Sometimes people say that water is removed from clothes in a spin drye1v ebf :ssel*2r by centrifugal force throwing the watelbe:s ve2* sf1r outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels w9xf(pl hu*gyv8+v 7haround a sharp curve at a constant 60 km/h as when it travels around a gentle cu(8vh 9hpfx v7lywg*+urve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does thllz1(rikgmp; +f,: ar e car exert the greatest and least forces on the road: (a) at the top ofr i(1;:mll ap,rk +gzf 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 ridinmtbiy,6fs7g gwc1p6qq ()j 77djy7 fl8ey/arg a horse on a merry-go-round. Which o7w78tdrf6imje bg(y 6a j pg y)lq71,scq7y/f f these forces provides the centripetal acceleration of the child?

A bucket of water can be wh3i)wh otca9ib 27qhc9d 16zh9rd q.xzirled in a vertical circle without the water spilling out, even at the top of t3z ci9hwz.qd6hc)b1ri ad2xo 9h97t qhe circle when the bucket is upside down. Explain.

How many “accelerators” do you have in yof1ufg k u5jm/cjvt)/uq,qbt z.i((o 8ur car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleration vb /1uft/o8()(cmi5jt gq.uuj fkq, zs do they produce?

A child on a sled comes flying ow t,+stsjqs* + zovsg*i2 6te97/ uuqhver the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (sw/set7 sv6,z9*u 2s hqgi*o+ttj +uq he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a;nqmf)69dzlq21 c u3g5wmnt fb82 zhyvcm i (7 curve at high speed?

Why do airplanes bank when they d zf+6hdam6* 1,kb vsb4, lbboturn? How would you compute the banking angle given its speed an*b6m flbb,o dva+dhz4 k1, s6bd radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pxa9 3:cvn5nf s90dyd cd8ei/zlane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the 9df y 8ce0nz/:9c3 d5sdnixa vyard. When should she let go of the string?

Does an apple exert a -in vxinn19/cgravitational force on the Earth? If so, how large a force? Consider an apple n n/-vnx9iic1
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moow ;3qm kxn76gh8h6x(gwgm 8nj n’s orbit be diffe3qn67gnh gxhk86 wxjmw gm ;(8rent?

Which pulls harder gravitationally, the Earth on the Moon, or bawp *i 0t. l :0a2s we9dt;1i,/tiqshpq.gll the Moon on the Easptt2* ial/ew1whgali.,sd 9qtq0p.:0b l i;rth? Which accelerates more?

The Sun's gravitational pull on the Earth is n+mt0d5q+ v8g:) dsl:, ki*pytt j bapmuch 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.]n+d+,j dq8tv ly) pgsm*b ta:ip0k:5 t

Will an object weigh more at the equator or at the poles? ywq)f+* sdgu)y8q nk:0x y je,What two effects are at work? Do they oppos)fnegu, * ydsq8ky:xy0w qj )+e each other?

The gravitational force on the Moon due ) sc rs,fg,, ,yexxjkb/ds1iw4 +uxy3to the Earth is only about half the force on the Moon due to the Sun. Why ics3y1xe x, )xidf+r,sb,yksuwj g4,/sn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su 1)y3wskl0pzp.dl, .l zdrhl* a5 cl5ln larger or smaller than the centri. lszdk0)3a ll5r1zlc .plwl5d,* ph ypetal acceleration of the Earth?

Would it require less speed to launch a r-0yk.7fif za1 /fxdg satellite (a) toward the east or (b) toward the west? Consider the Earthk rff- 7x /g1dayzfi0.’s rotation direction.

When will your apparent weixt ci8 s+42ka*t6:pe3w kcfo ight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, ap st+ 2ec84cwi6i *3kfo :xtk(b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend e+ / qr3nchsa(long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rhn3a/eq r s+c(otates, 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 of.

Explain how a runner experiences “free faldnbva0r0gs3rzv70 n(l” or “apparent weightlessness” between steps( nr0b03a svz0rg v7nd.

The Earth moves faster in its orbit around the Sun in Janu yccw5oz, )cvdg- wqv.*e;1dr 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 producing the seasons — the ma zv og1d w5*ec,r-dcwvy). ;cqin 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 havec-o 9h um:pi1tzka0s 8 a moon. Explain how this discovery enizkct9 1ap0u8o h: ms-abled an estimate of Pluto’s mass.

