Sometimes people say that water is removed from clothes in a spin dryer by ce0 tcbep3j q5as+qkpo1z0*i 7 mntrifugal force throwing the water outward. Whe0c7sbj3 a1p 5qzptoi +qk m*0at is wrong with this statement?

Will the acceleration of a car be the same when the6 iq ywzo6e/2mq-eg(d car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spo2w6q-g/(yd 6 mqee zieed? Explain.

Suppose a car moves at cj)b30 fum4s hkonstant speed along a hilly road. Where does the car exert the greatest and least forces on the roabkmus)3 04 jfhd: (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-qf3zwlo5yh93jm )b 7x* komc9go-round. Which of these forces provides hmj97*ykqmw 3xo9)czlo b5f3 the centripetal acceleration of the child?

A bucket of water can be whirled in a verw yxy -ug6;wi,tical circle without the water spilling out, even at the top of the circl;u-yyi ,wxgw6 e when the bucket is upside down. Explain.

How many “accelerators” do you have in yow e0c*nbi9+ y3cutvh5w(b9j a ur car? There are at least three controls in the car which cawhnv bjca+(0ty u9 c5e*bi3w9n be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comep/34mzga uxj5 s 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 hi3 m/u4jzag p5xs 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 wj 1 g/8j0z+4i)-x oyianzdwch( ffb 4ahen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you comput n0x98)on0avn.q obpce the banking angle given its speed and radius of the turnn.9bvpoq80 on 0n xca)?

A girl is whirling a ball on a strels+y9 ybs eg0t: r,g.ing around her head in a horizontal plane. She wany,+ 0:gt gsyr be.9slets 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 string?

Does an apple exert a gravitational force on the Eartt ky:bhoh(*vnq:2+s ph? If so, how large a force? Consider q *y bont:(h:v+hpk2san apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways j5rw2 ulj4 j- q8h1uliwould the Moon’s orbit be dif-8jrjwu42jlu51i lqhferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moo7tw:o*d*co5ybbg+ q wmj0 p z/n on the Eartmz*7+wq:to0/bpjg wo cd y* b5h? Which accelerates more?

The Sun's gravitational pull on the Earth is much ll/2qy;u sgb en;-chm /arger than the Moon's. Yet the Moon's is mainly responsible for thqny m g;u bs2c/-;el/he tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at6re-gu: fn)p l the poles? What two effects are at 6p :-fl ner)ugwork? Do they oppose each other?

The gravitational force on the Moon due elp vps (a1,f;to the Earth is only about half the force on the Moon due to the Sun. W1v(, p ls;fpaehy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Ma7yk e9,4nfmur rs in its orbit around the Sun larger or smaller than the centripetal acceleue,nfrmk 947yration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towy21wq- oowgo5gi f)h;ard the west? Consider the Earth’s rotation directiog;oww)-21i g hofq5oy n.

When will your apparent weight be the greatest, as measu 9wb;: ls 8rddyn8d+bqred by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accel q88+sw;dbb:y n9dr dlerates 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 long periods in outer space could be adversely affected bye2.* ctt ic/mz2sp,ig 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). Exple 2ii2c,g.t/c*mp st zain 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 “appar znui3lbd/ p+)ht27 :kpqah 2hent weightlessness” between stnz2 th q+kh h/b:pual pi)7d32eps.

The Earth moves faster in its orbit around the Sun in January than f- tkd ce8bi : u2eccr4 5vi2oea/:t.pin 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 main factor is the tilt of the Ea2:eibt5 ue a:f/it4rp2c-e kv8.cc dorth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known untikft ;t )4ajfba4 q ajnu/m, jz(nq,a,)l it was discovered to have a moon. Explain how this m j4qankz t,ff,a4tbnq;)/u aj ,(aj)discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger wp7db xk4xz sz)0. s(xthan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sidekzp 4d7bx sxs) .x0(wz of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 olo4mij er* 66 :all7g$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelera dcd1 crk3x9d/t w,h-jtion of the Earth in its orbit around the Sun, and the net force exerted on the Earth1c-wdrc kx93ddjh/t, . 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 rotates unif+n g2si-rqux3a-ol 3f uim;4 wormly in a horizontal circle (at arm’s length) of mfulowi;+gsi n- 23 xu-4raq3 radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfacodcm 8ry, b85hzvl (.0lwlw8 ue, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terlmw,ouczw0.d (5brv8y8l h l8ms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay1:7olbeocx ep 5dlp(/l -hmumd) , 5mw on the edge of a potter’s wheel turning 1m, o :chm5dlx/e-l pemb(do pw 57ul)at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revo .7zb39i3goq8 uwh 7q c9iz/)wzo2v cfemtn3a lved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00iwvco2o q)tqh 93u73.be wzz8n/3ac9 fgz 7 im $\mathrm{~m} / \mathrm{s}$ 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 wbg;x(thph rii vx 21a93 d(ob.ith which a 1050-kg 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 independent ofixv dhptarb9ho2 b ;3xi.1( g( the mass of the car?   

