Sometimes people say that water is removed from clothes*42txz d yssqv,s)-wa in a spin dryer by centrifugal force throwing the water outward. What is wrow2v4,x-y qd *as)tzssng with this statement?

Will the acceleration of a car be the same when the caxkii , g.++upesp;5qbr travels around a sharp curve at a constant 60 km/h a e5k.uspi+g,qx ;p ib+s when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at cdhdp 4k; fx u42lm*xpt4eq,8 zonstant speed along a hilly road. Where does the car exert the greatest and least forces ond;4pxh4pd8mzq , lf4x2uet * k 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 forces acting on a chij3ldw,4e0/k i5 pwt fp)jkft6ld riding a horse on a merry-go-round. Which of these forces provides the centi,63ptd f/5lt kp)k wj0 f4ejwripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the ud:y +4nh4i,rfjhb8 p water spilling out, even at the t4dhri8byp ,hj+ 4u :fnop of the circle when the bucket is upside down. Explain.

How many “accelerators” /hcgo yw9b)a ,aa9 +yvdo you have in your car? There are at least three controls in the car which cg ,)ayabwv+ 9oy/ach9an be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a sme l(zsp42ks2v all hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Exppvs le2skz4(2 lain this decrease using Newton’s second law.

Why do bicycle riders lean inward when sb08c .7o v;c-xoi6a) wyca re2bf i.erounding a curve at high speed?

Why do airplanes bank when they turn? How woul/su bi:u,m,8 fk gp5tjd you compute the banking angle given its speed and radius of the f,/gutj :sm,k5ui p8bturn?

A girl is whirling a ball on a string around5hz gw41pxm *,h0wfjm 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 thewmh1,0wj f 5mz*ph xg4 other side of the yard. When should she let go of the string?

Does an apple exert l.om hm1x.ng con39;;h 4mckca gravitational force on the Earth? If so, how large a force? Consider a.mm 1ngcn;chl c;3ox kmo4.9h n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways m j -xfm,an+a*5jwr5t:mfw2g would the Moon’s orbit be diffa j:f2 n55ww*garmm-+txm fj ,erent?

Which pulls harder gravitationally, the Eat,.wnmae+9s 5x tegl1qd6l +e rth on the Moon, or the Moon on the Earth? Which accelerates mor6aweg l+emd,1.5 txe s nl+q9te?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tt5tv21ik m ybq/1ai 4lhe 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.5 tlkv b1ymati1 i42/q]

Will an object weigh more at the equator or at the poles? What two effects ari(- ux (q zrow.s/l;swe at work? Do they oppose ersx(wi.s;l/ozuq (w- ach other?

The gravitational force on xzwoj)r1k /t7 the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t1ok w/xz7rj )t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroundj c2-6edhc7 ju the Sun larger or smaller than the centripet j-he62cj cd7ual acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward t9wpz .;h nl5v0(28it tt yj) 5ipcgcmghe east or (b) toward the west? Consider the Earth’s rotation direction nigm);j(gh t9ctpy0. piwtvl z2 58c5.

When will your apparent weight be the greatest, as measured-ivg)td -+u k8 qjtn :nrh4wh 9b4dk(q by a scale in a moving elevator: when the4tk:d 4rqt9w )+v guq8 -ndihhb-knj( 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 periods in outer space could b3gj8iub/g 6sfe adversely affected by weightlessness. One way to simulate gravg36ufgib 8/s jity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weml3dz+z*nk 0 iightlessness” between steps.3 *nklmz0id +z

The Earth moves faster in its orbit around the Sun in January than in July. Is tx*ej +c-sju4;v- fes)k6 ck erhe Earth closer to the Sun in January, or in July? Explain. [Note: Thkcex cj-s6 ;+k-erj4)fs*veuis is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to haveyp4w,nr;yywyd9ih,1w6r tu 8 lk * uv8x ccd3, a moon. Explain how this discovery 6cvw;y4u x9 y8ckirty*1 , lnh wudrpyw3,d8,enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on thek rmo k976/lp cuj.b1bksj4+x Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the k bjkujr .14 o+/96mx blsp7ckcenter 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 1980 o2*fl ,g 4xyk0q7irdva(j0t w$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 h *8dg h/ mkq)/ smo4*q-locvearound the Sun, and the net force exerted on the Eartec4s-mlk/d* g/qohm8qv*)ho h. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rnq/b bw7vz*ltg ;;bz :otates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cab7 ; wg ;:lbt/qvbz*znlculate the speed of the discus.   

