Sometimes people say that w-n06zxiq+*j 3jwwti fater is removed from clothes in a spin dryer by centrifugal forcew* jw0 -nzjf3i+6qxt i throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the q3u cb2w kk6 :.ff)df6)wdcfhcar travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the 6d wq.cff f6bhf)kd:u2)w 3cksame speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whelzh:,zystjg whrz*w i-t782 s,/ +xfw re 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 th8stxg,+ ww l iz,w /-sh7hzt*: jz2yfre bottom of a hill?

Describe all the forces acting ogav;o +l58i,k ,jlzr/jt r,mdn a child riding a horse on a merry-go-round. Which 8 r5jld,rtjoki g; a+l ,,/mzvof these forces provides the centripetal acceleration of the child?

A bucket of water can be whuxb(qv3d+ vn *7fgn4m rxgd 9)irled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. vgqvuf4gmn 9( +d)r7*3xxbd n Explain.

How many “accelerators” do you have in your cam0qvg( (ncytls- lnou:2g5k5 r? There are at least three controls in the car which can be used to cause the car to accelers tm5 lu nv k(qg-(n2:ogyl5c0ate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest o g 8vka*53gj4 vkavm0wc rw6ukjy027xf a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), bu 7jw2 vaa rck0y6g*4k0jxgkv835wvum t 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 leanzjlijj. js3 7d;+0doy inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking amtnhdjw4h54qxn2/ ,g aakx8 3 pc.o i7ngle givd47.anw 82xotpix/ m4 gh3 caqj 5,knhen its speed and radius of the turn?

A girl is whirling a ball o(p,1+vt d dnkbn 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 thb(+dpvd1,kt n e other side of the yard. When should she let go of the string?

Does an apple exert a gravitationa sd/ b*m)u jenn/3;uijl force on the Earth? If so, how large a force?i; s3/n)jdujem*/b nu Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whanvdjx6,ukpf4 )l 8 g+ot ways would the Moon’s orbit be di4 p8ofvdx6,gnj+lku) fferent?

Which pulls harder gravitationally, the Earth on h.gw 9,irg( mythe Moon, or the Moon on the Earth? Which accelewg mi .gh(yr9,rates more?

The Sun's gravitational pull on th6vazy v 4th lch:+6jv 3uld -3,mm9lgge Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenmtc-y4vh v3lz+vlgh,galjmd:63 6u9ce in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at thexf,f uu. mi7ck zpau-1 1w8qn* equator or at the poles? What two effects are at work? Do they oppose eachfwuiua.k1x1 pu 7c-8, qf*nzm other?

The gravitational force on the Moon due to the Earth is only about half thew5-lf mxa-) tm force on 5)fmx-ml- awtthe Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accele 4*xc6wa eswix 9gj88cration of Mars in its orbit around the Sun larger or smaller than the centripeta *g8 iw w6e48cs9jcxxal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east ow4fdq20hlqd zu* s 4d0r (b) toward the west? Consider the Earth’s rotation direction.q2sdq 0h f0d l*uwdz44

When will your apparent wjusk/ r* 9ps9 xx7)prbeight be the greatest, as measured by a scale in a moving elevator: w/s9xj bsr)xpk ur97p*hen 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 affectewlt 1bt;af4 4vd by weightlessness. Ont at;14lfvwb 4e way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). 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” o -ldbd1nniv 04r “apparent weightlessness” between ste-d i0 lb4nnv1dps.

The Earth moves faster in its orbit around the Sun in Jax; 1gndf6 y1t-6ygrdcnuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relad6gcr f 1dyg6-1ty ;xntive to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a momi e7i g-v3u07 ttq*b:ydc) qson. Explain how this discovery enabled an estimate of q g77t-3ye*mti v c:u)id qsb0Pluto’s mass.

  The Sun's gravitational p+)8axci;ap 5 9oxlc7 4idncvuull on the Earth is much larger than the Moon's. Yet th7x dclx c)ip +5aacn uivo894;e 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 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 l uikv td724-va,na0h 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 : db5obi*x5h.vnrcs92e my9caml/ 7 bits orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assumb29:behyo5.bs9mm7cn /c5l*vrxi ade that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifovnt /1/. cd2 btvypvzcv6 pd+1rmly in a horizontal1+pvt16.v ccdv dznvtyb/ 2p/ circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is ifj fy(-0 sql m.c+:hbwc i84ypn orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , t0( bip.h-+ :y l4mjycfqcs wf8he gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerssih+c2 0tr8c vo+t74rm1r u xation of a speck of clay on the edge of a potter’s whe4 ou1hxt si 0c7r+r 28svrctm+el turning at 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 vertical circe*xzw ah 3,e:rle of radius 72.0 cm , as shown in Fig. 5-33. If its zheax:re *, 3wspeed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radiusf bjfy9mgyz3d8 -) gt, 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepez9 g- t8gy3y j)bmdff,ndent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and x6+(h5 gdtty ak( zz4fgnh-8ythe road if a car is to round a level cu+kn(fg8t6 y5x(dayz4 z-h ht grve of radius 85 m at a speed of 95km/h ?   