  How large must the coefficient of static friction be b4z e/b ovww;ush )g64zetween the tires and the road if a car is to round a level curve of radi z/w6 4e;bsv4zow) guhus 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter piljtsy2 ct 62m-ocm(p5v ots is designed to rotate a trainee in a horit2sv -ct y o2m5cmp6j(zontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    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 variabt g;wztsqf h2p(-+n.jle 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 ;s(w2 -thzfq nj.+pgtthe coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at t/ uofla. r(x me7fpcy3h*.q+che top of a (qp3fue flxca+y7.o h.cm/* rcircle
(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 (includ wt( ,eto :*0ccmsrrd1(3 0q/ad jggqsing the driver) crosses the rounded top of a hi(gdmr*0st 1qc,e dwoa:q j/3tr0s(g c ll (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-diameterd bj 9,yxmrcdni+/3 wr8*; bng Ferris wheel need to make for the passenb;dxy j9rndbi*mg n r,+c/83wgers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Atieh *pagi-/ad6rjq +fhq 1w : hi,g,+f the lowest point of it:-iwhg,hard1i/a g+pje6i q fqfh ,+*s 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) must a centrifuge rotate if a particle 9.00 cm from the qt:rd9 1(8xv5 zj/mw (bmrgs qaxis of rotation is to experience an accelerat9zq m1 vrxgw 5m(/8stdb(q: rjion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopleaqt:4nmn3 w.x are rotated in a cylindrically walled "room." (S:3qwan4t m. nxee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a aji xq7u 57 *ddjkpw8-frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to7*- kjujw75dqipxd a8 a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of c6zr*i;feml/9 , d6aprrad / rthe ball which ri,/pfdr erar z*d; la96/6mcrevolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fao (os, 3kr9mf*vg x;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 x xsqs3.ez++c* aaue. $ 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 vert e)q1;mymvzw1zrp :w 6i 0frl*ically 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 ce 88;bo1nw/yj ( qxcb-bv jj,s07zq,sp im oo;mntripetal components of the net force exerted on the carm8ssow(vjp n qm08-by qo/oib7;cj, ,1z;bxj (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 acceqnp2,bna9 jjv0w rt45lerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slippin tj q 5r0,nwp2j94bavng or skidding? $\approx$   

  A particle revolves in a horizontal cirpqzsgktr/:o+ cijo a8 9p*0z,cle of radius 2.90 m . At a particular instant, its acceleaztkq+ ,08:9 isg* zcpjoo/rpration 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 asswt50;lphkdm 0h1s 6 spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if ps6m0s1wh;sd5 kl0t h its mass is 1350 kg.   

  At the surface of a certain planet, the gravits y+2jaqr ca;*ational acceleration g has a magnitude of 122ra+cs ajq;y* m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity o6o w 3jd1qiv3un the Moon. The Moon's radius is 1.7 w3v 3dioqu61j4 $\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 Earthm-w4 ;y k.g-/ all+ kyj4pxhlb, but has the same mass. What is th/4lhyk4 jw l-kybxlp.-agm ;+e acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rah3g 65w/bqsr9:x(w1x nlcxkd dius. Whabwcq9rng: dk x1x3l/6 s5w h(xt is g near its surface?   