  Suppose the space shuttle is in orbil/8qs i e52so vng80un zeqd)b;rawr4+ 71jo kt 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripeta1258)q7q e ngj/4woeounz;8ir0s+v rkd l a bsl 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 acceleration of a speck of clay on the edb-1b sf+v0q; fl:cgtg 4x 3oipge of a potter’s wheel turning at 45 rpm (revolutions per minute) if xc4 : qg+b0vg;b -stp1lf3iof the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate /3(2ox2vswa +uk lwbw in a vertical circle of radius 72.0 cm , as shown in Fig. 5-332(wb k3a wo+ls wu/vx2. 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 wi/va+. 6a 3erugoo c3v1a +j)yl dku8qith which a 1050-kg car can round a turn of radius 77 m ondi/6u 3 vcrq+oye.g1aao ulk8 v3j)+a a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be 3wms+-xwyz3owigz 43between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h4 wy3-izgo+ s3w3z xmw ?   

  A device for training astronauts and jet fighte6)7 q1n: gx-ixfpv5v5 z xardgr 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 x 1av5znd vf)g:x57q6xr-gpi 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 axispdpe /3hf5phyr/n9vnt: 4 *iz,e 2tbz of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36,d /hpzbezy3pi e:t5f *294 p/nnrhtv 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 8gbyuo8 0f9awztep -h3h/oz2 a roller coaster be traveling when upside down at the top of a cieu8h o8f0oya92 zbtph z/w g-3rcle
(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 kgnud*f 37lrgmio:gyno9 h /+k) (including the driver) crosses the rounded top of a +hk nniml:uo d 7*og)g/y9r3fhill (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 Ferri1iq)lzcv0du5m3 1 d2ms g8 bdws wheel need to make for the passengers to feel “weightless” at the23sdc w10 d 1dz5gq)iulmbvm8 topmost point?    rpm

  A bucket of mass 2.00 kg is whirled 2zdpuq( cqd++u 2 jip(in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the2i+c +u2qjq ((zudppd 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 iigys (*)8g ncfrom the axis of rotation is to experience an acc8* ini()cgsg yeleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walle1 i zcr0(b5inwuw.v, rd "rnz iv0r cww, 1r5(i.buoom." (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 ws)(xv p,8 bw7upoc2a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a d(78xs ow pba wv,pu2)cangling 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 , preciqy;dw50)/udf t p ypl r16pd2fsely this time, by not ignoring the weight of the ball whi5 pu/rwy ;p2ld)6tp 0fd1ydfqch revolves on a string 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 8*rmal;ss i dy,r+.s*c 8 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 masses -, +k rb34jymm1n47mptpkqxj$ 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 verti3:jsg u+(n1uhl/q ki xcally 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 componen upmu -8 hzp u.p32oucwh1.jq4ts of the net force exerted on the car (by the ground) in Example 5-8 when its sm82q uwz u.1po-hj3ph.uuc p4peed 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,dogin-x 1 8-g hr8p:rq 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 cp d onr:18-8hri-gqxgoefficient 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 particul8;7x+i(o5kqgune dvy ar instane7oq;+nixvky( 8gu5d t, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Ea1 j 1.2k+cmysi,hosip rth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ifps 1 +ioc1m i2.jh,ksy its mass is 1350 kg.   

  At the surface of a cevl +d a-z10uzqrtain planet, the gravitational acceleration g has a magnitude of z+uld 0a-1qvz12 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 gravit;ir ow*n(p tnns-2r)ny on the Moon. The Moon's radius is 1.74-nwt2( n;)p nnrr*si o $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has q )rzt cj-.9mia radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its t9qirj z.mc )-surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, buq1s**it x6qg ct the same radius. What is x1*qc6q* gist g near its surface?   

