Sometimes people say that water is removed from clotmd:a1z sy3k0y hes in a spin dryer by centrifugal force throwing the water o: a0z3syyk1md utward. What is wrong with this statement?

Will the acceleration of a car be the same whkgs:y6f7 uak:.kge9 yxb6kj(yj3v k9 en the car travels around a sharp curve at a constant 60 km/h as when it trav fkkv:u eb99s y(6gyk73yak: jx6jg .kels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car ek/43s+n v tep,kn/ mqexert the greatest and least forces on the road: (a) at the top of a hill, (b) at an4 vemp q/s/kk,ent +3 dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting,bwjr0h8nj9o1o ,i qlw q x3wf8kwa. . on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelera, 1 q93o,w.0 8w.xjhniol jw rawkf8bqtion of the child?

A bucket of water can be whirled in a vertical circle without tg0 pj;cbl+mq0 q/zm6the water spilling out, even at the top of the circle when t;+mm 6q0 b gzc0jlt/pqhe bucket is upside down. Explain.

How many “accelerators” do you have( .csatn9gli ) in your car? There are at least three controls in the car which can be used to cause t i(.clas n)9gthe car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crx rqhvgepzmp3s6+a67w) gr 06est 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 as he goes over the hill. Explain this decrease using Newton’s second pzhp m rqa366e)07gw+g6rvxs law.

Why do bicycle riders lean inward when rounding a curve at mus0 qp6sb5 s5+ef/ej high speed?

Why do airplanes bank when they turn? How would you compute the banking angleq (i)7fsauz:a dsq+5q given its speed a:sai7s d q +ufqaqz)5(nd radius of the turn?

A girl is whirling a (by 5b ta(uzm 0x8-h3c y,zsmogeo pzdd, +2u*ball on a 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 should she let go 2zs3do-dhcm+bguz m,x t*5e (za0u(b 8pyo, y of the string?

Does an apple exert a gravitational force on the Earth? If so,7m+d b34lnthb how large a force? Consider t3d b7nmlhb4 +an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubc9kv573-fy a vztn5 kurufj14r+dbb9le what it is, in what ways would the Moon’s orbit be differen atvfn3zkbc 55 r7k9 fj d49byu1-urv+t?

Which pulls harder gravitationally, the Earthu 7sc6y7vj gm,bd 4xx4 on the Moon, or the Moon on the Earth? Which accelera74 v74y,xdgbcxj mu6stes more?

The Sun's gravitational pull on the Earth is much larger tham9k xic 0p6j)0 de3djbn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider 6k90c i)xm jpjb03d edthe difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh 6c;s)h tr/(qvr2qr g(ss.tp+dnv8tt more at the equator or at the poles? What two effects are atvg trqc/8 (r q ;h+sns2)t svd(rtt6p. work? Do they oppose each other?

The gravitational fo/nom0nyn /ynsyznz-9; 0,iixrce on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eaz yi,y/ yn0mnn x/-nos09n;izrth?

Is the centripetal accelerationinu.,;xlozj 9 of Mars in its orbit around the Sun larger or smaller than the centripetal acceleratzl jn9;u,o.ixion of the Earth?

Would it require less speed to launch a sam0;6vfxk g s0xtellite (a) toward the east or (b) toward the west? Consider the Earth’s rotatix fv0 xs0g;k6mon direction.

When will your apparent weight be the greatest, ax2;qe :fm*whvdm/g; a s measured by a scale in a moving elevator: when the elevator (a) accel / qgfam h2vew;m:;*xderates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely aff4 srz- tyn)f-thv41alb3o( n;;yt bmzected 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 othef-h (toylzsr ) 4b;tv ntzm;n1a b-y34r aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlem jd +k+xk(v r9py4oe:-k;ocessness” between steps.:e94ke(d jr kok+vox;m-y+p c

