Sometimes people say tha ocxdm)n7fsv) a9;vg7t water is removed from clothes in a spin dryer by centrifugal force throwing tfx)ng) ov7avs 7;d9mche water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the 8mu3;6g rz1bwnl b* excar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle c;mz*1w8er 3bnxl6g ub urve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the7n3yh6;klrpcj d +qr. car exert the greathk+rd; ypqj3n 7 6lr.cest and least forces on 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 forcesbetn3 (/ .brrs acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accele sr(n/b r3.tebration of the child?

A bucket of water can be whirled in a vertical circle without the wc0t * gmv04d,pxv 4texz,b4l gater spilling out, even at the top of the circle when th4gc,dx bgm0 t ep*v 40vtz,4xle bucket is upside down. Explain.

How many “accelerators” do((4( yi kl gz-ilsuu6t you have in your car? There are at least three controls in the car which can s (yu-(l 6i(t u4zilgkbe used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crehw;8yh7 4d0gcib8opxpzhbd 8(:ig 1zst 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 decrease using Newton’s secon7odzy0 p8x:hbgi4bc18phi;z(gwd 8 h d law.

Why do bicycle riders lean inwarvf nu3rrli* yd:15 c/fd when rounding a curve at high speed?

Why do airplanes bank when they turn*z y8ltaa)evrtm d5, u;. bkq9)f sk7w? How would you compute the banking angle given its *y)wkm tt7u lrseq59a )z,;k ad .8fbvspeed and radius of the turn?

A girl is whirling a ball on a string aroundihwp7y9s g-.m ax4 y1a 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 shi a-y s7g 9pm1wyx.a4he let go of the string?

Does an apple exert a gravitational force on the Earth? If so, h-b1-v40fku m dnxn4o gow large a force? Consider anxbug no-nd1 k-vf04m 4 apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it isoq7wtbt -52 a +lshie;7pb;j p, in what ways would the Moon’s orbit beppwah bt2+q57;-o se7;ibjtl different?

Which pulls harder gravitationally, the Earth on the ebsj5e6z*bsvj)* p z ,Moon, or the Moon on the Earth? Whicj vj s) ,eesz6z*5p*bbh accelerates more?

The Sun's gravitational pull on the Earth is much p m4ce ys/.2oin;i j;duaot,/ larger than the Moon's. Yet the Moon's is mainly responsible for the mt.u4 i ps/ya,;o/c2n;o ejidtides. Explain. [Hint: 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? What two e p r+(r)d+ofvyffects are at workpr o)vrdf +(+y? Do they oppose each other?

The gravitational force on the Moon due to17xsx -r0b/k,mkr5ozblaq* w the Earth is only about half the force on the Moon due o*z/-lbm k0 5xrb1 s7k,rwaqxto the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su,i yhm- nirkb ee(7m77n larger or smaller than the centripeeik7hr(y m,e7i7 bnm -tal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eascx 5m0wgj;1acxp aw44 :5zlxct or (b) toward the west? Consider the Earth’s rotati5x accw01xcw;jx 5l 4:amg4pzon direction.

When will your apparent weight bexap cx(y en;y,vi0z-ov .6mn7 the greatest, as measured 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 imoya-c.(z0;xn e,7 vny6vxpspeed? 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: .jhx/9 ysqy,(yj ond could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauqy/x9 (djnjsyoyh: . ,ts 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 experiences “free fk kmq06ftw**ee me+o;all” or “apparent weightlessness” between stepseekfqo**0 t; k me+m6w.

The Earth moves faster i-pz bg (/x,mdcn its orbit around 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 tilt ocp zdg( ,x-mb/f the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until i,m. vi 4q ;ygvqjpfmd-y k/u::t was discovered to have a moon. Explain how this discovery enabled an q4gq:jydyi, .:mv p;ku v-/fm estimate of Pluto’s mass.

