Sometimes people say that wlrku04 f+v c7yater is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with th+f0vl4r 7cuy kis statement?

Will the acceleration of a car be the same when the car travels arol+w 0 *vpi osd,8b tsd3.mhx5xund a sharp curve at a constant 60 km/h as when it b03p,domix5l hw stsx*v .8d+travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a*f lmgh h-r 55 c*i/uq,:pigqm hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between twimqg5-* fih5lq /h:cg*pmu r,o hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rowi x2 j)rbbq25i dkh4qa n8t*;und. Which of these forces provides the centripetal acceleratiib85;ht2r jiaq w 4q )kd2x*nbon of the child?

A bucket of water can b5p 2jwu,z e)jv dnni-*6p f j2prr+6jne whirled in a vertical circle without the water spilling out, even at the top of the cir2u5j w d6)pn6fei-2znvn+p rj pjj*,rcle when the bucket is upside down. Explain.

How many “accelerators” do 7: e1hisp)rfd)rfy c3you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?: )f is)yrre7 d31hcpf

A child on a sled comes flying over the cre1fx vo,x1i f5qst of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease axffv ,1iqo15 xs he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when ano++iwv, g+53g 1rs9o1vdd owfy ,d vrounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking-,;y: .s+dhxa3 b gkdny- nyoi angle given its speed and radius of nxg: ,yi.-s yhndd-ya +o;3b kthe turn?

A girl is whirling a ball on a cw7l8e4 vl 4npa+e+tw 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 shoul7nv t8ew4lc+lw a+p4 ed she let go of the string?

Does an apple exert a gravitatetx1r-2lmxw w8b6bjr6sjmk- 57pz4oional force on the Earth? If so, how large a force? Consider am46r18mxsbrkt6 zp -j5jelx bw7-2own apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubl36yyee 3e q55 s8j2qvhwwtqg7e what it is, in what ways would the Moon’s orbit be die7 w2wv538j3shye56eyq tg qq fferent?

Which pulls harder gravitationally, the Earth on the Moon, or thy6kj7cdr*r ;/b *osvpvsn06 ge Moon on the Earth7kd/sns cv**bj 6o6gvr;py r 0? Which accelerates more?

The Sun's gravitationl 16o*wkzq.feal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationalef qzk* .ol16w pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at tgkh5btp*e21 ahe poles? What two effects are at work? Do they oppose *t 12h5 kgebapeach other?

The gravitational force on the Moon due to the Earth is only abouv- m7m l ur)h-0z7ttngt half the force on the Moon due to the Sun. Whmt z-ng-7m7) ltu0rhv y isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Marsd)ng6ji2jm:kpsx + +z in its orbit around the Sun larger or smaller than the centripexg)6k2:+jmidzp s+ njtal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward theo gb)pi5,o:ye east or (b) toward the west? Consider ty)ob ,:pge5 oihe Earth’s rotation direction.

When will your apparent weight be the greatest, as measuredo 8.br(ok **lt cph9mt 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 you*9ktolc*t 8h pmbor .(r 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 couldol tuf,f*e9gsn,v1f9kw -2eb 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 fee9bk vse f2w fu- 1,te*lgfo,9nt, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “ pupbdjggk; 4,/,*nveapparent weightlessness” betweeg4du;,/ nevj p *kbp,gn steps.

The Earth moves faster in i;;xporg;6 em its orbit around the Sun in January than in July. Is the Earth closer to the Sun inm6r ;gi;peox; 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 8 hl13rnk+i olnot known until it was discovered to have a moon. Explain how this discovery enabled an estima o38+ lnhlkri1te of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largere r36aolqiv-e 5,p p5f than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from o5plpq,r5-e faove3i 6ne 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 11hxxx 03 *6m mp1spabt980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetalkqk+lr + rtop+tl 5s8m;n7jy: acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle otrokjl8tk7y5n: ;splm ++q r+f 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 uniform9 w0z3lz0td4lx3rd yz ly in a horizontalt0w lzz yr4dzlx339d0 circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shut *f /vxq6 povzdy,2.bdq+h 5gvtle is in orbit 400 km from the Earth's surface, and circl/fq2vo bhpdg.q xvvy,+d*z65 es the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of thzz9/mz jn ies79/,u daoa. .f 2u)afshe acceleration of a speck of clay on the edge of a potter’s wheel turnin,792i/z9edfuu a n sfzz ) a.sm./ajohg at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uni4fl cws1x4ga9 form rate in a vertical circle of radiu1w449 lgxcsa fs 72.0 cm , 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 wigjq88uw63 ba7ja wv1 cth which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction betwee8c1w738q g bvju6jwaan 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 qlku9 d7 yuy96)ui:h eand the road if a car is to round a level curve of radius 85 m at a 99e:yk6qi7hy uuudl )speed of 95km/h ?   

