Sometimes people say that water is removed from clothes in a spin dryer un g .ig2:1utg gnmfva p 0ov io2c:3kr76w++zby centrifugal force throwing the water outward. Whatgprcai27z02vtg +gu6k o ::ui3v n.1+mogwnf is wrong with this statement?

Will the acceleration of a car be the same when the car travedr 4ua/ st(ezro,:nc ,.v1fc: -bg noils around a sharp curve at a constant 60 km/h as when it travels around a gentle cur ts.ez:/v-n rfri, douacb, (41:gnocve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whh zpgb rqw50url)71 3zere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level suzw35lh zr7br1q0 )p gtretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-4 0,t-4/pyva kris6nqcxk cu ;go-round. Which of these forces provides the centripetal accc0c4 vn /ps;u i,6ykx4-trqakeleration of the child?

A bucket of water can be whirled in a vertical circle without the watp36mw 8a8s nbrc f7n-wer spilling out, even at the t 7w 6nbpmw8c8fas-3r nop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cy+q a.y0ipd1wm5m 8o .gm/vrhontrols in the car which can be used to cause the car to accelerate. What are t5i 0. vm+dqwm8 yog/yrp.ham1hey? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill n /zbolsz j hj84,bevf+7h2g6, 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 ashn8,f6vb/7s+jo 4g b zl2jhze he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when r/rbhtuxq,yy/; ibf2 1ounding a curve at high speed?

Why do airplanes bank when they turn? Ht8dy o49l hij(zqyk2u,l;ph 4:c7oq y l5jxt;ow would you compute the banking angle given its z;kqyjxoolqc 5 jy(t 42 ilh,h9y;7dl8:t4u pspeed and radius of the turn?

A girl is whirling a ball on q -dsm o(f(1vyn1hm 1ja string around 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 shouls n1md- o(fj(hmqv11 yd she let go of the string?

Does an apple exert a gravitational for8:-di:7vlcac h-izo sce on the Earth? If so, how large a force? Consider an apph-a:ii zc- dl:8vsc o7le
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woulp1g0u;lv slkznu37s 2d the Moon’s orbit be differesps0v7ln1zk gu;l3 2unt?

Which pulls harder g s4unyu3ss g3rc);4fw7epu:sravitationally, the Earth on the Moon, or the Moon on the Earth? Which acw3)essf s;pc734:4n suryu ugcelerates more?

The Sun's gravitational pull on thcc09agg* hg 5uq8fr9ve Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Erc cgq 0v9g5uhf8g*a9 xplain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at tmyx68yve:rn 0:itn n3 he equator or at the poles? What two effects are at work? 60 8:eiyv xy3ntnmn:rDo they oppose each other?

The gravitational force on the Moon due vxlbe- ceq 4 lkw6xs.j8v04jdh2f -6fto the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the0h-cf6 veld- e.b2wj4q4fl6x 8vkjxs Earth?

Is the centripetal acceleration of Mars k dvhnr5i as 7ac1*p8*in its orbit around the Sun larger or smaller than thris 87 5pv kc*n*daah1e centripetal acceleration of the Earth?

Would it require less speed tc;m(a /sg d95+p2lvzoi avy8 qo launch a satellite (a) toward the east or (b) toward the west? Consider iq8s2magvd(59/ cayvo pzl;+ the Earth’s rotation direction.

When will your apparent weight be/rl/ kc5iny-f the greatest, as measured by a scale in a moving elevator: when the elevat/y-ck5r i nl/for (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely q.ir + y7-v1vkr4lwstaffected by weightlessness. One way to simulate gq tswir-yk4+7rl1v v .ravity 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 gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessk2:dh g+so k( wr*psngbz ,)k6ness” between stepsk :d2*+)k6s ,(wz bnkgrhopgs.

The Earth moves faster in its orbit around the Sun in Janu)jzd lq6 k9eq2ary than in July. Is the Earth closer to thejl q6z2kdq )e9 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 of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon.0yab (wr a+f1j Explain how this discovery enablfrjby 10(a+aw ed an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ear .qk:ouz xk 2uwr58 -bljhy1:dth 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.hqlw-:2jky1x bodzr5 u ku 8: from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19m.eb j:4ztn wv7 7to.o80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 u s;nqc*,+nquooa9 ;8zt x5up jr(f8yof the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on thz nn,j fpa+8(uu qt59*;osryx ;oq8cue 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 unrn2d2 v4y:. zr,grh r f3ive-xiformly in2xz.i4-her yfrg23nd vr :v,r a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in i mgjdizu 0)a21x3/r forbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutem)03/j2rdixaiu1z gfs. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of th rd:8mg4 cobzgr*0/ ,b:yplv* q4bbn(i u gvf2e acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’4u4/bm:*rf:q8 * gzidbov ny 0,gbbrlgc(p v2s diameter is 32 cm?   

