Sometimes people say that water is removed from clothes in a spin dryer by cent*pjsk e i37qi)yo4g*-vfby2bripbkj) q* yigi23fy7b-s*v4eo fugal force throwing the water outward. What is wrong with this statement?

Will the acceleration c0xt5xhme-y)fku3v zo/, u 5j 1zuh;h77aths of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Ex uv1-hy)x s7oct/m5,he 35;hk auxzt fujzh07plain.

Suppose a car moves at constant speed along a hm8ky*a54isiw2i1f b k:n kt.silly 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 two hills, (c) on ik4n:ti*amwik k 2s518s.byf a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hor d-4wxw* ; *ewjl t b/ndmp(/1hrua8xbse on a merry-go-round. Which of these forces provides the b*x8nl/x h e(*ddp 1;-twm /b 4wajuwrcentripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the8 dpw-ab,bq;0jx ds/mgs 9t (i water spilling out, even at the top of the circpj tq/9s-isd dbw; a,0 xbm(g8le when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three co xs)8s s3ot+rfntrols intos3+fx ssr 8) the car which 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 crest of a small hill, az7+/8uucv:* g)uvr hkyno nl*s 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 ther gluk7* hn:+/o*uy8vunczv ) hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high wqkg8,yt* mj 7 8icxcir,x.qyst025mspeed?

Why do airplanes bank when they turn? How would you compute the bankik u mn.(+ fgwwnxa vou1bo,q :8cye040dluj4 0ng angle given its speed and radius of the t+un.g0bvl n c 1ok8o(jq x e:uywdwu440f0m,aurn?

A girl is whirling a ball on nr)h .)z,zaczud4z itiy1 l02a 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 0d,z1i tyau4zh.cn2zr) li)z side of the yard. When should she let go of the string?

Does an apple exert b i)d c mzct9*l+w0elwg:w u1+a gravitational force on the Earth? If so, how large a force? Consieiw l1w0t*)mgzb w+ul +9cc:dder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublf/6pap :ig 4j+vb;fdyd*h 43el4ivdk e what it is, in what ways would the Moon’s orbit be differe4:g;fp e /4*lhdfvd jka+dpyb4 i63ivnt?

Which pulls harder gravitationally, the Earth on the Moon, or v6uup/gmtp)8 u 5a+lathe Moon on the Earthpav6uu8p/mgl5a) t +u ? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tiiznt 0o2) i/v27r dodhe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference i0z 7i2odivort/i) d2nn gravitational pull from one side of the Earth to the other.]

Will an object weigh more atr c72kuowcx7.+e7s1 f pbtf3r the equator or at the poles? What two effects are at work? Do they oppose eab+coxw17u c. f7te72rp s r3kfch other?

The gravitational force on the Moon due to t-9qib (tigm;b he Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pug9ib (m ibqt;-lled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger orkzb7uusqs8u . 88 rga*u z(*sf smalfu8s7 r *ub*a. (zzsq8ukusg8ler than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eas4mit+m ;r;d7lvb0fm dt or (b) toward the west? Co7dml;d vmf 40ritmb+ ;nsider the Earth’s rotation direction.

When will your apparent weight be the gre/r /so9nnu 5jj iumv0h.b4c6qatest, as measured 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 hr4s 6q 5j9mni.v nj// ucuob0case 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 couls xeac) (uq7o*d be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the asto (xc7eu*s)aqronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appn)jim20wh1dizz y /c)arent weightlessness” betwee1ch/)i 2jw0diyz)zn mn steps.

The Earth moves faster in its orbit around thegh(x2ux2, suw rstc9ed: 2w)i Sun in January than in July. Is the Earth closer to the Sun in January, o(w )x2 s:c g,s2 tuid2rhwu9exr in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known r *z3, ; /zb gv9rvfty;whc3we9 at)ewuntil it was discovered to have a moon. Explain hogtwva3; /wht9* 3z9c z;eybr)wvr f ,ew this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth i g3q4 w.(bur )cwreg1xs much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hinbw (.wcu3egx4r) qgr 1t: 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 1980 gmeb ; u6j5vf*$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accel;6-pckt ) qjsyeration of the Earth in its orbit around the Sun, and the net force exerted on the -qkpj)6t ;c syEarth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus ah/ rbp 3uaqk;i1a1- 5msw rh4fs it rotates uniformly in a horizontal circle (at arm’/4qku-;sipa hrhfr 3mb51 1was length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbitknnq)otc1k9*f6m3d , i u038nos s ncn 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the f6n9tnu m3on8*1k3, ic0ssq nnkocd) centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spwonggvjky0, ( k2jy,9 e+gr;i i45h eieck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diame+n,e0 vg4 gjkr yjy,ki29h o(i i;g5weter is 32 cm?   

