Sometimes people say that water is removed fr8 vqsfl2mi/k :96g gpgom clothes in a spin dryer by centrifugal force throwing the water outward. What iv8/:gg 6 2glsmqk9 ifps wrong with this statement?

Will the acceleration oqt d8cas4 xqe,69q;p df k5tj5f a car be the same when the car travels around a sharp curve at a constant 60 kme cxj8 qqta4 d,p 655qsf;9dtk/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. u j0;1 /m (teda-fztbzl3t4pl Where does the car exert the greatest and least forces on the road: (a) at the tflzt01;e dmpaz(utb4tj l /3- op 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 au 2r6o;v-jlr2amryj,l-o :rq child riding a horse on a merry-go-round. Which of these forces provides the centripetal a- qa l2lj ;o ro,2urm6:jrr-vycceleration of the child?

A bucket of water can be whirledg:8j3 ud2+p adc05gjr-ddak n4 n+pwe in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Exrd dn8k + g5-pj:0cj+ ap4ne3dgd uaw2plain.

How many “accelerators” do you have in your car? There are at least threc tv+db.z *su1e controls in the car which can be used to cause thc 1z+tv*u. bdse car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smallh6vuh:i cs+ rv0kn 1q7.j o9dz hill, as shown in Fig. 5–31. His sled does not leave the g.kch6r09vshj q:dzvn 1u+7oiround (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 whi * hjo,hp9q9( my,lkhen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angleti2d6 9v0 un6 tmdkbj2 givebtj kdtm i6n20uv26 9dn its speed and radius of the turn?

A girl is whirling a ball on a string ;l(8d;)iz +48lgieaojd(; qcc z1nqkm sjs t4around 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 side of sqit ;4s l(oz mle;)4j1a gzj (dc8 +kn;8qcidthe yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large0rauh w/vy. 8y a force? a0y8h /wyrvu. Consider 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 orb*bqvm5cut6 .dit be different6vd*q 5mutc.b?

Which pulls harder gravitationalwm3g:sr esf+ obji3w:hc+;3 nly, the Earth on the Moon, or the Moon on the Earth? Which acceleratesrfnhs w +bc m33 g3:iwjoe:+;s more?

The Sun's gravitational pull on the Earth is much larger than the Mou+ q.p(b btao-w8x0r don's. Yet the Moon's is mainly responsible for the tides. Explain. [Hintbwo+(-q xp0 8.rdau tb: 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 o/qz0(fqxrf 1xb )tv 9two effects are at wo1q0(ftz ox)/rb x9qv frk? Do they oppose each other?

The gravitational force 4+ln4) . tnetxm4bogn on the Moon due to the Earth is only about half the force on the Moon due to the Sx4ot. etmnbln)4g4+ n un. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger oitr p / q5vt7al 1em388 )-fqslu;vzyxr smaller than the centripetal acceleration of the Earth8tl y831zaxu e7mq)q; -l5fs pit/vvr ?

Would it require less speed toxw n(-rba+*q jfi l2t3 launch a satellite (a) toward the east or (b) toward the west? Consider the Elrbx (3a+jifwt2-nq *arth’s rotation direction.

When will your apparent weight be the gryr+:l jxvm x40 m5f0oi /ud52xf)rkr:gmaee7eatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates 0re: 2mielm7x)/: 5fvkygar05d jxu4mfxro+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 spendjumnlg):aubu*n )z( : long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spacemu:au*ng)zl n( ubj:)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 c3 wtmwrjg/ft f24-8d3uga fni k/*5j“apparent weightlessness” between steps*f8cgr2j/j gt k/ndi f-uw33t4fwm5a.

The Earth moves faster in its orbit around the Sun in January th3;i(jo;f 3errj.d lmfan in July. Is the Earth closer to the Sun in January, or indlr. orfejf m;(j3 3;i July? Explain. [Note: This is 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 ut u0ni+f4l:v9z dc mfll. **buntil it was discovered to have a moon. Explain how this discovery enabled an estimatl* * nm:zul0 fuic4dfbtv .+l9e of Pluto’s mass.