  The Sun's gravitational pull on thig*t52eg wi4 a4 *lhjhe 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 child sitting 1.10 m from the center of a mer2*i ij4l h5t4 weghag*ry-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 6un t+pu8jtc* tifl* *-fa0 tk$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Eartq8 .4awyl x o1ds6g(nrh in its orbit around the Sun, and the net force exerted on the Easa1gy6xo48wl r.d(qn rth. 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 as it rotateqxnt+ my bi(i j:+ab6a9d/d7i s uniformly in a horiz(baimd/9q7 d:b6 j+tyx+iai nontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km w0. 3bpv8bzhtp g)hn3 from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Exp. 3b3h)wv8t0 pzgpnhb ress your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude fvays4v 8- p4rof the acceleration of a speck of clay on the edge of a potter’s wheel turning at fvva r- psy48445 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revol2 fzijs- 2xlj0;o r5lnved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in 2 foznl-sr5 j j;0x2ilFig. 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-ki;xz, /ake f80s t d klmg4l2kd:9v0azg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result i9:4xdzl 0fsekk ma8 az 0dk/;,vl2tg independent of the mass of the car?   

  How large must the coefficient j v d/u;nli;b;of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speedljv;/di;; bn u of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotazbtq )0y*gfp) te a trainee in a horizontal circle of radius 12.0 m . If ttzbq fy)) g*0phe force 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 the axis of a rotating turntable ofp a.(i2jyio2h variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is oip2 2.aj i(yhthe coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rolleihqk,;* gvsmx)e q,f( r coaster be traveling when upside down at thes*ihkg ,,(vm e; q)fxq top of 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 (including the driver) crosses th-wppexa7j7 u 5j0t ,km.x7fnjrhp* *ie rounded top wprx7p0ajk mhti* 7e*-.pn uxf 57j,jof 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 minute would a 15-m-diameter Ferris wheel need to make 6;a(j8z,s,kysv// gypz tscbfor the p /sg,/ zcsysypk(,8v6bz ;tajassengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radil b+t ig9w2).4 dwn7 w,dsnsbqus 1.10 m. At the lowest pod7w+wnt2sds qw9gin4, ) lbb.int of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) musi+ tl9h: snr7 j(dyqg8t a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience any+9jti 8( dgq:n7hr sl acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnizil6u6wptt41z 33h z6v (nhjpval, people are rotated in a cylindrically walled "room." (See Fig. 5-35.)6i1tzw(63hvh n zppt 3zulj46
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 tablbae2u-oct2a rfff9k ) 5y8kn,etop, and is held in this orbit by a light cord connected to a dangling block (mass m ) e 52 - ta c9kyo2,fkbr8fua)fnthrough 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 th tncm.d0uw f63is time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particulat du6mcw.3fn0r, 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 perfec v2ouzt8x/dd -o bbp9-oia(n8tly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses , 5vuefdd/:x pe:eqo6$ 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 7z/cxrha5 g1e-gdqjf2dg6o 2 ss.k5z 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 comle dyz1n 24g,kponents of the net force exerted on th4e,k zg2ndl1 ye car (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 accelerates unifotf.ux9:)mrgwki696 l3lfm -flk a)k jrmly 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 cg amlkxlr)m.i :w 6f-3l fk6tk9fuj9)onstant 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 h0,7yp-xoabb l;bq4on orizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05 q-o; xny bpabo407b,l$\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacez )u ub,6+hepuclj/c rq4z8hs70ptp 4craft 12,800 km (2 Earth radii) above thp+j 8/ ,bhlzt pec746 u4zq)r chu0uspe Earth’s surface if its mass is 1350 kg.   

  At the surface of a c u.x2y: :5;ko oga7pw8vjdpx bertain planet, the gravitational acceleration g has a magnitude of 12 mu5;pa:xv ojo7 .8wkyxb2dgp:/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'q:hyj,29b0vp(jdz si9 1c qi/xfm:kts radius is 1.74k:h miv qjf(its21:0d czyjxq9,b9 /p $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same massa13 z29 vtpt4o izc4v jq3io+s. What is the a+tvs3t 3qpj 4 2iaz1zvo4oic9cceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timesqw7 gn (6ug+vy3gj72cak( vfs4rjv;z that of Earth, but the same radius. Wha s7vw ;ga(( 3vv72jgycrg6+f4zuk njqt is g near its surface?   

