Sometimes people say that water is removdi xj3a +n9g*xed from clothes in a spin dryer by centrifugal force throwing the water o x +jxd9a3ig*nutward. What is wrong with this statement?

Will the acceleration of a carmum-lms-oh h. ih1-i* be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same suh 1 i-s*om-. ihh-lmmpeed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car wvdf gb7cne3;7uw8 a, exert the greatest and least forces on the road: (a) at the top of fcga 7v,w;eu7b8wdn 3a 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 horser(mv g;,qea0u on a merry-go-round. Which of these m e0,v(grq; uaforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a v6pp viaxk)y1; 1oj4x4y1gcqa ertical circle without the water spilling out, even at the top of the circle when th;pj pgyv4i yx6) 11qxok1 ac4ae bucket is upside down. Explain.

How many “accelerators” do you have inoggsqgl kx3xq8 .p ;8. your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prox 3q.8spq;l.ggkx g 8oduce?

A child on a sled comes flying over the crest of a sma3 ufh8:lke7 tnf rezo b)4eq3/ll 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 this4 unzf7el3: eher )obt /kqf38 decrease using Newton’s second law.

Why do bicycle ridersk4e5q72:gki a/k ifke lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anglar*w* fp,h p hq myf1(y(uwk66e given its speed a 6 (fry*hu fy1m6w(wp qk,pa*hnd radius of the turn?

A girl is whirling a ball on a string around her heqk ,h*,v snmvylf.-z7 ad in a horizontal plane. She wants to let go at precisely the right time so that the ball will hi*ykm,sv zflnv h.q7 -,t a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitationalr.oq+wx/ g:4;b vgynhcj0.w j force on the Earth? If so, how large a force? Consider ang:nw xb4+ hgvw.yq oj0/r.;jc apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it o(fkvd:b0wk j t658sbis, in what ways would the Moon’s orbit bedksjw6kv: (0fbb5 t8o different?

Which pulls harder gravitationally, the Earth i . c-.2v-cln2mi o3gggv9u ppon the Moon, or the Moon on the Earth? Which accelerates mor2ig 2gvlon .-gp uvi -c39.pmce?

The Sun's gravitational pull on the Earvda7 ie-h+ecpd1+ d .kth 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 sidedhp1e e.c- vak+i+7dd of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects r1pmoyu2vs 9*3vm 5/m di v4klare at work?4vml pi2 /rk13v95 muvsody*m Do they oppose each other?

The gravitational force on the Moon d6th e7xmlti 7gec.96wue to the Earth is only about half the force on the Moon due to the Sun. Why isn’ ceh7i6e7g ml9tt .6xwt the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suo ffw04tl1wm9 n larger or smaller 1ff4 l0w w9motthan the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward bf)nf 0o8( hxux g9*je7/ldtah l+ cs;the east or (b) toward the west? Consider the Earth’s rotatx*o )0f;(lnelfs/xjhga7h9b t dc8+u ion direction.

When will your apparent wd -twl+:4r u(emdhw:seight be 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 speed? In which case would your weight be the least? Whed+lwd thmsr:(w ue-4:n 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 spac+p:eln.p*o/ qqw 1ogge 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 f:gpqe+*opq o.l n/g1w eet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bn(w*er+gob (p etween ste o +(gwp(e*rbnps.

The Earth moves faster in its orbit arounbno( ty8/hw/yd the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Ny /nyw(h b/8otote: 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 hajy n50bn sjkly f(.-p:ve a moon. Explain how this discovery enabled a n-j.yspf( 5nlk0j y:bn estimate of Pluto’s mass.

  The Sun's gravitatio 5n9s6d 57l0ytjjgs c;;uf k5maj6rbnnal pull 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 yl9afg m6r7tcjdnj5jn u65;ss0; k5bof the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1,rb7s(8szi7 5wdb zfbsv/ j,a980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 5( csvwe6qgm)om0.- fukbb *o of the Earth in its orbit around the Sun, and t)6vbw.*skq(o bc-0uoe mm 5gfhe net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniq:y+n3+(y;zp/o rsv09: qux.(x tbkzy ypazs formly in a horizontal circle (at arm’yy9 +x vnz3ry p:;a/+bspuok(q.stq y xz(0z:s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orb//n5 5dz ydeq:yqkc.f p ouyu9ht/. u5it 400 km from the Earth's 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 of g ,uko qy .e:n/d p/yu. hzcyqf9tdu55/5 the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay 63g yxpmg7u)y ka4 s( *jh,wgkon the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s d3ygp)kgsuhjya( ,4* km7gxw 6 iameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform k xij;14he 3wvmfl 8em8-adl u14tcf+ vely21 rate in a vertical circle of radius 72.0 cm , as shown i;fy v4dm eu 1811h-3exfmcl iv je+28kllatw4n 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 radius 72lwxyy,n-o p /7 m on a flat road if the coefficient of static friction between tires and road is x w -2,pynlyo/0.80? Is this result independent of the mass of the car?   

