Sometimes people say that waq: d d-.tzno,vzwq+a*ter is removed from clothes in a spin dryer by centrifugal force throz+d*d w,av:-nq.qot zwing the water outward. What is wrong with this statement?

Will the acceleration of a car be th v5l0nb -ulmj:e 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 speed? Expla5 mbl:vul -j0nin.

Suppose a car moves at constant speed along a hilly road. xqcbqb9 8ee 21Where does the car exert the greatest and least forces on th1bc92 qeebxq8 e 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 chia2- 8mh*t c+q rmivo2w:p4gmdld riding a horse on a merry-go-round. Which of these p4omvgmcwa :h i82mdq2-t*r+ forces provides the centripetal acceleration of the child?

A bucket of water can be whirled i8j xs:,blfiqm, .9.szjra 2v nn a vertical circle without the water spilling out, even at the top of the circle when the bucket is frj:.,vs x.a,z q bm2l sinj98upside down. Explain.

How many “accelerators” do you have ( in4y+ s6a esn na4.x3ompm8m sea)7gin your car? There are at least three controls in the car which can be used to csnspxe(mgoai4 emy 6nm3.)7as48+n a ause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hil f)7 kdm1 (aqh )nkrtxrw6-gse2kh(-l l, as shown in Fig. 5–31. His sled does not leav w lfm(drhk x))t26h(-r1 kan -seq7gke the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speed eanuy,x3dtlyh+( fx e 2x.v9.w5du(l?

Why do airplanes bank when they turn? How would you compute the banking angle g +wl,yn3z / 6 ts,w0hogs nepfq-:7dlfiven its speed and w3zelst,+f,- n:ods q/ w 0gy6p7flhnradius of the turn?

A girl is whirling a ball on a string around her head in a horizh(+uav)f(9fqg yq :syk1y i:sontal 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 yas:vyyfqy)(1sqk +g : 9 hu(fiard. When should she let go of the string?

Does an apple exert a ;q7ow- zxot uk.2 zg(yxt u5y3gravitational force on the Earth? If so, how large a force? Cozto3 7k.zy5oyu( q wgux t2;-xnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double i3+ xtoo; 3cohwhat it is, in what ways would the Moon’s orbit be differ;co o3ho3x+ itent?

Which pulls harder gravitationally, the Eart*ekahy 2e:tu p0 ,cx-th on the Moon, or the Moon on the Earth? Wu p,-e 2a cxyeh:0kt*thich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the M(ey s-txqyps()7q k g5oon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationa y(x-7sgyt p5s )qekq(l pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at .jtz ew,w x2k nj6m5n+the poles? What two effects are at work? Do t,nmwe +j5 jxzn6k2.twhey oppose each other?

The gravitational force on the Moon due to the Earth is only about half sdn y7bn) p-0ithe force on the Moon due to the Sun. Why isn’t the Moon pulled away f-7yn i)s bn0dprom the Earth?

Is the centripetal acceleration of Mars in i fd+ltfh /qs;omg /:+ 1ykiehuy -,d/rts orbit around the Sun larger or smaller than ttq:/f dmu1d / ,e-y/rs; lhihgy++fokhe centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (4sa3 ux. epozl ,hg15id5dw b*b) toward ez5 b1oxal,ihd w5p3.usd* 4g the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measurekw 5 3kbscnik.7y0 sa2d 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? When would i0 n.ybksk72was 5kci3 t 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 sp nc, ,7.4n2x tnvamjsface could be adversely affected by weightlessness. One way to s, vs24nfxamcn .j,7tnimulate 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 gravity you can think of.

Explain how a runner experiences “free f7:,sqnrz hc :dall” or “apparent weightlessness” between s 7dq nr,:sc:hzteps.