The Earth moves faster in its orbit around the Sun in January than in July.qnxgnb*mp6471i ,)hvzs )ns m Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor i7q),vnngbs4 )s*xpim1zh nm 6n producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explaie +1u2l5e0q pkqfj 1ivn how this discovery enabled an estimave iq0e2f5 klpj11q+ute of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than t o,az345z8dek;ham6 b )yjd9sfub- zohe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitat,4 b9;ezmu8oho5fz6s) jyzb d3 akd- aional 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 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 o(t g jrg:z:-t 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 ac t8 hy4s):d(kijt7en)2gkecp celeration 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 thatgp7 (4)cyh2)8sietnkd:t jk e 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 ro:cbw1zo3vzz7 vm g h5zfflb8j 8l9;p1 tates uniformly in a horizontal circle (at arm’s length) of radius 0.90 lzhw 13bb:z7v f8 g zz5f1pom vj8;9lcm. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbitq8/ ghqd+j;flwgz(dd0bg :8w(m, uv g 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of thgg mgj:uwdl0(z (bwq/ +,hd ;8vdqfg8 e 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 edqq8)5m+-s )oak* jji5rlh qosge of a potter’s wheel turning at 45 rpm (revolu +qo-mq5ls* sro ak) jjh85)iqtions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a 7i +2+v n)aye5ii eaw8punbk*uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its s872ebnuw n* ipvai iy+5ak)+ epeed 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 w2)xiypyez4 ddn5 9, kphich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and roadpy n 4e)yikxd,pz2 95d is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the rghj8(u/dou3t, w w+ waoad if a car is to round a leve(wu8 odgjuh +w3t ,/wal curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is des-+mcnkba t *5a8l7ksh igned 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-*kat7nblhcksa + m 58 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable fgxb9 k,vgsn+ (dn/8d speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntfg v8dx ,/kg9n(dbs n+able?   

  At what minimum speed must a rollejiwt-3 gvomn i3t8+iagxlw z t.3-b 4-r coaster be traveling when upside down at the top of a c3o vgg-txbn j wz.it- 4li3w-ta3+8imircle
(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 the 7grw/z/b a vi3rounded top of a hill 7a/ rbvzgw/i3 (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 wheel need to macew30c lk 5).mawnin4z la,z:ke for the passengers to feel “weig) c,: ecn3nml azla.450wwi zkhtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circlby4k-) igl- sue of radius 1.10 m. At the lo -gsul 4by)-ikwest point of its 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 centrifu28 0o xuhp8)lay+.ber kvb8dvge rotate if a particle 9.00 cm from the axis of rotatio.y pao rvh8ve8+kbx28bu 0dl )n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically w (tygs/ga (rz8alled "room." (See Fig(/gszt (8ryga . 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 frictionlessav d w*9j8c,og0qro a/ air-hockey tabletop, and is held in this orbit byoj,dqvc0waag*or 89 / a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignc5*w oh/msek;x (rn +qoring the weight of the ball which revolves on a string 0.600 m long. In partis(c+xwo/q rm *h 5en;kcular, 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 peqcq82i)o med-t5vhg*.2rt 6h0tjrw krfectly 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 7e2-wc0zyvkp $ 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 vertically at rjcr63 iu b*f*7 ndz2l310 $\mathrm{~m} / \mathrm{s}$ . 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 s2r,o4bw . :.ihec qso h0iv(qcentripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed i:iq 4 .hoes0s2wh, roqi(bv. cs 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acc-cvqfnuui(bh 8e,f+f44s ecgp ; x)n6 elerates 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 constfvuinh 4c)qspn(e 8 f;, cexgfub-46+ant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partt (uaw h:c,4((0 pbnmg sf9sbaicular instant, its acceleration is 1b aht(s(b0u:fa(m,4 p g 9swcn.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 spae/ ,b 31gon b(eafit4bcecraft 12,800 km (2 Earth radii) above the Earth’s surface if its naif oeb1,4bge (tb/ 3mass is 1350 kg.   

  At the surface of a certain planet, t:vur l(hcak * bys uw9/2*e6lbhe gravitational acceleration g has a magnitude of 12 m/s(*leb9wvys26b u:la* /ckhur $^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's raql c3fb odzst..o 5-rdb,v icevn9: *2dius is 1.7 qro,9c3 d2 .zb* vfcn:b-ol5stde.iv4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planemel w u0 j;y.d6(a3qyut has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfm; yj q6adluu .03e(ywace?   

  A hypothetical planet has a mass 1.66 times tha.r3 s-r.om43a 3eiq gxs-uoj/8lotn vt of Earth, but the same radius. What is g nearae rq3lj o--r nxm.g.so3v3itosu/ 84 its surface?   

