Sometimes people say that water is req--*areqf q nhgeo.rj;1 gm1.moved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wro. rjeqf1m*;g r. -eqo a-gqhn1ng with this statement?

Will the acceleration of a car be the same when the car travels aroun+hkf jexa4*++t lqas +d a sharp curve at a constant 60 km/+haa *j t+ls xe++fkq4h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does t3iwyie 7wrqa6x87 ex,he car exert the greatest and leas8wy6ii3ea x,wxreq 77t forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting onn.)fiowp* yhoy j8/4m a child riding a horse on a merry-go-round. Which of theyw8j oo *n m.4/)fyihpse forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a verti91zmk /s3i,4 o ylpnszcal circle without the water spilling out, even at the top of the circle when the bucket is up19iz y op4l,3 szmns/kside down. Explain.

How many “accelerators” do you hhidipp ed3a (psw 4wu 1ty3jy92i+ l1/ave in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they13djh pt 1l9i ( /ywe2 ypw3i+sau4dpi? What accelerations do they produce?

A child on a sled comes flying over the:nstw)kc7axc*37som 6km ;jk crest 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 decreacx)mso a;wkj* n:kskt76m37c se as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hm4buyb-.wixw 7;g(achra iy.)w0gv ) igh speed?

Why do airplanes bank when they tur/ /d opr7 dy3ds;rf3npn? How would you compute the banking angle given its speed/rypdfs/37 n;d3 rpd o and radius of the turn?

A girl is whirling a ball on ahtjlzu-lko 7x /,tc/- u-lij / 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 tht --/l okjullu/cjxz / 7-,tihe other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forcea6 nd3o 5kaqdf2*ytfv mqee .7sf;4r) on the Earth? If so, how large a force? Consider an a*q am7dkq.sf63tdn)ve ra2ffoe y ; 45pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what ah7bre v 2-bf4it is, in what ways would the Moon’s orbit be dire27f b bav-4hfferent?

Which pulls harder gravitatid5eqhe8lg5 ; 1qs+5mde)o lnlonally, the Earth on the Moon, or the Moon on the Earth? Which accelerat+ded18glle;l eqsm5) 5 onqh5es more?

The Sun's gravitational pull on the Earth is muc q6m, io/ebzg5h larger than the Moon's. Yet the Moon's is mainly responsible for the tides., 6gmbzq 5eio/ Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pol xf aw59 )ouit1 q/eat5tj;a(res? What two effects are at work? Do they oppose ) q e; 1a/uaj9 w5(ttix5tfroaeach other?

The gravitational force on the Moon due to the ts9/i ekt/scg,q98 nn,kvw4c Earth is only about half the force on the Moo8css twc,i n4 gt99kk,ne/vq/n due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars indvb (e i-,eqmax, (+vd its orbit around the Sun larger or smaller than the centripetal acceleration of ddb,ee(iqv, m+x-( va the Earth?

Would it require less speed to launch a satellite (a) toward thw fs5tga 4u s/5m.ca6je east or (b) toward the west? Consider the Earth’stmw/uc g5.a a6fss45 j rotation direction.

When will your apparent weight be the greatest, as meax ff5) n rs2:br0+uzmg)( mxlzx 1xg4dsured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the samd :4xmr) 5zff0)+m1x(rbs xugn g 2lxze 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 adverseliblycb8 dr mt 1nwq/v8 -q*5q4y affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think on b5/ d8yi8mvq b14-q*q lctwrf.

Explain how a runner experiences “free fall” or “apparent weightlessness” m gq6)s ikam*.(bz hch c; b5-vg0f)oqbetween skz5))vomb sc6; - *. gh0cbqg(amqifhteps.

The Earth moves faster in its orbit around the Sun in Januctbuuy sr(62bff;v u8ab*/7v4h k:mu ary 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 prodf/ uf2v(u:y s4m; b 6bucbur7* 8kavthucing 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 mod xr/ev:v3jos/,/rk son. Explain howdr/ ok,sr3v:e js//xv this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational p6srgogo72qvxdw)-( xm p 7zr7ull on the Earth is much larger than the Moon's. Yet the Moon's is maisoz mgp-o72 x7w vrqdr6(g7)xnly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 19rl on5dp5z1t 7bgxr 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 accelf/o qn+4hsj r:eration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What ex/snhf r:+4oj qerts 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 exedf7zbo lls(0ubc++uf6grb4+ rted on a 2.0-kg discus as it rotates uniformly in a horizontal ciubl s+70 gdb+lo (+ cuzffb6r4rcle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's qkpiakrqg(jxx9:06* surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spakpjx*rk6qa( : i0xg q9ce 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 am xmmeuv m04uz mjx+i6)p:)1 jcceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (re+0mie1vjmx z 6m:mxuj4)ump)volutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unabrjw; l37vdqx rk 0.)iform rate in a vertical circleq 7wba)l3xrvrkd;j. 0 of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can rowpjr ,gp7ndal 1v*c ;6und a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thisja,vd 17w g p*nrl;cp6 result independent of the mass of the car?   