  A ball on the end of9-: gvh bn9kxr a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3 vx99 r-:kgbnh3. 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-ffyu p5rc1x43 kg car can round a turn of radius 77 m on a flat road ifufrc13yf4p5 x 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 coefficient of static friction be betwetqqpt+jm ; 4f1oqsmwt1* n,c frq(w 6-en the tires and the road if as q-mwtf q ( wtcqnrjq1;*f+p4,o61tm car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed**.zq7sfff mb* 1t7zlm/ ja wh to rotate a trainee in a horizontal c t hm/7f.z1bzqs jwmf*7 af*l*ircle 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?    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 variable yp 7fs(yzj 3g0speed. When 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 coefficientgp07z ys (3yjf of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dogksaxa 0 nln:111w/qy wn at the top o1a/1 ax0ksn qlnw1g y:f 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 cj24dqbq7 bs+ 950 kg (including the driver) crosses the rounded top qq7 j2 +sd4bcbof 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 minute would a 15-m-diameter Ferris wheelcf tvq0.kik-;gxchqq5n74/ b e4e :be need to make for t45g ;4e 7 fe/-:cni. khbv0ebqktcqqxhe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled d: 9swt+m+,73. vdsm hgou wulin a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket 9 slst,3:7mmuu.wg+vh+do dwis 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 fromz gvh/t zy;33,/yf tpl the axis of rotatpz3yg,/ ;v/lztyf h3tion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot*dkfw s 7nuq,8ated in a cylindrically walled "room." (See Fig. qn8w sfu,7* dk5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a f -u/xl4cw9 zc+ck(fxerictionless air-hockey tabletop, an+ 9k-u4 wf(xcccex/zl d 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 , precisely this time, by not ignoring the we prun7 f)zo.8xw4 ux9b-o,hra ight of the ball which revolves on a string 0.600 m long. In particular, find the magnituxx p89 4wro bzu7,)arn .-fhoude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 75l. ;2rdb *svlzxqe:xp5sypl5 fy.i0 , $\mathrm{~km} / \mathrm{h}$ , 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 massesjt)h-ba in6md4 h6bt uzn47b* $ 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 mk4ua1 47wvtoganeuver 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 anl mh; 9;ezfjg6q:.cgv- euoi 0d centripetal components of the net force exerted on the car (by the ground) in Exa-; g60cfvmoe; 9hq.jz :ielg umple 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 p7u)6h lsh ehwiz3z7-rxg -t0500 accelerates 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 c6h-el3p 0zrux7ih thswg )7 -zonstant 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 ovs:(s5gh vvd;f radius 2.90 m . At a particular instas(5;vgvhs: vdnt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earthpld6hxnwq 44-w b/p 0o radii) above the Ea4l6h/dqopbn w40w-px rth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g haa nf v y 9uaar 9mkf(7rjtj/):30k/tqap*1isjs a magnitude of 12p: (719rfkt*/v0jj)af a9nyaa3tmuj r kq si / 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 is 1p1 tf4. b0obha.74h41bbftp oa0 . $\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 sayt:k lk)r0 ohk-rh9w t 3:2zihme mass. What is ttkw -it hykholk: 230h9r )zr:he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bg/a1ht/vw u2nbdx14 (xni1+,tp 5 mvxpo ee u9ut the same radius. What is g near its sur gb+2vh5onwi, v// t1xpm1(ud9neaxpu1xe4 t face?   