  Two objects attract each +uk2jpz )u2ye.8 crg hother 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 acceleration of gra5gd6/ db*, n gns5mekuvity, at (a) 3200 m/m ,dkb nn es6gdu*g55    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance nl0rl( /md 7ga l,-ivvfrom the Earth’s center to a point outside the Earth where thegravitational acceleration due to therdlvlai0-l(/,ng7mv 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 into a suc1fp c9hb*m 7phere about 10 km in radius. Estimate the surface gravity on this monsmc9f7h b*1pu cter.    $\times10^12$

  A typical white-dwarf;uat(g0-qaqj b9fn : p star, which once was an average star like our Sun but is now in the last stage of its evolutaau0bqtj-;f ng:(9 pqion, 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 weig 6ijn;e9ir ,d*vl vg qy+*:csqhtless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them ac+9;jq vieq:l iyr*d,g* vn6s nd 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;,eo+ e j(7ultd k.nrir q(7xf 0.60 m. Calculate the magnitude and directionjk7(trfux+qe 7r i ;ledo ,.n( of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years nihxs8p 4k.9qmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn,9xkq4sh pi8n. 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 mqv;;kh v vf ,2 fv;g8av3diy/Mars is 0.38 of what it is on Earth, and that Mars’ radm;3vq 2fk; vf;/ ygvi,8vvad hius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using uv l ;uu0 li(2qmj*u-wthe known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Ke-0uuimq vu2 w(j lu;l*pler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sand.yv qx98ltizi(a7+ tellite moving in a stable circular orbit about the Eart(7 ya xqti9+zlnvi8d .h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above j/crh :g3b(h-kd1 6um 2v dqvbthe Earth. How fast must the shuttleu2j ( bv 1/ hckg6qh:3mddr-bv be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants )m inm io3l2,bare to experience simulated gravity of 2m,no 3m)ilib0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for aas 0wmz/-n(kn satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Doe -znwn(mka/ 0ss your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to/e 7uraz:y/ee:agy e1 be launched from the top of Mt. Everest to be placed in a circular orbit aey17a/ru/:egzyeea :round the Earth?   

  During an Apollo lunar landing kqllx n3p.x ;sj am135mission, the command module continued to orbit thesx3 5npa1x;k q. ljlm3 Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. 7 :gr)q h8s,uji4qb wcThe innr4qqu:s ibw) g,8hj7cer radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in pd4 ;/2zdykvki lpg8: diameter rotates once every 15.5 s (see Fig. 5–9). What is the 82 dk 4yp;igd p:/zvlkratio 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 weight of a 75-kg astj r- c.xt 407rzdlqt+oronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) mojd .ct+-xlr40qzor t7ving 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 mae:rq p 11 1r7mzn.zlywss. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway bm p.r 1zqyreln11z:w7etween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight l kd/t;/2j ijwof a 55-kg woman in an elevator that movji/ w/d ;t2kjles
(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 ceili8ax38gw em cd1 4kjmv3ng of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What wd g81mav e43jw83c kmxas the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite;6vrajy i9 7f0rejz+biv ,a7s orbits very near the surface of a planet with period T , the density (mass/volume) of the planet is s 6jzv iv7a07erf9,b i ;+jyra$\rho=m / V=3 \pi / G T^{2}$ .
(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 dl4pr.7b o 83tjghx+ys ) to determine the period of an artificial satellite orbiting very near the Earth’7+x4 yojl 83.hspb gtrs surface.    s

  The asteroid Icarus, though onwz .v8y1wj k9flb nmr7 -wz;2zktj5 m-ly a few hundred meters across, orbits the Sun like the planets. Its period is vz1brf2k-j j8wwy-; z mtm9zlw.kn75 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancq3b sde1c , +rufvn yhk38:.co/q.q rte 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 ve6du .dj mx.m z/du)gf b9ar6r*ry 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 farthest distance from the 6uar/)fm 9 . .uddm*zbgrx6d jSun.]    $\times 10^6$

  Our Sun rotates about the center of d*7ihd6 /ehi3x 3ha*hs:f rhdthe 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 meax7mq vro-gz --n distance for the four largest moons of Jupiter (those discovered by -ogmq z-v7x r-Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon.v8(mwei4)qp .fog bnts5 5t3 z p5.bt5o vwgzm n e(8s4t)q3 if   $\times 10^{24}$