The Earth moves faster in its orbit around the Sun in Jan8jh a,buslr - )a*1pcl,vb0qcuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a f0vql1ra)alchc -* bujb8s p,,actor 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 ;f cwc+l;bm 9dnot known until it was discovered to have a moon. Explain how this discom cw+;c;9bldfvery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. k27+xme zym8aYet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of +2 8mm aekz7xy 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 travelino)o- m ,3rj( r neynzns*7mnkbg17pn8g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in itszxkj 5lo5fq, se0a6zr/:f8wc (6w jda orbit around the Sun, and the net force eoaeq6 z(xd0,6sj5 :cajf58wr/ kw f zlxerted 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 exertea+j ht: p +r 3du*,xsx5jhdia2d on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 d3jpxrj2sx+at+d*: 5 i,ahhum. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfacea1(i: sf vcbcp 1yznqy*2y; k6, and circles the Earth about once every 90(ky1a p6i 2ns:v;cb *zcfqy1y minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerat j+r*cvg0q +r bxy((/tjfe z1pion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (rxpgz0y qc(1rf b/j +*t ve(j+revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved he *r)j9pmgjev /e+-vat a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sper/e p -hvj+v)gme 9e*jed 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 5pqt h:rv29 re-4hhiy fmgdfcm*-) 6m9f ju1jof radius 77 m on a flat road if the coefficient of static friction b*-v:rhg99 6t mhufidyefmpqc frjj21m- h 54)etween 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 between the tires and thhjrnx6-qm6u 5 xi./;xigudv(+xy1-7kue a jb e road if a car is to round a level curve of radius 85 m at a speed of 95 6b 71uyrgx+u/exu6india(xh; j- -qjx5mv k .km/h ?   

  A device for training astronaut2k dv0 o29c4,tckohi4f qxsb:s 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 wes 4 0 q4t:cvibd2xo,hfkck2o9ight, 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 s0 as4du*jow8vz+ 5fmqpeed. When the speed of the turntable is slowly in4fvm8sz0w+ d5 u joq*acreased, 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 trab5. uedqi+vzs-+ j 0wnveling when upside down at the top of a czv-e50 w++qbdnj s u.iircle
(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 qm x-ut/xs*9bthe driver) crosses the rounded top of a hill (radius =xt-sxu b*/9 qm95$ \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 wo*hry)a k)br eg -z):nauld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weign*)ea y) gh-r)zrk a:bhtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of o r6 0me:c,4)taiuxxeradius 1.10 m. At the lowest point of its motion the tensiex6ie uc0oaxm:r ),t4on 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 cw11bg oko6 x4t+iii)jt/*hyy entrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelerat14 ot)tiy j ig ybxwo6+/1*hikion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylihc3d psa8 ; ujtgsdc+(i,6e9 6 jg4bnyndrically walled "room." (Sedj; ysdc gc9a(b6st8 gnu+ p4h,63ijee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frica xh+xv97it ,9( pi cudv3gwd,tionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dan,i diw dvuht+7cp, xvg9x9 (a3gling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight o2yt u w3ze;)iff the ball which revolves on a string 0.600 m long. In par3;wu t)2zyie fticular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked y.4qxu)k6 b3r,erht n 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 masseszv p0;fzing,- $ 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 verticaw(zk7c+j lrb )0:i, 0fq4e gtcc ,0ma mrak3mhlly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net fm(tr)ooq1ej73 pgw4 qorce exerted on the car (qrq t7j3 mpw)oo(1ge4by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acce 5g(t36yp 9jlc xxk zd6xl5 s;i6hsp/mlerates 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 radiamy3 xl 5lch 5tskdg6;s66zp/i x(pjx9l 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 ciradrm(9 95kvr( b;mv igcle of radius 2.90 m . At a particular instant, its acceleration isvmr9m5(g kvb 9ird;a( 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 12,8 l 2 5heu:6m*d;mjrprp00 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.6p;er mdj*pm52ulh r:   

  At the surface of a certain planet, the gravuh;fvjbi)w+hw5e(w6d g m31ditational acceleration g has a magnitdum(+ bv w) ; efd5ww36jghih1ude 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 r,t x-i2wazis.g 7izx8adius is 1.7aw-2i iz, xg.7i x8zts4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 shwn; gj*3tga 5a2:;s oo*ei wtimes that of Earth, but has the same mass. What is the acce ;:gos;wa* henw5i3sog t*2jaleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ear+h6t0jxqo gu) th, but the same radius. qx)+0tgh u jo6What is g near its surface?   