  How large must the coefficien)it h ki;dwh0q04p-vr t of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at ap;k i4rviw) tq dh0h-0 speed of 95km/h ?   

  A device for training astronauts and jet figsxza4x s2u c.*hter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on h2ux4x.z css*aer back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variablgt9.7h lc9dse7,p ci tjnj :w7e speed. When the speed of the turntable is slowly increased, the coin remains fixed sewjt7 cpl7j d . 9c9n,t:ghi7on 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 traveling when upside down9 i+yd a8ms 9hwa1d68tyy vge8 at the top of 9 wiy9dag v+tdahm18y s688ey a circle
(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 m/vr)) mer0(f,i ixly driver) crosses the rounded top of a hill (ra mimi )l/yrx0)rfe,v( dius =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 woaohgl+ oe 64l7uld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weight g o+hla7lo64eless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical ca09dwrre6h s3ks1wub+ 8e5 jcircle of radius 1.10 m. At the lowest point 9ra suwhw +d 6ec03er8j1bs5k of its motion the tension 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 centrifuge rotiqx6pc 22o,1 tav -ktc0d2od eate if a particle 9.00 cm from the axis of rotation is to experience anopa2c2 1qi 0dtx e,ko6d c-vt2 acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cak p,ljmm m w5g77+2zaya5:unbdwxh- /rnival, people are rotated in a cylindrically walled "room." (See F/k guwj:-7bzw7hm n,2 amax5 dy +l5mpig. 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 :s4z sqxbg;4k rotated in a circle on a frictionless air-hockey tabletop, ax;qks 4 4:gzbsnd is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , pre3 zis x65n q7 jmmq9hob2hiy0/cisely this time, by not ignoring the weight of the ball which revolves on a st3 z0q6ixohqb59j/ n7msyh 2miring 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 3k mkd9-qkv/bm 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 masses 7a a l7r9/ 5*zqzwmllv$ 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 vertically at kxsf:g ks6yf b23)-a(ha/cts310 $\mathrm{~m} / \mathrm{s}$ . 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 onq263qk 3ifjtx the car (by the ground) in Example x k3 f36jqtiq2 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going froctd,d k mk9t*r2q*h vu) 1w,vjm rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and r )*tvu c,tj dvh2 r19,q*kdmwkadial 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 of radius 2.90 m . At a particupk3uc79s - wxodngx/-lar instant, its acceleration is /n79xw3 skpxdo-ugc- 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth ra qi-vj;v* bh9)ef,9shbglu8 odii) above the Earth’s surface if its mass is 1350 kq fivhbe9 o-, v)lg9 8b;su*jhg.   

  At the surface of a certain planet, 2noebjk(.e 9z90wb cw the gravitational acceleration g has a magnitudeezceb9 0.bonj k2w(w9 of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius ish(jv/nzrb w i5p3: :lg 1.74 :wjnp hv/:5b( ilr gz3$\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 sameas;eh.*a 7,x lmgxpq*e6 8z5 umxfx2k mass. Whakulq6z8 7spaf2eh *ax,mxx; e.x5m*gt is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same)ia, ecs;w, /-dso dle radius. What is g near itwc e)ild; -ed s,so,/as surface?   