  Two objects attract each other gravitationally with a force of 2f+ i( sq.adh-xwq*6c f.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 valu/njry)7j g tb7e of g , the acceleration of gravity, at (a) 3200 m bjn/g r7y)7tj    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth s*ep i2k zup3d3mrsbcft/(t3 8wb:s/ where thegravitational acceleration due to the*3 8rtsbt:uf2 pk3ed w / sbc(mszi3/p 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 packed intop;gkd4xt hg)+ a sphere about 10 km in radius. Estimate the surface gravity on this m;hx)4pt gd+gkonster.    $\times10^12$

  A typical white-dwarf star, which once was an averaggokyeyhxmk 54 u3 :z25e star like our Sun but is now in the last sta5yg z 5m :hoeykuk423xge of its 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 astronauts feel weightless while orbiting in the space szc7/x, 63bn xg*yf4k3yxw mzahuttle. Your friends respoyx473bg6nz k3yxz*,xwac f/m nd that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square o uk 2csu/chf :o7 rar0gu,:8sif side 0.60 m. Calculate the magnitude and directikur 27c:i8aruho/g s0fcs,u: on 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 li .kn bxzuwx/,8ne up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are /uxb8 zk.w,xn $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 t8 vpl)pwa77tehe surface of Mars is 0.38 of what it is on Earth, and that Mars’7vwlap )7te8 p 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 v:jcg+ ta6 p :r,akkf8the Earth and its distance from the Sun. jr6kt:g,c +:8fpaavk [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about hfk0 wk)sd p 9d3,jrp7*kz2pu):o fkathe Earth at a heigk)kfp *:s,ofprdhpj 2k)73kzd w9ua 0 ht of 3600 km.    $\times 10^3$

  The space shuttle releases a ( nlx f/h66oes:r y(dzsatellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occx:(n6/6 fhd zeys(rolurs?    $\times 10^3$

  At what rate must a cylindrical i8i7f55xh r0gi gw0sbspaceship 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 foggbf s0i 0i85h7rix5 wr one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takesuih0llf 1mons,e833) h/k -amnqq:iv 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 tf k8i molin)-alv:n33, /hhu m s1eqq0he 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 launched from the-w9xyfjdg(6yx; - fbjn7d/bx top of Mt. Eve9f ny xjb7dyb;x /(wjd-g6f-x rest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the commabhsv xgi3 k),wm)9u79 kcrsak )gx l2:nd module continued to orbit the Moon at an altitude of about 100 km. How lonc, 72rhkw39a:igs9)g xmxkk )v lb us)g did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit v;bs k)995tjebueh 1sthe planet. The inner radius of bvb )s ee;hts9jk15u9the 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 (se.)0 nlqan. hyze 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 bot q..) n0hynazltom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42004 wy62;dzoqy cgo,c0c km from the center of the Earth's Moon in a space vehicle (a) moving at oc4d o c wc,zgyq6y0;2constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. The +6s0joy fgx,6 vjg.mdy are observed to be separated by 360 million km and take 5.7 Earth years to orbij.jsm + d6g6o y,v0xfgt about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator th7+p1cw+xt) ro8od g wxat px dw+cg+7x r18oowt)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 fr7jvz+:: cs6ecn5x (r*xo ne ubom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (mag6ousxz(+r5 7:b:cxcevn*n j enitude and direction)? a =   

Show that if a satellite orbi.qck)jn k, h)*cos zg(ts very near the surface of a planet with period T , the density (mass/voc)n, *ksqkc zh)(oj .glume) 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 deter :2o jvmot+-aa:3g xhwmine the period of an artificial satm -+gt23x:a: vhajoowellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits tfu;a,+2zl1jrncn6r y oq9)lh he Sun like tz9ur );lc6l fh1nr 2+,a yonqjhe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of f1 sekc4.b:nq4.5 $\times 10^{9} \mathrm{~km}$ 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 lb. 8gxap/h7he1mpe onv( r hbm9r+ +bbv.c3+ years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s8ga.mpe+pbhmv hrb/7 n.v x(31 b+b+oh9cler 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 o tlgp0wk /(tq0f 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 for the fo be5: m0if w2vi+(x;yzr+jfj fur largest moons of Jupit+bf;(xi e izj0vrf5:yw2+fmjer (those discovered 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 the known period and distan 6i zws32u8j7ck9w*ggl- xkurce of the Moon. w u-*s8j9z 2xgg637cwrlik ku    $\times 10^{24}$

