Sometimes people say that water is removed from clothes in a cww; rt9 s(is;6g(fif spin dryer by centrifugal force throwing the water outward. What is wrong with this statemen6w9 fc;wt;if (r ig(sst?

Will the acceleration of a car be the same when the car travels around a sharp ces v0y*:k d4s 13isbrqurve at a constant 60 km/h as when it travels around a gentleqv: sdsk4yi s1r 3*b0e curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly ro-( )ezbw 90j,n5k x exidkjz(ay,4 nrhad. Where does the car exert the greateszhrnxj9-b0 knxjaw k ,(i(,e 5y4d)zet and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the fore v-.2ez9vqr 4gqe8 ilces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of th l4q 2g-evv9iqz8e er.e child?

A bucket of water can be whirled xe;(sog , y2klin a vertical circle without the water spilling out,l;2e os(y ,kxg even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Theec1hjs7mgq:;) wzwxv: b :ys.re are at least three controls in the car which can be used to cause the car to accelerate. What are they xhbqyw; :gezj:) 7.csw:1m sv? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig) 86 gnep,lbd9du 1f63 ajdvna. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normv6ulpdbn 63an,j)g 1de9 d f8aal 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 whenotnc3vf8fh)u 03wd lume)i+ g60ce4f rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bank)y gwn 03su/ :a;xfrnw a6,o;wxeb1 bjing angle given its speed and rj;xr fa 36sw;0ao:n/wg )x1bw u,nbeyadius of the turn?

A girl is whirling a ball on a string around her h :q2 am;iouvpiu 6q ,7aj6zo*cead in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit 2mqa,cp 66:ivq j;uouz7oi*a a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forci(xiqi qp +c)45 7-miua3qknwe? Conx(+wci kqqiipm )iuan74q3 -5sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were docf r1g9g o(qv :o-5dtl iepe0i c 5kmx;)o/;hmuble what it is, in what ways would the Moon’s orbit be differe)cdp /c9(x 5;1o vg0:eg -f5 mie qliotkro;hmnt?

Which pulls harder gravitask5 po;hwj* x9tionally, the Earth on the Moon, or the Moon on the Earth? Which accelek;95jx ohpw s*rates more?

The Sun's gravitational pull on the Earth is much larger tha(c:h 5mf(.l t )fhwtpan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the othemwpac5:fh t) (tlh .(fr.]

Will an object weigh more at the equator or at the poles? Wha 5kfe(4r08zpyz) fqvj3 kn2swt two effects are at work? Do they oppose each other?82kfz )sj (5eq0z34nyfkpw rv

The gravitational force on the Moon due to the Earth is only about half x50m g(eclj6kekn f29the force on the Moon due to the Sun. Why isn’t the Moon pulled away fromkj2km65fx(e lcn eg9 0 the Earth?

Is the centripetal acceleration of Mars in its orbit around tht sv;a6un-3n6ix tz4oe Sun larger or smaller than the centripetal acceleration of thex;aotint -4us63 vzn6 Earth?

Would it require less speed to launch a satellite (a) xg- aw yfa-6rlzk,l.o)ay/* stoward the east or (b) toward the west? Consider ta )zf6k-als w* /y-yr,oxlga.he Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in jdk7n 3rey 2;uoh 7m9ja moving elevator: wher3yd9; om7ueh72 knj jn the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periox dl )e p+e * vhbm9n6 jk67t7/*mkx6sxhjyj;tds in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity vl6 ; y9kj btsej *x mnjph6htk)7dex7 mx+*/6you can think of.

Explain how a runner experiences “free f2i(qyeylu26 uall” or “apparent weightlessness” between sliq( e uuy62y2teps.

The Earth moves faster in its orbit around the Sun in0d 7efrnq8jm m49b4 t3swoxg 5 January than in July. Is the Earth closer to the Sun in Januarmx rq9s75fw4j 80e 34bgdtonmy, 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 wakt j tcx i9:(mb3o, q3.mqpu4cs not known until it was discovered to have a moon. Explain how this discovx op t,tq.jc(c3 iub39 km:4qmery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eartj9k;on rrn - ja,h3tdb. :b/swh is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.-k:brr;3sh.nja 9j w/dtb, no25 $\mathrm{~m} / \mathrm{s}$ . 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 travelinwk v++a/a clym;i(.ghg 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 its orbit ao)50akisc-r4oj pn1rnq-b( f round the Sun, and the i-(srn4fo-a r)5obp0 nc1q jk 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 disc:b bketlsyxs. h,35 3g0ds:y jus as it rotates uniformly in a horizontal circle (at arm’s length) of:y35lys:dsb hk0exbs, 3.tjg radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 0o0 uo(s6arvm9we,cn km from the Earth's surface, and circles the Earth abou(a6om cv9ns,0r eu o0wt once every 90 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 accelerakcep36g m4txe- al2 )stion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diam e3am) pks-t62eg c4lxeter is 32 cm?   

