Sometimes people say that water is zc k6sr:yml7il2c6 c0 removed from clothes in a spin dryer by centrifu60y2l7csklz m :rci6 cgal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the cahlgibp7 t/iw gdoofl6.1 4 /z19c2hgur travels around a sharp curve at a constant 60 km/h as when it travels around a gentle/ ho tf9dbzgc4lwl 1. iiogu/127 6ghp curve at the same speed? Explain.

Suppose a car moves at constant spo: mky zgjm27r.4z:.alr6x:e3r1c 7f au pou teed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hx63u.lk .yr7go p4c:2ar otzjz1mmau e7 :fr:ills, (c) on a level stretch near the bottom of a hill?

Describe all the forces act2usq /q4tf:l ping on a child riding a horse on a merry-go-round. Which of these forces provides t2t:ql4q/ u sfphe centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water -xcpl8cv8yx a:4 8kr fspilling out, even at the x- lcrckx8ap8:yv 48ftop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lea wdkhgvv+0(so,ha 6e1,ee; u iptxf9bin +*5 ust three controls in the carif;insh9 kxp,wb(1u v+0,dhue 6ve aot*e+ 5g 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 cq )61sosd aen:;r 1gomu5+bhnrest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he gd1 5;: nrqesnoa6h m)bgu+so1oes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward zd;:, /ifyfzxwhen rounding a curve at high speed?

Why do airplanes bank when thmbss .hd* g+2fey turn? How would you compute the banking angle given its spee*fh+s2 bmgd.s d and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.,,mivva6 kpl b :w1kk) l;zssl90 pkn. She wants to let go at precisely the right tim;0l s:kmvsp nv)1 6pw,lka.li,bkk 9ze so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert afglgy0s. b.r,ar 2p0j gravitational force on the Earth? If so, how large a force? Consi.g0f.gl rrpsb0j2,a y der 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 yn3u )i 4,sy:e;ze6pwq0s*uk h6hlcr be diffky eshircs: *q6y4 ,w3n;0l)u uzpe6herent?

Which pulls harder gravitationally, the Earth on the Moon, oryqqz(6 qkjz2 ev3/ys6 the Moon on the Ea y(z6qve2j s/k6 3zyqqrth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the f6e; u7klg k+5wtbqk3 Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint5tl f7qwbe 3k;k6kug+ : Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are/xq; w ruhx b4h(qqodlon6xs ek8 -+(* at work? Do they oppose ehe6w4+x olbuq -dr q(k*o8q/nx (hsx;ach other?

The gravitational force on the ocxvid 13**;b/ vqaaj Moon due to the Earth is only about half the force on the Moon dued/;*aic3v1*vbqo ajx to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratioqf(pr 9ohf8p0 fq8 q4bn of Mars in its orbit around the Sun larger or smaller than the centripetal acceleff(qqh8q 4 90bo8 prfpration of the Earth?

Would it require less speed to launch a satelli wn0r(f(ni; mcz0w-aute (a) toward the east or (b) toward the west? Consider the Earth’z c(wnw;fmn(ua00ri- s rotation direction.

When will your apparent weight be the greatest, as meaj9y- rzv:ttxb tsnvgm5r*9 ( +sured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when youyrtx9sb( m59nvtr+t :jv*z g- are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space co,1;zky i 6zmy1tdper-uld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceyer1i,k- p6dmztyz 1 ;ship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent .z b .xuiszpi7 z+1susy8z8 u5weightlessness” betweenz usz.z8i.85i 7usy1u+ spx zb steps.

The Earth moves faster in its orbit around the Sun in January thv p/px.dwsr8illd6 j.7bfvv 9 c,4+ab an in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This isd 78 ,xvplafbvs46wclb p dr+/. jv9i. 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 until itzlezh dvz- 1vht5 )n5:u.so0d was discovered to have a moon. Explain how this discovery enabled an0h5vudt5- zzzh :o. 1denlsv) estimate of Pluto’s mass.

