Sometimes people say that water is removed from clothes in a spin dryer by cerve b+9tgbpe9edpfc 8p 0g 9a*5 mwg9:ntrifugal force throwing the water o0p9ebvedwge5:f9pt*rg8 9 pg9cb +amutward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around- s3yk*/mgom-s 5d tpi a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Exism-/smdy5o3 tk -p g*plain.

Suppose a car moves at constant spf r -ktvc(af2-eed 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 hills, (c) on a level stretch nt(f r -2cva-kfear the bottom of a hill?

Describe all the forces acting on a child riding g)0q2gnhi.g33 )tvbn bh(l zfe :y0fna horse on a merry-go-round. Which of these forces provides t3n3enzg0.2l )hhb)( it:ffggbvn q0yhe centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cyo9k8wu9lwz3 ay::q qircle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain9u:yl y3k:waoqz8q9 w.

How many “accelerators” do you hy.jkr:o;cm3x ave in your car? There are at least three controls in the car which can be used to causm;kj 3yrx:c.oe the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest o,bq5 ckpk ck2t8xyd3.f a small hill, as shown in Fig. 5–31. His sled doesc yqk.cxb5pt3 28 dkk, not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when yjam1qn jn;j((jl4 d-0c/fvd rounding a curve at high speed?

Why do airplanes bank when they turqgtpp q 7+rk yysa* :f9.0sh0:,kltqc n? How would you compute the banking angle given its speed and radius ofkrlq*0y0.fkqch,s p 9sa:t+ g 7 pqyt: the turn?

A girl is whirling a bal r( rfl+py5h/(k5p;vgdq6 lmal on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other s l5f/rgp(qhp;k ady r(l6v 5+mide of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large oxm(pz6/ ;hawa force? Consider an apxzwpmh;/a (o6 ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dou.vox qk38yno .w,i8chble what it is, in what ways would the Moon’s orbit be different?3 c.v ,.8 knwh8oiqyox

Which pulls harder gravitationaehs+lkf/j(o 8 g g0db(lly, the Earth on the Moon, or the Moon on the Earth? Which accelerat08+hkbfl((/o ej sgdges more?

The Sun's gravitational pull on the Earth is much larger than the Moon' ,dw22u)so rpms. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Erm swou ,d)2p2arth to the other.]

Will an object weigh more at the equator or at the v,gll t8./3 6rtax 0a:jnm* gxp veem8poles? What two effects are at work? Do they op0lapt83n:* e v86l.r mm ,ggtxxva/ejpose each other?

The gravitational force on the Moon due to the Earth is onm7+bka.j c 4:qdgoyf/00 p asc2ov7q wly about half the force on the Moon due to the Sun. Why isn’t the Moo+7abcvcjog7 : 0oq dwsy.m/p02f4k qan pulled away from the Earth?

Is the centripetal acceleration of Mars in8 (4mo j3kidmrx6:o o )6p ns*bca9bmi its orbit around the Sun larger or smaller than the centripetal acceleration4:9om3nimmjis)a 8db rb( x6 ok 6*pco of the Earth?

Would it require less speed to launch a satellite (a) towardbormx(t6: +nb(8zes j the east or (b) toward the west? Conss b ( :nz+exor(86jbmtider the Earth’s rotation direction.

When will your apparent weight be t 5fh,aonzk,13ok b n0ntr5un1he greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In whicknofk3nbo5,z t1 51ha,r nnu0h 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 periodsx*p,hql5rf 4)k 2khos/l5dvn in outer space could be adversely affected by weightlessness. One way to simulado*)5xp/ 2kf k,qs4h lvrn h5lte gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” ozb fxr 3k6+*-/rqwckdr “apparent weightlessness” betweenwf-b6q z cxrk*/+kdr 3 steps.

The Earth moves faster in its orbit around the Sun in January than in July. 7a8950i xw k bbaulx(eIs the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in px0weiau bx7 k(al95b8roducing 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 it was discovered to have a moon. Explavhp.;1vc xrt9g/x q xqo6b* t,in how this discovery enabled an estimate of Plu x * .xvb;xh69gt,ctq/rvp1oqto’s mass.

