Sometimes people say that 6oe;+xhda xbs72y3na z8. iklwater is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wroaax6hzy; 82n7sdbi.+ olkex 3ng with this statement?

Will the acceleration of a car be the same when the car travels around ah2d3j:hqt l ;-taw:t e sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expla:dqel-:ht ; haj32w ttin.

Suppose a car moves atnvnbi5vi z95.(,jo l pv.oht be.)z :b constant speed along a hilly road. Where does the car exert the gre v5:njoh.l.e 9bbpn.bv ztv5(oz ii ),atest 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 forces acting on a child riding a horse on a merry-go-rounqrjct)h 4l6+v d. Which of these forces prov )t6hlq+j rc4vides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cia+y -wfz +fh 9(yy3dja ozho9st-5)ykrcle without the water spilling out, even at the taf fz +) zy(dyjy5-o9-ykh9 o+h 3sawtop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in youhjfai7nz99-72bjis v ,i3fomr car? There are at least three controls in the car which can be used to cause the car to accelerate. What aszii, -fnoj 2h79vmij 37fb9are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig -1tvhu,liutj2e b1;b -hd/mg. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest andu 1ihm/jlte-,bb2u ;-tv g1 hd the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hi76b dhpa5b e) 22nbkeagl5o1egh speed?

Why do airplanes bank when they turn? How would you compute the ba9j67) h:t uyw g-jahfenking angle given iea:jt) 67fuhwh g9yj -ts speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizon :b9puvv;sh 7wtal 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 let go ofuw v; 7:9sbpvh the string?

Does an apple exert a *rr vzr 4f-4qgah5 s+cgravitational force on the Earth? If so, how large a force? Consid + a-zg*r 4qv4hrr5sfcer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what 9967ucwj eeuk it is, in what ways would the Moon’s orbit be differe ew9u67kuecj9nt?

Which pulls harder gravitationally, the Earth on the Moon, o,w; b(2tzkccs9a wkk (r the Moon on the Earth? Which sw29ckak,(c(twbz;kaccelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon' tb+7icx*dgkk hq06p 7s. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider thpc 7gq x0kk+h76*bti de 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? Wp8.ssmj (9zizhat two effects are at work(ms zjz. 89isp? Do they oppose each other?

The gravitational force on the Moon due to the Eart 6mqx4mid:etnn ;yovs,,/6qy h is only about half the force on the Moon due to the Sun. Why isn’t the Moon pul,i6dynv nqq /4sm;6 e:, yxomtled away from the Earth?

Is the centripetal accee u6h p(u12wwp;qk7mxleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eartuphmu2 wp; 6xk(1e7q wh?

Would it require less speed tuam9kvb-d n ,f wb*/fh)( z hh05emsf)o launch a satellite (a) toward the east or (b) toward the weh )b nuv(fz9sa)/f5m,h -bk fwem0h *dst? Consider the Earth’s rotation direction.

When will your apparent weight be th4ia hoovu65x-wc)e *le greatest, as measured by a scale in a movin)cu v- wo54l*eo6xiah g 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 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 13m rgtksi v*a(2glqqi4*8ivin outer 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 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 g4i(vqkit21 r*sm*vig g3qa l 8ravity you can think of.

Explain how a runner experiences “free fale- 3c3b( jyh )wo-lbmil” or “apparent weightlessness” between sti) c(jelo- h3w3m- bbyeps.

The Earth moves faster in its orbit arokp-crn7:hy5 w und the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not muckcn57rw- p:hy h 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 wasolm6) uxu9 z(fe*jk74x vl1nu discovered to have a moon. Explain how this discovery enabluuz1 )l 4jfvkmn 9lox(ux7*e6ed an estimate of Pluto’s mass.

  The Sun's gravitational pull on xs 6js r:kn acdf3umg3,sw1sx+;f+ j) 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 u:,)sfxgk d+;jss3 nxf6 mc +3sr j1wa1.10 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 traveling5 j :z:quz/th .5a9q6qpro xfz 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 centripetaa,4ru(j l.lrp+ya-e zl acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earlzy.ar+e u( lp,4 ja-rth? 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-kb zx/75x qgx qm .s,lfcyq26(tg discus as it rotates uniformly in a horizontal cit7fbx5 /yl2q gm,xxq.s (q6czrcle (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' 8s/f8qw7k ofhs surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms ofq/ohf s8fkw8 7 g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of+dd,rhv.v 9kz fh*bvg n ;vm7 knf(.7e a speck of clay on the edge of a potter’s wheel turning at 45 rpm v n;vk.7dr7*+hf vz (md v.ghbf,enk9 (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end ofp (kw(/zmwb u: a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If wm b(p/uk(: zwits 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 c)j,kyiv a j5w.or6f 9tar can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires 9yj6 a, vf.riok5)twjand road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficim5 - 5uosd6 y/(x my6(qsmo/acba)n kaent of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95kmqm scnd5)a6ks (5uax6mmoy /( a /y-bo/h ?   