  The Sun's gravitatio qq-9b*fe-s lmnal pull on 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 other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed -sq b9ef*l-mqof 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 travelin/ sma c3/ *vo q:t gxxy+vzxn:3mzd6l0g 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 Ear )sc3kk/7hazi th in its orbit around the Sun, and h3)k zi7ac/ksthe 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 exom ,u xqc9g:0 uf;jwcjxju mt-3l2;f3erted on a 2.0-kg discus as it rotates uniformly in a horizonl0oxg2mc:u 9,j;w3-umuqt j;f 3fxj c tal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from t37+b aa jytz 6qx:iu,y*spxx*he Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of qxab* ai+yx* tz67upx,s 3:y jthe 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 clay on the edge of7x6 yj2ymwok1.ad,z1,r bc/i v+kgku a potter’s wheel turning at.61vdy7 /i c2,o 1u+b,wxkmj yrkkgza 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertica66sq0pecr *3 eenw; r:9sbks kl circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed 0 epc:eeskk*b;9qr s6n w6r3sis 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 wi s;h( g;cuzqwmq79lr7th 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 of t7shmq;qg 7;(9c zrlwu he mass of the car?   

  How large must the coefficient of static friction be betwar-1 cf6-b)bw7fid vb 7 drew/eg0 ct4een the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h0v baw/r-6 wig )d7fe4bt7drf eb 1-cc ?   

  A device for training astronauts and jet figrp-bs 1ixo:3*j4y - ti:u jxqgiyy /w.hter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force :y-qt 3- igjy/ruxso4 jpi:*i.1 yxbw 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 th3 amdti c (fu7wo;+(nie axis of a rotating turntable of variable speed. When the speed of the turw( o amt7+;iuci(f3ndntable 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 the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must ,b 7r;z9uzbnw1/m)nm dm )v+jptz:tn a roller coaster be traveling when upside down at thet+b9v1 :t/u)m 7z)nnrwjn zm d ,p;mbz top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosseoz j8 e7wtqe 0/t*x/p+km.obns the rounded top of a hill (radius =95 7mbetw0ezo 8o nx .*/kj+pqt/$ \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 nee n,-1jk w(bosw6abm: qvyz9h9d to make for the passengers to feel “weightless” :basv96o (wqh 9wm1- zbkn,jyat the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius;e o zijb6+v t+ y:/uhedkfk.8 1.10 m. At the lowest point of its motion the tension in the ropv;b .k dt8 o+jihufe+ z:yke6/e 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 rotat nch bu:p4d94ke if a particle 9.00 cm from the axis of rotation is to experience an acceleratip4d:uhk4bc n9 on of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated7ngxt jf.3p* t in a cylindrically walled "root3p x. tn7g*jfm." (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 on a frictionless air-hockey tak. d.y;kjgj0 dbletop, and is held in this orbit by a light cord connected to a dangling bloj;ddjg0 . y.kkck (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 weightfb5 / .rwv58xcuarcpupsp-. 7 of the ball which revolves on a string 0.600 m l/ f-5.wvp.uxc ba5ur8pp rsc7ong. 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 perfectlyp,rpzq/i -pb3 f*7g ev 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 l3g sihi2yft6c6cg 7*$ 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 maneuve lm s2nst1(hm m*kfd.)r by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centrinw,je ( +f ;f,*ko 8idmpjz+vtxqp1 +qpetal components of the net force exerted on the car (by p(;fe+8+ kqw,q ixvto z jn+md*f1pj,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 accelerhb.7lr3.t j cne wp:aiy* )p,dates uniformly from the pit area, going from rest to 320km/h in a semicircular arc wip)7t*p w lejrb.: aih3cy .dn,th 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 radiusbdsgq 5,e,2 yb 2.90 m . At a particular instant, its acceleration is eg, qs52bydb ,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(m u1llj)(yc8 b nyx(5n7srt s km (2 Earth radii) above the Earth’s surface if its txuyb)1 sy m7s( (r(cln j8nl5mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mwfz0ixz,yy9 gdn;8* jul)+ ai agnitude of 1n*,yix8azd y+0ufl; w z)jg9i2 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 on6gz4-xpkd/ wh the Moon. The Moon's radius is 1.746xdkg4hpz w/- $\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 ofsek-d m l/1rriuezc5/yh0,r0 Earth, but has the same mass. What isy/ezd/h50 ,0rl rieu1- csrmk the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eartpleix**4 + ovrh, but the same radius. What is g near its sur**olxi e4 +vprface?   