  Determine the mean distan x6l6o1rs007loi 0eui.xuly t),jpbn ce from Jupiter for each of Jupiter’s moons, using Kepler’s t 6 ,peu6)uso0tixj0 ll rnbx iylo107.hird law. Use the distance 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 co y- vw(0kk9xrpnsists of many fragments (which some space scientists think came from a planet that once orbited the Sw p-xy 0k9r(vkun 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 "pll )r+sd;qch0(5 mep fdf *6qmlanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temdrs0c5q;mf f6 q+dl( meh)*lpperate), 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 bwusl3dr2m25 0 cgv oq(y 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, whdrcumqwg25ol v 02 s3(at 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 wi,hn mav9v9 sx9ll the acceleration of gravity be half what it is axv m9vh,99ns on the surface?    $\times 10^6$

  On an ice rink, two ska5t:7t )vr m.x:q5k yzex:hev gters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual mass.etxqv x m::h)5:v krt yeg5z7es are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent ,*pe xnpxol14*b5yftgkq3 h9acceleration of gravity at the equator is slightly less thantkq* 3fp 4blgexp5 nh9y1,xo * 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 spacecraft ,6wbm gdzt5l) traveling directly from the Earth to the Moon experience zewbm t5dgz)l6, ro 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 bathroom scale in anrpuw+(pw5bu s; u5zb . elevator, it says your mass is 82 kg. What is the acceleratiow+urz5 pw (5 bsup;.bun of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular4okp6 :rm ti5gh-4l iq 1s-a /fbva0thikn70 b tube that will rotate 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) if an effect equal to-g06a0a 4n5h-/1rkpfk svbm h qilit7 bot4:i gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hisdp0dkqt4:0 dl44)blo d rt/r t aircraft in 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 in terms-tvp1yj vgvrp *o730 c of its radius r, the acceleration due to gravity at its orv3- ypvj071 vcgt*p surface and the gravitational constant G.

A plumb bob (a mass j+aq(hvxg(f :4-h6n2j wp ugem hanging on a string) is deflected from the vertical by an an ajqxeg-f( g(+2vw6pnh j:u h4gle $\theta$ 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 coeffic gyo)+/g2 em/sopels9r;mtm 7l9los/ient of static friction is 0.30 (wet pl peo9 ) +lm/sgm/g9/er7;to ml2o ssyavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast t jp3u9g c.fs6hhat objects at the equ69 g3j.c fpsuhator were apparently weightless?    $\times 10^3$s

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

  A train traveling at a constant speed rounds a curve of radius 235 2mkoifkh t+ze tv ,hh*8h::9im. A lamp suspended from the ceilingti8 vtimze 2 ho+*hf9khh: :,k swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massn5/6 u zyqzbi1w0)koa/n*itc ive 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 at the equator of such a planet. Use the6 /i0ia) n1w*5ok nzqcuzb/yt 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 presenst 9m 5o/pdy qu3/pw0jce of an extremely massidsyqwj/ p 05mup9o t/3ve core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown8v5qig d4qmi*ab1;) :usagu/ w gh- js* gsrc- 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 gbw j 1*5m)ucs8*:g/i;s 4-qhaqgv g-s uradi 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) utilizes a group of 24 sate+x8/aprw0ph w llites 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 nau8/r+ww p0xhpa tical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), anm ir19.n o dz*j+wq/t7)fpz after traveling 2.1 billion km, is meant to orbit the asteroid Eros atzjo)anw/+z9rnmid 17*f. ptq a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in :5*scwo ,6yf9jhwft x need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 c ,w6y9 osff*j:5xwth 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 me7uy w4wd+ rog,an distance from the Sun?w,do ur4g w7+y   
(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 t13u.jea ke6h no be if you could actually "feel" yourself gravitationally attracted to someone near you. Make rea.3kue6ja 1nh esonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centergm l (ckrx.41o of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years (4kocx .mgr1l 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 gtm ) k-0 hob8pyqc82r0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the -p mcqoyhk0rgb )28 8tsquare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earf6mtrr 00 ,pobth $ \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 swny+0 s+oqzjw 0- ,pr/z5 6 rnhf8jyaqweep second hand on0 azfqr ,pyw- hjys nj0w68z/r++ 5qon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start tu(y)wm 78 qv7rn, smqeo swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a compm e8)ruynqw,q(v s7m7lete 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 radiubhm dm w 1u3 jv.7s+vwi06tuq+ cxds8(s R in a new highway is designed so that a car traveling at speex67tu+d+.buhjm 3dvis8(wqm 10w sv cd $ 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 ofk azrd;j6ie8 0 the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provikrie8j6 ;adz0 de the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$