Sometimes people say that water is removed from clothes in a spin dryer by centr-k5crdf1 87ox sh xgp5,u6zhj ifugal force throwing the wat k-h5j8d15gc 6z fhx x7sopur,er outward. What is wrong with this statement?

Will the acceleration of a car becw psud:g;9n pe q.u7bg0zll3-b;:j;9 lz k bp the same when the car travels around a sharp curvlb:uk eznqugl99:0b cw p;d7l3b.;p ;pjsg z-e at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constantd. y2rmg)sz.e1jh4hlw m;2u x speed along a 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 t4d ;r x2swejmy1.)2z guhm.lhwo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horsgs ot-j brr9*gp /zr)v6pv;t*e on a merry-go-round. Which of these forces provides the centripetal acceleratio ;pj) -*tbor pzg vgs/6rv*t9rn of the child?

A bucket of water can be whirled in a vertical circle withoup 3l- z *fdgz1w40j4g6qvtipft the water spilling out, even at the top of the circle when the bucket is upside down. E4qdg16*z 3pwvfz 4-jtlgf p 0ixplain.

How many “accelerators” do you ha 2wxipoaz(0p ry7czauc,bu i v/r +78*ve in your car? There are at least three controls in the car whichz707c2+/a*uw ar,ivipzy8ro xpbu c( can 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 cre b3 vm skgw89gybn5-/e( w)yxjst 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 goe9v-)8 wybk geywb5/jsmxn(g3s over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high nkda u b,w:g((2ce2k5 hakuj4lmp/qn* i /y +kspeed?

Why do airplanes bank when they turn? How would you compu5gbc/x9 sk8whlib/, vte the banking angle given its speed and radius of the tuv5s 9xbc8khgb w/i,/l rn?

A girl is whirling a ball on a string around her head inrg4u+ujd 9 )snt)( j5:ptads jv)*aan 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 r5sa:j+g)dntptj jv )sa4)9a(du*nuyard. When should she let go of the string?

Does an apple exert a gravitational force on thex(okk/j8j 0 ja Earth? If so, how large a force? Consid(xj/a 0k8 jkjoer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wer5 .7px9gp7vae az4;wpst)qeh 7,iiiqe double what it is, in what ways would the Moon’s orbit beat4;9 7hsiexqw .geiiq5, pz77av )pp different?

Which pulls harder gravitationally, the El-q b(smvst-1) l-m onarth on the Moon, or the Moon on the Earth? Wht m(m)s ql-o-n1-s bvlich accelerates more?

The Sun's gravitationgud2i6 kbp ffk4/-: fpre.6 zaal 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 gravitational pull from one sig ru.k2-6/fi 6:dzpe4pfa bkf de of the Earth to the other.]

Will an object weigh more at the equator or z;j :n isbua3:at the poles? What two effects are at work? Do they oppose each otz;i n:3sb:ajuher?

The gravitational force on tm,s)q.i :w b9v i;*fvfh oh 4:tbcjs25ae:zid he Moon due to the Earth is only about half the force on the Moon due to the Sun. W4* ob) s5t f;q.2 iaz:fwhscm:hj9diiv,e v:bhy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or avyr gz ign* r: t9hhb (fldke2:0-,*ksmaller than the centripetal acdab 9ry* 0er-:z nvgh :k2fk,lhtgi(*celeration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b7tse+ e(sp;ludr2 7 fvewzy: )) toward the west? Consider the Earth’s rotaterdzse sf+wl7( 7:u)yep; t2 vion direction.

When will your apparent weight be the greatest, as measured bz.es 7sy /xi3(rmmnc/:0rp j-z evph*y 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 m3./*x(syvjzprep e rmc z70 /- s:nhiyour 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 affected by fyox1o, mms*wy w43e7 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 fas y74xm oy1mf3,e*ow wll, (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”7,n m,tna g:ml or “apparent weightlessness” between stepm,tn7m gn,a:ls.