  A device for training astronauts and jet fighter pilo f-;. r dd-guofdc/:t3wl cnt2ts is designed to rotate a trainee in a horizontal circle of radidof3wlu.cf-/t2:g ;rdn d-tcus 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 rdp) e+caig0(axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntabl c (ig+dp)ra0ee until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsvr.3 h:o,oo pq, cdf/bide down at the top of a ovro:, q ,codhp.f 3b/circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the ze :z3 a.ku) cyb).sxrdriver) crosses the rounded top of a hill (radius rzueb3 :. a)ysk.)zxc=95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel n x2nnuct9-kjbnu*cf )5x;5lceed to make for the passengers to feel “weightless” at the topmost5c9n2fn-u b;c*5 cun)tljxxk point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ow) u ck5p(wle4f radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is kw4 e)( cu5lpw25.0 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 rotates*9x8 ao5lf5qtw 4kgu if a particle 9.00 cm from the axis of rotation is la*5gkwu 45x89tqfo s to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivu g ;ajp5aa9wzwta,9j1 c1na 3gf q7b7al, people are rotated in a cylindrically walled "room." (Seewabqaz w,fn9;c g73auta9p 15j 17jag 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 frpkmx 1f-3q je9(powk)cg7i2 zictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a -q97kzg1ip ocej ()k32wpmf x 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 , preciv8/fe/o* .ej xgdt- 5o1op kifsely this time, by not ignoring the weight of the ball which revolves on a s/jtifx.8 1*opeo/d5 eg fvo-ktring 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 42ndqas. ythc4/ 5rhx m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesr 3m.unrh /ci9 $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving ver o7oa)0rcg; fz 6fnz7etically 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 centr8tqqh9( syw,eg4b +d8o cxiz6 ipetal components of the net force exerted on the car (by the ground) in Example(4o8,+q i egwbytzh8 xdq6 9cs 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 accelera l9f31mj xmun*tes uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the*mf93 mln x1uj 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 1ihb8k v.h p ut(pkvlh:.y7w9circle of radius 2.90 m . At a particular instant, its accelekpu. t:vyiklv78h h9p.1 (wbhration 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 12,80.uym vj9w: tibb :yvzzb;/7y2j. 6nbv a6(yqp0 km (2 Earth radii) above the Earth’s surface if its mass is 1350 :y b p.aybvyj :w6 /b v6t2;n9uzmi.yjvz(b7qkg.   

  At the surface of a certain planet, the gravitational accele 6fihu0u6snygx; li-2 boqj:to 25j 4zration g has a magnitude of 12 :;x 0jlijifu2b-y 6ns6to5 4quoh 2gzm/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 oga+ 814 p:+fusi gjaimn the Moon. The Moon's radius is 1.7i ai41jgp8s+:fm a+ug4 $\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 ha03tt(6ahcct ks the same mass. What is the acceleration due to grktt(6 h0c3tacavity near its surface?   

  A hypothetical planet has a mass 1.66 times th1s ;wpy+g9cj zat of Earth, but the same radius. What iss 1yg+wp;9zj c g near its surface?   

  Two objects attract each other gravitationally with av68/ krptwx3w ini:; 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 acceleration of grav k3sk27(y uru) 2teg+d*lpdnoity, at (a) 3200 m e) koyg us*(dtl u2rn7p+dk23    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth w8nztp8ql0a scnta 5v8e9 i16l( hq.j,ijo8q khere thegravitatijqqsn,h l.z6il k9tp518cqa8ev 88 o0tinj a (onal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha o m-ywbn/vsk-+4r),j8 idcrt xcp5m lp:s-u(s five times the mass of our Sun packed into a sphere about 10 km yc-r b( c5: m-s4/dilmwj-p+8upo)r n, vxkstin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sta(qtz :wo54if cr like our Sun but is now in the last stage of its evolution, is the size of our Moc54 :zwi q(tfoon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining weol, h epk7k *q3u5ug3hy astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above t5ko7 e 3* lh3eugpkq,uhe Earth’s surface in terms of g.   