  A device for trainingd8favub8 yqbb1)5q 8h astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.8 bb dvq fu58qa1h8)by85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating s g,1g:iu(wlf 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 coefficient of static friction between the coin anlg(1f :g,is wud the turntable?   

  At what minimum speed mus)9wfb;twk 4q3egkkfi,( 8vm ut a roller coaster be traveling when upside down at the top of a 9f)t;f kg v(kq ib8u4w3kemw,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 ofvmll rc 6.vf4/ mass 950 kg (including the driver) crosses the rounded top of a hill (radius =9r./v6vmlf4 l c5$ \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 whe7k (e 2yt6o)b(k6dcnyz niy v5el need to make for the passengers to feel “weightless” at the topmo6nb v k(yy2yzcktni(657ed o)st point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. blqx 3zn2-uk;At the lowest point of its motion the tension in the rope supporting l ux z2k-;qbn3the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from t-03tlr nx-ee 8 q:ug8,ub znvhhe axis of rotation is to experience an acc -:lu-h8, 8zb 0u nxqrge3nvteeleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot8a3 p3ttgx ej+ated in a cylindrically walled "room." (Sepj+3x3t ga8 tee 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 rota l(wq44;r+v/senw :pcn uix 3xted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown;si/rc4 +nn:xx4lwuvwpeq 3( 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 non(yviqktm k8+g7 70kxt ignoring the weight of the ball which revolvesnyqkx0m +k8i ktv (7g7 on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is 0jmzwaqxyr y9*:e4 /mperfectly 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 masse +)vl(qb3.ax3lh 4yed*kd cw as $ 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 divyc( f1dtad o87 w,pdpy2 da5g6ing 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 thie:; jbm *oa+nends4xn2k6t2e net force exerted on the car (by the ground) in Example 5-8 2 sxne*6nma :b;k no+4de 2tji 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 accelay7 2f,dxso ,kerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turnk,x27yds o, fa, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a p 5mr 6f4ymurztukpc1l qd8t..5jj 9 l7articular inlclfmqjr4yk jt. 8d5 rt mpz9.7uu561stant, 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 spacecraft 12,80usm;x/0 *sp 1ct(a fkm4el(ni7mc.mx 0 km (2 Earth radii) above the Earth’uaenm.* ;sm /4xmmx1(klcp0(ifc 7sts surface if its mass is 1350 kg.   

  At the surface of a certain planez cad1lw b2+zr s8bk91t, the gravitational acceleration g has a magnitulzb18azw ds2+ 9krb1 cde 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 accelerv yl 8zcw eisn6-c2tqch t87--ation due to gravity on the Moon. The Moon's radius is 1.74- 7lczvq-e8cstit6c-y w 8h 2n $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a r -zvq+ivb sapf0p*n )6sa+c 0radius 1.5 times that of Earth, but has the same mass. qsbn0zsv* )f+c-+i ppa0rav 6What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a4/fvtnwlmc sue0h yu1 3 ij41: mass 1.66 times that of Earth, but the same radius. What is g nevms3 4/w0h ljeu:i1c u4n1fytar its surface?   

  Two objects attract each other gravitationally with a for q p(ibufz 1tkx4.9chtsy1 g2+ce 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 , theuv86d (3vuc4qh lj l*g acceleration of gravity, at (a) 3200 m dv(4lc8uhu3 lqg6 *jv    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the E1lcz)ho5+l1: cv au/h8l tsn;eykf, b arth where thegravitationakus h :tyec 8 lcnz ,lh1a5o+lv/fb;)1l 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 oui(*y4y 9*-hwuyybfyc ) q j*ctr Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster. yf *yyyuiq9-tjcw (* )hcby 4*   $\times10^12$

  A typical white-dwarf star, which once was an average star like ourkj 8xttzj 2yvlh 94n14 Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass tl4v1y 9xthzjkn482jof our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining wh8sgjkz ;.ku1a seuf33y astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker e j3;f3zu .gs1auks8kup there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calrlfo9-z ;;8l m muy9n8o5ypf0r:idmjculate the magnitude and direction of the total gravitational force exerted on olo8:o z8uyfim9pymdf;0 j5m-;n rrl 9ne sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up o74;u7bzanaji8i7 yii n 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 lazu7i a8 7 jn74ybi;iiine (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 surf5q(/n2u4g y8 vanjs(q l p/b5pm2kkz face of Mars is 0.38 of what it is on Earv( qknml/2upk j( s5/2qngbp4z 5yaf8th, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kn l/s4tg4ermt(3r a6tzi * tv0zown value for the period of the Earth and itattrli3ttveszg6r *44(/ 0 mzs distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of al-p 18 dj-i0zheax,j f satellite moving in a stable circular orbit about the Earth at a h0 p8-fahx j dj1i,-lezeight of 3600 km.    $\times 10^3$