  Two objects attract each other gravitationally -3 *u cz,qw nr:tyci2mwith a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g/ 9-)n f2(hdinsk bcdo , the acceleration of gravity, at (a) 3200 md)sf b ockh/i2n -n(9d    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside thz o( ayzzo95ai: wlx,krvb173e Earth where thegravitational acceleayr:a5obo(9z ,3ki1x lz w 7zvration 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 our Sun pack l)z7+uyep-:ubs.s 4uhi,ahoed into a sphere about 10 km in radius. Esty)bs+s,7uhh4uu -.io l:ez apimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Su6zchw. vsej67n but is now in the last stage of its evolution, is the size of our Moon but has the maj6ch6z7wv .e sss of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauti9 fw.u5pm b6dzyzd6 8s feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was jz u md98fb6wid56pyz .ust a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sispskq+-2ti f.de 0.60 m. Calculk.+sit2pf q- sate the 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 same sidew* ms1t.)nxrrb2ju7 xcpt2b*: da sd. of the Sun. Calculate the total force on the 21t.x:bsmd*7j .c)upbns 2xr*wdrat 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 gravityk6e6p ta jcp*8 at the surface of Mars is 0.38 of what it is on Earth, *tj68 pke6p acand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value foc jl.9).r: znq*a5orcx bgew3r the period of the Earth and its distance from the Sun. [Note: Compare your answer tocrz9b )ew5 . *3g:jqrnxa c.lo that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movingryx t 3 tuj;s 4te( lidv6-7vz0b:3nwe in a stable circular orbit about the Earth at a heigvzu(;e:3t07vi rsj3-tdyt xlebnw 46ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 gg fj,079vuqm km above the Earth. How fast must the shuttle be moving (relative to Eargv0 ugq,mjf7 9th) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants yy nc2w,(/u 3po1ozawa br.g5are to experience simulated gravity of 0,yrwg15c/ay. up2zbnoo3w(a.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it te3e+e bq: y qcno;o7o1akes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the massqo ecen7:y 3e o+1bq;o of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to bef io9o 0jw5qgnw:xo hwm; ha+*6tq3a: launched from the top of Mta6w3j :i0*+ o q9mh5ntxa:oq ww;fg ho. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued t/ :*4sr 4xjg5zy og1co +kxxvwo orbit the Moon at an altitude of about 100 x rsx gw/4 4xkyjvc*5+ ozog1:km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that 15s/hzw pyh4torbit the planet. The inner radius of the rings is 73,0hy5t41hpwzs /00 $\mathrm{~km}$ , 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 (;:.gk.55eyqyk+ ;uwayuey hdsee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the boq ;g 5dy;.e+ uyhwa.:kyyk5euttom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of tho mkqrw7x /cr-p 18a0qwz;d9p e Earth's Moon in a space vehicle (a) mw/q;8dq 7o c- m0wr9krappxz1 oving 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-sv4eg)x g/u c,bm8q :;uj;w ubgtar 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 pointjg b4qcue):wg b m8u,;vxug;/ midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weigh r c.gl.df2yzv8i 70r8ze xyk1/bm9/ zmh4 bljt of a 55-kg woman in an elevator that 1.0 c z.k/lvlyjr h zr72iey89b8x4mf/zb dgm moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. T46ach ywtqg.5he cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction4cthw6 yag 5.q)? a =   

Show that if a satellite orbits very near the / tnly:9d fb, khn+q4gsurface of a planet with period T /+n:kl bnq,d9t 4hyfg, the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine t3vqb++ijvgx m/ upjfd xe7,)9he period of an artificial satellite orbit/u++gx3xpj d9v vim)ej7qfb , ing very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits tl3 gduzt )yf3n3e,1yd+ rlow+he Sun like the planets. Its period is 410 d. What is its mean distance from the Suunf td +yzeld1wgl3)y,3 o+ r3n?    $\times 10^{11}$

  Neptune is an average distance o gzqo3v/ te a3ys;/n+cf 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close tn- t0vjgi s 93gi7dob4o the surface of the Sun on its closest approach (Fig. 5–39). Estimate the djtgn7 s -vbi9 043oiggreatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxk: 5)j6gb3 z xddgpg6hy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for,k7(3h-s5v5zd 6z+l lamuqqqr3opg, ps,ug e the four largest moons of Jupiter (those discoveredo +s7s l6lgpd3(q a5pg, umz -euhzkqq,r, 53v by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from t5 x t**hpofax)he known period and distance of the Moon. fpoa*5h*xx )t   $\times 10^{24}$

  Determine the mean distance from Jupitepn:q..rp q t +o+6m9ws rhjwr8r for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values+.ns+ r:wrmtrwqo .j68p 9 qhp 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 (which v64*hu6i f d)-hw rhtrsome space rhf6)v-*riw4d ut h6h scientists 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 describes an artificial "planet" in the form ofbapo/ l0fzx7:; e5ycv a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the cl:ec 50/avzofx ;p 7yblimate 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 gorgeyn5j3 wccrc 3 g,/u*th by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is c3*w/cguj53n tcryh , 5.5 m long.   