The Earth moves faster in its orbit al(zv( bgj:8mrtpi g8 (round the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt ofvgl mzgj(p(ibr (t:8 8 the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hav8 jn 0add1eihi2,1sq he a moon. Explain how this discovery en0dqiaes,d2 h 11j8h niabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moojyn5 fo* ( +si 5e-yub;hwofl 27n,bjcn's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves wit ob5 s2yw,ienn-7 yl(j+co5f;j *ufhbh 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 j a6llfqjnv9x vey)a;9,gj : .1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its c/.) myz6kud j74u pndorbit 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 cir) m7kd6d/pzyn uc u.4jcle 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 4*w20 ckl0,qsap upxtexerted on a 2.0-kg discus as it rotates uniformly u* ,q40 0wlp2cskaptx in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km b8 0ef hemdt1v.8drq.from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in te1.r f8.dqh 8 0dtmbeverms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude zb4+f 46j u :9ctpbdguof the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minu4j4bczu6tp9 d:u bgf +te) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical)ur(rv)l:6z,zo dw jsyf +m*r circle of radius 72.0 cm ,szj+ol)*udr rf:6y ,z(mwv)r as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of radiuni pv93cl gb;angt2 5qp0t9s.r*)u dys 77 m on a ir5pgn pt9*adt);03cv n9g.yb sq2lu 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 between the tires and op:6*x5)w ix1wtk mtw the road if a car is to round a level curve of radius 85 m at a speed ofo1:tw6x5 pkxw*it wm ) 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate adif7dy1( 9 mjxp kur9: trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back ism u 1xr ikjf:yd799dp( 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 axis of 2hm( ba) e+oqk 1)fj.tc1whf 7g0g mtua 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 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turn.matqo7mfh 0t1 g2)+ kj c1wufg)e( hbtable?   

  At what minimum speed must a roller coaster be traveling when upsidey w)v6:qzxf8h down at the top of zvx8w6q) yh:f a 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 mq4bws:ayz2 *i37b bn jmy6/ykass 950 kg (including the driver) crosses the rounded top of a hill (radius3 kib*4y 6j2a:7qnwyb myzsb/ =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 gxbrum: e)+ 5iv7d6 dlto make for the passengers to feel “weightless” at the topmost pointdbre:l5)+ umvdi6 7xg?    rpm

  A bucket of mass 2.00 kg is wil6bky/yf4 : bhirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supp iy/y4b l6kfb:orting 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 par l fy/om0g a(4dr0pq+xticle 9.00 cm from the axis of rotation is t q0rla (f +gdxy4/op0mo experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricalrh 0qn bz0f*id:ha95lly walled "room." (See qr 0dl5h:biz ha9fn*0 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 )x bdoz- 4px0aifb5 wv4o +,.0 c*sfyco is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central ovpw fy s*4do+ f b5ox 0,b4ia.-0czxchole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring t ci b)kb0no69zi bnzivg8*n85 he weight of the ball which revolves on a string 08bvb8 i9 )n5 6zgiok*zbn0nci.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectlyi;enekk- t ;(c 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 massei:)d 5/ 7)ntsdrihgff s $ 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 maneuu2p+f,ic nm 8)z9xrh6m0+wcglti yg4 ver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compoo u4 jx6zy+3ggnents of the net force exerted on the car (by the ground) in j+yxg4 z6go 3uExample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly fr9q2uzs 1lnct; om 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 coefficient of stati;cl2s z9untq1 c 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 vwnq9d9p d 5)k eyy)o*2.90 m . At a particular instant, its acceleration isn)o5dq dk *v)99pe yyw 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 o)zi6y u :tt2v:u.dm2vvi r ,ikf Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is6 u2vir) ttm,z2ydiv uk:i:v . 1350 kg.   

  At the surface of a certain planet, the gravitar8 p.86 r8zmj uh.ooqdr7wayw-*3mjr tional acceleration g has a magnitude of 12 6pz.hmwu *.8- rrrdrqmoj 8 joy37a8wm/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's ranaql)+h;fh fd3 .gfm8dius is 1.73 .qlgff dhfa)n;8+ mh4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a rad:.sqa15 wsura ius 1.5 times that of Earth, but has the same mass. What aas5 usr:q w.1is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,8dnmaoa6 n9j268oh x 7;arzx c55efv z but the same radius. Whahrnfaxc5 axzn 6e ao5d8m ;vj6872o 9zt is g near its surface?   