  The Sun's gravitational pull on t;;cmz3n uz k8zcz8 4jxhe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hixc48;3zjz8kn;zc m zunt: 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 travelin5r s+b.kb/ nebg 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 centripe4yfvryy1w-5o w7ohssbt6j n(.me . m:tal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle4v.hsm6:ryw 5 owjy b -e(n1so.f7mt y 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 d/ids s5k5cf* discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 ikdcds 5 f*s/5m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surs,g mcz*bn2xf ,l*ny3face, and circles the Earth about on*x3nsgy2bl,f,m z *n cce every 90 minutes. 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 ofzy2+c2e(yx*siu tpky:0kr r8 a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wicxk28 *ury:tes pk (y0+yr2zheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at d )t 9sgm4nqqu h1p23ha uniform rate in a vertical circle of radius 72.0 cm , as shown in )14qq pht 9nu h3gmsd2Fig. 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 1ym1zklwo l9,)xb 29 ntdxf 5vd+s,fycan round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road i z ,1bys9lo,dvtdx5y9 wlx1+fk n )m2fs 0.80? Is this result independent of the mass of the car?   

  How large must the coeffilfwi :+1hcxw38 f7v pxcient of static friction be between the tires and the road1w73i8 :xclfxw pfv+h if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter piloh-dk ) dal hc+r/t6e)zts is designed to rotate a trainee in a horizontal circle ofedc-)/)a +trh6dklhz radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    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 of vart3orn9 fw (5x/h krw-biable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reachk3htf w5ox bw(9r/rn -ed 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,suzs(+6og+ nzx dcb, upside down at the top of gz,b n,+c6s+xo uzs(d 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) cn qsx6e3wn. o*rosses the rounded top of a hill (radiueosxn 3.w* n6qs =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-diameterg: h430 pdgy gh)o9rcq Ferris wheel need to make for the padphhorg:q 049g)g 3 cyssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ob qb+:k n8sx6kf radius 1.10 m. At the lowest point of its mo nb+q6s8bk: kxtion 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 particle 9.00 cm from the )1+i1rzqpz/4 bb smiqaxis of r mzqz/+ 1qs i)pb4r1biotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carni(5h2d4oy gqdt5 03smio u m(cgval, people are rotated in a cylindrically walled "room. q(3dd45com2uhgio0y gtm5 (s" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is hcoih9 e49 hy68/ytrku8 za3f rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a 9/h9zuki34efthra 6oy 8hcy 8 dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of thevto.)wm.y 7xl ball which revolves on a string 0.600 mtx.l.)vo7w y 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 traveling njsh6ug/ /s/kr 5(tiw 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 massesjns o)d3j pq /gi5 i;/om8.hqew)ubo/ $ 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 vertically at 310a)0 y*pygmau vvj4 y)2 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net fon5a5l bw1 vy1qrce exerted on the car (by the n5 bq 5lwv1ya1ground) 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 uniformly from the p*9+v/ek (dqnkwhio5 eit area, going from rest to 320km/h in a semicircular arc witoekh/w ni 5+9dq ve*k(h a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of 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.h)k,dh2q0i2:tto x8cre fov -90 m . At a particular instant, its accelera hofrke t,0xv2:qocd-8h) ti 2tion 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 Earthmjalgopz(ep,c w 73521op7ux5blr. e radii) above the (oluz p c5lr,5 emga12wpb.77jpe3 xoEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the ;9v m98rqwvmw2j : kucgravitational acceleration g has a magnitude of 12 m89vv crkj;wum :2 w9mq/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 ;fw-w3l+ds e7/pizjv Moon's radius is 1.7jipz -d3 7+e/lsw ;wfv4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical plane+upt)o+ fpf ,, ;:llhmbxe0 hvt has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration duebe+o0,v xl+:h,pf h )fmupt;l to gravity near its surface?   

  A hypothetical planet has a ma *.)fcgloqqhbsy*i+n *)0aatd3+ vqtss 1.66 times that of Earth, but the same radius. What is g near its sdsgf ltq )*oiban+hq3*v*a. yt+cq)0urface?   

