w26m/de+ hd8utdbqy3 km8m: k609).
(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 Eartnmbzu1 iv *t;cf ;t0((m6giruh from the known period and distance of the Moon. z0*u (v1b c;tmtn mu(r;gi6 if   $\times 10^{24}$

  Determine the mean distance/ o2t6-jgjky,bepvr h1 v3:t v from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabvkj 2t:-h3tgr,y bovp 1e/v6jle 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 fragments (6l;bc zxe7ugquq )q5+ddc .na-c6s r1g,t2ud which some space scientists think came from a planet that once orbited the l)cz25.qcnq6xa ,-r61ubc d7 u +guts d;dqe gSun 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 de*aph rmxb4 5j1z y25voscribes 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 quamyvbrjo 5*24 hxp51zickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a h brfrpui o4qw-763t-* sd.lzhanging 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 tod4r-ishu. q3pobl w- *r67zftlerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration+yr9 po 6a 26cnull)mr of gravity be half what it is on the sur9lr2nloy+cmup 6)6r aface?    $\times 10^6$

  On an ice rink, two skaters od 5(:gxr(vy( )y o ihd+-dmonnf equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and theod)-r5(y(vonid dy mx : (nhg+ir individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent ac mh zpc,)2iae4xa7*vb qacvo2+ ,x:l nceleration of gravity at the equator is slightly less than it would b vh2bxomax ), ,cp:ea*n2zqli7cv+4a e 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 willhcprmnp +qh6.v/+n b-kh-do . a spacecraft traveling directly from the Earth to the Moon experience zero net force because 6hm.nh pnq/-crpvok h.b++d -the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,)k.yikw)o-8a0h zy v( hle:uk but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the eyy l:uzi)k(w -.vk0 ka8hoh) elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abouthjsocf),vf 40e(k (tj its center (like a tubular bicyc ft0v4k)hfe,( j (scojle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43).zu03k z9eweug )p5.wn
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the nwfwqs q -4: nwue kwg(*+d10facceleration duwwwwg 4fekq:*f(+d-0n s 1q nue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticak0htd 5xp.h i(l by an angle.dh0tk p( h5xi $\theta$ 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 1fzi1:ov b ,u.jb pczg )pre0;If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curfo)ze: 1vbj1r,cu; ig0.pbpzve?

  How long would a day be if the Earth were rotating so fast that : mgp. g 9h.fwc: x70aei8mhjjobjects at the equator were apparently weightles ci wx:ea..8ghhjm j:g097f mps?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart z(2 as/qkf67kjo.e in-jsrs6 of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of acj(d 7vhhy 4(m +s-z(pl/gyqradius 235 m. A lamp suspended from the ceiling swinal+ z-ymch/( ( s d7yg(vjh4qpgs 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 9uyb 9qi73 zbfclaimed 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 data for Jupibq3 uyf99b7 izter: 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 pre ft o1siv76rg us ,6mqf+ks)*ssence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting v+su)k,mf7*ssogi6fq 6 r st1 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 his:ncs)j ,s:wx+t4mr dll and valley shown in Fig. 5–45. Both the hill and valley have a radisx4std: j,)nw :+rcsmus of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilxs;89erc e6abizes a group of 24 satellites or6xr bce;e9a8s biting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Renxld.wmasw2 -ygxl .)1 dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a. syl xaxmgw.-l1d2w ) 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 spac+ 4na4t yzkw;re shuttle pursuing a satellite in need of repair. You are in a cirway4r+t4k nz; cular 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 period of 3000 years. (a) Whk2tqt .kycex8 tu/0n 1at is its mean distance fry ktxuq.2knt 0ce1/8tom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "fee98rwg9.jcuc 5 3hf);.y+z kls n rgxywl" yourself gravi g n5xkw+u) 3;r .8ccyshf9.yw zg9jlrtationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroumr.lf (o;w9obmw 1x) knd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about (m x1.o;9mw wlfr bok)30,000 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 squag0r,d k)o x/oyre 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.)okrx gy,od 0/    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg os*c l mc6,(5pfm6gejd rbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienc)3 ktoe,0 ie(xgdbc/med by the tip of the 1.5-cm-long sweep second hand on your wrist wa(k0di bcx tm/e, eo)g3tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing lxc u-g1b2+ 9f2 oodtja 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? [Hint: See Fig. 5–1t+g9-bo f1dl o2 jx2cu0.]    $^{\circ}$

A circular curve of radius R in a new highway is desig*; o(t2 r5uevhrx(ijzned so that a car traveling a2 oeruz j(rt5;*ih (xvt 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, t,pyau6s y3xwc/ d)s.5 *x0v l3gq bvvthe Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the vs)vly up.,ty*3sc65q/w30gxdvx abpassengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$