Sometimes people say that 6fsdqk 8-nf89 c2efcq water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrongc 82qc6fes-n9k f8f qd with this statement?

Will the acceleration of a car be the sam)cuzj0v7g trsb 5x j2i) ++xkxe when the car travels around a sharp curve at sb)ijz x +c+kgtx)5r0xu27 vja constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at comvy4t;bju,cny5iy i 4u v-n4 3nstant speed along a hilly road. Where does the car exert the,-yc4i yb;vvuytu jn 543min4 greatest and least 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 on a child riding a horse on a merry-go-rouip v );vml6tv1nd. Which of these forces provides vl ;16)vmivpt the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spihz hbi)dy+ :4p;+ubgklling ;pih+ g b+d4)hky:bzu out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three c2j *h6abxj0n ovqza.,ontrols in t2xjb6aa n0hj*z,vq o .he 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 q1z0rs 9beh (foh6kyad, yu 9)flying over the 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 sl,syhhd(ya 9ukq6zb r1oe)90fed decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cv w13q 2kf xf1,rrc7blurve at high speed?

Why do airplanes bank when they turn? How would you compute the banking an/05/ ayg a0 vpxkgehh6 pbx-3ngle given its speed and xgb0/ yhk g/npx6ph5a0 e-a3vradius of the turn?

A girl is whirling a ball on a string around her head in a horizo1w z*g7 fayol h.82 ;yunojn7zntal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the strywy z 8jfao1. l7n2;uzh*g7on ing?

Does an apple exert a gravitational force9t q(xs +lj/sd on the Earth? If so, how large a force? Coj9+ls(tq d/s xnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit 5xi; ctmf5uqu le( s79eh)4)j/mrqcp be disqicfu5/(m )p)xej met7hc u9 ;rql54fferent?

Which pulls harder gravitat0e1+dlve.jw6l+m el g ionally, the Earth on the Moon, or the Moon on the Earthl61 0lj d.lee ++mwevg? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet t97fxcob du(: rko3kjekl4u4ev 1b,9b he Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of thebc1kokud9 b(v9lo:37,x rb4 ukj 4fee Earth to the other.]

Will an object weigh more at the equator or at thic rirp7kx+/1 bl5 yge:*ntm 0e poles? What two effects are at work? Do ib :xr0+1ltcyeimrp 5 /7n kg*they oppose each other?

The gravitational force on the Moon due to the E3 j lboiz4ujz : 86leoqp52:nrarth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth2j5zli6urz:: npq 8o34j l obe?

Is the centripetal acceleration of Mars in f4:7x-iyr i soits orbit around the Sun larger or smaller than the centripetal afisiy4o:rx - 7cceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bj cgw()t(jw.u xa ()aj) toward the west? Consider the E)tj ).a(ja wjxc(u g(warth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scalkptg69a1p3b t e 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 thg3 b6pk 9ptat1e 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 :k mhm (htar44k x7n-d 98cxk5w0uvtscould be adversely 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 ohvk04 x(d 5x7tmk ak-:n4uh 8r cw9mstn our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “avdke:m0wr-ol ;va 20(0onwcl7l 8pzf pparent weightlessness” between steps8l ; k pwdvcolnm0 lzv:2-w(o ef700ar.

The Earth moves faster in its orbit around the Sun in January than in July. Is tu()axp qybmqr9o:j ejt7w31 o.vgc5;he 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 thacy x9uoj5;b m7w1.pqrj(eq:t3 )vo g e tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expl1z pkz4cn,ur5 ain how thi n4c,1 u5krzpzs discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on t,+ h:xmu5aalche Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A ch lam+ 5c,aux:hild 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 js, 4-mfkochy:vhnm a3j g9u(+ol0- l 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 accn .k grysc,hoc8zv/6+p(og, aeleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force6ypcngg8 a,ohc+ /.s( koz,rv 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 exertedors+ i l7u th:yyppa2uwm5(61 on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speewy m2yuauipro1 p +5t(s7:6lh d of the discus.   

  Suppose the space shu)t0y,znrsm e,y4ey 6 dttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minun y6yrs4)y0dzete, ,mtes. Find the 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 q-: jmut s mil-f7az.2pd y/:tspeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s did famq2lpmuj:-t-7 st i/:y.z ameter is 32 cm?   

