Sometimes people say that water is removed from clothes in a spin dryer;:tkjhgr1n3( )yt3zazzvd r 5 by centrifugal force throwing the water outward. What is wrong with tr3zr:) (kyd1zj h53;nt avgzthis statement?

Will the acceleration of a car be the sa7cel .g8cawc3h,:o we me when the car travels around a sharp curve at a constant 60 km/h as when it travels around a ge78 go., ehwleccw:ac 3ntle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hillyi: /3awn kjsw:,n)wkn road. Where does the car exert the greatest and least forces on the row:s,n/an) knkw3iw j :ad: (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 horse onz-8) gt:n8+dt fzavt k 2h5ksq a merry-go-round. Which of these forces provides the centripetal accelenq tza -5tvkh828gt ):+zkfdsration of the child?

A bucket of water can be whirled in a vertieh+vsg 3ovl +4cal circle without the water spilling out, even at the top of the circle when the bucke lhv4sv3+e +ogt is upside down. Explain.

How many “accelerators” do you hqttwf g (i;**shaf(a s/xc/xr+nnk13 ave in your car? There are at least three controkq f(ah*(asrx/+/s g 3;xni twc1n* tfls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyint4gmb c*u jc)/g 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 btgj )/u*4mcc 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 inwaq:(f f5d8i bvj az(nc,rd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking an kuo6,,cj:-b wi o:cu-uqxqm*gle given iiu: q-o:*o c w jbu,mcu-xqk6,ts speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizonv5,f:v el 2gndtal plane. She wants to let go at precisely the right time so that the ba f v,lng5:d2vell will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational (ewjkfj i /:bz trf0 k2:go07c4h,zktforce on the Earth? If so, how large a force? Consider an apple ekzk bc0t/2 4krgi f:(ftjzhoj0,7w :
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tg,fgx sp,e+0d he Moon’s orbit b,gpedg sx0,f+e different?

Which pulls harder gravitationalc/.wbamb1u1jr1 -,a;sx nzl e ly, the Earth on the Moon, or the Moon on the Earth? Which accelerates ;1a bn.er/1ulw- csz mjxa 1b,more?

The Sun's gravitational pull on the Earth is much larger than the Moondy3 dp;v:y2bs '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 ot3d:p;b2 ydvysher.]

Will an object weigh more at the equator or6 ,02tkfv fn ejjm(7b9mttp8t*dhnk; at the poles? What two effects are at work? Do they ot7fv 20et tk , jknf*8tmn9p dm;hb6j(ppose each other?

The gravitational force on the Moon due to the Ejk 6ln-d m5-agh/87kx u;v abvarth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earthm j b7;6lv/58hnak-kxdag u-v?

Is the centripetal acceh .hjtz1uo9yr/be8d/43 vw zc9xg q1 vleration of Mars in its orbit around the Sun larger or smaller than the centripetal accelerd9yoqv3 1g81/j / zert 9h4xbwh.zuv cation of the Earth?

Would it require less speed to launch a satelp:sejbwk:) 3 +0 ng lejarj(;rlite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dirg a3(sj+j)b0pjrke l;ne r:w :ection.

When will your apparent weight be the greatest, as meas(zcij8.r,vhx ) ;azuoured by a scale in a moving elevator: 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 theo a; ),r8c(jzzi.xvhu 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 outerjkc.f- up92/zk vv9uhb-r4 c l space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on thekv- u bzv.f2-cchr4l/pu9jk9 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” 5i2ws:la k(cgjf2 zerk0 w4f0 or “apparent weightlessness” betweeng 5ws2rai zcf04 j02(kwfl k:e steps.