  Two objects attract each other gravitationally with abdx8iw. fqy8pe*hl - 9 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 grlfyk(. tvtl2bwr.v9 v1ah6 , uavity, at (a) 3200 m lblyk(,vv92ut . atw1rv 6. fh   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe:o*tzk3 3ay qhre thegravitational acceleration duyz33h: *kto qae to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivat rv7fw8p3-*tliv 3a7 or72sx p riw h:-kui8e times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfa7pvo7 k7wipx i ut3-a8irr:rvs8fltah2w- * 3ce gravity on this monster.    $\times10^12$

  A typical white-dwarf spyr 66ztd 69zstar, which once was an average star like our Sun but is no6 6trdszz 9y6pw in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting,upfugz/3/tc2 * uxew 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 acux2 f,/euztg/cpu* 3wceleration 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. Cal;n,s jq,mjquw (x8fc 3culate the magnitude and direction of the total gravitational x ;un j8 mqq(,3jcs,fwforce 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 uvi4. -2onwnskjz, j;tp on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four plan.wi-jzv jnsok; ,nt 42ets 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-psoig2se55m gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3mes52p-g 5 soi400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th zwv1naw8zu xh8b6()n, u te2ye period of the Earth and its distance f nz2eyhb t16 xv n8(),wa8uzwurom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circu* hsupkbl2o y3-p3b)u lar orbit about the Earths3pp )hu bly-*uo2b3k at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orby*y: gkb8ui 6cit 650 km above the Earth. How fast must the shuttle be moving (relat bugi*ky6:8cy ive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindric7jw ndlux, ;mh:tu 2p+al spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m,p utl2xum; dj,7+h: wn and 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 circular7h7n u 5lwvrmuy/5ch4 “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 n5w4rym5h7lu/ uh7vc Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hartg2*nun4 o;lve to be launched from the top of Mt. Everest to be placed in a circular ol*our2 tn4g;nrbit around the Earth?   

  During an Apollo lunar landing mission, the command module (f4x 7ndm2 yw: wsx8k lj49pzhcontinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onypfw4x8w9s 7khjm:4 n xzd 2l(ce?    s

  The rings of Saturn are composed of chunks of ice that orbit t fri 8sy -rmm+p8n ;/w)uny8bghe planet. The inner radius of theim;rn 8+n8/ urg)p-myybw8 fs rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter + m)dj3vz:xoyrotates 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 (bj)zyxo d3+m:v) at the bottom?
(a)    (b)   

  What is the apparent weight 9pmuzu0//y /qhghn 8 64wkiylof a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space veh/uqkp6z 8/m ni hwl9uy/ g04yhicle (a) moving 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 equal mass. The5c,.giftc 9klor e*4oh*7zj l5 5wtqyy are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is theo* *r5ofl 5he5qwct zk9g,ltij74 .y c mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman j 2*zg+gxmocjlga 00/ in an elevator that mozj g00x*oc+lgm2 g/ja ves
(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 su1ny m 7o,6y2 f.byxtslspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elev y 2lysnxt6m.7b,yof1ator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface, +k/q n 0 wc*1hrgki0jhwhcqr lr*a:)9hzw9c of a planet with period T , the de q+qr 9 nkkl) *wgh*0jwcr0,h: cc/rw19izahh nsity (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 thez0. dfftv:5kunou)a:2 w y4y cq bnp71 Moon (27.4 d) to determine the period of an artificial satellite orb4qnn k 05z)vu 7uyo:tff21pc.dab w:yiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, )38)r6cyb -xg9gzhmwh(dfjas 2r lh 0s/ t 0faorbits the Sun like the planets. Its period is 410 d. What is aj l6r)-)sgw9byrgshh z2xf/a8mh0 f(tc30 dits mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distxnbk 3n03f3x gance 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 *owluj9 jam)6very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthe6a ul j*9)jmwost distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the 4ck:gd 8ruddde+yqm:x.mg . 0center 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 maunr8g *m n9e3xk0ir k)ss, period, and mean distance for the four largest moons ofk)9mr 3i*ng8 r x0eknu Jupiter (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 fromr2w m,e8sb; dtg3 m4/ w*ipccg the known period and distance of the Moon. gt28gr,d4ww3b* c/ im;s mpec   $\times 10^{24}$

  Determine the mean duq, f xz (/am4 xn:yiua 3/p7ndwkkc92istance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuesx xzan9 u:u(2pw3k/ikfa m, /cyqd47n 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 be (). 0h 1dudqtpj6gpmltween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the S(p61mgu0)pd q ldt. jhun 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 b e, q:exqnkm;pp0t3 .,6(wxdr u/ wnbform 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 Eaq/6(p wqwx :ekrbx0db un,p ne ,tm3;.rth-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?   