  A device for training astrona(4 +vc*bxei7 b(yxbrk uts and 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 wei(ierkyvx+ (*b4bxb7 c ght, 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 ybgcy h-9+ 0g0ft .4ylucky: mcm from the axis of a rotating turntable of variable speed. .9y:0l ybchu0c4mfk g yg -+tyWhen the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tra4n ;(qdb-2gvat m* gluveling when upside down at the top of a cirav d-q(;2mug *bntg l4cle
(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 tr4i6b-y i lyu5r5nw9ohe driver) crosses the rounded top of 5byyo45-6il r riun9wa hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel nt1wd0s8 bnp 6djgv3e*eed to make for the passengers to feel “weightless” at the topm3dw8vt0g*j de p61 sbnost point?    rpm

  A bucket of mass 2.00 kg is whirled in a 1zeid9 gifp-ot0l x):8yl wg4vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buckw9:0f) pll gy8izg i1x-dteo4et 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 centrifuge rotate if a particle 9.00 cm from the qh3pjo0pxvz*,f3 .sj axis of rotation is to expezp ,jv sq.0 foxh*p3j3rience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walko- kz6+ ga.zhled "r.k-z 6ga+kho zoom." (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 +yf ,9xyoi2sx 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 )xsiofx 92+ y,y 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 thz w p9)ghrkuhh zri-bws(:z(v,*i,uc9 k; ,k ye ball which revolves on a stringy,*kbcw hz9h rw:(u urv9iipsz (,,gz; )- kkh 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 radiuap1dvs:z f 7j-s of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massehb :xd4nw65i 8-epdy su+dx2v s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving ver,te mf9rz3q q)tically 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 ceb rbjd 3e;5hx5ntripetal components of the net force exerted on the car (by the ground) in Example 5-8 wbe5b;x5 h3jdrhen 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 accelerawic.bj o:pm6x6fu4of r p*(3ktes uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. Ifjf(im*6436ckw.p bu ox :of rp 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 hjtm- qk;:-csgwx, g s9orizontal circle of radius 2.90 m . At a particular instant, its accelerjsgg s9tmk wx,q-- :;cation 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 hgmm / ie(hkbnge8 10m n;f+r: gikm0(of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its kkn( mi;ngbg0/ heem0hg 1mf( 8ir+:mmass is 1350 kg.   

  At the surface of a certain planet, the gravitational acc v6(t/u pgqu5 ,sv8t(7ewnrcyeleration g has a magnitude8rt7 yqw5n e ptv/6vgsc(,(uu 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 Moonbm w(cnu.1 l/z;ta+nm's radius is 1.74. +l1can zt(ubn/mm; w $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planekkic * t1iu n5iy md*6/w .ti1x) rj*kl-jom8kt has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its su.ywcltimxuikkmi 6dnk i jr -) tk11*5*jo/* 8rface?   

  A hypothetical planet hasi wd5 jnm n9u6xur6 fud((;um; a mass 1.66 times that of Earth, but the same radius. Wh5;d9nmumd uw66((r j ;ixfn uuat is g near its surface?   