  A ball on the end of a string isl397h0scwh c96nqe qm revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in F hc0 96weh7sc 3qm9nqlig. 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 oslzv)iwjj94zf. p /9:eo8recar can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is lo/ri):9489eo.jz z ves pjfw0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between thero 2eh:q8 +pp2 vs;imp tires and the road if a car is to round a level curv8+pp:ei ropms2 h2v ;qe of radius 85 m at a speed of 95km/h ?   

  A device for training astrona+h prq2f7n d dmrtk*d,6z.ud9 uts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her ownd d z,*2dfmd+7 69tuhpk .qrnr 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 axib f.9nq:vnu .is of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpq .9n b.vuf:inm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coas+9snt+(mof dt .d q3cnter be traveling when upside down at the top of a circle nd sq(+ m .t+3tfdon9c
(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 rounded top g, k w3m y3pv:(ioax9wof a hill (r,wyvp33w9(xa kg iom :adius =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 Ferr af2 vu3,6wqa8)nmv omis wheel need to make for the passengers t,ua6vm8v)wna 2qm3fo o feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 n+g/uq5d *iw 8uup,l (udacv*kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the ropedu8vuc(*a w* idqnu/ ,p5l+ug 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 r-tugn2mtgk).dj8 e jq9m1 iz2otate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 11-jmt m t 28djqgze 19.)igunk25,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplfr v x2wxhfm* 7lxp(2;e are rotated in a cylindrically walled "room." (See Fig. 5f*2rx;hm l7(pv2xfx w -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 frictionless air-hockey tab :u9crs kuo9znb4m( :oletop, and is held in this orbit by a light cord connected to a dangling block (mas::u(r9c4bo 9su n zmoks 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 timeb j;117nl gkzj/ ljfj+, by not ignoring the weight of the ball z l/;gj jj j17+bkf1lnwhich revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travhoqa5;/xq2c4lgy1p z l9cr7me j(t :jeling 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 bkm0 khbz5rc s. 7h*-d$ 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 ee lill v9pkmg yr*7j18.iyc/*vasive maneuver 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 components o -m o;orwcmmb 7hclk)n5-)ck 9f the net force exerted on the car (by the ground) in Example 5-8 wc--o5kkbl;n wm c9 ))homcr7 mhen 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 from the piwew) pmwa-vmvesw.( de+x 21)t 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 flw1.e-2m ew)xswd aem)vp(v+ wat, 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 part3 98fpbfss)* kmnnpq, 7uyz-uicular instant, its acceleration is )fn7uu8p*s fnk9zm,p3sy q b-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 Eartt6m1y )zo hzen86ejl: h’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 k: l)mt6 8ze6nyjeh1zog.   

  At the surface of a certain planet, the gravitational acceleration g hastgu / 9, yol-::ywbvqx a magnitudb:l,x/ytu wyq9-go : ve 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 on the Moon. The Moon's radiu4 g/*hweshje - 8uui6ts is 1.74 jeuh* 8h6/usi4g -wet$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet harbtf24 of-a(rs a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to grav 2 (ftbrafr4-oity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bup.hy9jxxzn ubmo-d n.rze;wp 74i. /9t the same radius. What is g nea dxx. jppnbumo;w ierz9 yn4-zh./79 .r its surface?   