  Two objects attract each other graviq6*unp pbs7tgycg v9x9 3 7tc n a8qo-mlla;)-tationally 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, at (a) vqj m)h4znxhh9; 9 f5y3200 m; f99jnyv)5mh4 zh hqx    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whlw.r1z tfnwf8b3aq.g,x( m-ut(5rw a ere thegravitational a3q(gf.a br.( wanzrt u15m,wt -wxlf8 cceleration 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 suo*06zh-ip- s0 hpjo)oyj/oSun packed into a sphere about 10 km -p *u zoh6 0jysoph-isj0/ )ooin radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once +5 u6hjn/wvxju;bvm7was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfax/jhbu;7uj+ n vwvm56 ce gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spacems2y-bys0md i90r3l z 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 sur3 b0rz0i-syy msd29 lmface in terms of g.   

  Four 9.5-kg spheres are log+7l:rvaa wvsq ;2kx5j:qy v4 cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravik;vjr7 5a lsqv4x::2qvyga w+tational 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 on the same side /ynw 80ec n,4 -:cid(s zrjkovof the Sun. Calculate the total force on the Earth due ton n(4d ve z,sk0-ji/c wyor:c8 Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of graviiib0*gp(fhmaj mt o)n03z4i + ch,an 8ty at the surface of Mars is 0.38 of what it is on Earth, and th0bh*i(tnajon4c0gm )+ ,aizm 83 pfh iat 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 dbk :j.l-* mudof the Earth and its distance from the Sun. [Note: Compare your answer to ul jd.*mkbd-:that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a y +sf7b +ymaw9satellite moving in a stable circular orbit about the Eaybwa+m9 f7 s+yrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a saybtnmb .9tewui 5* .:vtellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) wuv*.bi mbtet:5y9w n .hen the release occurs?    $\times 10^3$

  At what rate must a cylindri/x8b t2alc)zn,tz5h dcal spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and giv,8/ l5txzh badn2) ctze your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbiti epyz7off5( pn1,9ec the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of thezofp1,p9ef(ec y57in satellite?    s ~    min

  At what horizontal velocity would a satellite have tooi, z:e kt;a4a be launched from the top of Mt. Everesoea,;k 4: ztiat to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missio8u /k/2x5dq+hmw m*pdfpuv h+n, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go aro f/mwpqmu/ukd xh+8d+* h52vp und the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inn*d8 q/lo; :7uexzi kdde:;oz*eu7dd i/kld8 qxr radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s t,7zo *i m1uejdvf 8l:(see Fig. 5–9). What is the ratio of ji8of1 eum:v*zd,7t la person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center6)4v.fkneh afzl mi4 4d z,c,2 fhv(wu of the Earth's Moon in a space vehicle (a)f4c)le nah62dk, v.z wuimv, 44 ffzh( 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 massg7zwe/0v cs8e- i+xg eup(8jz. They are observed to be separated by 360 million km and take 5.7 Earth years to 7ep(s0xwzg+ evce8 /u g8z i-jorbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read forsr9dip( qau3+) ncdw2 the weight of a 55-kg woman in an elevator that msd2d)3nuiq(+p w9a r coves
(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 f) bclof(;boe- j4yar :rom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Whabfjbo4eya:(; c-l) ort was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with perivab1 mofu j*,w+ v w(suhqu8p5cl1-*qod T , the density (mass/qwvulu-ca bop 1 f ,*1hs8juw(qv5*+mvolume) 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 determine the peripd88 u gv.g+si;wl m1nod of an artificial satellite orbili+m;8sggvn1 uw d .8pting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik: .fdabxm, ef;..i oine the planets. Iieaom,fxn.if. : .b;d ts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.h1yqwun/; 0ri w is) r2yj1gpl.0y+wi 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 comes very ca87e .cji m;fylose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nea e7 ;8yca.mfijrest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centeg*z wty0j1 :fhr 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 masx*m gbsyfa5ento* o9st-i fb 9.ad,0,s, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 160t e.9o *b n-bsoyms, iaf*axfdgt,5909).
(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 thea5b kpuf +))*/4 uu6 fkgtcpwh Moon. h+tu6)fc/kg4)uwpf k* bau5p   $\times 10^{24}$

