Sometimes people say that water is removed from clothes in a spin dryer by0:tjr6,nr38qel f z qg(rq2wi centrifugal force throwz0eqtl ngq(6i382 wr:rj,r qfing the water outward. What is wrong with this statement?

Will the acceleration of a car be thyzrta9p:hr 40 2lj-f me same when the car travels around a sharp curve at a constant 60 rf a2pm rz0:y-4 htl9jkm/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constaf6rxq26dfpu 1nt speed 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 near the bottom o frf6p216qxduf a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rmv m0gq+v cqk2b/hel jxn314:if*7ug ound. Which of these forces provides the centrip*mnu0 emqvg3 /j724xv kf+l h g1i:qcbetal acceleration of the child?

A bucket of water can1 v5kep7y0ukw be whirled in a vertical circle without the water spilling out, even at the top of the u1 k0wkpv57yecircle when the bucket is upside down. Explain.

How many “accelerator*9:qcaj/ ikht8mmdr ny- l;q1s” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acc iaj: 9mr1 h8qq-*ydlctmk;/n elerations do they produce?

A child on a sled comes flying over the crest of a small hnr)-gg9 qy.mdill, as shown in Fig. 5–31. His sled does not leave the d9 ). ynrmgq-gground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speed?8a 8(1 5tjoq67vboocqv (iwob/z,x wn q9/whe

Why do airplanes bank when they turn? How would you compute the banking w ;8wray5mu w-angle given its speed and radiu ry8 mww;-wa5us of the turn?

A girl is whirling a ball on a string around her head in a horhl1v773c gg(dw q iy+tqh ,j8iizontal plane. She wants 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 oh8c+w dih 1y3, qg7itlv7jqg(f the string?

Does an apple exert a gr4o/7ganj ajp9pv)l j2avitational force on the Earth? If so, how large a force? Cons7vg jol4 j9ppa2n)a/jider 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 orbitqn4eeonwz a o7.5(4 iv be differeoew.anei4z7nq(5 o 4v nt?

Which pulls harder gravitatio)4v:d-t1xxski(t m a5o;tne mnally, the Earth on the Moon, or the Moon on the Earth? Which acceleratestm:k sadte vt 1)(54xim -nox; more?

The Sun's gravitational pull on the Earth is 4u ) t2ssc.xiiq7k0og rrm:-xmuch larger than the Moon's. Yet the Moon's is mainl.2smr4s:7qt x0r)ik iu -o cxgy responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh3fl x681zzq(0umej x ln )qu.u more at the equator or at the poles? What two effects are at work? Do they oppose eacn1zxm ujq3.)fluelz086ux( qh other?

The gravitational force on the Moon due to the Earth is odjs.vm 1r 1o4bw;t fk:nly about half the force on the Moond. wovmkt4b; s :1j1fr due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger n odf9j 9cgb)dx1j96dor smaller than td9g)c o99xn dj6jfb d1he centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the n/k , hp vp)xukt762tmeast or (b) toward the west2xn, hptmu7kk6t pv/)? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measuredk haxb0kpr8 qhiyki ,*111 xp6i6; pzg by a scale in a movingbxap6i6qg *r x iihkk;18p0,zkhy1p1 elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when 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 by :er3h j8es5tc lb8r0s weightlessness. One way to simulate gravity is to sha th 8l:0re 3sjercb8s5pe 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” or “appare g/yl9v)rc+7yjn0poxnt weightlessness” between steox+ p 0cnvr/yyg79l)jps.

The Earth moves faster in its orbit around the Sun in January than rz.qqoojya1 i (o +:l3zyk,)wkefac 2x h/.5lin 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 seaz/lo5(kif a3q:qy+o l,y )zcro w1e .j2ahx.ksons — 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)acezc0*dwxfeo9, x* moon. Explain how thisowecz0e9ax),*c fx *d discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mucgh4vyrln112w:zeyy/6m/lj i wg 4w 3ch 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 Eartljw4i n c3v:1r w4/ygyz w26/he1glmyh 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 19dqji18c +gnt 880 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratio;v5d62z5o1nbhja8 qd-qrb noypgh +8n of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Eahaz6d;+88ry- g5bqno j hq2ondbpv51 rth'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 exerte+* c ex.gkj4gad on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) oxga *+e c.kj4gf radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and y2e on.lf,u6j circles the Earth about once every 90 minutes. Find the centripetae,. uofy26lnjl 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 clay on the edge m5i;4c ud s1veof a potter’s wheel turning at 45 rp;d 1sc eivum45m (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolveo-z m 8pc2d;ccd at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is zm 8ccod-c;2 p4.00 $\mathrm{~m} / \mathrm{s}$ 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 radius 7436amekjg+2cj h ing77 m on a flat road if the coefficient of statimc4ena6+3ijg 7g2 kjhc friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the c kzhk 7v66i58f *uuptffh)m3voefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 muzpt6 f3) 7mfvu6i5h8*khk fv at a speed of 95km/h ?   