  The Sun's gravitational pull oo 76)orgl) pmun the 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 otheroo)ulg 6)m 7rp.]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 travelinfh.zq w(1, r :egigl e7hdp.9vg 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit9-7sqkwv fc z0 around the Sun, and thc- kw9f7zsvq0 e net force exerted on the Earth. 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 discdtv-wq9myo)j6m c8ul y*1jbxxd- rxb2wx60,us as it rotates uniformly in a hx - xb j xyydbr*xw6)0 6vw-q, 928lojmcutm1dorizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 40m94r94 /of ;ei ounp. cyecov:0 km from the Earth's surface, and circles the Earth about once every 90 minutes.. 4cvoy 9i/foncu 4;e:pem r9o Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of ce6dgl sz) mt/x3qp59 elay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter 39/x lees6zqpdm )g t5is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circuujuasr/:u2why k /9ouo ,y lr**8 r)mle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is klmu9rhu2*o)uu ry //:s*wroya,8ju 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of rh9e5g8h q 1mecadius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass o eghh59mec1 q8f the car?   

  How large must the coefficient of o pr,y:e2y:p( w tlv-astatic friction be between the tires and the road if a car is to round a la ,( rlpw::pvyo-et2yevel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to ro27c 4x (1uqv(qn7, n xm)pkple2und xbtate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 time, 7p nqx)bdu4ue(n ( 22xmp1vlxqck7ns 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 cc-fdru )-t4grqna8v h f,.z 9em from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turnta-8e rnu-49tfrv,cad .h)z qg fble until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed musur3 e qni1m6o*ef,0dh. : aoctt a roller coaster be traveling when upside down at the top of a cir eond3fcr :muq*h,0 1.6aeot icle
(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 xbjdo7* jly(evnt3 6,the rounded top ly,xno t(j6v ej*b7d3of 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 /f67sfrrm y*u to make for the fms yu7r*f/6 rpassengers 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. At th 0v3r s+xtsha5e lowest point of its mo3 rt+x5vhsa0stion 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 rotatemy: ., k9shcjd+*o r.i ,etfl j,mkoc7 if a particle 9.00 cm from the axis of rotation is o7 jem, th..fi+ :m*,c9 oslrdkkcy, jto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "r; a ,r5ahli :; fgawx7rdqiq19oom." 5;gwq 9ra rad1:xaii 7hlf;q,(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 rotated in a circle:t47quuy yfs: on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through as tyf u7:yu4q: 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 thee*n+;bno8qzic n . 8so weight of the ball which revolves on o*bnq.nse8cno+8z ; i 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 i5f7iyml)q 7ja dz9 -ctw3j+hcs perfectly 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 wl(k6z j e*m*nj+wl)a$ 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 v4qqz.pnw4l:y : cmo1gw rb;7mertically 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 com klgbvbzt-ik q 4hau4 )a u+l7*0.htd9;k3j ucponents of the net force exerted on the car (by the ground) in Example 5-8u+u-akttu04 hc .b7;j9 zgbivalk *4)q 3lkhd 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 uni may507e6h/oim+tzsmformly 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 t7/msyi mto+6ha0em5zhe tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular :*mju9m 3o,t mlibaq1insta :mqja*mmbt ,9ulo3i1 nt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a p1*wk w7n zkkm).iln ygx:8zzi).rp)spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ).yrl*8)w1ixpn k kmw) k nz:.zgi7pz if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mauwzehe(e(+e ,:/t,ctiqb( qv gnitude of z(,tq+ewvbq , ieehc/ ut(e(: 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 8p;qb i eidlmuoo). 3r8sh -r) 1.7;rsrb-o88i)deu 3ql ipo m)h.4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radqojgxtgbl lsapi( 14 n )l9+d.116gqaius 1.5 times that of Earth, but has the same mass. What is 11 t sqdno 4(9glllbqg)6 i1a+jgxp.athe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that o l-/;gq:s,dekdbz9vk f Earth, but the same radius. Whatvd/9 -sel:,;k gdzb kq is g near its surface?   