  The Sun's gravitational pgnz 6l+se 7zqokgi).8ull on the Earth is much larger 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 agns7ie6gq8z)olk .+ z 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 9h ;n2fj)v7vd qo acee 3qti(-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 accelerati x;an 1ulfh1b)y ( dx*th7d6xxon of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the nh(u7xabl16xxdt 1h )xf;d*yEarth'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 unli82g a ytp6t)iformly in a horizonil8 )g2tya t6ptal 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 Earth'skb dbx(kwfyr ug*c8+l( )+ f3p surface, and circles the Earth about once every 90 minutes. Find the centripetal accelerak+wrd*)y xkbg((f8lfb+p c 3ution 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 accelerat0d sn ej;rx8-eion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minut-n r;sde80x eje) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stringdbpuh.y3 iq 2+ is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spee uiph d3+2.bqyd 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 tur rc- qv:sgjkx qz+co43w 2 ortap53;9nn of radius 77 m on a -zp q:ats9wjrgq +co2o 3nr3;x ck4v5 flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffici9* bb11k v5tspces c+gent of static friction be between the tires and the road if gsbek1* 1 vtcbc95+spa car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts andryvftau4g/-z iq n 40x ;dy0-d jet 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 is 7.85 times her own weight, how fast is she rotating?yiz ty4/d-qv- u40n;0arfd x g    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turnt m j/vs )(x4 lekftko9rwii sk.2fy 3/lh58+hvable 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 ank ysv8o935mli.l+)4s vf2tk/h krw/ x( jfehid 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 bqb,+;r)fn irle traveling when upside down at the top of a cir)rfbl r,n;q +icle
(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 :+ 6fns9 s5nbc8dc hgzmass 950 kg (including the driver) crosses the rounded top c+ :dbz9hs86 gn n5cfsof a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per mf omnbr)/b7)q*r+v n einute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightle)q* boer rm/+ nvnf)b7ss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vxp1km6vw: p j4ertical circle of radius 1.10 m. At the lowest point of its motion the te kx:j1mwp64pv nsion 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 centrift ex bwe6.n72fuge rotate if a particle 9.00 cm from the axis of rotat7wf n6ee2.xtbion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a(ypx l* p 2)fvixmf45 bmu+p7sre rotated in a cylindrically walled "room." (See Fig. pvx(f+plp7) i 2 *b mm5sxfy4u5-35.)
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 rotatu w.o-:d34m/awjq mm med in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connecteuo4m.m/ dw :w-mqamj3d 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 time, by not ignoring the weight ofm :v/rip6a k+n the ball which revolves on a string 0.600 m long. In particulink6mv /ar+: par, 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 d72itq ;5dzmue sr7-q3b4rmi 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 massea1hnw/sf r:2 8pgcu 6ps $ 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 mak4psc;/ krjz,neuver 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 cer5u3m7t b m*;5 ohnjfpntripetal components of the net force exerted on the car (by 7*upmmborht53 j ;n5 fthe 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 accele 8:jrvi-c-klgmv,:* j jxr9 xerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius8- ki:jxrvj:gjm-v l9rx ,*ec 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 circle o7 ln52dwjc)u n 9 s676btsfwtrf radius 2.90 m . At a particular instant, its acceleration is u7d6swn7s9w)6t j5 rbf2nclt1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 12,80tcv;p t1wh6)a0 km (2 Earth radii) above the Earth’s surface if its m 6vap ;1)whttcass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has;fv 9v2owfx0s a magnitude of 12 m/s of xs;wf20vv9$^2$ 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 is *eo0 jj z,v:;c/pjn dd 1.7p* jdv; ezj:jdn,co/04 $\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, bozh.+blo7o d( ut has the same mass. What is the acceleration due to gravzdo+ ohl( .7obity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eao2 z8 qk(uys9irth, but the same radius. What is g near itu9 sizoy2q(k8 s surface?   

  Two objects attract each other gravitationally with a force of 2.5tknjz 8l10u )v*-ktqpb:ah(i $ \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 accelerasef -h* xp)f.d hyqco b(xnu7xt:3i99tion of gravity, at (a) 3200 m -ehfn tu bx( ) 979hx *cp:xdi.q3syfo   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from .,qnnl u;3a;0q essm,sej gt,the Earth’s center to a point outside the Earth where thegrav,l,s;n,eusm3 teg 0sjnq.q; a itational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ob/ pd )*ftn0vice) ,eua79xpsur Sun packed into a sphere about 10 km in i, ne / udaf0e)*sbvx9c7t pp)radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf s1mv2droz9x x*tar, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our rx*z1m x2od9v 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 while orbiting in the space shk jw w(q4z0+j +wou+m*l/dj yeuttle. 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 suwd jo++kj0z/wm qj(lu*4 ew+yrface in terms of g.   