  Two objects attract each o:tj;5io 6oe ya)d qq1xther 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 o+wbqo) -t i9vnnr .ljj:. sah/f g , the acceleration of gravity, at (a) 3200 m hn. l)toj/s+ jar.vq bnw:i -9   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth ibdb0i9bb5enc)+ /da’s center to a point outside the Earth where thegravitational acceleration due to the Earth isa9+0e5dni b/dbcb bi) $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed id.w9l ;fkjsf )nto a sphere about 10 km in raks wdl.jff)9; dius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averagvwfb : 0*f*froe star like our Sun but is now in the last stage of it:f0* wob frfv*s evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronautsg8/2 l.sgmwg1f:bg;l) 7,jej iz. dpqlt ;zl f feel weightless while 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 l,/ qfl:zs jglegbz w1it.l78g; );dgf p2mj .250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcu* ,-/zg2o3greys oc p4w+gjjulate the gwj4*u/-pc+ g2,e ojygos rz3 magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the e w e1xjhbml17:b iydf)j+w *13b /ujzsame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumin1/ l* b fyeum1jw73iwedzb:)hj b+jx 1g 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 jyvumv;.0gn,0ouuiosrg-:6 9n9 se q0.38 of what it isru,u 6ngoengvqvous;ji 90 ms9-. 0 y: on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the ysu/b,u +hh- uie9++vzr:p vo okr7l .Sun using the known value for the period of the Earth and its distance from the Sun. [rpo 7.h , hu+uorz+v-us:ky 9 liebv+/Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satell)n m6nx5p+yw fite moving in a stable circular orbit about the Earth at a height of 3600 km. 6n ypn)w+5fxm   $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 klfm* l8k 0 m37cj;vzqpp7)e csm above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?*jvl3;)mscq07kcp8 zmf e 7 pl    $\times 10^3$

  At what rate must a cylindl, mg,;+ nyjbirical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for omn ;,,bgijl+yne revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “erboq zb:7uvj:3 n a/+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. Does your result depend on the mass of the satellite? o u+:qr/aenz:b 7jb3v   s ~    min

  At what horizontal velocity would a satellfy19+w cr6)67:/qesw gi a6tbvtcp mnite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the qb1+wt6 6gien )cf /69rvmap :tyc7sw Earth?   

  During an Apollo lunar landing mission,ag yq03a(j ek14c/2totigu7 gpp: w3l the command module continued to orbit thc7a/3y3 pgk1tep ul owtg2:ji0 a(gq4e Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The innwnwdwjc, xhw)+ v78u6 er radius of8 wwdxh 6j )wvc,wnu7+ the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. mrqdfs,,nf/ 5js5p 8r fh5re)5–9). What is the ratio of a person’s apparen8nj5 pr)d,rs,f/fmf5 rs qe5 ht 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 tvpxbs wz;3* /qhe Earth's Moon i*;xw3 / vsbpzqn 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 njwwb15g:cwk5j 3y-q-star system consists of two stars of equal mass. They are observed 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 eagc 5w13-byjj wwk5 n:qch?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman ind7a;vaw2p3pjo8p lg/2btkh 3o m;( dx an elevator that mov2; v2(x3 ddwpo /apo3ktapmh8bgjl; 7es
(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)3jycza)t5t( , tv1fdhj9oc ,cwpyv 1 the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acceleratestt9 dc jj(pfw3a,1oc) yt,yzhv 5vc)1. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelld(ojga ;,xmq4 +o7nl fite orbits very near the surface of a planet with period T , the density (mass/volume) of(mxdagqnj, ol +74 ;fo 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 (2cavt1b m- zu0:7.4 d) to determine the period of a01:vmbatu z- cn artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,km(jhqbee6o ) (hq: /r orbits the Sun like the planets. Its period is 410 d. What is its mean dis(h)jq:k/( mq 6 eebrohtance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of7t zcd+3:.cqti;t(jc)zh muw 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. Itr-cg*obvkg4nuf38 eoo ,d 2f9 comes very close to the surface of the So-vcko nubf,ggo8r*2 e93f 4dun 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 distance from the Sun.]    $\times 10^6$

  Our Sun rotates aboutj(x 6un sab1*mki(rz 5 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 mass, period, and mean distance f)-;ooglt 9juwe(:gqh c v0,zaor the four largest moons of Jupiter (those discovered by Galileo in 1609).,qzu(a eto:j-o w vg90hcg );l
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth f0 v.y+mt 7v nnrodkcef8rpe/tys2 ;3s(er4,h rom the known period and distance of the Moon. e pye/r ohd r4(t07fynkv vc sr.23+mne,t8s;   $\times 10^{24}$

  Determine the mean distance from Jj bd-jflw*b) 4.uv0 fnupiter for each of Jupiter’s moons, using Kepler’s third law. Use the disj4lj)b0dnwu .ff b*v -tance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frag.6ykm:h t:vp hqwytg r05q)a om1.7jxments (which some space scientists think came from a plan ):jha kmhg1. ty7pwoqvy:56qm0 x t.ret that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the foyn5wy /u1b3(mn i )9zo bgxc4ca)n)mfrm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noo ix m/u5nw4y9zo 3a)c gnyf(bb) mc)n1n). 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 arcg khaxy.jpe 1u9m:) 0s from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 mp9u :ehg kjy .a0)1xsN 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 ai ,ir5m(3c ck8ze o8qicceleration of gravity be half what it is r38ii oc 58e (kzmc,iqon the surface?    $\times 10^6$