  How large must the coefficient of staticx( 5ointmo- ,kzo8) gv friction be between the tires and the road if a car is to round a level curve of radius 85 m at a5ozx8ot)i,m kg n( vo- speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to r1dgow; jp 3n)el+81;f sz gvms+cc2gyotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?y j+)ge m2wp3gs8;vlc +g1;s od1fz nc    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 rotatil nxn- m/z:0kpng 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 anlmk/ n- 0z:xpnd the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dh8;lucfj;(* zng h ce2erk7 ;down at the top og 8hel72*uf;necc(hk;rd jz ;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 mass 950 kg (inc7me,h:oznioo+;j .spxp 2n r. w7-dtoluding the driver) crosses the rounded top -+p d:oxwton.s,m 7r;ihnozoj7 e. p2 of a hill (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 miuajxz2:7; fwrtiyug4 zi3 p78nute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” a:pyjfwi2g z73 urt;7a8 uxiz 4t the topmost point?    rpm

  A bucket of mass 2.00 kg is whirle u.ixewst3 ( yzw2 gwh-7.z4rhd in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the y( wg37ex2s wi4h.zr-.tz uhwrope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axis o7.g tkywimvm+q*l8, ff rotation is to experience an acceleratiowql + fmmtg,y7*vi.8k n of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled z1mxw.ybf *d0 "room." (Seey*xfbm zd1.0w 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 (v. of cbpuw99c*q7puct )rp: a circle on a frictionless air-hockey tabletop, and is held in tuutwo p 9q (*bvc:c9pf)c.pr7 his orbit by 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, byzmvk jeld (,v2w pkwfvya :d/9w, u8;8 not ignoring the weight of the ball which revolves on a string 0.600 m long ,mu8:jv,/vz vkdday f (9pww;2kwel8. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly z)o9z8u up qr05-y wh;cp;yvzbanked 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 masse + ooxybp l5u6e7ij(,cin)3em 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 maneuver by dzxcb:wl+ 1 jw+iving 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 components of the net floka+opf +.x/9vg a:a orce exerted on the car (by the ground) in Example 5-8 when its spee/.:of+ oa+vla9g xk pad is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis yr++7 oo j b kbh;k,fu8cg+qx:500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient o; okufrb,:+c ++ ykj 8bhxg7qof 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 ciq*umum;i wc8/z;orq ; )j-e jtrcle of radius 2.90 m . At a particular instant, uimw jtezuj;;cm) /q; r* q-8oits 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 Earth’s gravity on a spacecrafa4i0ytrqz 5ve0h1rj dpsr31 ma,(,dgt 12,800 km (2 Earth radii) above the Earth’s surface gh ezp,j4s0a,1 ( 1ri30q trd 5mvdrayif its mass is 1350 kg.   

  At the surface of a certain planet, the gravit7drp 5meg(e/y ational acceleration g has a magnitu/7dye pg 5erm(de of 12 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 gravity o*sm i6nzjcb)c+/ 7fvnn the Moon. The Moon's radius is 1.74nv bj fnzm*)+ /cic67s $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius (.mh)2a.ekn5o ndykd 1.5 times that of Earth, but has the same mass. What is the k5y a).d h.onmk(2d neacceleration due to gravity near its surface?   

  A hypothetical planet jh + 48kkat0syhas a mass 1.66 times that of Earth, but the same radius. What is g near its surfacets8 0yk4jk+h a?   

  Two objects attract each other gravitationally with a force l b1dce7f+tlys h8b3vdc 40r2 c(ecv+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 acceleratiz1g l2hvgzu)-6 aac- qon of gravity, at (a) 3200 m-) za zcg-lqgv62 h1ua    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point o7zfdeh2 *va7x utside the Earth where thegravitational acced7x 2vhf7 *zaeleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into e-;4kfrdcp2h ge-cf7 a sphere about 10 km in radius. Estimate the surface gravity on this mo4-;fp-ec7dce2 gkf rhnster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but aseocr-a.tb-6 yz7. t is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is thtsa7 .abc -e-ty6z ro.e surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feea,aa +ll4t)/nghl g84 0jfynr l weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms oa ay +ntg/llfh 0g8,4arl) nj4f g.   