  Two objects attract each other g8a(+ :jgisj x-mwwv5o ravitationally 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 oy wr,aghr .lw/+oe .5df g , the acceleration of gravity, at (a) 3200 m r.,waoh gw5e +yldr./   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth.*cy zm g 6h*uln oisb5)j2s-x ph:0i1yhov:m’s center to a point outside the Earth where thegravitatix mbhosh) :s162 jlgh50c-vziyn pm.yiu*o :*onal 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 Sw epl5 corf.65un packed into a sphere aefr .5 wlc5o6pbout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like ourgxhy e wq;-1wgk8g :-q Sun but is now in the last stage of its evolution, is the size of our Moon b; qkg-ghwge 8y wx:1q-ut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whileho1bf29wbz7i+; r zwu7s l )+ ugi5.z aj0rfcs orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up thereif zgws) s0rhfb. i1ab;jw +z9c7urzo+u2l75 . 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 located at t:umxza6h*ux l-q-9 nlhe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other threel hzx :xa6m-u-q9*nl u.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mo r8z)th0i4js 5 4tbkifst 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, assuming all four planets are in a line (Fig. 5-38)ktft hi4irs5 0b8z)j 4. 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 atarcrv ) .2uay 6i/yoi4 the surface of Mars is 0.38 of what it is on Earth, andyary i/)4 6ocu.i2arv that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ea169bzmdj y/u7g)3b gc7ymxg (i. yom brth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examp63 c m ggx9byy71bjb ).uizmg mod(y/7le 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about hugg 2ozarp)q s576q*frlry47.sri18q bn l2the Earug1h7srqa.soll8br 2n i2 qr5qzf 4p7ry* g)6th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a s)97 vybfe7ru matellite into a circular orbit 650 km above the Earth. How fast muye vf9bm) u7r7st the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship 8uj(ku6n6w f3i- xx lmyszyu c8n5:*mrotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, ixuuj 6x5- f 8ucylksw*6(:8y nnmm z3and 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 alf uepx u*9d9; 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 youru; f*u9del 9xp result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be lau.b 7,3ad9tyjf.gxlnd nched from the top of Mt. Everest to be placed in a circular orbit around d 7f,btg n.j3xdya9l.the Earth?   

  During an Apollo lunar lwi9xem1,cn u /anding mission, the command module continued to orbit the Moon at an /1ncw ei,u9x maltitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thaz7,fr / lshlz6t orbit the planet. The inner radius of the ri /zfll7, zrh6sngs is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–90i2p zkra zw5, 7fawi,). What is the ratio of a pzawpwk7,i fa2 irz0,5erson’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 x3y3kx ;uqxm0astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) x03mqu ;ky3x xmoving 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 o hpcu4acuq l0,z1q9 vwclr,3)f two stars of equal mass. They are observed to be separated by 360 million km 1pqq )hlc3 ualu ,, r9w4zvc0cand 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 weightmz4r7x8wu*u e of a 55-kg woman in an elevator thatu4w mxuz8*7re 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 from the ceilifeqzl -72 oux4ng of an elevator. The cord can withstan -zfouq74lx2 ed a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very neavktjdx1 .ivb3e 5/nh 2xu-+ntr the surface of a planet with period T , the densi1. n xt5 2/utvj x-3nbeih+dvkty (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 pwr f:kgdf9p *)-p naq.dd:c -weriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Eawp dfdc :.-kdw * rg-f)anpq9:rth’s surface.    s

  The asteroid Icarus, though only a few hundred meters z vzj0zi: ,xuy5 :io7eacross, orbits the Sun like the planets. Its period is 410 d. What is its mean distance :yjzzx ,zi 0io:v5e7u from the Sun?    $\times 10^{11}$

  Neptune is an average distance of6+ln)9e+2 xse 37xlkahf ukjo 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-bt t2n93aj :/xwq gej 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 neareg9jnbeq 23wa:xtj t- /st 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 t iu (kpcc)*;dcenter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for t ; b25g.x dk*9mfbrx/po 1 rj2oma)jsche four largest moons of Jupiter (those discovered by Ga jg1xb rkmds.2o 25*9 xf)rcbo;pm/jalileo 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 o b dz9s4+yhxv9f the Earth from the known period and distance of the Moon. s+9y4bhz dxv 9   $\times 10^{24}$

  Determine the mean diq ldol,+z26+kn p2rur7pvx ldyjy 3 1+stance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tablezuy++ p2r+7 36 lxpd,1joknlryv 2qdl.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments1jtp:o ,nqq6hekeh71 d(x p v) (which some spacepto, hq6x(e1q e:j7 phn)v1 dk scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "lg -v5mctf.c8r-p1 gvro4 -zgplanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always nv-g p. g -5c8 r4ztlc-fmgrvo1oon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge b+d sk/3 (wyb dzzbm9sk w,-yw*y swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long. +swkw m/,b3db yz9sz (yw*kd-  