  On an ice rink, two skaters of enxm5ro4 2 r 9xc,seof-qual 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 their individuanrfxx5r -4,eos92co ml masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appalls (sat3qoxc e.861f rent acceleration of gravity at the equator is slightly e613 .loq(xctsfas l 8less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spal7b4 h9tm w5yy1yb+lw cecraft traveling directly from the Earth to the Moon experience zerw45h 1 blwm yt9yb+ly7o net force because the 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 bathhxxo0j69 uu j*ayv ,1yroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direcxaux jhjvo9,0*u1yy 6tion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboutn )nobju8 p402fqge.d 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) if an effect equal to gravit nqg.p8n 2 4djeo0u)bfy 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 (Fiz(0dakhaun8j ae:-.l5g 2iww, :yjw1sol 5 xzg. 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 of its radius r, theyd 8v e5i-;jcn acceleration due to gravi5i-n dje yv8c;ty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflec /dt10:8d2cjz clzq h dtazh ,q60fbm2ted from the vertical by an angla1qbtjfcdzmz 20/:6t qz h8d,dl h02c e $\theta$ 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 fy d)g3 mmv+/uxk4m*sqor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car sa3 qk /4gxsum+*v mm)ydfely handle the curve?

  How long would a day be if the Earth were rotating so fast that objecxl 7:ae k+d m/7;o7ovqq04osou6fq vlts at the equator oquod7oq a+f : mk v7v0lx6;e4slo/7q were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of s cy;3t12 e5)bi6;ip ocm+lmzqc3emi 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 co .iu;c/ru i7w7qif/xvnstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an anglef/;i7xvuui. 7 cwr/i q of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mast p s,5u;h lejc09b7yzsive as the Earth. Thus, it has been claimed 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 ate b; 5yt9plh07,jcusz the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an 4/;aelnir; ri z/*g rxextremely 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 cloue lrgizx/ *;ir/nr;4a ds 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 ip .prg3(1ye4ehvu wl ;j/tie/rg 1hb 8t traverses the hill and valley shown in Fig. 5–45. Both the hill atg8 l/p br1;v upe1 ejwr(eh3 gyi./4hnd 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 at A?

  The Navstar Global Positioning System (GPS) util*619zrym 5eb)wfsqn e izes 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. *q b fzn5s9r6m1y) eweThe 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), after traveling 2.1 biuqgp.clu 001s llion km, is meant to orbit the asteroid Eros at a height of about 15 km . Elpus10u0 cgq .ros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repair: eyn 9 4rqq(s,qjbu3fdy 7.ay. You are in a circular orbit of the same radius as the satellite (400 km above the Earth) :4qryy,b 3(9y.a j qfenuqds7, 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 3000g0*+8 7u fzw)jcrxfteq( pu:ivjq3n 5 years. (a) What is its mean distance from tz5*jfu:)pwi( 0qxcvqt+ ur3neg87 fj he 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 nev 7ifm9a/d- ae)mvmj5 ed to be if you could actually "feel" youv d9iamev/-75 )jmamfrself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.k1jy pc3 dp/z5 5-46) at a distance of about 30,000 lightcyp1zk5/dpj3 -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 n1-8iqk e- 2gjrs :s;zz6 kxxrk1 0bglcorners of a square 0.50 m on each side. Find the magnitude and directionezir:68s1xlggk qxkjs zk21 n0--b;r of the 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 thed75 yjd5ix4hc 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 experienced by the tip of the 1.2r csqi3 p i,ec,j8f(v5-cm-long sweep second hand on yov, 28 qj3,i(fsi cprecur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weig.1utv9 nml-x gy1qh0xqg0d. vht 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: Seu11qvxmdnx 9tqyl.h-g0 vg0 .e Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thds,;d k2 o* ji,ih+tzq s-y;jfat a car traveling ,,*fji+shj z;kdoi -d ty2sq;at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of wru4lk;)xkcay)e 6n+ :i fid(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 experienc;di kkl:)ciux4 6(fywrn+ a)e e 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.$\approx$    $\times 10^2$