  A ball on the end of a string is revolved at a uniforaxki 8w3 bhr6 yyjt5 0;vp4y*wm rate in a vertical circle of radius 72.0 r4kbxhj0pw *at 6yv i;3y58wycm , as shown in 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 tu*n(* c 2f :uiui(yhsezrn of radius 77 m on a flat road if the coefficient of static friction between tc*zu(ii fy h:u *2e(nsires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of stat1u +imntpwf/9 ic friction be between the tires and the road if a car is n uiwt1pm+ /9fto round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and je em5y vrs297(zm(xogjt fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she ro5 s79jm2(zvox g(mye rtating?    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 thvrig/,yi7,kl e axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable unt/g 7lk,,viri yil 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 4 ilhx0 1448 dhzkln/njjyw)ka roller coaster be traveling when upside down at the top of a ci dz1/j xhw)lkl44jynih8k40 nrcle
(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 driver) crosses tq0m3esyx9 jn -he rounded top of a hi mne0jq3-x s9yll (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 wheel8i* 9m. ej+wh/ibf mqb need to make for the passenger hj*i8iqwbm e+ mf./9bs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle v q :+1nhspp da)k+ tw,npr8ae-aug71of radius 1.10 m. At the lowest point of iqhw 8n-gtpd s 1,u)a:epkvanp1 7+ra+ ts 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 rotate if a particle 9.00 cm from the xh8 cl+ dv8b9)p6+bfk,uwtm l axis of rotation is th+x+m d8vk6lbb8f,w)cu 9 ltp o experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at3 xksm; *** gasqh1mcl a carnival, people are rotated in a cylindrically walled "room.*;g3m lh* 1*ascx mskq" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionlesv,lda7 :q/ rpppxf) , q5wg;gjs air-hockey tabletop, and is held in this orbit by a light cord connected to a dangli fr:qv;l/,p ppxjdqa gg,)75wng 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 igno oa*1eaj1+4 lh5cerz6x,qqop ring the weight of the ball which revolves on a strin+ 65,qzoer ahj* xopaq1l1ec4g 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 m is perfectly banked for a car travelingosyuo /(bmz,0r 20mt rokk:qjv*- ;vi 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 b fwih5vkp,7 y,q q :4k .or 716gl0ffd1wosdf$ 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 manbdh:;j pq.t 8geuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal co 4w(nqlyw2y( jmponents of the net force exerted on the car (by the groun(yjw2w l (yq4nd) 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 accelerates uniformly from the pit area, gtd1b( s:tp rdg 47w1pcoing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, wcw:pdgt (dr p bt1s471hat 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 particulai9zati -ki +m:c-xmcv/q xc* 0r instant, its acceleration i/a-c c0-c:ikmzxit *9x+mivqs 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 g b -688h7ymnwkt 5ngxvravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s su-8h5xwtnb kny 6vm g78rface if its mass is 1350 kg.   

  At the surface of a certain planet, the4 nn4jdsu28 mc gravitational acceleration g has a magnitude of 12 4sd2umn njc48m/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 only3fx o:w6x 3r the Moon. The Moon's radius is 1.7436rl3 xf:oxwy $\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 Eart8z -57pcsc pehl 22ijfh, but has the same mass. fe28pc- s2jz p c5il7hWhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but t2 cmrmvkpja3 f*l uk:vif7qe,bs*.69he same radius. What is g ne9s2ijbfkk q.*6a3mmclu, : vp7r vf*ear its surface?   