  A device for training astrx3 p,oc ,ffra a9v6rx-onauts and jet fighter pilots is designed to rotate a trainee in a horizon- faxv6af o9,rcpr3,xtal 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 -hol,gx fn.l3+vr pj* of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficienv.lo rgp+-n,l*x3fhj t of static friction between the coin and the turntable?   

  At what minimum speed must a roller coa/,8 nryu ;2nfoiydq:r ster be traveling when upside down at the top yroinr8 uqfnyd2,/ ; :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 m:/ t* ovmkr :mjtzth/2ass 950 kg (including the driver) crosses the rounded top 2r*kttm:/jz/o h mv :tof 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+ez7 8p v1+j0lfxo, fdkwy7vl per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at twf p70l1 8xlz++vo7fv jk,ydehe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.108q 37ww+y y wc;,pplp3vk2q(mw x.dyz m. At the lo;3m lwy ppyp8,ww.c+x (yv7dwq2 qkz3west point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a)ucnh +6ci06ye- yk mn centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,00n6y6ykuh)i +c-e0c mn 0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotyn:ueas yq6a3.b-,y9n x4t i hated in a cylindrically walled "room." (See Fig. yie4 qtnh3a6.9nya ,-s :bxuy5-35.)
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 tl/ eb x /ho3zl,+pfr7rotated in a circle on a frictionless air-hockey tabletop, al37/f,ltrbezh+ op x/nd is held in this orbit by a light cord connected to 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 weig;lyzw xkj83 o4ht of the ball which revolves on a string 0.600 m 38;ywj4zo kxllong. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for hn/gqq k oep*),9l) ulwknc/: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 massesnm9j 8t n(q0buy8zdo0wg tkpq4 f+-d( $ 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 div3 t567d skhym,m)afrk ing vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exere6f;prfx* i9ahe oa f* ga,*(wted on the car (by the ground) in Example 5-8 when its spe* p ;faeriwe ,hx9 gof*aaf6*(ed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniform5n hcu , (u.eg tnm9x5m/u/dkhbr*7+cxpt9 b yly 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 stau/nu9 ,/h9rpbh7 dbx.m(ne*kcm 5gc+ ytt u 5xtic friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pa3b kh18)69gtih rxw) oexr0sf rticular instant, its acceleratio x)6bfogtek0sh1i h)rrx839wn 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 Eartv5h)k 6qjvz 57bopwx3 h’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. 7)hvo wbjvpz 53k q65x  

  At the surface of a certa e*qqy7jh:l eqx6m rp 8lt.zz(v(6n ,rin planet, the gravitational acceleration g has a magni:m txynvqjel(.rz 7l8( 6 *e, pqhzqr6tude of 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 satne07kx:c3)6bfki s 9vhu4 Moon. The Moon's radius is 1.7k7bxcuv)h:0 sste6nfi4 k93a4 $\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 cwhp 8-l czq,3that of Earth, but has the same mass. What is the acceleration due to gravity near its s, wz-3 q8lchpcurface?   

  A hypothetical planet has a mass 1.6x sujk cc-p9gy/c: a0/6 times that of Earth, but the same radius. What is sc g0aj- uxc kc9p://yg near its surface?   