  Four 9.5-kg spheres are located at the corners vy1b a3h(h +a3yw;p:5vgrby(/7n8 veuywqub of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exee/u ;gav81y (w:wqpy (bnub7v h ya35+r hvb3yrted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sf )(oo( ba;qkuame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets a q(bfuk)(o;ao re 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 . z8wz7pfmdd1eyc9xyh ;gq-2f +qb5 d*u ki/i the surface of Mars is 0.38 of what it is on E ekgd5mqyc1 ;*iqwbzxyzi82.d / -9u fhp7f+darth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth h+b4 t/t m 1r6aa9uhk l2jks/oand its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.hrjab+4a m t1l/kuo 29 ht6ks/]    $\times 10^{30}$

  Calculate the speed of as5w2( tq7nwj m*.haqe satellite moving in a stable circular orbit about the Earth at a height of 3600e57js2n.qtm( ha * qww km.    $\times 10^3$

  The space shuttle releases1s+gvi g77g4t kpu6l+zg3at- z k9hfa a satellite into a circular orbit 650 km above the Earth. How fagaks-7g4 97ugt1 h z+6ktv l+gaf3zipst must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylv+d8bzdxo ) +:pu/ (ig yp6gln8d.etq nv 5-clindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give yc 5:+/l(d ed+ng )t.voz-6 gnyi8v8x qubpldpour answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takesn9m kb.9b-l9aw cn t/u for 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 smal9cambubn9 k t/9. -lnwl compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satelli )k)rmz3vs: dhte have to be launched from the top of Mt. Everest to be placed in a circular orbit a:v3 )shmrzdk) round the Earth?   

  During an Apollo lunar landing mission, the command module continu p8+lo2kev7 ik- jk0.;q7b2ivbqss vfed to orbit the Moon at an altitude of about 17 es8-lvbk2iof2vvksi;. qkjq b 7p0+00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed ofxbb jpa ,,w,ed iy(10g chunks of ice that orbit the planet. The inner radiuyp gj0,bi,bw1dx,a e(s 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 diameter rotates once every 15.5 sh9 e( j-w3e rltat2qo6 (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weig ta9(rewote3-q 62hlj ht (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wh089wx0 jb 5q0oeerhieight of a 75-kg astronaut 4200 km from the center of the Earth's x9jrw oh8 qe00ibh05e Moon in a space vehicle (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 equmxlsszdri pn1;8,w ass /v y,mlu,:5b-.c+ ical mass. They are observed to be separated by 360 million km and taki,mp w, nrc58,aiux; y:szl/1ls+s sd-.bvm ce 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-k1t 3hpwjav8 9)tkmu22vt -v*oat73xw guke+ cg woman in an elevator that movesu 8w a+v)*vht-tptecwx2 gk 39uv1ok 2t 7mja3
(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 ce76mp)i c8u yukrrwq4mc02rbup yx063iling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the el q ryp 0xum)wpb r6820k76i4uuycmcr3evator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfek7;-vhi:wol ymu/) i ez*v4uace of a planet with period T , the density (mass/volume) of7-/zu i :* yevoh;lmvu4iwk e) 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 thu*9 4jcfn5j (pydg sf;f,p+b deu:s 0jm/tic:e period of the Moon (27.4 d) to determine the period of an artificial satellite orbitingtfj b:9u mc45/sjjpgp (cy0f fesu:n, ; +id*d very near the Earth’s surface.    s