  Four 9.5-kg spheres are located ais2fl;uz08p )zi 0to bt the corners of a square of side 0.60 m. Calculate the magnitude and direction oftlzi0fp0 b oi)2; 8uzs 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 the planets line up on the same 8 ,(tv/lbsd qn0kmz(bside of the Sun. Calculate the total force onqd(m(ls/b 0 bz8t ,kvn 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 surg-y kbl 3h78vaface of Mars is 0.38 of what it is on Earth, and th8yv-bgl73h kaat 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 xhno 7nkz g9d lc.m)n9/w97uaEarth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16o9xwd )n7.c 9am7lz/nuh9gkn .]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about tu ic +mjmp8j17he Ear pimj j+c781umth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circubitxh):1i6 *) txemxmlar orbit 650 km above the Earth. How fast must the shumx)xxte 1i:mth *6i)bttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experien(zuj+ xszmx1xzrqm /n-9- *d6xs;ygf ce simulated gravity 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, Figm9n q-m/u- sxj szx( +;zxzdrx6y1f*g 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth547(hc mg;b f,n)cfe1fw m kbu in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of(bg c4) e 7,5kmhcfw bun1;ffm the Earth which is very small compared to the 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 launche*f -:p vnbm*k9ehxv3x*5 nes cd from the top of Mt. Everest to be placed in a circulxb c*svn fm*:9vhe *e- pn53kxar orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit the (bh 064c/hgdrz.m aue Moon hu/r edz6hc (gam.4b0at 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 chun1sf m+ilkymb1ii9iw :z 6h,1 eks of ice that orbit the planet. The inner radius of the ring:mii,+hb6 k zy wf9s1im i1l1es is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once ez/ 4iqr5dpe+ pvery 15.5 s (see Fig. 5–9). What is the ratio of/dp z4qp e+ri5 a person’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 le c2.rhmjrsrni0sl)*y 84 5nkm from the center of the Earth's Moor0 j*s )l 5mrh 2.lrscy4nen8in 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 o9 )ml3,k(.s iecoe4ddkv2: ilbytp- uf equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yeae2k4ivditkom d: pl. ul s)c,b9-(e3yrs 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 weigv 1zbaa zne;*c23q. pmht of a 55-kg woman in an elevator thatn a*ca;vzqepz13b m. 2 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 oh p -.8wwhwz4af an elevator. The cord can withstand a ten4hh8 w aww.z-psion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pefe,3 gyg8 vww3riod T , the density (mass/volumey8egg33fw ,v w) 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 per2abz )e4*- lb9fbl5 xq-gos zfiod of an artificib*belgqf -x9b a4s zzfl)2 o-5al satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbwcs3zxn;c0,t its the Sun like the planets. Its p0t c,3snz; wcxeriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4kqj *3kqo0b r-.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 hl2e5vm 6zcub-6g 4 fovery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. I e625cg-v hbzfl6um4os 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 the center of the Galaxyvf 5p7xde ye;7 $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 ad ;qrf*50zp-biz8wh uh/rh3 distance for the four largest moons of Jupiter (those discovered by ;rwp 3zfdiu-zhr/* 8h0b5h a qGalileo 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(0ojs4weoty . Earth from the known period and distance of the Moon. (0jos4owy. te    $\times 10^{24}$