  Determine the mean distance from Jupiter for zrd+hij,k .hdyi 64 9geach of Jupiter’s moons, using Kepler’s third law. 9hj gz. r,kdh+ii 4dy6Use the distance of Io and the periods 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 consists ofqjzlx;,* kvigh, wjv uf6/6occ1ff .( many fragments (which some space scientists think came from a planet that once orbited the Sun but was , i;/lc(gwqv6f jzffkuhv6*xoj., c1destroyed).
(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" iqdjsliu+;*r( tx4 bw1r*7 ie-wk m8 svn the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the dkx vt4dm;sb1-uwrlw*7 8iq*(r+ iejsistance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging ini05pja)h0)ue2.8 wge rj res f 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 pr)sg.ej8uf 0 jrw 0ea 52he)ipoint 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 accel1 f x:q.fvtyq0,q1 dvferation of gravity be half what it is on the f,q.ft0qf1:v dxq1vy surface?    $\times 10^6$

  On an ice rink, two sjw.ps+ ih luhmef/-o*f b x522katers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and 2* x 5beh/.+fsmlu2i fhw-pjotheir individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once )ypt +t5p1dl)o2xtkvper day, the apparent acceleration of gravity at the equator is slightly less than it y+kp 5ol tdt)ptv 1x)2would 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 wt9gd(hpbg0 5:d1 k ildill a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal k1p:d 9g lh bdtgdi(50and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in9v1mpg 71ci ke an elevator, it says your mass is 82 k7 gmk1c91 viepg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulab :su4h.k jvjn8s:go-r 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 the rotation speed (revolutions phjngk8o: vs. sj:4-buer day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–l5j.0326f qqywg7n1zwiqc gh 43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms ofg9sj,m x 33mu7pcritqjc19m -;c zbg ) its radius r, the acceleration duebgz-j3i9p1 xg 9j ct,cmq7m ;c)3ursm to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve ,x-7y6msx xhgzrub j8jy(t -)rtical by anhx, 78z-m 6r tys)x bygu(j-jx 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 speed of Iyx0v2- ij: iblf the coefficient of static friction is 0.30 (wet pavement xb l:yv2i-ij0), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that9 scmu sf+61fs objects at the equator were apparently weigh1s mf9fs+ u6cstless?    $\times 10^3$s

  Two equal-mass starsa 7cf.dw.v x0k maintain 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 constant speed rounds a curve of /bou1s,fka.n) r e3vpradius 235 m. A lamp suspended from the ceiling swings out to an angle of 1sn,b f v)u1ope. a3kr/7.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed s-e/ rgah vb-:that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive sravh-- g be:/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 Hubbl8nn2bbj/3 doje Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87,bd8nn o 3/bj2j so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant ;-w,u.co 8ifn wavu;d 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 withoi onduw;, a;fv-uw8.cut losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili6wid80q2g3 bbkh5htfg j6/py zes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in 2wgt60 p86hj dbi gy hf3/qb5keach 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 vx 13rb; 3z,zvtt.8yb 71xfrddos2rh(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Ero32 ,31fdzr1xbbt rv .xysrzovhd87 t;s 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 tj0;x xot davzc7i7 b5y)fk57 satellite in need of repair. You are in a circular orbit of the same radius as the satellit77)fay xt5o5b vi0x;7z dcj kte (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 pe6f g, id87ssmn1 dszw7riod of 3000 years. (a) What is its mean distance from the szs gmsd1f8 77w ni6d,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 x)p qfb-4j6 oiof G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reafp q)i4xjbo-6 sonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a d/x tst0qt1us* y*1wt eistance of about 30,000 lig1yuqt *x*w1e0s/ts tt ht-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 (ii1ov8 rr aym7sb)6/ekxu;l7+qnkxsquare 0.50 m on each side. Find the magnitude and direction of the graviti8 m ey;xn7)as+/k(l 6 rvuki71xrqobational 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 a tg( kcn w8bx607s;9 u+sscdmkg orbits 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 experiencedis4.7j8rk9k l bcfa:m4 it /hsk.z0kc by the tip of the 1.5-cm-long sweep second handlf/ks.cbakz ik4k8 74tjc 0.is:r m9h on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start :v0bkni+zz+q to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a cqv+niz 0b:+zkomplete 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 i +2y.iirl wce2n a new highway is designed so that a car traveling at wie2l.2 cr+y ispeed $ 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 hdv ew3 .m 4l k-.ibptb-gwdx0if7m0 3cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centrip7bmd - bf-p xkvil.degt.h0wi0m4w33etal 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.$\approx$    $\times 10^2$