  A ball on the end of a string is rev3uens5 r s/ndqabk38 .olved at a uniform rate in a vertical circle of radius 72e358q/3rn s k.nbauds.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 round a +ukdmty.ded8iojb xb9*l 4x. 1eib )8turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the 1t.okb8+) m x9ydixul8jd eb ed*i. 4bmass of the car?   

  How large must the coefficient of static friction be between 2f5eat+ 1 i)vl.a l1fu2agnykthe tires and the road if a car is to round a level cka2 1 f y+inf)va. l21gl5taeuurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighterjh gv30ho.pr2 pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the fo03.hjvo2g pr hrce felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from thj 6 ,sojt+bzvk5tln,5 e axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a5 tbts 6z,5 j,l+vokjn rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down y/p2xlwja 8m0at the top of a cyl2a/ x8wp0jm ircle
(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 (includingv c yhvt- pgk c7o(noh.c5/2h nw)-js, the driver) crosses the rounded top of a hill (radius =95o7c/vc-5 kot2vg h n(c, )hyh- pwjs.n$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to mae dj tpdx0+u 5me+5q7bd;o 11 hbxh-xrke for the passenbdudmbjh h50rt1xe- px 51 d++x;o7eq gers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is.h4.2 v qrw5unrkrv m, whirled in a vertical circle of radius 1.10 m. At the lowest point of its mo v2h4r ..5v,umnkr wqrtion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a zft4:dk cn8)vl fxz:0-iq3 m rparticle 9.00 cm from the axis of rotation is to experience an acceledzk8ln:c fr4tq3-: )m ixfvz0ration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a c ,:-mic ggt8f+of*qfun) j1dsarnival, people are rotated in a cylindrically walled "room." (See Fig. 5- f-),jcqt u mng:*fd+o18fgis35.)
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 tav)q6 qe06 gey-ac(ebyo8ci 2m bletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hol 2q6e6m( -aq8vbce gy)0yieoc e 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, fte 7kdu13qm, by not ignoring the weight of the ball which revolves on a string7 tmefu1 kq,3d 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 ban9dr ogas-7w;6t/bmauked 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 massesjch9 n*9zz/ik. pnzmkbdp l5a7. c86 c $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertic+; btos q-,rbpally 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 ne ja i+.+q*rxoqt force exerted on the ca*qaj x+ +irqo.r (by the ground) in Example 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 accele2y5d 7 i7:xmgxdmrdh+6hr6g krates 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 acceleratiod:my7xr 7ir+5d62gh mhkgdx6 n of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rd l3 go0kwm1 xo3xvo4.adius 2.90 m . At a particular instang3 m.wol x43vxoodk10 t, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth l :5 8 g92emneljcsi-uradii) above the Earth’s surface if its masc8l u-n2eeis9mj5lg:s is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a a7ef.by ba s.t:t5k +:algab1magnitude of 12 +saf k .tblg:.e t7aba:a1y5bm/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 q6bmxl/m9g (5 -33ctwy rril j2hej(rdue to gravity on the Moon. The Moon's radius is 1.749j623( xhtl/ij (cgm l- bwqre3rmry5 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radig) ;zly:k:xxmu3qi0 yus 1.5 times that of Earth, but has the same mass. What is kuyyzxi mx:g3 0lq;):the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that offdc+b )ny-zgf- *n yx7 Earth, but the same radius. What is g) -- 7 *zy+ycfxnfgbdn near its surface?   