  Two objects attract each other gravitationvnb l0j7 dg::/ vkm-yjally 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 gravity, at (a) 320 g 1vrko 6uxc9d+g/wg40 m wcg+4dg9 /rkox v 16ug   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centee:+tq.i 2koe7 sa2cmgr to a point outside the Earth where thegravitational acceleration d7ske:tm+ieqag2 2o.c ue 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 a sphzuntp*iyzy ,t48s 9-b ere about 10 km in radius. Estimate the sur4 i,n u-ptt9 ybs*y8zzface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but iih c1xh/ m *t2gam 2e:.bdt*avs now in the last stage of its evv*b a1h2ctgmm .dxh iae*/: 2tolution, 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 astronau-cx v4i6ci5 g:ww/9 yyg *t 7z6evadnbts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravityid66 xtcv74agv-ebi5 /gw :z9y nyc*w 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60/dhfdq,.4ind *bg5y jji.c 4 w m. Calculate the magnitude and direction of the total gravitational force exert,n5i4 b.jdj*4gdh i ./dycqfwed on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thez v u8sw 3rkwm5bm 3hpef(c3*(ki9a8j planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The massesb ha3 (53urme8mkik*z8j3vsw c(9pwf 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 surfacx/h-ujxo 3 .sie of Mars is 0.38 of what it is on Ea.xio/x-s uj 3hrth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the u:/ kxt+jhmn0ag6 u-lknown value for the period of the Earth and its :+uk6a gj hu-xml0/tn distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a:mj /pwb (,lg2nv9a0u- dh iyc satellite moving in a stable circular orbit about the Earth at a height ofpav/d2g hic:j blum0-9,n y(w 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbi r w.:vdqx6kr8i.x.q)vmx nw 2m y0h)tt 650 km above the Earth. How fast must the shuttle be moving (r2dxmrrt .)6wwk.. hvxmyvx :niq)8q0elative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cyline k0(6ikm5qod+t0dz ndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your ansizn6ok05(0mkd t+q dewer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes f8 ;ah pna 44j:;ua-2ue * jkxgiitm;ckor a satellite to orbit the Earth in a circular “near-Earim*j-: p 8a;tcixak k44ugj e2nh;a;u th” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite r 1z c(jj;56zlv zmt 4u0ymfx:k1sc :mhave to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? 1jsc y41r6 z 5m0jktzx;:vz(clumfm:  

  During an Apollo lunar landing mission, the command mz lp +jw72.rzpodule continued to orbit the Moon at an altitude of about 100 km. How long l +zw72jpp zr.did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit tj:b0b:j0hvvmd m-zp0ie .v )vhe planet. The inn.m bjpvhdv:z )00bei:0m-j vv er 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 diameter rotates once evev8 x biup*g gel0hrhgb/g6h06885 nsfry 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, and8bg6/85gf6bgxn ihhp0sr 08eluv* g h (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fr +q +b kn68c66gb(v l:fxtld f*vti3inom the center of the Earth's Moon in a space vehicle (a) moving at conkgni:6cbd8 bi+6l xt*f+l(t n63fqv vstant 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 consist x53em .vezne.s of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 me5.vn e. xze3Earth 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 s:zq4b.g)k:/ bvai*yf 2hsr/ l ips+fthe weight of a 55-kg woman in an elevator that moves q/ hz s*24f)v +s:gk:yi alfibsp b/.r
(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 su ds49xg6csi (, vp85 xbkpqb9pn*fyi -spended from the ceiling of an elevator. The cord can withstand a4 x- (ygc ipv fb9kp8p9*xnq5,6bsdsi tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a plan faqd13za: 3njet with period T , the density (mass/volume) ofd :jaz3a 3qnf1 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 ofwf1kth4 goy ag5 ) jm2lm:a5rph3i .b0 the Moon (27.4 d) to determine the period of ag1)tp.jg40 fmbkwm: ya r3l25hhoi5 an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though on+imv,ty vj.gf -qe j)eic;q67ly a few hundred meters across, orbits the Sun like the planets. Its perio-7efg)+6vy.mev;j qctj, iiqd is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis2a/i /uu5) b8rwteuae tance 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 year,yf1zw+lsd5t qr / liil 7 op*rhe97h0s. It 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 stil+*rilldw roiqf zhpt 91yh,/s757l0 el “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center ofzzk 9 lnm jv)7t4(qc.o 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 mass8-; xz0li nqei:7)nw fyeog v;0du 3zf, period, and mean distance for the four largest moons of Jupiter (those discovered by Galli8)-gq3n: yv x dofi7zfn;; euwe00zileo 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 pe 6hc(nrk*t zb/1o+yw2:*pv hcme lil )riod and distance of the Moon. hoebhtm1lz) ( *2v pcwr:i/nlc+y * 6k   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kej6v,tadfagy h:gwmn i o).gq9i- - q 93.rx*sqpler’s third law. Use the distance of Io and the periods- ws).xr69n mdii.ta3- y:gqj gqq*ha,ovf9g 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 fragments (:gd 3u*zxiwc) which some space scientists:w dzgic3u )*x 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 augh4f ihyx7 e l2/ge6/d )5rwgn artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the ihe25 y4w6liux 7dgerf/)/h gg nside 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. rcov+:+mhf p5m: 3ams/y/ vobx .cjc4 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 lowep5ja xy+v4:b.3+mm /hcc: / rsfvcmoo st 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 of gravity be half dbhu5s8m 8v3w,n 3gaxwhat it is on 8w8mx3ahu sb5vn ,3gdthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands ay0to06 g lxp: /f-pndmnd spin in a mutual circle once every 2.ly/x: p6 o -nt0p0mgfd5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the aph2yi /gtrfr y6 n15q-qparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitth/nygqy fr-56qr1 2 iude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from thi6 6boyj-8isze Earth will a spacecraft traveling directly from the Earth to the Moon expeb6-y s68 zjiiorience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass isgeno7/zd5 sb - 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleratin7 zgdboe s-/5on of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will b 95g* pyyxe7kl7 f0vsrotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube h y77vk by9sxeg p0*f5las 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 aiwa39q gllldh t1( 3/ylrcraft 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 wzr s5cir9b; nd /*4ka cd 6ivnm,:y)aplanet in terms of its radius r, the acceleration due to gravity at its surface and m6diwrncyi b;vr* 5ncs/ad kz9a)4,: the gravitational constant G.