  Two objects attract each other gravitc0k di(kze: y- n+3vrtationally 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 v ntcdr9v7 57viogjy**wva*p- w:4qixalue of g , the acceleration of gravity, at (a) 3200 m7 - *4p*:9g jr yqotd5vcw7wivnai*vx    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsidgq5,4d2hm*tsrn2hy,n(va;6k h gf rfe the Earth where thegravitational acceleration due to the ;gf64h tf*2,a h dnskrn2y(m,q rvg5hEarth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spheret1z0jfp c1, 9,cvhizl about 10 km in radius. Estimate the surface gravity9z vjpzcihl10,,fct 1 on this monster.    $\times10^12$

  A typical white-dwarf star, which once was af:4 s g8ppm-b csig64jn average star like our Sun but is now in the last stage of its evolution, is4 psg bc8fpm6js-:4ig 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 weightleyu/d isw(5v3z3vj n zv .6csw.ss while orbiting 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 vy/zzc35 v .jwus36wn(s id.vkm above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres imrxxp6 +c )j.are located at the 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 threepx)mjr 6x.ic+ .   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the S g+be/,xr0hnd0v*i f bun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in ,g+h0dnbxb i e/ rf0v*a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the sut-hqhcbec 31c4df yj7qoh/ ,6rface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Marsqdet1 fjh7h3 -6coc/cyq,hb4 .    $\times 10^{23}$

  Determine the mass of the Sun using the kno /1mtt,4qi muo o3wka/wn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 3o4uo/w,kt1 mm qt/a i5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite15w9cj;v7ck lhm8 4 q,wzpsg j 8ozv9f moving in a stable circular orbit about the Earth at a height of 3600f,q8cvzw5jhpwcsv4 g9 kzj 79lo;8 m 1 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ea) x1vi rayl i-4r+tzc)rth. How fast must the shuttle be moving (relative to Earth) )cv4xltzi)r yi +r1-awhen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants lcoxq: c59n 4 k8oiu3xare to experience simulated gravity of 0.60 g? Assu8l 4o3: k xnquixcc59ome the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the lnb 5hdf l uixlkkx:l;7s +-3-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 onul:ld5b-x lk 3kl-ih; sxn+7f the mass of the satellite?    s ~    min

  At what horizontal velocity would a satelw l 733ff qmhcjvf p(3(76gvuulite have to be launched from the top of Mt. Everest to be p(f gv(u77 vf 3qfwp336 lumchjlaced in a circular orbit around the Earth?   

  During an Apollo lunz:6;ed 1kj wapobxgvqv7m3x /e7g5b0ar landing mission, the command module continued to orbit the Moon x1 7edkoj 0:6e 3bx57mq/wvzapbgg ;vat an altitude 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 iceqw,6*,-f4h tsmp gohu* mdse5 that orbit the planet. The innermspo65uhfgsmw,-h t *dq* ,4e 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 15.5rhc)wm:ho5)p tn813q 9f h2 p yx,gnch s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real :8yqwht95mf) )cnh 3 hppgho2r1, cnxweight (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 of s 3q 8w2,zyc dh7kqvi0nj-+xithe Earth's Moon qc+x iq3 8ihw0d2- vyn,j7szkin a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star satak ;tql w/2foz,2 o er0zl;9ystem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to le20atzaf ,oq/klo;zt ;w 92rorbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-2 vkf2wlg+wmo1s kmrg3, s/h0kg woman in an elevator that movem1/ o vmr2 wlw2+s,s3kg0gkh fs
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elg:o;nu+n, jr p7bo icaxw7h)2evator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (m)hr:n 2,7b7+na oi ;pw xgujocagnitude and direction)? a =   

Show that if a satellite orbits very nev7)8-qnr 0s icc bi7rvar the surface of a planet with period T , the density (mass/volume) o)bic8- rv077svc ni rqf 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 perieo5g j+gv* svoy ah0:a+2xq r.od of an artificial sate.*gv+ra2y5o q+ gsx avjh0:e ollite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hund ( 8i )ejljkl9-sj av*m(ft+)uukun0 gred meters across, orbits the Sun like the planets. Its period is 410 d. What is its m)l aj+-( ) u9tlmejs8gki*nuvjfu0(kean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 7.+tri+9ptlp3) yk b ebsj,rq4.5 $\times 10^{9} \mathrm{~km}$ 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 evez*yg mg 1a5b,wry 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it z m* gawg15by,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 t )pslprsm8;vls-/ k z/ s5n2rthe 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 f+e:pw;lr(r y distance for the four largest moons of Jupiter (those d( y:p;lwr+rfeiscovered 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 o;jkfsfv/u o9+5 -kfwEarth from the known period and distance of the Moon. kf u;w-95+/fo k jovfs   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiteqg28ym bttu*(/ j(;b l pxh7f6rdpjj- r’s moons, using Kepler’s third law. Use the distance of Ipbp;(d2tl8 *-jf(h6yx7tm bju/q jrgo 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 tdnnx*vurgw;3o 40a ( Jupiter consists of many fragments (which some space scientists think came from a plann o *(vw n;0ud34rxagtet 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 thee6i q**ki+bg/9y xmdi form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), xdm yq*ie/b6g+*i i k9and 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 croswai z1i*a,fre(*t3 pls a gorge by 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, whawli,zetpi1(r*f*a 3 at is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravit5so h; g6/v(/c,l+qiavoi +ox fcqiu5 3xqk5 ly be half what it (qighc+vfl;oxqqc5/osuo l +/ 3va65, xik i5 is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutu:gryt -0,i:in*xgvcb al circle once every 2.5 s. If we assume their arms are each 0.80 m longy- cr0,*x it g::vginb 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 accel k8,gm/xidq4x eration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g isd8mq xx k,g4/i this?    $\times 10^{-1}$