  Two objects attract each other gravitationally with a; y- b1.nbh0q1i eedgd 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 gravitb4de .kpo6f xo t08pt vxx45-n8 nvbl.y, at (a) 3200 m4v.5x- fbtopd4vk8oe p. 6nt b0nl 8xx    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to6zcjvvis,/w hub bi990(sl2o a point outside the Earth where thegravitational ac(bcs9/ wlz,26 jhi9uboviv 0sceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packe. s6y3cfg gc8yfnha3 2d into a sphere about 10 km in radius. Estimate the surface gravity3nfggc.h y632s 8 yacf on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avn /b4x k2;nqflerage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravityn kb/n4x2fl; q on this star?    $\times 10^7$

  You are explaining why astronau)luuk5aq82l y ts feel weightless while orbiting in the space sh8 a )yqlulu2k5uttle. 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 the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a sqmjw t07w+fny7j r(p ;quare of side 0.60 m. Calculatj 7wp(7tr ;wyq+0nj mfe the magnitude and direction 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 most of the planets line up.bs7e,s9w 2sbg.j xm s on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four plsg2 sj.,wm e.bss7xb9anets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what n78k2pie ihc) 8 5rngzit is on Earth, and that Mars’ radius is 3400 km, determine nz) k8i7hr8g52ci pnethe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ear4q d8/znpce(pvx3 r y4th and its distance from the Spqnc x (e/d3rz8v4 4pyun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mocx61q i u hok3ttu-qpcey-vzv61j 9++ving in a stable circular orbit about the Earth at a height of 3600 km.6c tk++uvocy11jt-x9u e zq ihpqv63-    $\times 10^3$

  The space shuttle releases a satellite into a circular orbita ,r:j y:c*7ns+no /;gs khhe( lwn4ti 650 km above the Earth. How fast must the shuttle be moving (resnan/kn ;h cl :7+w(*:etso, i4rjhgylative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical space2pgh,vcr9 ; pjship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m , cphpjvr92g;, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes forl ky5ja54)v.jllpi 1ke5 n *xs a 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. Does your result depend on the mass of 4s)ke5jvjy5.xa kln * i5l1pl the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fron*u- od8ewg t7m the top of Mt. Everest to be placed in a circeoudn8- 7wtg*ular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conticwqy +:ih29 2k6dbkvr x lb:1jnued to orbit the M ijx9lh 2cdk21 b k+:v6qwryb:oon 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. The ae;d25ues2(qle v m8m inner radius of the rings is2eqvl;8ause dm25(me 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 rotat xhjj h5 bukd3:aoarc8g5 p98-/zwjv )es 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 (b9jx -zhu5pokawa/)jg c8b 8dr5hj3:v ) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of *.q2e+inagko 2 +7uwu5iiva 1d hek5kthe Earth's Moon in a space veh .v7q51kkoaheu2di *i2ewgnika+ 5+uicle (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. They ar;7b kykoc5*-jbxuhl3 e observed to be separated by 360 million;7bhjx clk 35uy-b*o k km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fogoivsg/qkvm +qi * d+;c 8(i br/el4u1r the weight of a 55-kg woman in an elevator that moves ric u* 1e/+d gkv(;qiqs +bo8m/lg4vi
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an ,wtxhjk(j 879t v / qsnf4i*oselevator. The cord can withstand a tension of 220 N and breaks as the el 4iq7s*h9wjfx8js,tkn / vto(evator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with perio5gdksn 2( (u ea-bq2nad T , the density dn 2(aaungbsk (5 eq2-(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 ; 1rofz04as alehkcwt96 ut /.of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s ;6kaea1 wf/4r tu90ocsh z.tl surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits te8nqv,f bp* ll:n*5c0ujufe ,he Sun like the planets. Its period is 410 d. What is its mean distance fro*ef e fqln:ulcv5 p,ubn*8j,0 m the Sun?    $\times 10^{11}$

  Neptune is an average distance of t g w3*nrt;s/k 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. Itz,jp( ;rnz ;gw comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is 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 isw;zrz ng(pj ;, half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center f ipxi+0w72hmq 5xek+(a c7ww of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass,byso1bmp + 9z7 period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609).+p9m1 7szybb o
(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 z )ve2qn +mz8/5hzao ndistance of the Moon. 2qh/)5eo8 +azm nnzvz   $\times 10^{24}$

  Determine the mean distance from Jupiter forhgek314peshdj e 9*9hyx x;x 6 each of Jupiter’s moons, using Kepler’s third law. Use the di;y3edx *kh4j91g6s exe 9xhhpstance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmeb-hy rkfjd,n29k* . d)7jcctgnts (which some space scierdjkbn)9 -gyj.dt,2 kcc7* h fntists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a ba2 5ngz7i v97ttltt2l ynd completely encircling a sun (Fig. 5-40). The vtgtyzi n772t5t29ll inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig.b5qn tv h3*ztfn0 n0m: 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 hi bf v50 3*t0n:tqnhnmzs swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravityisy )yg p;2fe5 be half what it is on the surface? g;2y )p is5eyf   $\times 10^6$