  Two objects attract eam:x bq2 t4p)qjch other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valx7 gwz *pny*euw/3k t*ue of g , the acceleration of gravity, at (a) 3200 m *3ny7xz wt*w up*/ ekg   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center te 8 4jd7c*m6:c(x nr5iki+x uyldibr(o a point outside the Earth where thegravitatiikx e lxb ndc(di5+:74* 6 (jrruymc8ional acceleration 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 6 czl:-+ocwz32g/mhb 5fogv lmass of our Sun packed into a sphere about 10 km in radius. Estimate the surfl f l:25c c+zmohggv oz/-b6w3ace gravity on this monster.    $\times10^12$

  A typical white-dwarf stajuh5m73*d*q6uj fevr r, which once was an average star like our Sun but is now in the last stage of its evolution, is tu7 6vhfm*3 jr*5ju deqhe 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 astron o1/r hzb5kob3auts 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 isnb/5okr h 1boz3’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 mwp0lnqd t:o:6d0 dvl9. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thre:v0ldd0 ql p9onw 6dt:e.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yebit*9 +lhut d5ars most of the planets line up on the same side of the Sun. Calculate the total force on the E lbtd i*ht+59uarth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of iasjx03 le*f( Mars is 0.38 of what it i0l*aje3x( sifs on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass ogd t+b6xu*3ju f the Sun using the known value for the period of the Earth and its dist tugx63db*+j uance 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 satellite moving in a / n4,*knw03 lehdlw 8otf f3hl7drv:mvt:nd9 stable circular orbit about the Earth at a height el0t:/ nn9:towwm8vhln, d3l7 v*h4ffd 3dkrof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the aujqvkg 1xubh k,9/7k+ 9l e;kEarth. How fast must thebk/9u j + 9;kagkexku1v7hql, shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants a)suq3x d07+hefujw:-n bibnae* (8n l re to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your ans+f- uq d3hu0nans8:nixl(e * )e 7jbwbwer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the E1umx3a-yv)t . gceq/yarth 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 the sateua v g./xyt3) -1cyqmellite?    s ~    min

  At what horizontal velocity would )s 6)mz*:wlg0bo ol n/m,xj1fasfb*o a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit afb)jf:oow 0/lob sz)m * l6m*,asxg1n round the Earth?   

  During an Apollo lunar landing mission, the command modu 27wy04:d 34 0kg 6tixelzep +:yi m8movqoputle continued to orbit the Moon at an altitude oqttz4o0peupgy:m+043mk2 6yvlei d x 7w8 :oif 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 thj; aehv tl 32:7;ac v/j0quxxme planet. The inner radius of t;at 0m37xjlqj2ux e/h ;a:v cvhe 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 s ij0 * sir0kmp+w yl10c(see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) rkwipmji 0lcy00* s+1 at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronoesz 4x0n s1cb gwe3b2 rd,/z2aut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velo/w ges2rnxbbe4,21 zc3dsz0ocity,     ----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 /1)i d q1i*lh (hfvgfdof two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth if *1 hv1 (dqd/hf)ilgyears to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale ream2a2r e7 h*s x.mu6nadd for the weight of a 55-kg woman in an elevator that moverdm7x6e*m a2na2 h .uss
(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 fromdcb p3da8trnt86ong 88aw 5 v0 a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (mt odb0pa5w3r g8 n8nv8t8a6dcagnitude and direction)? a =   

Show that if a satellite orbits very near the surfazxmrkor2 vo,joo8 4cy5v.2.q3lh v+kce of a planet with period T , the density (mass/volume) of the planet m5rykv.o24vh cqor8 .kol3zvx 2j ,o+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 ofj ahl,pc6a0wp91-sf u the Moon (27.4 d) to determine the period of an artificiap-6aw,19 lc0fs ajuphl satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hu5mbvcd*xespf)9 eg1 g 0o8ip p zx131sndred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance )xppfed 90gg8mi zpvo xe1 31 c1sbs*5from the Sun?    $\times 10^{11}$