  At what distance from the Ei th nb z(s9- 7;,i,i bcrejegp(4pag.arth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposit9 eji hpzg-t,e ;rs.ip,(nb4 ac( gib7e forces?    $\times 10^8$

  You know your mass is 65 kg, but wh+/szuj5d. p kmen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directjs/d5.um+ kzpion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro yhqxx,m93 qlh.i.y )ctate about its center (like a tubular bicycle tire) (Fig. 5–42). The ciq)xilh3my9cx .yq. h,rcle formed by the 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 aircraft in a v0e s;fy 5gl*m;zj8q+/t:m ;xh9dyndn 9a zbhkertical 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 avnan *fb8r*7 planet in terms of its radius r, the acceleration due to grar bn7*nfv8* aavity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vers;n.hqaiu53z u +qx c9 j3)qestical by an ans)ne 9;qquuhsci3az+.3j5q x gle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficie1eutc8aw/ 2lk1p mqvay9:l4t nt of staticl4p2t1caa9lu8 q/mk1 wvyt :e friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the e5vt 3vz* 7 :/yxuqrkzvquator were apparently weightlvtqrz*x: uy5 3k/v7vz ess?    $\times 10^3$s

  Two equal-mass stars maintain8moz-)t2hvh z 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 qm-bo ymp urc+;f/rxb8f+5(yupbj. f;nm.q 7rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to afqf7;f5 nu+8 b;pp c/-mob yr+(qu..mj ybr xmn angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 time96egy3 slw1wt(rbhl.s as massive 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 survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jgerht( 1l 9 wsw3l.6byupiter: 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 presencefn c3ofm2gs :be z:vn71)no*a of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core tf3m bzcn*17a 2s:ov :ng )foneo 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 valley sho 0r)z5g05 uhp5vo iowrwn in Fig. 5–4g po5)or50vwh r05iuz 5. 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 without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelnvu m/lse +6)alites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine )evl+6n/saumthe speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), aftepn ptv3fr480rr traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km r0vp84nt3r fp. 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 cjb ...xs+uyg;/.vq- u,kp,pw bsy eyin the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behip+veusqb,gj. -scy.,.yw u kxp;y.b/nd 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 mea)x-rmt -kz* kgn distance from the Su kmg)-z*xktr- n?   
(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 youw+0htt-fux(-ig qjg :fqz h03 could actually "feel" yourself gravitationally attracted to someone near you. Make reasotxh fz0j :qifu-w0htg-g 3 +q(nable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (F0tm4zz zjd n. isiy8)9ig. 5-46) at a distance ofi0ysj 8mnd9).zt zzi4 about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side. Fwfdq fky* s r/b/ -e we0um,5xys/4s.wind the magnitude and direction of the gravitational force on a fex5 sm /ywf0e*sf, .w4wu//k-dyq brsifth 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 orb h7hjdacjsq 7+ v5fa+1its 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 the tip of the 1.5-cm/yl gpn: . r6 xm9erpx.;es1eb-long sweep second hand on your wrix9; p:l/m1xp6 serb..ryneegst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing 8uq-qd c;g0/x2fsi kg 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 fis s ;cduxqi28g-q k/gf0hing 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 cau-g 6: ag.niozr traveling at spee-u n.go:a6z igd $ 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 tig4ktx3 kod-k:lo dq(*lt of the cars when negotiating curves. The angle of tilt is adjusted so thatdd oxqk- (kokg*3t4:l 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.$\approx$    $\times 10^2$