The Earth moves faster in its orbit arounlt;pe9e:gthyrc+5te4 t1f:4r bd2a c d the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain;14erceg tht + 9tfy 5 2cbp4lt::edra. [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 have a moon. Explain) x gn7-iwz7vl how this discovxw7-)gn zi7lvery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larnkp-m(fqyw,ha )s2 ,z )nwcn8ger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitach)z8,n 2)-pwky,s(aq fnwn mtional 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 travelinhuzz 1--oy( ;h +y)fibeefh3gg 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 av9j0iic:nzt m .6uw )oround 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 circle of radit0zcuwm. 9vn6i)i : jous 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 rota i;)bm7v x2gaw-r3geutes uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discuge2)wv;-gb7 au3 r ixms.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, andk/f1 kwh)yl/-x*y c wd circles thekx*yy1 d/) wcf-lhw/k Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spex(dr8+7e0lmzcan 4 a dck of clay on the edge of a potter’s wheel turninea47 dx8rm n(cad+0 zlg at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string ign719dly so:,w2;t( hctkc0bfj kr4 fs revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shonohkcd0 fk;2,b7:s9l 1gfrt(4twc jywn in Fig. 5-33. 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 round a turn of rad w/)j *hx uvvo13z.jrniiy 3a/ius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of)h/z i/aj jiw vor*nxuv.y133 the mass of the car?   

  How large must the coefficient of static friction be between the tires andvodyvcg652. yo5,5s u:kzlll the road if a lsdv clvy uz5o5y2:6.,glk5o car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet f(n8 p4ceu4ny qll6u0 ag 2+azcighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If thez(aunayq 406l+4clg8enc2 u p force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm frizs+a 3*kn,k5sy j lr881f fheom the axis 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 akr z8i,kf jf yhn*l+5 e1s8s336 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 upside down a01;,rbqa fn .n 7aehsdhdh ()zt the top of a dn)1fr hba ,eqd0sh(7 h. n;azcircle
(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 rounded togrh z u63cl+l(7fe p9ip of azl6 (ghe ufc3l97ir +p 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-diam.u)6 6,ezf8sdcqpp (hybtdf -eter Ferris wheel need to make for the passengers to feel “weightf fh du ,z.q-p)bd(s8p t6ce6yless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirl f+;hj/yic f*zed in a vertical circle of radius 1.10 m. At the lowest point of its motion the tensio; zi*f yc/f+jhn 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 centrifuyy2w ol z+ed69. q0pyxge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration ofyp9wq doy+ y2z6.0elx 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrxjht9*j:xi0oqocc: i 0 yf0x4 ically walled "room.o9jji400ith: xc of x*: yx0cq" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictios4o(1bt+7ueekrc x7 onless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling blo7ucoerseo +bt1 4 k7x(ck (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 time, by not ignoring the weight of thomp4z0iboj2t ar; f *1e ball which revolves on a string fj*b ozr0o41m2 pati ;0.600 m 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 m is perfectly bankb7dhvu,1c.oe yo4 nz3lq6nw4p 5pz;ked 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 massest +,xsfz5 ba2y :l+sbl $ 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 efi 5psylvpm -n g:t:f)-ob,/uvasive 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 centripetal components of the net force exerted 1utj(,h 7gx nv2vpus0 on the car (by the ground) in Example x2 jtpg1s 0 huuv,n7(v 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 c1 fkn.ygq8 f3accelerates 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 t c3.kf8qny1fghe 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 c0gehl 7c*yfm ;u 7jy1uircle of radius 2.90 m . At a particular instanuu*7ym lj0;fc71yhe gt, its 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 Eaa3yg i)s pd+eixu;a/ (rth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s se; u3(gxii/d)apy+a surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magniwwmlql( g0go;c 00fg n663vpgtg(nlv ;l066p3q0mfwocgw 0g g ude 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 M 4irq de:i:n5hoon. The Moon's radius is 1.74: i:5in4dqehr $\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 samegd e.qupiq f93(fw e:5 mass. What is the acceleraqp :93ud.qf5gweei( f tion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66j:aars l lt1bng-, 3rjma-2 1m times that of Earth, but the same radius. What is g near its 3rsl:ant-,gmamjr1lb1j 2a - surface?   