  Determine the mean distance from Jupite r3v(q)pync5.o8;;s zx6ft)g hyjtyer for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given; jnf )sv);t8rh yyeo qty5.3cp6g( zx 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 c*u/;q;vibi (u7ughd vonsists of many fragments (which some space scientists think came from a planet that once ov guh ib/*v7u(;d;quirbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes xcwgdlz *c77j p93m o7an 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 li*7xmcz loj7c3 7 gwp9dke 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 skpi)y-4s8 ckp xtp3,ukpbx4c48h j /uwinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable ofscb pxk k)p4i83jyup4-4 8h,upkc xt/ 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 Earth’s surface will the acceleration of gravity be h ;uurx+(k; pvralf what it is on ukrp;;vu r+(xthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cih72.**pk *grayy- zte4aq t7rr3p qto rcle onayo k2p ra*r47z*-.tq hqp3 t *yetr7gce 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 another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acc4hs(cl xl:fin )e8 c(bfyn 2-ixc7t;v eleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate ty s(f4i) cc vecxl8tni :nhl2;(7-xbfhe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dip d r6a* c7-bg(kyt g)vs3+ru9ewm 8nyrectly from the Earth to the Moon experience zero net force because the Ea+ps wg-398 )tc(ngm*vbd eu akrr7 y6yrth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a ae9h500a5 mdjtg53x g-dbsni bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dire 5abdsihe-a 9dm0x n5j30gt5g ction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotn9rje6rv6i zedsu24q 17wv i0ate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day)0 4i1er7uq6z9 sjniev 2dwv6r 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+/8y3 4 jpc hyjfkelcbesb*gp0mm-*63).
(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 mj*/ 9fsnuw:4 li0k z 3t:ldw6uo,txk uass of a planet in terms of its radius r, the acceleration due to gravity at its surface o3, k w9utwu sit4 :*6fln:kx/ uzld0j and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defojx;k;-ub8 :k1yi jsikp8px-lected from the vertical by ax:kpb8i;x-kk-us y;j1 poji8n 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 co43q0+6sa g8qjm 3 rh jd/domgiefficient of static friction is 0jjmdmgg /0q38q ad36so4rh+i .30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotat1gang a /zu(3aing so fast that objects at the eq/ag 3(naag u1zuator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant xo1jly n;ckj-5cv2+odistance 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 curve of radius 235gz6irl 7 2lth mv(ods36ow75m m. A lamp suspended from the ceiling swings out to anmihwoolv m52l( 6dz6 st77r3 g 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/my/etbc z.m5 psd701j ivth *, it has been claimed that a person 0 d tb7eih*5mm/1t.s/cyvz jpwould 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 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 Spacnm59fqr6a*,l fd ma:grg /5hwe Telescope deduced the presence of an extremely massive core in the distant galaxy M87q95rr:al , *df h/mfg6wagn5m, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trave-x, de f+h,wg61 e7 adu1oqmlkrses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road atd61 hea kg mqe17,o-uw,xdl+f A?

  The Navstar Global Positioning System (GPS) utilizes a group ofz3pzp bm3 *nosf;*z/m 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the po* ;zzpbfo*sn3/3pmmz sition of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), aft6xx2r6e )hfr *bj9 gyder traveling 2.1 billion km, is meant to orbit the asteroid Er 9 6erjdy)hr6 2xfb*gxos 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 spacpxl7f0xygj3 7k 2h5mme shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but70jlx23xmgh 7 kpmy5f 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 ofuvv r;4 fkw/:ln3 p4myk+ wi0s 3000 years. (a) What is its mean distance from thy v;k+sp:k 4l0wvmuf3r4/w n ie 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 "fe ysltv/;.tq9pl.b9w2d zz d+s el" yourself gravitationally attracted to someone near you. Make reasonable assumptions9t/swp.bt vs; q 2 .llzzy+9dd, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dista*v(c +ktonu3l 56jgs kncelngs jku t*3kc(v+o56 of about 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 square 0.50 m) e/9a -;upz,b8qu xxaj b5k9pzjl8gd 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 sidebxj9 du )kap9 8pu-5 /x; bej,qzzag8l of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth* su)g th3)1hz(oscd3 iwm2wvc pox,sf;9-v r $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep jo r zry0wa uf ,:,l0iuik+k++second ha f0u++y :+wz,,aioj kkiu rlr0nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get n+3uoe yy y*p 86g iurf)22qzvbored 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.2uq ypun*+ )63 e8 iyzvroy2fg What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius ba2 )v) gxz3t ,cnyy63zqtu*k R in a new highway is designed so that a car travelixc3)) 2uz,zgy*6b vqy ta 3ntkng 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 Aar b.v:0 sbz r/+kv7lucela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a r rasbz/7kvlu v+0r:.b adius 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.$\approx$    $\times 10^2$