  Neptune is an average d6pokbs0re dc6-b0 tf 1istance 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 dg4lrb:r5m,try nx.y, 0ips;roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest d,5rb. rsn,txpg y ;r04diy: lmistance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of vnb7je1w)hy 0 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, period, and mean distance for the four largestu dbwbca9h 4jkk 2q343 moons of Jupiter (those discovered by Gad 3au4b9q kkj2ch34wb lileo 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 ofluy-ha-6ky z1 the Earth from the known period and distance of the Moon. k1zhyya-u6- l    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitec*mol8 y0 /l oxt in9m61wo1vvr’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Com 1im1v6/ wm8oonlc0*x to yvl9pare 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 frags+a, h; ae0dzp1z f f6t0/a zzg.k0cszments (which some space scientists think came from a planet that once orbited the Sun but was dest; zfcat+d ,g1 a06h fz0z.kz/pzs0easroyed).
(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 oxtxe/.ew a3o1 f a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that3oe e./t x1wax 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 inl, ilzk xg4.x azl877e an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? Hik g 8zl lx.4xz,e77ails mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelera(cv.y26zf4jx9 ju hlktion of gravity be half what it is on vj( xhlfjc ku4 9z62.ythe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mastcqdrkb 87)p:rg 5b7v s grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard arbr7 r8t:g)vcpbkqd75 e they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelroluw5: ,ly1wos/n6 k eration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the mak6w n:/o yr,lu5wso l1gnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will akejwn/6 n/r sbolh.c5fr:6 j6 spacecraft traveling directly from the Earth to the Moon experience zec5/njk:s 6e6wl. ornrh 6fb /jro net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a ban3pw v985m rsothroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of nrms 9w58o pv3the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a-jfhbce l l3.6 circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What muslf.3 j ec6lhb-t 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 uy bovn ,c/0k+aircraft 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 b1;iw* kltr4zia0 . ztits radius r, the acceleration due towz1lak .04zitirb;* t gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectf8 bvn8.j l,31 cnrep0o;toie x,ta+led from the vertical by an angle 8llo1tnn0a pe3j.8o;f iv,rte,x b+c$\theta$ 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 tb2 r (p)qao;oche coefficient of static friction is 0.30 (wet pavement), at what range o2b); oc(qra pof speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objeco ;rhkj99tjl5iko ns) 1, z7fxts at the e k7ir51l,n9 ;osfxz t)kojj9 hquator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars mainr jo1+ailf,-a ux* b0 5im.nogtain 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 constaw c6 0,thq w*0 yh7mrvaut8hp)nt speed rounds a curve of radius 235 m. A lamp suspended from the cei0htpm*y8 wcth6q7,a h0vwu r)ling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eaqe, by9)eh -(ybbv8rqrth. 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 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(qr9yv qy8eb-b )e,hb $\times 10^{27} \mathrm{~kg}$ , 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 presencent)i et.+fb(32la m7hz7 q-n w5ri siq of an extremel)ashfwt.73+ riq lmt n27iinz5 (-qbey 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 clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley qj-tx1kos0 . s q4:r+dux8nbg 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? (Whj-sdu:sg kx1xrot+0q b 8.qn4ich 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 Syst l+suo/c/ llkd/ v5ii4em (GPS) utilizes 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 a45/ ko /i ivlcsu/+dllpproximately 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 Aster:df a)ot6a7zooid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroidadf:t ) a6z7oo 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 spacr0-vn5 sj x6i*o sp2uwe shuttle pursuing a satellite in need of repair. You are in a i j-v* o6uns5s2r0 xwpcircular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What-s:c-l f)dkp w,7 k1utxok8 gb is its mean distance fr:u -78f k 1p,bdo)kcw-tskglxom 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 actually "feel" yod np7(-c(i8v q k3gywxurself gravitationally attracted to someone near you. Make reasonable a3kix-(qg 78(dpc vwny ssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the c3 p pmnpf24v2 jl cic0u,v3*jcenter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lig c0iv j 43vc3mf cp2,jln*upp2ht-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 0.50 m on each h*c*1 u ofl9ps )x5n. uzifjcw* +co(lside. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at thecn j9s)f *l fzx.(u *olho*5iwc1+ upc midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg or73zr(r xmpc)xrc;nji y9d; lurj)-t7bits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long cb9,9h0 p seca w.w.aisweep second hand on your w,ac0wwh9. .sa ce9pb irist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swgp d5m x(ls/;ling a sinker weight around in a circlmgl5 x/;(pld se below you on a 0.25-m piece 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 radiu78xsg bj.h n.ik1qb2h s R in a new highway is designed so that a car traveling at.bjb q17s 8xhh gin2k. 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, utili7mfh tvf+i;oini) .b- zes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is b)t-ifn i.7vh;f+oi mnot 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.$\approx$    $\times 10^2$