  Two objects attract each other gravitationally with a force o /ukcnb*z. cj8f 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 acceleratio lj):xd0sj7ion of gravity, at (a) 3200 m i0loj s7 dx:j)   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance si r,hobwhd7ja2( 0s :from the Earth’s center to a point outside the Earth where thegravitational , bo7hjsaw: rds2h0i (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 mass of our Sun packed into a sphew,p ,9l2 ctvwjre a2 ljwvt,, wp9cbout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which onceg6 rgxmg; yc):)a;ls c was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the c:; ac6rlgyx;g)ms ) gsurface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orhmz 6 sj4ltt7l oh+t.to0.+fape s*d5biting in the space shuttle. Your friends respsmt5 *.oeh6 l+04 laft7zotp .dhsj+tond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locateow ardy-,rk;2g/,.6c t tere7(on6bkw gej-md at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sph o/6mge-errnk, b k t rycg6a.edtjo;w(,2w7-ere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plane0iwr2nh y+lb 2ts line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and y2li rbhn w+02Saturn, 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 surfacb ,jc yw7w8-cue of Mars is 0.38 of what it is on Earth, and that Mars’ rayc -8b w7wjuc,dius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usingzjhytbyju 0 xzy651/5 the known value for the period of the Earth and its distance from the Sun. [Note: Compare youxj zb5tz1/y j6y hu5y0r answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abn 1c3t x3bq-wa3f tpk6out the Earth 3kf 6w3cx-ba3pt 1tnqat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a c)(j3v g;im0 qz.ya6hlbaf0yeircular orbit 650 km above the Earth. How fast mue); gaz.fyi(6 0jm yqvh0 3lbast the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylinlil+5,yt(xk 14m q shfdrical spaceship rotate if occupants are to experience simulated gra+4l(1 t fxl 5ky,simqhvity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in vxyg2 s *p wa,7(,lzwpa circular “near-Earth” orbit. A “near-Earth” orbit is one at a vzpp,(*x,wagy s 27wlheight 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 have to be launched from the top o5e*0rxx gwo/,ke k5r(zjy (ne f Mt. Everest to be placed in a circular orbit around the Earth?gkz 0(or*5wjy5rxee n, ( exk/   

  During an Apollo lunar landing missi w1wd,ua:pt8 mon, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onc:tdw 8,um1 pwae?    s

  The rings of Saturn are compi6o51h ie4vdjosed of chunks of ice that orbit the planet. The inner radius of the ring1eohi4 5vj6d is 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 rotatern-l(xs/oyu nj;h(4)axpi9 es once every 15.5 s (see Fig. 5–9). What is th j(lrpy (xxoe);a/h4iu 9 n-sne ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200gwr2agh 7hq+ y4vuv39q:w/1ez8i bzn km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, :v24rh9 +a eznqg1wz i8b uqv3/7hwyg    ----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 systevfw :kmu *oi)-* ct;2m fvs*cem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betwekmcv:ut2o*i-f*fc ; mewv*s )en them. What is the mass of each?    $\times 10^{29}$

  What will a spring scg81ilxrivzy4tib3v9g e : g(0ale read for the weight of a 55-kg woman in an elevator that movegt1xy3 9vgr gz i(b40i8:eliv s
(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 9g gp acoz b0; uzy72wm-b1eq.suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevpg- 9qbeoab7 c 0z.yz1wum g;2ator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period k 3od+e5tavn9,llz u*cs k8k8 T , th*e53l+ks v8l d,n 8ak9to kuzce density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon ciqh;5* vmo5x (27.4 d) to determine the period of an artif ;*xoc5mhq5vi icial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metersowqmu ( -xew-3 across, orbits the Sun like the planets. Itq( xu3ow -w-ems period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan+ . hl)wbxkr;qce 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 ou :tl7x734ttiz7 o *s;ayghdyears. 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 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 distan7o4iz:saouxt3 lty7dt7h g ;*ce from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of *x :z:ao/3c wsehern+ 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, a k2(krdv9w5h) pl3wkds qrt+3 nd mean distance for the four largest moons of Jupite9wrvwq+ pk25r) hk3sd t3l(kdr (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 the Earth from t bg+lz-9sm +*,eqzeb the known period and distance of the Moon. q,+b9eme+*zl zbst-g    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiterqe7u0m; b2ra6 bkyk0w ’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tablek yerk0q;maw2 60u7 bb 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 betwewh*dxz/v2*:qa 8 a uevo4l ob2en Mars and Jupiter consists of many fragments (which some space scientists think q *42b/ 8vex2vwhu z*a odlao: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 d4u oxl/fz*ap 6escribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to 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 year6 /paxo4l zuf*, in Earth days?   