  Four 9.5-kg spheres ab935:/hnx if:ugo: o z 8oijprre located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational forz9g5:8bo orpuij:ho in3x:f/ ce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Shf dg n;c:p3 f:4*24tviygtdmun. Calculate 3tifcg2: ;p*:4y4tgm v ndh dfthe 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 acceleratna2l- vo.cj *emygn* :g(. xcoion of gravity at the surface of Mars is 0.38 of what it is ona(ccy- :njeg n*ol.g2.oxm * v Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kng 34xh idgoe 3a5ibry 38;5hanown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usi3ibrhd33hag5ex5a ;iog8n y4 ng Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit n,lvy 1(zr0;1qek aduabout the Earth at a height of 36dv( ;ryez1qnkl a 1u,000 km.    $\times 10^3$

  The space shuttle releases a satellite into a ciwt azh*(xuq 64ro 57 bho27twwrcular orbit 650 km above the Earth. How fast must the shuttle be moving (re72wahqoho xrb6tw ( 4t5u*7zwlative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if owsyiiom1wdh8:4 * qc(ccupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and givo4ds:*mi1i cw8( qwh ye 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 El ph(ie4spny. f zt(/9h;hsnt;p d*)larth in a circular “near-Earth” ;ef .t;zsn/pls ti*yn(l(hph4hp9 d)orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hz*b,g4g 7v mouh :2cigave to be launched from the top of Mt. Everest bz7gug 4mc*higo2,:vto be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command mo1stygu- q )q;fdule continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the M1)- ;qygt fusqoon once?    s

  The rings of Saturn are composed of lrllh--,1* xw nkkk(h* oqoo;chunks of ice that orbit the planet. The inner radius of the rings w r* 1qo--lk,kkolhn(lh;x*ois 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 diame;9tq /o,togqekt- ,)x yp4jryter rotates once every 15.5 s (see Fig. 5–9). What is the rxjyqk -t;,t) rog4/q e9ot yp,atio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent g/ 38rnhwmk,d el;9dqweight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at core/hklg 98;dm,wd3 nqnstant 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 o j7 du1ros1bf5pb4x,bf two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years tbj 5us 1b 1pdfrbx74o,o orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weightb+/)*- ydi(iqx+x/u nrp1poznrt7f x of a 55-kg woman in an elevator that m/xi(upnf7/ixrn* qdz -+ bp)oyx+ r1t oves
(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 e0*ojeq wa)8; sdd98y2j ffth cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 qd2j8a oy;*fj )wds0fh 89eetN and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near9 y5;,y zafeos the surface of a planet with period T , the dezyo afsy;e,5 9nsity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the perio67o;0 v2ngb6 hbxgby8p) *tcz y j6gcad of an artificial satellite orbiting very near tg7b80x6 )g p6c6bt bazg hn*2yovjc;yhe Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits theyrv8k 2r i;39z k oqn2zll.7pk Sun like the planets. Its period is 410 d. What i8pz zli2k7r2k y.3 rlo q;knv9s its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of .msuyfc)gqs5p/+ h -q 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 vel 1j rdkr)4goq nn*m g:9h1in+ry close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance o*+jn 1n9g4r g1idrn lh)ok mq:f the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gal:vvvgu h(;) qqm60r9 f3hhhz 3gy wdn5axy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 h w33fhzfd4 dx0 (h)pw7gc.sl distance for the four largest moons of l) d7p 4wxdh.hcg3h3w( f0s zfJupiter (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 a8yd .q:vj0xbo*:fmyy3 zd*( p a ib2dpnd distance of the Moon. v*z38iafybdpdbdo y(0: q:j*xm 2.py    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,rqw2 1-07vgzv(v 1 xty pijp,p using Kepler’s third law. Use the distance of Io and the periods given in Tablxwtvz- vqp 1(p,j pg0y2v17i re 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frag(h.cuo wlcg)c4mcq 1rdc*e,ov s /-k q:ovu(6ments (which some space scientists think came from a pcr1occ*dgk(.)hoqlo ,c:4c-m euu(w/6s qv vlanet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the formgx, cvf*az7n( 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 Ear f,xcgn( *7azvth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig.njsvx2q 6p+x -rf-d m- gbe1c7 5–41). If his arms are capable of exerting a force pn- -76s xc1xj2+mqfbe vrgd- of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the 4lbw8t/7 e(ktxc 1pmynez3;2eet z y 9acceleration of gravity be half what it is on the surface? (ztekly4c8/x tm 3eezentw ; 17b2 py9   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hay8 eignyfpbw;;v: 7up;v/i, ands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80u;va/8 v np,; wb; iy:7ifepgy m long and 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, t cvi+yom9. n(f+u0q xnhe apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimn+i.onv uyc +0 q9fx(mate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earts)psm8e9gk ydxw)4 , vh will a spacecraft traveling directly from the Earth to the Moon experience9k xs))8s,mpdvgwe 4y 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 scalehdob 1*lu )gz4hdu/ z4 in an elevator, it says your mass is 82 kg. What is the acceleration of ho/ l *1duug4bd)zh4z the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists3bj1gsq96 nm+(r: zm kl-tr os of a circular 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 gravity at the surface of the Ess:t3o m r(nz1jlrg-b mk6q+9arth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lopf31g do;t-o36c/ou n u kau5xhtg8 1rop (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 89vbkrk lke;8 of its radius r, the acceleration due to gravity at its surface and ek rv8kk;bl98 the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical4ph 5tt-.* kkcs5gfr x by an an5fxt khrtc- s *g.k54pgle $\theta$ 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 coeffir*9al.fpw, d :cea)hpcient of static friction is 0.30 (wet pavement), at what range of speeds ca c:ad9 r.,halp)efwp *n a car safely handle the curve?