  Tarzan plans to cross a goasrl2r;j/f; s83sy63jgn h g mrge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the viner s6gf ;3gh; mnalsrj/jys 823 is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of 5oi u37bwlvo ;gravity be half what it ; 3 buv5oow7liis on the surface?    $\times 10^6$

  On an ice rink, two skt u- 9pi7c.avaaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 u.aavc i97p-t kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatesy a5b .i *.-x hsruf7xel0 h8kmu8zb6m once per day, the apparent acceleration of gravity at the equator is 7zbm 05ku-emy.h fr88u.i6 xlhxb* saslightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dirwfdp-n ( * .msz7bgq;s/1xgafectly from the Earth to the Moon experience zero net force because the Earth x n.-gdfzmaqs;s/p b1(gw f* 7and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bkz)3em -0qow aathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and kmqea0-w z)o 3in which direction?     ----待选择----upwartddown 

  A projected space station cs(v3 d2)fdfek0rk hzs.ezz4z20/fh c onsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube hesz f3.rf)f0h(dz/4zsc22z0 e dhv k kas 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 vertical loop (Fig.i wxgc3k)s cvpq3)kt13 ,9ucz 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 zz(x5euoa01 r ;s4pbpa planet in terms of its radius r, the acceleration due to gravitr;5pa1 (0bzzep4xo suy at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string)0:b+9 rrafecn(f lqx m--*kul is deflected from the vertical by an u+n f rqlmre fkxacb--(*09: langle $\theta$ 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 ojy+omhy2 t02cd*jea8f If the coefficient of static friction is 0.30 (wet pavement), at what range oe+ajo2dyj20 tmh8yc *f speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so lcb rwgy1b7lin)zv)*sgpmh+5 (d34 5 il9d gafast that objects at the equator were 4zmii(5 l3d5 )rg anwh) g1yv7d b*+slgl9cbpapparently weightless?    $\times 10^3$s

  Two equal-mass stars h9e;0;dhal u+nkbv /nmaintain 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 el upke+6td, 9ws2mjj0,aaz1a constant speed rounds a curve of radius 235 m. A lamp suspended from tjwem+69 eupk2 zta1, 0la j,sdhe 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 Earth. Thus, it has be7t cpwdst/, .een claimed that a person would be crushed by the force of gravwc,t7t.epd/s ity 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 Space Telescope deduce* vo8kxkbopfc9m0d4x:fky+d-bp)u 0 d the presence of an extremely massive core in the distant galaxy M87, so dense that it couldfmbybk04k)d0f* d+ oxpv-o9x 8: kucp 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 val8, uv fdn) bzrjol61o/h;fup +ley 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?) Explbvo6 lrjp+ ,uf/8hudn; f)o 1zain. (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 ojdq2 :vgve5j5f 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 nautqj5gve5vj :d2 ical 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),5(cgg uu+v)eb after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a uvug+ )ebg(5 cheight of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shutux3 d zgzyj* fo;ts849qg42rntle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 kms*9n z tg8uxj fd324yo; zg4rq 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 year.c )nkw2m4s wrs. (a) What is its mean distance from the S4w s rc2)nk.mwun?   
(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 actually "f6san*dw.b(kganjgjr2, ,fj0 eel" yourself *ja(rg0a. ,w,g sjn6f2nbdk j gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-403 p( boiby,zz6) at a distance of,b zip03zyob( about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a sqczo3 bk8tmh2/dxl 44hcw*k 6 nuare 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 b ncd3mtl/ckhxz* ok64wh8 42 square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ou839mlo zmfl6w ;twi o/tn 2w*8sj0cwrbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep s ctd hr3d grw3q/94t3aecond hand on yourt9a3d /4drwq3rtg h3c wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and star0o knu gk/)z 5et0i;kht to swing a sinker weight around in a circle below you on a 0.25-m piece of figk 0iz nk0o5 u/k)e;htshing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tramh l. )) kwfh,lsv2h*hveling at speedh2h) m.v), hlhf* wskl $ 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 trainllf5yk7/ q1h-sstmk zf30w,v , 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) Calculate the friction force needed on a train passenger of mass vsw5,/t0fl7q 1 zk-mylhf s3k75 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.$\approx$    $\times 10^2$