  Two objects attract each other gravitationally with a force of 1e cfb-)/aqyh8 4xtcm2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at u56doo6*y)a k 3clr o. hbcv3d(a) 3200 m a*c3.)6hrd b o oy d5lkucvo36   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the v-void sx)qm1fd0: q-6y ;p xbEarth’s center to a point outside the Earth where thegravitationa1; vxq sq--fvioyb :d)60 xdpml 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 mas 2flfzw,f mp*+4 d0dkss of our Sun packed into a sphere about 10 km in radius. Ep4s 0dlz+ kffm,d*fw 2stimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which omrl neo4 5m) ,uxtsw6:nce was an average star like our Sun but is now in the lxoetw,n s)4 m u5rlm6:ast stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbduall yp)2; 2 adg.uk3iting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.y)k 2 aaugll; pd.d32u   

  Four 9.5-kg spheres ai(t lqy*g,uk:ft0 c;are located at the corners of a square of side 0.60 m. Calculate the magnitude and t ,;:g(lqu0yk*fc ita direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up. r() lk y*kwjikkt98,uhz5 sibdr/0e on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fu/e ti*iw jdkzlb(0rr9,kkks8)y. h 5our 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 am)n9skiov96dyld r t0-:is/rv a0d 2lt the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deteo/ i6rki9dl0dd- t0rm nyv:v9s)lsa2rmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the zgm)5rojmj68u+uk*r-dl pw 6known value for the period of the Earth and its distance from the S g6pmurl kd or6-m8+ujz*j5w) un. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving ink*m *- btejtu.d+r 5dn a stable circular orbit about the Earth at a height of 3.n duktjbtm* e5*d+ -r600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kme0w4b s.(c;o5 y cho(vig dhw9 above the Earth. How fast must the shuttly.b5hhd0c(i( ;w 9soveg4wcoe be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants ara* iwhak).t; 44oy juwe to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Qut *i; h)aa4yokj4 w.wuestion 21, Fig 5–32.)   

  Determine the time it t:b/ idx2ys+ej akes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “si/y d2b+ e:xjnear-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launch2)yp uje mg-5hldy3/b8)pgpied from the top of Mt. Everest to be placed in a cirbyj)p8ig-u egy 52dp )3/lmp hcular orbit around the Earth?   

  During an Apollo lunar landing missrk + 24f6l2xa zcqprp/osjswf2wz.90 ion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to rxafs4w9. f p/2q6 z 2zkpro2lcs 0j+wgo around the Moon once?    s

  The rings of Saturn are composed ofrv,xbo4yb9 .m34id k uormf07 chunks of ice that orbit the planet. The inner radius of th u9r4.x m io74,3yvk0b rodmbfe 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 ro rd l(*5vxdx8gjs;x,ytates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her yvsr 5xjlx(,d8x dg*;real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center 2iz)lnao : *sd+4l rytof the Earth's Moon in a sptl+ n zd rao*s2l)yi:4ace 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 equal mass.()5ky -o .hoimeo( *q9 ehtf)fdgiwmp h;4 tj: They are observed to be separated by 360 mi f o4iqi(:m-ktgpj m h.e*w eh;d9f(5t)ohy) ollion km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the we-;, 1xtmxq wvlight of a 55-kg woman in an elevator tha-,wvxt;m xl1q t moves
(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 frxc 68t5 8* vrvfwtra9mom 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 (magnitude and direction)? xr*69cfvarv8t mw85 ta =   

Show that if a satellite orbits very near the surface of sul xl +l4 ,4l; ga.idajtq)a7i xjk6.a planet with period T , the densitgdll is .i7,;j .t4ljx4 qa6 lx)kaau+y (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 (27.4 d) to de nl; wkl;o ;ke)htka6 /pg)i.q kdy8.etermine the period of an artificial satellitepoel;)k ; akykk;tw6ed..n )q/il h8g orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a f5po e)aisj )n8ew hundred meters across, orbits the Sun like the planets. Its ppo8i5)s )enj aeriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 jl1ky5j0w xs0nz7 da/$\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes vwpqba4ls 9v;pc 2ff +6ery close to the surface of the Sun on its closest approac4s cq+fwl; 2f9a 6pbvph (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 distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G w9obatf s1en7 m) im)byk9*offc.g9/alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,ltk,mk 3x)lv/r3 zyg 1 and mean distance for the four largest moons o3g r,ylzxkmvk)/ 3 1tlf Jupiter (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 the known period and distance of the Mo2txaxre,0v2v2mdm8 k7 x py-fon. 0 px2 ,mvyxeda7vrx k2-8mt f2   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s m:haqfm+n clpc24 +/lcy8y8fdoons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in th8lfypm2/l+ hnf4a+ 8 y:cccdq e 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 Jupitq f4w7.67 28 tvoju(0 dwzy6upbhvhxwer consists of many fragments (which some space scientists think came from a vf74jvwx. 0hqz8d h6uw2wyo6tu7( bpplanet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of z dscxr *oll 6f5b+3*ta 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 enougzb+t*lfrlx5 6d s o3c*h 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 6sf4a c6*b :l9 ki g5bg(iix.ubvfhc- in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 14:bgg-6f*u4c(b9v ii s hf6xa cli5kb.00 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 acceleratioy:4:dr- 9 uo(w.d ahee,(leubomhfy*n of gravity be half what it is we( : *ly 4mfde . ou:r(ay9beh,-odhuon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a muh4va*uyd7a5c;jbt s5tual circle once every 2.5 s. If we assume their arms are each 0.80 m long and thei aj4hab 5 ;uydsvct75*r 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 accelerationdvt(-/uk3hb )q7 yo9uk jx h)v of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this efft7udo k3)u (yhj vhq/k x9bv-)ect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s x9:dhbi2fxt(pacecraft traveling directly from the Earth to the Moon experience zer:tfx2x(id 9bho 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 bat;96npzn9qpj qmg /t 7fhroom scale in an elevator, it says your mass is 82 kg. Wh n76ztpj9;fmq9npq /gat 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 8 6pkw/6uuf agrotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by tha6pf w g/6uku8e tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his k9jjf- ndqt:(m(ql 9. km mgd1 /3niliaircraft 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 pl g(- .hqtqjm2yzldllw s7d 9,:9dei 6n(fscc0anet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constantzg9:enh d-0sdqmc7 (q,yf(djcls 2itlw 96. l G.