  Determine the mean distance fl j6jh5/+lxg zrom 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. Compahxj/ll z5j+g6 re 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 c 2+ dtktt2s 5o+azzj m+8vl;wconsists of many fragments (which some space scientists think came from a planet that ondtmw5z ozvt s +t;k28j2+ac+lce 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 artn:,mp2m vre- kbjg +nin(cq .qoj 7q9,ificial "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 ma72,qp:nr- mjce .vb+j(ng,kmn o9qi qke the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in 7vrs im17f7y/zhaulzsz 7+ 0aarp65lt3rs4 d an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of7370p4fvr 5+a7m s 61rdylluzarz7hstiz/sa 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 acceleration ofqxi3b0xng, ,4kz w)w l gravity be half what it is on t)i4,l,z x 0ng3kqxwwb he surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gmb,m d1wdq8lln/;hnzt1+ q d+i0x- fqrab 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 kg,x fzmlt;w+lb 8ddq/+-in ,0nh d1q 1qm how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatqio3//ye3ns :f dzcq .es once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What es qy/q3cz o/id3f:n.fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly upb,4 o7g(erc ;yep5 ffrom the Earth to the Moon experience zero net force because the Eap7bfyee 4 u5rpc, g;(orth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you pgzppai grs/ zv9)3le8p3 ,e* stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dirp/8,*vp3i zlgea9s p)zr ep3gection?     ----待选择----upwartddown 

  A projected space stati)pl v)3fuzlf0tkj41 ff )2sfh on consists 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 (revzhfu f01 k)f fstlj 2f)34)lvpolutions 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:x)7 0 ujj0caje)fq:x2y e eei. 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 tzns 9b o;dcq56b2ubg. erms of its radius r, the acceleration due to gravity at9b;g2u s6 5.qbobnzdc its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) 2upq w7;62wmvau 9ltn is deflected from the vertical by an angle qw 6p v2umlu9n2at7w; $\theta$ 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 forkv19cj8 r/ libefi g33 a design speed of If the coefficient of static friction is 0.30 (wet pa8 erlk bcjv3g91/iif3vement), at what range of speeds can a car safely handle the curve?

  How long would a day bn *vd9;+wyb muzp57 fr- ue)vbe if the Earth were rotating so fast that objects at the equator were apparently weightlmu+dzv r); bv9*5epb nw -fu7yess?    $\times 10^3$s

  Two equal-mass stars maintain ao;vw7 kdc8;tgtk je2th*gqsuf+-l 16 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 speed +v27bzsa3s) z8tr i i71.gszn2btl sp36q izyrounds a curve of radius 235 m. A lamp suspended from ss 7avlb zb87ig3.pz 2qzsi6)t1 3 y zs2trin+the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has beenir36hg xyr lpz q)fhg -86 sg*v,43beq claimed that a person would be crushed by the force of gravity on a planet the size of Jupitp36r hg6 *gl8ixfygeq,qb sh3rz -) v4er 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 deduced thl-2568 p9 fl znjebhage presence of an extremely massive core in the distant galaxy M86 zl -enfa5lp28bh9jg7, 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 spedd ji/b6q0w*o ed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Li j/db qdwi06o*ghtest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Syst cdl(1pu+ rnnul2 0h3zem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and s+2ndul3pcz1ur lh(n 0ignals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 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 traveling 2.1 billion k1a s 4azd o0:4)lhnipzm, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40as lip4d1 ao)nz0h: 4z $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 ne5a 6ri--vuufzed of repair. You are in a circular orbit of the6 if5-uazv-ru 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 year-lvracoxvtl+i(p/ab8 3 x j kse415 h+s. (a) What is its mean distance from t+ jtb x v e3p8x (54c-a/1loshakl+irvhe 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 8jz1 d1 yjgzgvg;1 of5 G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumpvfo5y1z1ggj zd18; g jtions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around ufk*la/ 7t4 f 2(78rqidqt,xndm7 uclthe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-y qr( 7q,*xu /ldkiat7 4cfnufl8m27 dtears 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 ,ue ucvq/:9 u4u1cnxethe 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 mc/9u,1xqu 4v uceenu:ass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orb*rlbi9 uf2pi-its 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 *vy)mvdqrz*t93jtdisqc v 7h5mx 0:11.5-cm-long sweep second hand on your wvm7 :hm x19s50 it qq c*)vtry*dzdvj3rist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighta 2 q*obv.fxr 3n)dq6x7;yp fm around in a circle below you on a 0.25-m piece of fishing line. The wei;x)rn y*q73o6pvfmfqab 2 x. dght 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 radius6kcullbs s e f:q,2;n l73r5ea R in a new highway is designed so that a car traveling n:7ecl fq2u 5ba ;l3l6,sk sreat speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of3 hg fcglhksjooe14( sl:bm j;,6r, ;d 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 cok,o : jos g,(g 4 c;le1fshdljbhr;6m3mfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$