  Two objects attract each other edpqa3w;(6 hgp+m, efz8+uzf gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelerat )h9dh/ m.wadrjt9ww( ion of gravity, at (a) 3200 m 9w/(adw)dhtrj9 w mh.   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poin x-im,3j tb5 wbgl )56ouhhb5tt outside the Earth where thegravitational acce)l mt,5btho hjgbx356 i-ub 5wleration 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 packed;g,l*8ro5 rgbvr q4f y into a sphere ab4,ly qbo*rvgg rfr58;out 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a njh-woo:u-nkzger-y9t; 42 nn average star like our Sun but is now in the last stagennu4:9 2-wn- gjyte-hor zk o; 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 w. qeo(j+z hx3bjxt i0-eightless while orbiting in the space shuttle. Your friends respond0- j t3qehj+xxo (zbi. 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 of side 0.60 m. Ca68 ymbdfx hbt fpkti721o6s4( lculate the magnitude and direction of the total gravitational force exertfmk 4b8p7 o(16btsi6 x2yhd fted 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 sidnw-y+9svpnowa 6 z: ,pk;(t uye of the Sun. Calculate vkas9ty ; n6n,(ywop z+u-:wpthe 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 $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what ipgb, g4e1rw --o nyms5t is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars-ym,wgr 45gsp en -bo1.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of 0ko1(u(4ka)qziv/a ;trcs bh the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawbvaz a tq4k(0/;kc1o) rs hi(us, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of4qn eu*m;0w3s v a*aeh a satellite moving in a stable circular orbit about the Eart u w*q*s4a3ah0v;nm eeh at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above a d7emr8s6dxl2 1j7w m5e5 dtqthe Earth. How fast must the shuttle be moving (relative to Earth) when the releasemjrt6m1l85 a2 7d sewqdexd57 occurs?    $\times 10^3$

  At what rate must a cylindrizq :p,, gzwrp:cal spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, ar,,:gqwzpzp : nd give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a ciryr/.hnwjkz f(0.cnn a n i)69cj4on3kcular “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 jc)3 rh.n/f iyn.zacn(kwn 960onkj4 Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to+u.skx+q +chob +v 9 acqp1a;o be launched from the top of Mt. Everest to be placed in a cioao s aphu; cb9 +++k+xqv.1qcrcular orbit around the Earth?   

  During an Apollo lunar landing mission, an kgqy v6/;hl5yab 1ji xu-;-the command module continued to orbit the Moon at an altitude of qya; - kyiha5vg1jn6l; b-/xuabout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice th. rjsmjn;* oxec,)8ae at orbit the planet. The inner radius of the rings is 73sea. rej)m,cx8 *onj ;,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. gfobxw8prcf)p 2aqcx) () 7x.uu0*xy2ogg e diameter rotates once every 15.5 s (see 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 bott.bwgfuua). 27 opo8gyx(0rq2xc *p)xcxe f) g om?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center o8 6(ez7c2w p+ abkxj tdtplib2k8m q)+f the Earth's Moon in a space vehicle (a) movingtalzpebkp2 i( 7+ j8 k8xbq6d t)mcw2+ at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of e vbaj sau7.a r/*lk;0dqual mass. They are observed to be separated by 360 million km and*u;kvaa.ar 7lds /jb0 take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman sd m6 5cd hj ulbtk ,npo*ry+)si)8yqr.n(5+yin an elevator that movs +nd6uymoik sd+5,*jlbrq) 5ncp()rh.ty8yes
(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 elevatohma)ro v uiv/s d8/h64r. The cord can withstand a tension of 220 N and bhra os6 /hm/8u4vidv )reaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pl o;ikaegl:c -ylu ,56wanet with period T , the density (mass/volumey,; u5kcw 6-ll:eaiog) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period o 1nsdqwhj4 s+ vn;uykc6 atjx09 p5+)wf an artifiqv0dajsks9 +1xty)6 h pn+cj;wn u5w4cial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hund 9tjppno s(8gd vtc2a;2hve.+ red meters across, orbits the Sun like the planets. Itsd ;pnv h8tj(ep sv92a.ct2+o g period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis,ci-:qdpbf- xhk:hpf*um; ( +/pph ps )bz0r ctance 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 roughzj sa25ee ;sp )zjm-+ vwu+u(jkqhr.;ly once every 76 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 +jk uje e5r(.s 2z); u+hazwqsvmjp;-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 th:t tr y2m.*mngsj5b 7ze 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 m,ae e3fj )6y.vxj2 vfoean distance for the four largest moons of Jupiter (those discovered by Galileo foaye) j,3jfv. xv2e6 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 f+qiq ke qt)vs(na0ne2. kv93 the Earth from the known period and distance of the Moon. vn9eq(qka nt) sq 0+vk.32 fei   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Ke8lupb lc6 f4phi2 1g9wpler’s third law. Use the distance of Io and the pep f l1u4cw 82hi96plbgriods 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 76a4jnhjde 6o consists of many fragments (which some space 7 do4 ajh6n6ejscientists 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 anr9pk rv8.s(mxb4 ,(xiwelbdt1l 8p z, artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days? sp( i, 9,m8(ez.4vblrbx81 w kpltdxr  