  Two objects attract each other gravitationally withj83cq 8vy3- m 5pbkznw 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 effectiva(le ;5g:xdi9j zp z5ue value of g , the acceleration of gravity, at (a) 3200 mi ;5jg u(5:zxl9apedz    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a po9wc ia ,2a vc ,0uxat)ao3f0hqint outside the Earth where thegravitational acceleration due to the Eart9 a 0qxvcuca of3)aa h2wi,0t,h is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ourpizw1n,mk))6 6wsiy q+ d,xum Sun packed into a sphere about 10 km in radius. Estimate the uw)qd s6 1) ,i6w+nyzkixpm, msurface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun buu. 7s) dbk,bett is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravtb7ub. d sk),eity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space shje2w:hqz2m) y uobn:gs)g56o uttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince t2o)j::u)e hg 2wosm 5qz6nygbhem and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of w 5wwyi/vt,n0a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thiwv,0wny/ 5 twree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planet t) grf+qv5(t6w*7tk ek/yodj s line up on the same side of the Sun. Calculate the to/)jtr(kd +vo7tyg t6* wf5keqtal 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 5)e*rs c3 gmiiof gravity at the surface of Mars is 0.38 of what it is on Earth, and that Marig m5cr)3si*es’ 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 t-g xym ) s;e/f+/g9lnvg twp;ihe Earth and its distance from the Sun. [Note: Compare you;m vtn;ggegpl9y+sx )f w/ -/ir answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite msu4 iyki61zh 6oving in a stable circular orbit about the Ea6k is6ih yz1u4rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releas(ub zl1gq3;izes a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rela;(lqz 3 zugib1tive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylisxlxf2s+c(),:ux znw x; 1nz nndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceshiplf1uc;nnx: w,+nx2x zx sz(s) ’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 satellite to orbit the Earthdyr - +hn;eszi z*d1qd: c3si- 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 the1 3; * qch-+sdd yezizsnd-r:i Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satebboy -/i,:x 4l9t mpunllite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?: m yuo,tl /n9b-4pbxi   

  During an Apollo lunar landing g-*yn .1ly*k iwuv7dvmission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? d.u-wk*yvvn gl*y7i 1   s

  The rings of Saturn are compose: suy(njgqd:: d of chunks of ice that orbit the planet. The inner radius of the:nj: sq( guy:d 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 oc(x jx7k fwvs:u/r(fh8+a td-nce every 15.5 s (see Fig. 5–9). What is the ratio of a person( x7-8hs frf:(xka+ d/jvu wtc’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of t49z aqlp2;w vthe Earth's Mozl 9;ptwqa24von 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 ag :l3pi ut o+6ogvmf*yp:(.rjs(ny ;v,xv1p tre observed to be separate l u gv:*( mnoo+vx sifpg3pty, r;1jv:(6t.ypd 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 for the weight of a 55-kg woman in an elevaouom4vzy30 l3 0s0fbh tor that moves4voz 03u3m0yl0hs obf
(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 ofq pc-mj8j2i/n an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (mc 8-/m2 qnpjijagnitude and direction)? a =   

Show that if a satellite orbits v:f(trp/h t-wwq/,gncd-o u *eery near the surface of a planet with period T , the density (mass/volume) of the planet igp(/-odt ,qu/t:w r f*-cwh nes $\rho=m / V=3 \pi / G T^{2}$ .
(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 an;xe vufr xh--)d the period of the Moon (27.4 d) to determine the period of arx;-x v -hf)uen artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orj59jjm6dn5hep2dcs v i qsk ky/f) (+7bits the Sun like the planets. Its period is 410 d. What is its mean distsyj/+n7p 2ev9jkd m5icqhs j6 f d5()kance from the Sun?    $\times 10^{11}$

  Neptune is an average d;iysx nkc1 *,zistance 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 yeacc m (tzn;gfb/ 3j2gf6i3dxv: rs. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distaz;c 26dc/f: g t g3mf(jvxin3bnce from the Sun.]    $\times 10^6$

  Our Sun rotates about 1qhh/wo2n fr/ the 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 massdx/ ;cb (3nkhb, period, and mean distance for the four largest moons of Jupiter (those discovered bb; 3 dcxb/khn(y 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 Ear)xdhqcim r(csd+ pm 4- g2j/5pnqe;n5th from the known period and distance of the Moon. q5jih; d p-xg cp2mq(n4cm+ n/ sd)5er   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moond7g)pdw*+dl l5rnfo, s, using Kepler’s third law. Use the distance of Io an d,7*ofgrlln)wp+ d5d d 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 fragments (ve3iri2)-7xx wmc qo 5 4dle,swhich some space sciem)4ri2d 5lxqwox ,3eci- s 7ventists think 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 describesrh vbf2e5i:gt(d q9( j an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the :f9h( rqtig(ebv5dj2 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 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 hangingrrc0 18dnp ne/ vine (Fig. 5–41). Inp n81d0e /crrf his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth3v:nq0m66 -(wh2dc v ed hpfgt’s surface will the acceleration of gravity be half what it is on thegd6-nvhwtcmh( ed3q :0p 6f v2 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circleb-t pd:7w,i:3ldgy uw once every 2.5 s. If we assume their arms are each 0.80 m long and their induyi:3 :-db,7 ldwgw tpividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates5o j 5f 2+xw5mob2vq5m cbpz*j once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fracti*b+wq5om 5jp5vj xz2m2cb5foon of g is this?    $\times 10^{-1}$