  Two objects attract each otherqx 0n- 2 r+ya(h/ lm)mi9lsiih 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 value of g , the acceleration of gravity, a92/bp+yt.swg ln od 7b7z lb3ec2t5 eet (a) 3200 meswp 57 o byl+bte329b2e. z nd7tlcg/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center0;ddr4uzgn -st3adw -*l6r g c9o et*u to a point outside the Earth where thw o-g*rdst3gz04ed *a 6ndu-;uc9ltregravitational 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/c/9h g.az;kca8 sosd the mass of our Sun packed into a sphere about 10 km in radiu 9 /c.aokd; hss/czag8s. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star k6l 0gfuc gm.jf.p2cr-)rxga5a;m 1x 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 thfmxgp c5. gr.1-a0 ) jga k;u2lcf6mxre surface gravity on this star?    $\times 10^7$

  You are explaining why astro3(m bgl0 vg.q+ny5ue ls:zp d: ns+:ihnauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was + 0yvhgn.z3su:bl lq5psm:e n :+gid( 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 locawnm; qlk:wz5 6dp eh:;ted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exe;m6pne5 wwhqld;zk:: rted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mosk;e8op-d f*lb l:3bih75itjt *jwu4tt of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, alj : i5h3tpk*btj7-ueo 8lwid f4t;*bssuming 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 surfacelvy63g5 gqea1m .vu1hs*o(14i tthgb of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 gomv1eb gvgq4sa* tt u(yhh.i51l361 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value f7m.w) :rkelb*ngyp 6gor the period of the Earth and its distance from the Sun. 6lwy)m .pk* 7nbe:gr g[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 stable circular orbit about7(2jba ae h+sd the Earth at a height of 36d2(a7j se+ ahb00 km.    $\times 10^3$

  The space shuttle releases a satel-9dtokeavg3ro:im8sgkght j *a, a 3u,b3q3- lite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release *t3gd8b :i9 gs aug 3mkkh,aoa,3tq- e-3v rjooccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are8*4yis u ;fybt9a3h ty to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m3yft4 ; uyhatsi98* yb, 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 ikv0o y.8u hnr g6ce;g1q ,7epvn 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 satellite8egqekv. p;c gh y7unr0o,v16?    s ~    min

  At what horizontal velocio (q hp(1(orf9vmsid+ty would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around1(vm opqof(+h9(r sd i the Earth?   

  During an Apollo luna cmlvln;0(1yf 5 uyo ns)is*u0r landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How v1i)nu ;(lcy*n00m5 sul oysf long did it take to go around the Moon once?    s

  The rings of Saturn are z:wg+ yfj /.xut8d.:joiep6x composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000.6pxd: 8ow xtu fjyj/ze gi+.: $\mathrm{~km}$ , 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 oncek(ki3 a8u 5pxk+ l/zye every 15.5 s (see Fig. 5–9). What is the ratiokpyx (e+8kzl5 aki3/ u 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 as (xx o,dc-t hoaqgz +:hcg:7o5tronaut 4200 km from the center of the Earth'sgco7dgz :a :-hx5hx+q(o,o tc Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equt7.lyc,s eov1jl;sk ( al mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point oecss 7(ltkyj v1.;,lmidway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring sce9xag jepu 26;4 bljm+ale read for the weight of a 55-kg woman in an elevator that mlm +64e;a gepjjbu2 x9oves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of or:8.1fibvvq d*idt6 q7unk*an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Whovvk* qfb 8.q*:ndiitd r 617uat 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 -cn3afm wbk/ixs)v; r 8n20omT , the density (mass/vol i/f3k cvomwn xb;s20n-r8ma )ume) 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 tg *szk o,)9:b 4tfb.l(rw /kcex)cl shhe Moon (27.4 d) to determine the period of an artificial satellite orbs) ktr .9x celwg,l:cf kobh*(4b/)sziting very near the Earth’s surface.    s

  The asteroid Icarus, tho- pkm;b imc17zozqo ot5 353rpugh only a few hundred meters across, orbits the Sun like the planipbmoc;rk 53 7tpqzo-5m3 o1zets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 2gi j l+te8aczbe3-9m 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It*ny+z8il f6r y 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 distancelf+ *yry68i nz 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 the Galaxy zsyn518/+1 qqenpkm*o- cgts $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 disc+kzbl 0ef) p-tance for the four largest moons of Jupiter (those discovered by Galil ef+b)pc z0k-leo 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 period and distanc,se-;ose /kju j3r f owbd:)f:e of the Moon. , )ok:rjo sje/d-fsf3bu;ew:   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jup;rb z,e2qv45o:*/df hcbwva m iter’s moons, using Kepler’s third law. Use the distance of Io and the periob/wzm5,b4f;: o hqcd2vv rae*ds 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 l a; / 2zey9 ,2ng8wtp2qeeug-jfnd3 iconsists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed).eq ftgij8 -a p,2du;2z gn23/ln9w eye
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a;snpma( (f+ .pkk 5yso 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 ry+p s(ka o;knps(5.fmevolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging ingwp f/l h99m9kp2c:v k 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 9w:ghc pk 2pkmf 9/9lvhe 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 2i 3s pnpuibk7/qg4q 1gravity be half what p 4i/ sip3q1bqu27 nkgit is on the surface?    $\times 10^6$