  Two objects attract each other6y 56h 1rrgswd* (haly 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 va .4c9 nn +8q:f8w,qfgx sqbpbique1w(lue of g , the acceleration of gravity, at (a) 3200 m nse u8p+cbgqq, wf:q498 q.i(nx1bfw    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pdi i +(2mue/iff4e*choint outside the Earth where thegravitationalehf due2c( i fi/*+im4 acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our oob9bps/9e a4bn4l;cbwvj :qll79 3a Sun packed into a sphere about 10 km in radius. Estimate the surcb vn: 94lbbbjeo93loawps/ 4 al 97;qface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wafx w )8njz,l3bs an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but, zw jf8l3x)nb has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronak6y h;brb9)z uuts 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 6)b uz9; yrbhkisn’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 si ;4 z(n2lfkotfan,h-g de 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the ot(,tzn2o- n4gah lkff;her three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years)hmyow..j t3sujp9:w most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, an9ushy mpo3.j.)wtwj :d Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity ag)r9 )hhcg.fieig 9s +t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determinge 9+ .)ishfhgi gr)9ce the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuzs:c a dce 6*owg3p-gra8/trvn. /-ai e for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’*c ro pr- 8ggaw3setv a6da-i.z//:ncs laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about tz14(q5fgz rfow,evbs:yc6icgb(7 u4 he Eaw6:bggsc4 ou(y eqr1zbf5i(47, zcv frth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases *k xjim+nuuk+:efz* 3a satellite into a circular orbit 650 km above the Earth. How fast euu + zjf*m*+xik:k3nmust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate iffif+-) : mbbol xs0sk(y 5cd5h 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 nee-5ys: ks5f)db +i0 bxcmh(lfoded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular a6m9mndoi59orvdp )+ “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small comnp9ri+o)amvm 59 d6o dpared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launcm- ( fj jjrwm0n-1jqlfr, na7/hed from the top of Mt. Everest to jajl/ 0wnf,j- 1(fr-mqnj r7 mbe placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbu 5btrv.+j+pbp4e(tu uz 7e: wit the Moon at an altitude o5tt7v.ee+rz (u p+ ubj wu:bp4f 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:g+p10dxrg 2lpq8y he that orbit the planet. The inner rag+ p l0xdqrhegpy:2 81dius of 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 diameted0:za r zkcd56d46phfq. l)nqr rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a .4nkzlfh r6c5d 6): ad0qdz pqperson’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from 9, wcz -ypowb- ,ufb7ithe center of the Earth's Moon in a space vehicle (a) moving at constant oy, c7fww, b--piz9bu 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 cou:z aa) k s540;a+lgwk5lvq0j jqae6o nsists 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. Whkz0ak:+5v ajq uq6lgl0;ase 5jo )wa4at is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevad( v/ ho8k3kiwtor that moves wiho8dk ( /v3k
(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 elev,9) i+r0mf3nk(wyalntw g k p7ator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s mit)rg,0fyl(7m a3pi nkn+ 9 kwwnimum acceleration (magnitude and direction)? a =   

Show that if a satellita7msew4)elo/ e orbits very near the surface of a planet with period T , the density (mow l /eams)4e7ass/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 x m,hcjy/*xbvlcpd)icz r 9st ) ,v-+,determine the period of an artificial satellite orbiting very near the Earth’s su lx9i,,-z*vc,rdj )vsbt h pm+/cx)y crface.    s

  The asteroid Icarus, though only a few hundred meters across, orb// rkghpp*z ym;yaf.6its the Sun like the planets. Its period is 410 d. What is its mean distance from the mzk6./;py rf*yh /p agSun?    $\times 10^{11}$

  Neptune is an average distanl nox)7(g*gc uu xdq16ce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very close l yk4583y *akwzic5toto the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nea5c5 a yltk8o4zw*3iyk rest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente6 ;o nh0;atdjhr 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 for the fourh33b apr;e r4s vr+f*z largest moons of Jupiter (thosbarves;*3p h +rzr 3f4e 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 distance oj , 0nxc44luxjf the Moon. 4ljn u ,0xc4xj   $\times 10^{24}$