  At what distance from the Eyyo p 7amu8pj1uhq-66arth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the m6yp86 puj uh7qoya1- Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in igvur,i pzz),io,) ,a an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,,gru, ,i)vz )o, zpaii and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat ;wecqv2w0l/5fy ;nc ae about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diametene2fc5a/wy; ;vlcq w 0r 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 loosbnksz 6 )pnz+k/w2m 9p (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 planet in terms vp:m*b1h 2nqo4ti v 6eof its radius r, the acceleration due to gravity at its surface 62 ve opi b4:*qntvm1hand the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vermc:;h:f+:xb7e2 g ou )yqckxu9:eosb tical by anhcxe ecqo2:;:) 7k u9u:bs+gy ob:xmf angle $\theta$ 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 coeff(q aku;cgk6/lh nv61 nicient of static friction is 0.30 (wet pavement), at what v(c hnl1k/q;n k6ua6 grange of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast tha vs ,j6,mpzjn/*n*mj vt objects at the equator were apparently weightles*6/zpmsv,n * vj,nmjjs?    $\times 10^3$s

  Two equal-mass stars maintain a conszu elw(,b0 z3etant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a 3 +oy bz h,jtiyl1sjlugo89 (4curve of radius 235 m. A lamp suspended fromjh9(gslutoy 314l, +8zj o biy 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 asq9wso9sy v0g r,wkb2* the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the qgow2sy*s0 r9k 9b ,vwsize 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 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 pre.xk/g ;wpig hci6(t2 usence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They2w ;ictu.pkg6x(i/ gh did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and val2it;dek yq3) vley 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?) Ei2y3)d v qt;ekxplain. (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 Sysu-v;ba1 v34v 1sqxs jopt l/9zh3bw2ftem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to 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) Determv41 opwutls32-v 1fh9 x ;qb3b j/zasvine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NE9v m-btm.af7yw l:ip1 AR), after traveling 2.1 billion km, is meant -mvtpw.9a7blfmi1 y: to 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 /iqco p)a ba63pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (iaq3a6/ pboc) 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 hi0fy/llqm 8nyz.:b i b s,hg6 .x qvgl)a(:n:mas a period of 3000 years. (a) What is its mean distance from h vlbsgl,fi 6b /::ym8 ng ly x.m0q:)nzq(.iathe 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 yo is,2av/rpmm*-ru aq 0u could actually "feel" yourself gravitationally attracted to someone near you. Makiammpa ,v/*rqs r2-0 ue reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center o+:fzug zv6i,mnh6)ed k 8nh-nf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-ye 6 ihv n:mug-)+8ekdnfz hn,z6ars 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 each side h9fp2b/b2ezl. Find the magnitude and direction of thb bpz e9hl2/2fe gravitational 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*w;tn/vktu,yat x 5 9a1 rr/zu 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 experien 0yiw,pu:.ya9wlm2nvl9:dik;w vp o .ced by the tip of the 1.5-cm-long sweep second hy0wi:,v;n.9wa:9 wydpvu o2k.ilpl mand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swin)snf 8nfb-s hsef,x*2 g a sinker weight around in a circle below you on a 0.25-m piece of fishing lin)hbs2 fffxe,s*- sn8 ne. 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. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is de w2k/p rdqeaq3j/abr6o4 68kvsigned so that a car traveling at spe 3qve/k a8ab6o 6/2k4qpwr drjed $ 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 whqx o(3rom0w:ooc3b x7en negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, cx3 (wmbqxo0ooro :73is 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.$\approx$    $\times 10^2$