  Tarzan plans to cross vl fqv25p 6(ky y8e05c3ujq rhd h0fw6 t7t/cka gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force ofkwp0t 3 5hklqhtyecy5v 6(u6 0 vcf8d2f7jrq/ 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of g/ grw03b z( ib3h+wuzyq43mel ravity be half what it is on tiug4l zeb33 h+3 m( qr0zwyb/whe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circleup)u g0w5gder4t5d ky:h4nw , huew) k:t 4ywundg4rg 05pd,5 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 pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accezqsa)gh8w6g )leration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this e8 zsg ))g6qwahffect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wilp9bmx- 9r1u kll a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forcesx1rlbkp m9u -9?    $\times 10^8$

  You know your mass isvcd9k2jk7 :dh 65 kg, but when you stand on a bathroom scale in an elevator, it say27 k:vh dd9jkcs your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate w8,u.+ fud6x/n7 b,sl balcpsabout its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter ofnfl 6l,b+ u sdwcxp u7abs,/.8 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 v kh1rd elx7b76mp/(tatti2 3 a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, t 5lad(.fyze-z he acceleration due to gravity at its surface and the gravitat eyzzlafd-(5. ional constant G.

A plumb bob (a mass m hangt 5erth - .8dqza+lc,ning on a string) is deflected from the vertical by an anga t 5dq,+ h8tnzcl-er.le $\theta$ 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 thes1klyg ut)aya; 7 27sb1(bau q coefficient of static friction is 0.30 a1ygs yku aab7()l2 us7qb1t;(wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast t0d4e8gjh1isz sn69u o-.u4cx5j ukhthat objects at the equator were apparently weightl z8u 4kjtudx0.su jh56 1o4hi s9genc-ess?    $\times 10^3$s

  Two equal-mass stars maintain a constao:nyi4pj;3qf y ;w *yjnt distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 23, s( jezmc0 eqk x6r,3xhhh2y;5 m. A lamp sus hy6rjz2 ,0(qk3x;mshexhe c, pended from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it krnysehohi 4.3;folt2 - +s; dhas 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 plah2tsdskoeh .; o+n3 i-;lr y4fnet. 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 presence of an /howi.. x3umms.1 8s6y( yenbpmoh( textremely 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 780x1/.uo(m6iwysbotn3.hphm y ( e m8.s $\mathrm{~km} / \mathrm{s}$ 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 shocgx7vj4n+n5kpf/ 9/ba.un pcl3- k muoc+g1rwn in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces aj b4nkm+g57 ru+fa1n u p.pk cxg/vl9cc/-n3octing 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 without losing contact with the road at A?

  The Navstar Global Positiwodm2ott7ao .)*qw /joning System (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 or*jt)oa m 7w.do/q2 owtbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, fmx o:2zap-j) is meant t-2fja:)ozp x mo orbit the asteroid 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 space shuttle pursuing a satellite in need of)u, k*bahdk9p y9 gxbhw64/ jy repair. You are in a circular orbit of the same radius as the satellite (400 km abo yd6ub4*9kx9 )/j kyb gwpahh,ve 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) Whatp;cg-abg0k 8(ymqh 8b is its mean distance fro hb0-k;(qagc my8 gbp8m 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 f1wr :wn szku) pn+9z5 G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make rnup 1 z9w5wnzr):fs+keasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-q :wq(*wl umo1nc7wlkl8t6,t46) at a distaq mn76 *tq, tl1u:(c8wklloww nce 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 0.50 m on eac: pfx4*tz0ua7yp,ehp h side. Find the magnitude and direction ofa4p:* pt u,pxeh7 f0zy the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the yd+d15y6ma; wp tm6ia 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 5 dkd0jil5fl3( 4jy- +lvtogn-long sweep second hand on your wrist i3do4y(jnkt 5vll-jf l50gd +watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in amdf3 ; o3 wv)jcd 1fme)gm9,bu circle below you on a 0.25-m piece ofd,3;vm fmgw 3jo)9edmufc)b1 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 p7zjzg : zru/ -z*svsr2,fzd s. g4-; az8icirradius R in a new highway is designed so that a car traveling at speed ssjcrvig4 .7z2 :r, g* dz a/fpz;iu-zrzs8z- $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when neyiqcjn j9 7qam,8lq vr4x4nv,h 1c, b-gotiating 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 (approximatelyy4v b-cc8lq49, h7vn1,ram qjnjxqi, ). (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.$\approx$    $\times 10^2$