  How far above the Earth’s sz1*uknlp-c7r (aq)4v .p kp pxurface will the acceleration of gravity be half what it is on the 4uz(1p a*qvpknk.pr)-lcxp7 surface?    $\times 10^6$

  On an ice rink, two skaters fp5oy13bl0 p- dq 2z5z7qmprnof equal mass grab hands and spin in a mutual circle once every 2.5 s. If w7 nf30 yqo5r p-qpdzzlm 25p1be 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 acceleration of gravity at :+)v0g,nmukp g3sd sxkw) ;hzca 3f8w the equator is slightly less than it would be if the Earth nggk,p 3w8;cxmfs: 3sd)) a h0kvz u+wdidn’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 spacecraft traveli s yr .qcv- sy0e1yx3hg;(*ibeng directly from the Earth to the Moon esvbyiehx yecys(3g0q1.;r- * xperience zero 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(9w;lusz bob;c;u dc , a bathroom scale in an elevator, it sayb9uc,swd b;;olz;u ( cs 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 about itsjh*vfgbzr a0979kr x31t)2xoqacac2 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 the rotation speed rxa cabj9tfc 9q 7rg) x*20o1z3kah2v(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 o by7j rn9(7tvin 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 3hb3. r27 cfs2 ft(hqsj7qseqof a planet in terms of its radius r, the acceleratistb q.es(f 3c sqr3j77h2fqh2 on due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is x2tbf 7xbs,(;n)gu4z wamf4:prwgw6 deflected from the vertical by an a: xp7;()a,r utx4 bzwsnb gwf fw2m6g4ngle $\theta$ 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 )33km zjgk2ds m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavemd)k33z 2jmsk gent), at what range of speeds can a car safely handle the curve?

  How long would a day be id ey.-hm)jy ktyp+9s. f the Earth were rotating so fast that objects at the equa+.kjm ydyh te-)sy9.ptor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a o as xj .3:0az g,p5zw.vrd5psconstant 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 235 m. A lampj0f+fy;iw qxg:uf/f: suspended from the ceiling swings: q 0fff;g:/jxyf+w iu 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*r b qk+i6 irnsrp5v99 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 survive more than a few g 's. Calculate the number of g 's a person would experience at the equip s rb+9rkrqv5n9i*6ator 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 Telescos jm2k.7 (fjcqpv6s tare c/:,pe deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (fro2.j/p v e,msqfj ccark(:67t sm which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and 4y bk2d ye9p/hvalley 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 hh kdy/b9e2p y4eaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili5ia w +61 ihi*o33s2 rejvc.uebfq 86j xkeql;zes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals traf2 o.3h qv5;+i6u3ikib*e 61xjce qerswjl a 8nsmitted 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 Rendezvous (NEAR), after traveling 2.1 billionzs d0rw9p)rk8 km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rough8)rrz90sd pwkly 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 satellite4 d1cui4l+ywq in need of repair. You are in a circulw1yuiqc4 d4+lar orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a peqmp3 (ui+ofms (4p1;e-m geih6soq4a riod of 3000 years. (a) What is its mean distance from tm+qo1spfiqee4( ia4-g6 ou(;3h s p mmhe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuall;gw 1jd)*ectey "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiondw*j ece1 t)g;s, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkyb)n7tkj2q)hb 5v/,v;i/ q-fadaiqwg Way Galaxy (Fig. 5-46) at a distance of about 30,000 lighdj2b7)5q , -vh /anq b igwkiqv;/aft)t-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 eacgkq )/qtz5 4fy,vwze 9h side. Find the magnitude and direction of the gravitatitq, 49zq yw5vfkg/ez)onal 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 Eart* rfblb1p:nb2r pn5 /th $ \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-cml) i dmn:3( cn53kljxlxu+9ol7m fr/j -long sweep second hand on youn/xlcux+i) ljll9rdnm :k 3m j(5of37r wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and startbb1fu1y xu24 t to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a compl btxf14by1uu 2ete 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 radius R in a new highw- +5rflk-z wser:,vb 6gv7h(m oumqh9r2le;way is designed so that a car traveling at spee;6grlf-:k rz emhr v w,-7(5lsvhqueo m 9w2+bd $ 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 Axyu0 2tq.)xzjr aj:8 icela, utilizes tilt of the cars when negotiating curves. The angl):jqi0 x z8tuyxa. rj2e of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is 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.$\approx$    $\times 10^2$