  How far above the Earth’s surface e4; yzg bw3twykm+:o2 ls5l u7will the acceleration of gravity be half what it is o3e:u+lswgkyt57zo m lb2 ;4ywn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sp9mf ky /dnt3u:in in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m lo /y:dn3f9m kutng and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once perke,j g/6;br h6tgez7d 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 fraction of g is tk/ee6jgb;,h 7zr6gd this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Ea xaq/y 6 )fk9atu7rqb11ud, vu0ks(idrth to the Moon experience zero net force because the Earth and Moon pull with equal and opposd/10) rq( 1uq9 daxik7sutbvfkyu6 a, ite forces?    $\times 10^8$

  You know your mass is 65 klpbz lp*.897sm+qrghv o*q z(g, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whirp7gv.l q m9o*h*l +bsqzp(z8ch direction?     ----待选择----upwartddown 

  A projected space sta tptfq.r ; xzp:h)3a0ition consists of a circular tube that will rotate about its cen: )0qrxt3 i;pazphtf.ter (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 gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft iwnvsp6 e,dfj99k.;2 .wj utks n a vertical loop (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 /pufe8c awf-elg*b-- in terms of its radius r, the acceleration due to gravity at its surface and the gravite-fu- / fa-wce*lgbp8 ational constant G.

A plumb bob (a mass m ha5n 7/ sr;bdp+l 7pndf1+crjf mnging on a string) is deflected from the vertical by an anr1 d; 7/fsb+n+7lcpn5 mpfrj dgle $\theta$ 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 z 93imd8y4-xw7oxs djspeed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds cz d3x 7i8-d jo4wyxm9san a car safely handle the curve?

  How long would a day be if the Earth were rota) 1q-y az2a5wwawfgf;-l:w ja ting so fast that objects at the equator were y-;5wlqgaa aaw-1:2)z fj wwf apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintaineyt5 e85so fuky;5w 5x/ dt+dm a constant 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 round,chmw74a ak udb;r +o 8+:3rthzyqbn(s a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of :3q4bromhbun;+wah cy z,7tdak+ r8(17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claime tf55en )(fgyz39j wkzd 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 5zej z9)f gn5kyt(f3wg '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 presence ofd(zqavt ;ai7r qx- ,x. an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (fromvz7 tarad ixx;qq(. ,- 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 traverses the hill. ugn/u+/e,kdgpo a4i 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? Expla gnp+,kg4eudi //uo.a in. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Posl 9 *bxqv03duzxj*z;.8*pxn fjvm/ yditioning System (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) Determine the spexduvx/l p*qxmz* .jfyz*; j8vn db30 9ed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Ren7)cczr.+6; a nnctowe dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abouew o art6c.)7czcn+;n t 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of re+ f7(ttixgj +h 6y8odsrx.x )fpair. You are in a circular orbityh8. +x i of+xsft()jdx g67tr of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dispyw3 3q:24wb)elp 6hti * gxlbh2x k2ctance from the Sun? 2 ib 3w bcl hq3whx2xy*gek l6t:4)pp2  
(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 gl 2n-/j x:wr)tml y+bof G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assum m +lnj:2)g ytrbx/lw-ptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the uu h84 v ijy6 j++x sltro631upu.pbz-Milky Way Galaxy (Fig. 5-46) at a distanc sui1rjuzxh 8ju4py++6u6vbt.3o pl -e 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 mt8avm 8t :g 62daqzwwfroyb 8.rqgf-2)sn q* , on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of thz:q,tyq*.fa b8mn2r dw6 t8-wf 2v8q s)gg raoe square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg o te w acxrg9)o*rc25n3bxx.,t rbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep secondxx yas-ul:f)w o;9p5n: g lh8f36s fbj hand on your wrist wasflx8 pb;ofjyx: h)wl sf 6ug-35 :n9atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arol es k43:se0utund in a circle below you on a 0.25-m piece of f t03:4kse eulsishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travel6 fnm-yl be9 ulkm-7 r3wr:di,ing arn, 9fmbk-u3 y:-7elrilm6 dwt 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 the cars when ntc, .71uhp+:ilw-bxalyvs0t 9x rh -regotiating 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 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 does0 r7cy 1h,-lu ttvw -h+.b:alx9prsx i 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.$\approx$    $\times 10^2$