A plumb bob (a mass m cin,x2(/wp ;jov.v .lvwsx8,x 9se yihanging on a string) is deflected from the vertical by an ,wvspso.xxyvi, 2 i;nwx9ljv/ c(8e .angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of s6erp8 oqhp+h ;tatic friction is 0.30 (wet pavement), at what range of speeds can a car safely ha+p 6h8h rpoq;endle the curve?

  How long would a day jf*:g3nbygu8be if the Earth were rotating so fast that objects at the equator were afggub: y8 *nj3pparently weightless?    $\times 10^3$s

  Two equal-mass stars .qri2,m ,jfu xmaintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a const;wzk.5ttabo8n sw2 n )ant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle w tw. oatknnz8s2;b)5of 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 claime;e r *oaii.;fq +dd2esd that a person would be crushed by the force of gravity on a planet the size of Jup+2;qd fre*oea ;idi s.iter 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 ded)t(6x nk ;8z9 dx biz9vx ew2sks1jq0gn7db)g uced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from;(209xw bnveks tg6z xqgkn8z1bx 9 dds7ij) ) 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 4z e,51)puvgmz3yoog,mpj)h speed 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? Lightest? Explain. (c) How fast can the car go,p1u mo)g3ghjz 4zv,pm o5e y) without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites ory/aj)-9q t(uz8 gi bmybiting 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 continu) a-ibyq9z/ ygtjm( u8ous 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 Re1k oz +8vane:l+pxbi :wr+i -wndezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 4++pa +b: o-:evrizwk8lni1 xw0 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 -z pm2b1h1frp 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 ber pf12z1mh-p bhind 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 isxl+rz ( t,rvu3 its mean distance from the t zlxu v+r,(r3Sun?   
(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 actuallon,/l1 vlz b0ky "feel" yourself gravo lkz1,vb l0/nitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy zfm8;dn,u(7cj cgcg01iooj6(Fig. 5-46) at a distandoc,o i7 mn81cj(gj f6guc;0zce of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.ikj/ v5 7-*(p o::ni+nmwf9 1epvq b a5dmozhs50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sibm5wk7(5eh9/qvp:1o ip nif- sadjo:*n z+mvde of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits tny,.3mcbg-3 8nlgi964avc j dl+mal mhe Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep sec. l8g(sfdszg4ond hazl gs d8g(sf4.nd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in axs1+ts. lfacg+ mhnek7py0in 8m:z 6 / circle below you on a 0.25-m pim0i6 zx cf/ 1n+ k+p:ygel8ts.shm a7nece of 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 radi3 :z,cosb y5wc*zx1s sus R in a new highway is designed so that a car travelsoxc3sb zy *,:wc 5sz1ing at 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, utiliz- w66: +, edillzbxtboes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius wel,: 6tol-i6xbz+ b dof 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.$\approx$    $\times 10^2$