  How long would a day be if vu:f4j4l j / 32xmvpevthe Earth were rotating so fast that objects at the equator were apparentlu:evvlm p /4f3v 42jjxy weightless?    $\times 10^3$s

  Two equal-mass stars maintno4*1-t+nfxgf hwv1 gain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speeann ) wy(3 5nf.f-zy8hunfcx(d rounds a curve of radius 235 m. A lamp suspended from the ceiling swingsnfnfnwxa.yh 8)- y(u53nz ( cf 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 Eartbnbx f5:b21qih. Thus, it has been claimed that a person would bnbxi1 :qbb f25e 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 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 Sp y qb-epqvf dw/l)zei2-.e( 8tace Telescope deduced the presence of an extremely massive core in the .vpq fb-ezi l)w/8e - etqdy2(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 v-sa v9l mk:g ::hsp4p 5vhpin1alley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the norpm i 1plsh:g45:nvh vka9-p:s mal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a9m 95 duiyrga4 group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by thesu5rm 9d4giy9a e satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after trave qrloxrm,)p2 ths36+) *l xcovling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abouxo3h6o,v+2ltmp qlrs rx)*c )t 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing5 ic4dilv/l 8t a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Eard/t 8ic5 4llivth), 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) W kav)r0h/blya0+l go/hat is its mean distance from ygl0 r ao0l/ vb+hak/)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 of G would need to be if you could actuavo583gq, k2fl d+ lsjdlly "feel" yourself gravitationally attracted to someone near y sl58+dkqg jdv23flo,ou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gazc +:-6amk5m6iaf vf. tf2 iallaxy (Fig. 5-46) at a distance of about 30,000i2aalma fvm5 fk.6t z+:cif-6 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 squa z z/xrx(4qf l zg)z.jza7mmh(45k cr1re 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass plac(z zxfhzcrl.zram7414 /mqjkxz) (g5 ed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500al 346d fens; c9:wgkc kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweetuncr(:pt,, vp second hand on v:( ctt pnr,,uyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker 8m c tadqr;:vp+(unk 1weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every: at1qvn d8r(;cu+k pm 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tra,q+-lqq;ak7q (g)tuj5sgyy uveling at sp -;qlgj)uuyaqsg q+( 5y7,kqt eed $ 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, utilizerehvmnz 0lmee. ;i (m;*zc.g8s 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) Calculate the friction force needed on a train passenger of mass 75 kgz0m ;.ei.nce*l v;gm(8rm ez h 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.$\approx$    $\times 10^2$