  The asteroid Icarus, though only -k ;srji obw8h4p+ xb33b-q doa few hundred meters across, orbits the Sun like the planets. Its period is 410 d. Wb3r wd43kxbo- -piqh ;s 8obj+hat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag.v20fj+ c rs /qsyqy5se distance 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 vu+ cbr1(p)i0vkqysrr-11 w5rr fyow7 ery 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 orbi ks+c frr 01p riy5v-(1ww 1ubr7)oyqrt is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ; je 2yrm /e)e sm),duxz*m2)bf*yfqicenter 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, pepwiqv)(y1/2a;rrj jeh vb3 . rriod, and mean distance for the four largest moons of Jupirjw;)e23/r jqvp(byir.ha1 vter (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 tgzp/v/j n 17nhz6iw7qhe Earth from the known period and distance of the Moon. z6qz7//g7 v phjwinn1   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kep 6 tip,b 2mfl dja;2jot*a+tv0ler’s third law. Use the distance of Io and tftptva jdat b j6,; 2i*0+m2olhe 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 cons e/t aua:r4e6jists of many fragments (which some space scientiaa rje4 /ue:t6sts 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".e-: r2 )g ely+i+ovmppxa(y o9(gbh q in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as oxo qv-b +ipr(:yglp+o ) 2egaye9.h(mn Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a go5e.uh hhir8 *qog j.hxiz +4.prge 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 tole4ih8u+jp.rgo ih.ze*hx h.5 q rate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Eara0 vhg+j q3: lbf-rfh5th’s surface will the acceleration of gravity be half what it i0 3f-:rfhl5 ag+bjqvhs on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands azh- h 9xhaw1xpqc(8 dx2yu,k:nd 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, how hard are they yx h9xkhx(:h 1cp,qwua82 zd- pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent alr2m(38 dp;t. ghf(y d2og pkacceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this e yd(.t;8d(fggl 22pok3m hrpaffect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from thiaub ew6 x7y*9e Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite ayubi* 6ewx79forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scr)h:cmr 4g0 mfn2*fgcale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whr cf m4 f:ghng0rc*m)2ich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate nxn7.tjh7vux.y+ m8c about its center (like a tubular bicycle tire) (Fig. 5–42). The circlejv7m8yn+t.chx 7x.u n formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43)b v /0fgb-(j+8 dvsh ihjmq/,j.
(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 o8 ab 79uj 86mh2csy.6 ncaenhaf its radius r, the acceleration due to gravity at its surface and the gravitational cons.se28c7 h8nju6yb h6cm 9naaatant G.

A plumb bob (a mass m hanging on a string) is deflected qwmqgo6e3mtep;em :u6pll0yz48 / k7 from the vertical by an aweoz/6mlmp teukm6qp:;ge yq730 8l4 ngle $\theta$ 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 y)t0j e:(drwlhoh ,8g*lna aoey g215 speed of If the coefficient of static friction is 0.30 (wet pavement), at what range o0t*y5l 1a)y dhgao hgoe,w8 n 2el:jr(f speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects ;e6q wdl1de0e at the equator were a0 1q; leddwe6epparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apgn :oyttl/o37l9g )lk art 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 gh u k )w7onyy6tg.v93*ljj6nsuspended from the ceilingjn vnk6g 7g9y*)htu36.jow y l 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 masxk tg;4vlv48v sive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive moret4 v;k 8vv4gxl 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 the presenclqe 7+o7 d+jjje of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas co7e+ jqldjj7+ louds 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 valle d-/jbmi9(/4ekj8 xz5 mgye h cp9sl/hy shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on t85h (l dm-y pek9 /i4exc/gzbsjh/9jmhe car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utm 6ndsy5lqf:a p/r/7 -4jdnrpilizes 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 w 5/r7syn:dpjdla fqrm6-/n p4ithin 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. *uk 2exk p.s8xuu/ vp/oh6noj0(0aec1 billion km, is meant to orbit the asteroid Eros at a o cpuv j0(*xhanu.kosx0p2eku 6e/ 8/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 space shuttle pursuing a satellite in need o,w sec i;)f+ +t ljfp2/ngqa+ d*cht; vap1bo8f repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25+ h+t 2;8)p dil ap,a/cotwbnvj fe;qc g1*sf+ 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 hs2gx );ib3;yw fm6onuv1+m / m63+glt qaavl kas a period of 3000 years. (a) What is its mean distance frwt+s vl iu2m y;q6336 +lmnkogma/;f 1)agbvx om the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could k yv*ullatu m61 f-**6rk 3m 92ejvdtiactually "feel" yourself gravitationally attracted to someone ne aut3j*lk1imv6 r u 9el6fty-* v*kd2mar 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. 5-46) at ad4f4 xo-* gzfu co,/fh distance of about 30,000 light-years from the uofof4h, g/cf-z*x d 4center $ \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 asvse( :sv7z/p t the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force o/vz(v 7sse:s pn 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 5p9(jz7h sfm vdnt7pqb 4c;+m7500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm(rl zn79hl0 rz5fmc o-ncjz5v31sg k:-long sweep second hand on your wr:-( z3zcj1lcsnrlkgn7 z5mrfo 95v 0 hist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkenc pguh:jl 7 3 ;2: kyag82,jlzzfbo5dr weight around in a circle below you on a 0.25-m piece o :o7g2c2ajz g8pu;, n3jdzh:5k llb yff fishing 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:qm.k(j 4was+cnm d5 k highway is designed so that a car traveling am(cm+n dq s 4wk:ajk5.t 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, utis j*ocp(s2jz.lg 9i2 vlizes 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 Ace9lsp*(i zj 2 cg.osj2vla 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.$\approx$    $\times 10^2$