  Determine the mean distance from Jupiter for each ocnvj qt3(.nrj7*p5 gif 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 in i*(3pn vtcqn gj7.jr5the 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 consi0f c5nxej/ wu/sts of many fragments (which some space scientists think came jfx w5/c 0ue/nfrom 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 "pj.ng;. sp3 tdxlanet" 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 dis tdpsj n;g.x3.tance (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 0c1mb32 cbg5ym0vp q bax.e7kin 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 tolmg7pb qx 5 a32kbec0by0m.c 1verate 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 d:d fv ,ics:lb+vl1x; surface will the acceleration of gravity be half what itd d,sl1:;vb: flixcv+ is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circattqk 9bf6 v6-rpl:;8m.2ec0vhc jwile once every 2.5 s. If we assume their arms are each 0.80 m long andm8rpq-k.l9be: cwt fi 6;v20htjc 6 av their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent apn;d mtl:/x x3 qs7sw9cceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate 93dl s; /x:wnx7sptqmthe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the tg*wf 7krt/9 cEarth will a spacecraft traveling directly from the Earth to the Moon ex9t/gf 7tkwc*r perience zero 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 i lww2ewp;n-: un an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and wu:pn; - w2ewlin which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itj, 5 *vvqhcbrj*(imn1s 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 spe*ih *vbr nj(1qcj ,vm5ed (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 aircct : lpeo;ny x)*1jgx4raft 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 :r97z w iklr-kh wd*a3in terms of its radius r, the acceleration due to gravity at its surface kk zha rw*73r: -ld9wiand the gravitational constant G.

A plumb bob (a mass m hannvf9 qhzjkv/qf.; e ;.rmd 20lging on a string) is deflected from the vertical by an ang;k vn.h0fvdleq q./2zm; fr j9le $\theta$ 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 isiuw kuxid7u2 .(e0.nc banked for a design speed of If the coefficient of static friction 7u.i2.xuuicn(k0wed is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating soci/hab 31vf6up 0.gbc fast that objects at the equator were apparently weightlessu hb1 vf6b3ac/i0g.pc ?    $\times 10^3$s

  Two equal-mass stars maintain a constant g 9nk66 x adtzju :8sou,tc51sdistance 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:4hpg 9hchq(u t 2yvp, a curve of radius 235 m. A lamp suspchpt9 upvyg h4(,q2: hended from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the(a .vqxji45o z d(ay7f 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(a.x id7 (vyz4af jo5q 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 Hubblh1b lh2s( 4zxee Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense thal(zh h2b es4x1t 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 rd+rvhulnja1jy. )o:. 3aca(k:a/tq speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact wit :3orrkja.(q a)a vjh 1.ydal:/+ nucth the road at A?

  The Navstar Global Po s1yyvn i0tv oyty):/ i p0)pzbvg.;c,sitioning 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 p. is v;vv1)yyo):pbnzyi,0/gytc t0nautical 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 Renh ax:8, ajx1p*nwi,b wn1 xxq0dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is ixnw 8 ja,whqx*bx,p n1:01xa 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 njz+:p y/p+ck ceed of repair. yk:zc /++cpjpYou are in a circular orbit 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 zv; ubad4i s+p * uggmpe4;)t;mean distance from the Su dga )bg44isup+;u; mp ;ze*tvn?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could y1ke.p k1p pu2actually "feel" yourself gravitationally attracted to someo11 u.kppkpy2 ene near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centerf tlk7i1u )ny23 jtg7v of the Milky Way Galaxy (Fig. 5-46) at a distance of about2itg7yjvt ) uk3lf n17 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sid +x xb,l: b+putnwfg*(e. Find the magnitude an(,x x t *:upwb+flgb+nd direction 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 the Eart6ftnj8da+vbv( yw0u ,(sz cr5 h $ \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 expew;t /84jw a 9bakn*fimrienced by the tip of the 1.5-cm-long sweep second hand on w8*kt ;inaf/w4ba9j myour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weig8wmrd bq)tnkmf 8780 rht around in a circle below you on a 0.25-m piece of fishing line. )m08r bf7wqn8k tmr8dThe 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 thatsix3b )7hu x4u a car traveli7u 4u3shib x)xng 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 tiqdn78q :y,eh rlt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force agai qyq8ehdr7n:,nst 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.$\approx$    $\times 10^2$