  On an ice rink, two skaters of equal mass grab haoyyq oddc *109nds and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m lqdo1yc y9o0d *ong 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, the apparent acceleration of gr 5kn8/lqxft :sc op20iavity at the equator is slightly less than it wouldcsix8 :k po0q2flnt5/ 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 Earthke4(xg. zm nc: will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? n4: .gcxzk(e m   $\times 10^8$

  You know your mass is 65 kg, but when you 7/ lmkv +pcayamd2 j)6t6ue n:stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the ad+ j mu:6ae/2yk c7)6lpavmntcceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will roc3k w: i 47q10n /xugykwzfmyy-q8y)rtate about its center (like a tubular bicycle tire) (Fig. 5–42). T1-:giyznw8/mqy)4 qrcwf7ykxk 3y0 uhe circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircrwnkrn6.-s9 hkuqbz0 qyh2; w)aft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r ;w 2iagt13-i,. hdie;gjgzhruo9 /qn, the acceleration due to gravity at its surface and -gi gq ohij;2tnga.h,3/d; iu 1zwre9the gravitational constant G.

A plumb bob (a mass m hanging on a6l4qw (0 qihqsf(m :np string) is deflected from the vertical by an angle nq ( w6:m(q0sl4fqpih $\theta$ 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 thef6 z+-w:hk 9ewv h(ecfrt o: b1p*uj7u coefficient of static friction is 0.30 (wet pfecpr( v f::*t-h+u9khjz7bw1 oe6wuavement), at what range of speeds can a car safely handle the curve?

  How long would a day dhe1lmw7,ex:v h o (ou:(-c etbe if the Earth were rotating so fast that objects at the equator were:mv utcohloe (-w h(d7 1,x:ee apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant d1 p bv)9gz*r/vyy+s,: zh+ac tykl;h pistance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp 06ulfwscio 5 :suspended from the ceiling swings out to an angle i0wo6u5 cls:f 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 been clb9hzp c1c5a y*aimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.ycc5bp* zha 919 $\times 10^{27} \mathrm{~kg}$ , 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 Tegan)ssq:6 s0n lescope deduced the presence of an extremely massive core in the distant galaxy M87, ssq6na:sn) 0s go 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 thy8wy i+ -p*.lrujzho0 e 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 heaviestw0*y-.z+8jli opuh yr ? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) uti*ago, 60d uiwtlizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical *,6owgt0 uid a]. (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 billionn 2e c3. sclqj:bgwyib*8,b+cfj (wx( km, is meant to orbit the asc +l x jwq*8b(ibjc3,n(w:. c egfsy2bteroid Eros at a height 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 s4rq3if)bp6gbp1 lf 0opace shuttle 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 km bfb ppqbol 6fi)30rg14ehind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What/ op.padfgj;1 +lo 9yd is its mean distance from /+ooj.a; d pd1lfpy g9the 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*b c 3:z,w lt0ffj.sius-ntk )1m1 tautj+q.k would need to be if you could actually "feel" yourself gravitationally attractkjta w *lm+1 bzs:qki.)t-0 tu.j u1ncf3fst,ed to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cente 0jdr5+v*:m 6pl4/xw hipzgf9zy ubs*r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from tz6**5 b:dpws rl 4gyhp/v9fxz iu+0 mjhe 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 c ck fg+9mqloob*4e5e) orners of a square 0.50 m on each side. Find the magnitude and direction of the gravitationceo boe*lm+4f) 5k9gqal force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg;tv hly( v)-czwh ;ou+ 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 si jb38p+3hp.b z0fi j 2 a9ch/ozybq8by the tip of the 1.5-cm-long sweep second hand 88qa zo3bbi .phf j/yz+29i 0bcjhp s3on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start tobl yf:e ,z9rq ub3,tiswc8-, k swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a com, 9fuqs-c,83elyibw:rbz , tkplete 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 newk)c.usd49kgi9b dbr ) d76w gj highway is designed so that a car traveling at speed.7w k b 9kj9brcd dgidg46)s)u $ 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 of thskc: 2*mgn*g n5p2bpzf yv5c h7/; jwhe 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 experm7zsfw ghp*;v5j5*ghn2 c :pb2/y kcnience 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 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.$\approx$    $\times 10^2$