  On an ice rink, two skaters oau7 db fc;x)pg(/o6c ff equal mass grab hands and spin in a mutual circle once every 2.5 scd7p uox)(cfa;b6gf/ . 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 accelerat bouskr *,n;1iion of gravity at thn , ;usr*bki1oe equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacky76a:h a z:9u)cj tvaecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with ea j :v 7ytauck6z:)a9hqual and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a esem)3b4,hjwu6 tcnq f m70i2bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration ofcq)hn6t3bm 2 ef0j4e i s7,uwm the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circularnigy)c uc)f i n1-.zp( 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 must be tf.-z(g ypc)n ni1 )icuhe 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;bb.rzw ky rxbxae;n2:o fme. *c3f 9; 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 forna 0* -ahan3vv the mass of a planet in terms of its radius r, the acceleration due to gravity at itna*h3vav- n0a s surface and the gravitational constant G.

A plumb bob (a mass .ikoex i+ (;efm hanging on a string) is deflected from the vertical by an a if;k.(xoe+iengle $\theta$ 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 fo :m,m*6lcqmfp r a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a caf, :6m*mcmpl qr safely handle the curve?

  How long would a day b5qoi tka.o8bs tv 86k)e if the Earth were rotating so fast that objects at the equator wa6k)tk.b osi v8oq5t 8ere apparently weightless?    $\times 10^3$s

  Two equal-mass stars main:0) 1x;xfz /txk7tzijr 7yqla*d:dl )zbkyx -tain 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 con-p ,kxzqacop8xrmp9)6 jae7tyd)3 u 9 stant speed rounds a curve of radius 235 m. A lamp suspended from thp amx9eazj- ,t8p ud73k96yo) rxqp) ce 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 has been claime 2jkb)x o/oa j8( z) /oibbw,zx8hk:qqd 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 )a,2 oj/8hzxb o8(b/qq ) : ioxkjwzbkJupiter: 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 presendc;mv 2 byxd.oa+ jfv;.nvg9qj0m6 -n ce of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clo b-dm.ga;cj20v v6fq x.; mdyovn j+n9uds 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 con3vmky+ky: ju(stant 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 with(muj ky:3vyk+ out losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites nm7lb5c1b ;z m9)7ccx/nfhg p 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 centicb/7hnpg5xnz c)c1 bm 7m 9fl;meters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after d pu n*)lot3f3pp9p(ttraveling 2.1 billion km, is meant to orbit the asteroid Eros at a heigh (tdfpl3tp* 9o pp)3unt 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 e; kej6z ( oqp(7lv ei:4eyrcfzcn: *)pursuing a satellite in need of repair. You are in a circular orbk fqep4e :v;nz e zieoyl*c):jc6(r(7it 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 d)oz5h be*8 i2 eu,frfperiod of 3000 years. (a) What is its mean distance frfed2 fh iu)re b8*,5zoom 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 - ky)gjyieic 5(lf446rgbg8 vof G would need to be if you could actually "feel" yourself gravitationally attracted to someone neabi4 g)fr6 kljy(yv84g c-g5 eir you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around t0n z r 2kkgnw,qr.pm3:0ec 4bbhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lig2m nzq3b ngk:.crkep0,rb 40wht-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 lo)7 fy+da aio,yzfbnfy7p)26ucated at the corners of a square 0.50 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 piof fad6+ uby ,7z2) ay7)nfythe bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits) m o*t(.senqk 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 exvn 0bfdgicx+ra v bz2-33t2/dperienced by the tip of the 1.5-cm-long sweep second hand on your c/rxfd23 3vv ndzt0-i+b 2 gbawrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weigd5ci 1ihs- d)gke+b- aht around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle c h +-siek-digd1b)5 aevery 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a nexer4m g p5g7j-w highway is designed so that a car traveling a47-p5 rjmx eggt 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, utilizes tilt of the cars when negotiatingads kuw)6usop-x 80+ x curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide-oas kx+ d)x0pswu 86u 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 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.$\approx$    $\times 10^2$