A plumb bob (a mass m hanging on a 394g 1 fjg1ot9leia8zb azav+string) is deflected from the vertical by an a l8azve1g499ao3t+ij1gfb z angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design rtkrsfw :5wm88d1; ku speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spe;wm8k w8sdtruk1 f:5reds can a car safely handle the curve?

  How long would a day b3vbnb l )8dts:e if the Earth were rotating so fast that objects at the equator were app8t3sl b)dvb :narently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanc)b cwrh6mtw3c z(a5i .e 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 curvrk966y bu)4jxjo6fen t-hg3ge of radius 235 m. A lamp sus o6rtbje3y g4u fn6j9 gxkh6)-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 mass4xq anf lz;ta9dp. 78rbmi-/kive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't surviv pd8-qxf a .7z;r94klimatnb/e more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extrog w4 0m rlg(tbr,(dw*emely 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 , wor*t(gw b( dlr04mgthe 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 traq5fa7x wc ..*.wqmz+bk,sn n qverses 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 acs wqx nqq.+fkc*nw5a,.7bz .mting 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 Positioning System (GPS) utilizes a group of 24 satellitelu/x8lfpt-5 f s orbiting the Earth. Using “triangulation” and siptx5l /uf f8-lgnals 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 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 Rendezt,)c*k l bb qxqwi./f(vous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height ofck lx,*i).t bwb/q q(f 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 rephlcg )jm4 :vn( fh lm826ag/joair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), buma82(j ocg/jfll h)h:vmn 64gt 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 is its mean dist-*.ufux,g2dvlgizzf i 6 l6c 2crd04rance from the Sun2dzvx. ru2f 4c0 l*f udg6zri,lgc-6 i?   
(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 tl1rs f pnl- vuba;2(*jwy 3/x would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like busx*j;frw/-nl( tl13aypv2 F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal 2ygz /ri9z7cnaxy (Fig. 5-46) at a distance of about yn7z/g 2ic zr930,000 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 l.ffn a: r t4p8 z2ukvnq.l*j1kocated at the corners of a square 0.50 m on each side. Find the magnitude and directif n8nt.4 jv.al2uzqf :rkpk*1on of 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 or dt2o/afr34yqu 6 (oaibits 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 r0 4)vqu d3pg*;o fw)yw lu1icw 6xvq:the tip of the 1.5-cm-long sweep second hpxgc )w) v4qr0; wvu *oidy3 q6fl:1wuand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get byg8sj d:z.pp 95vy0e b3j fo8+0 yyqdbored and start to swing a sinker weight around in a circle 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 fishiejf vo dq8dy0bp359 jbs8y.:p y+yg0z ng line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a x-+dt9l tna 2:vd4v-wlsusd / car traveling at spews dt-unal d :2vxdv-t +s/9l4ed $ 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 negoti nhu6yc b;m ynmhooe3 6;p/))mating 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 comfortabo6 ;)yeyp/3)cbu6; nmmhhonm le. 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.$\approx$    $\times 10^2$