  Tarzan plans to cross a gorge by swinging in an arc from a hanging viv(th5rt -j mkz2,kt6)ie 6gk8f8mzk k ne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the mh ,mk-r2v )kkkg 6kz zfe5im 86j8(tttaximum 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 surfacef 8g8wuu f:9;qev ofuy 0dwn .x+yt+v7 will the acceleration of gravity be half what ito+uqxy0fwte .wn; v+u8g987: uvyffd is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in 6e2xr*s pi8x wa mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anothe6e2rs x*px8iwr?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration oy0m 8.;sbzwq pf gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of thibyz.q;sw0 8 pms effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft 25zo zj8b/xnsy- qj8u traveling directly from the Earth to the Moon experience zero net force because the Eart njjs 8u-q582zozyb/xh and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand v9o hbvn+ y1x82wj;x xqn+ x)gon a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the ele qgwoj 8xx;vyx9n)+bx+v hn12 vator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tundkp,l ks n * ;y:4puw-u*eg65bfxz0ybe that will rotate about its center (like xzn*6* u45eb 0 pgkfp:l,;nds ywkyu-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 in a ed.*bzn-u rl8 ju7uu bj,x 4z)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 of its radius r, the accele4e3gs pwpn+l5g z.6 zexc,1q mration znxe+1.eq c s5glppz,4 3w6gmdue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertica70fi - nhx;cgsgd5 5vsl by an anglh5i5 0;g7gx nsfs vdc-e $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficientp4 *cvb4jvobq.4h4g a of static fricti c444h gvapq. *ovj4bbon 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 qbpm.4h5i-vl3 neu l6Earth were rotating so fast that objects at the equator were apparently weightlessm 5bi n.p e-uvq643llh?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.w3ehbkzw. 7t c -d-9jp0 $\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 cs ww- 4gb:0r6 o6td karv:t7slonstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swin4 s-otwrb w:adg 6v0:r6t 7sklgs 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 t.hw5d ta0ndb3he 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 nb dt30d. wah5would 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 th cla8q 0 ax*n7hlm0rr2e presence of an extremely massive core in the distant galaxy M87, 7hr 2mnr00a*aqcl8xl 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 hij ,jrs jxuq:b-xy g68pew,(7g5 ahe/vll 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 larg,sqve8e, xj7r: xjgh -g6bpw5yj au(/est? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of f qkojb0vmdv m (zlb69.r*a.224 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 “fb.0ma(rf2movv*d.b6kj9q zlixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvouk 5et45)pwlejr,oibalpt+- 9 s (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is e9l ieltrtpb5) awko,j +p 4-5roughly 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 repaiv62l6r;8u60qk3wswtxs7ep pws b b;fr. You are in a circulvw ;w7fpqu6b;rxksl w s 8p0t6eb63s2 ar 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 yearee n/v: fudb3kv6r odh7 ,k:6tdb h63us. (a) What is its mean distance frdur6b6 ehfu h kvk37nb,:3:v 6dot/edom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value okj )yh(5 au:idn q(n,uf G would need to be if you could actually "feel" yourselfh:ak( 5 jun)yqi n,(ud gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center or rko.i: 8xuk7ozq/gt,dl;h fwa5*2pf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-year o/l2x,k rd 5*uwa7kitpfh gz; .:o8qrs 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 aruq3qj6ulq wgzz vxt .7o r166 qou*di316oup0e located at the corners of a square 0.50 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 square.iz xu.6qqo3uoq *gqrj tou6p3v7zd1016 wu6l    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth s71cru 8ejg5aeb00 ba $ \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-longz zy) i vdnswtki3, 6429tspi, sweep second hand on your wrist watch?v,nzp w 3t, )i9k 6ysi24iszdt    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arncrpc+nh*d +x p: jr28ound in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. Wh82nc +hnc+*j rxpp: rdat is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius Rjoyxu dvqba*1 wjk) 0/mg)- hk, z8.jv in a new highway is designed so that a car travel.)ja kvwk,dboz8q0 1h)vujxjy* /g m-ing 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 traini a/;jg:4sprl;o7smo, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calcula 4rao; lj /:m;7sispogte 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.$\approx$    $\times 10^2$