  The space shuttle releasesw5 fgug1kvm m0*t8:pl a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relp u*:01f mg vgwmt5l8kative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spa:fi09cmm( ppc) ul dicgj00 1*-bigse ceship rotate if occupants are to experience simulated gravity of 0.60 ei m0 i0-19lspcmdj 0pc)*:c(u igbfgg? Assume 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 orb*av 0s v+qpl/qit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Eals*q+q0v v /parth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from than q++f9metm4(,bo roe top of m4nat+f o(r,eqobm+9 Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar lanpp4 .dcppa /3wding mission, the command module continued to orbit the Moon at pa4 ./cpdp3pwan 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 ice that orbit the planet. The gq,*qj.foxtfz + fjt+ q b ze lkwldl+6.8p/1-inner*p +bq+ xqq+ft6.8gk oj1lz d/ t,lwfezf-.lj 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 (see Fig. 5–9). Whatff)(s5z4;nwlk (5u0b kh 7otnj wquz6 is the ratio of a person’s apparent weight to her bjtl(n5q(zf fz wuuk ;h0 wo)4567 nksreal 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 centeb6qr w5 d 1k,l5ovub;rr of the Earth's Moon in aob r55w ;dv r1ulqkb,6 space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of .p y f9/lun+cdtwo stars of equal mass. They are observed to be separated by 360 million km and take 5.7cypf9 u/ .ln+d Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring sca5m0 txkpp: 9nm0tw8.gd8rp vxle read for the weight of a 55-kg woman in an elevator thatp95 0r0m . xmtwpp8:vdn8k xgt 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 susm: chuq;+ b62+kj ded fh+gkq8tljh)84 znk1rpended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elev:8+d2 l tqdnhk )j qg;m1jh4+8khk6eu czfr+b ator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period c0b7,xffm.1 en -r qllT , the d.7f0- blxce,1ln rfq mensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the rd loww.i-l 8;Moon (27.4 d) to determine the period of an artificial sa -loi.rww 8d;ltellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Suje w.xyp7,n )pn like tn)yj w7,.pepx he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagrm ;u wmoo/--ur52( 0eceude mgcv0 x.e distance of 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 comes very czfn 02j d;mr7i a4kt1t 1ljkn0lose 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? [nmtk;41ka d0 j1 izrf7 tnl02jHint: 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 cenr0kh / ybwv4;qbfbr9 2p, 6 vadh:a2ddter 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 mea,jo7.ibqrlh0 m-hy,z+ .isp bn distance for the four largest moons of Jupiter (those discovered by Galileo .+ ,hi 7 0zomrbb,p lsq-iyhj.in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of th - dnagxlgnkq.g*4o 1 2,tlfe/e Moon. oklnnqg-t4e d, /l 2g*gf.a1 x   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Juj -/fuoe(25q t1gqx l si),njnpiter’s moons, using Kepler’s third law. Use t-j 5tf) qjenlq,gs(/ xio u21nhe 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 Myc;;q mhg gf8-ax 8wr2ars and Jupiter consists of many fragments (which some space scientists think came from a planet th a ;gcyr- wx;8hgmf28qat once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bandebr19 mzhw 6v(/w fu0)gm.sln completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exbw.v 1w )mzne(s0 m6g/9ruhlfactly 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 llxbb gzr,, ir *5i. qde;so69a 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, what is the maximum speed he can tolerate at zlqx*r 5ib d egl.,bi9,;os6rthe 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 w;,k pooir -svqh.):tyill the acceleration of gravity be half what it iskspo,)oy q ir.;v-t :h on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal/jmmlu -7kpxwsn4 x)- 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 their individual masses are 60.0 kg, how h4-k/ jslmn-umxxp)w7ard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravit+ b rdurney*cbjb h -+(3c *r*,yhcq)ly at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate**h b+u*c (brcle3nryrjd h,)cb+qy- the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from th jo47 jtmb 1g+sxu;a8ye Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mou8obm4 +1s 7gajytjx;on pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elevat6(qn0 pwu.zhhxn3(u u8b7y5 aa.yddoor, it says your mass is 82 kg. What is the acceleratipqn odz yah. 5 .(hudx80(wb36anu7yu on of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists oq4jf kacab..* f a circular 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 rotationa *bcf4a.kqj. 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 vertical loop (Fig.5iy yty9m7m,a 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 p6)ui /v ymf7xud p0q2dlanet in terms of its radius r, the acceleration due to gravity at its surface and) uy7dq2v6xd/ f iu0mp the gravitational constant G.

A plumb bob (a mass m hanx a. d(ywd68pfq yd; at24uz,*x ctv8dging on a string) is deflected from the vertical by an anglf8p xdtdyuaydcz ;t a6xw8dqv,(.24 *e $\theta$ 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 coefficie pmk67zsi s64e2*n mh07rzfdent of static friction is 0.30 (wet pavement), at what range of speeds ca zf7z6r 60* nks e7mipsmh2de4n a car safely handle the curve?

  How long would a day be if the Eart )d;ynhkb+w g,h were rotating so fast that objects at the equatowbn;kgyd +h, )r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cvo/km 8m,tji4n o9pjxw7;. uo onstant 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 dtlm*/yo5lj / a constant speed rounds a curve of radius 235 m. A lamp suspended ft j//dy* o5llmrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as thetpky fbq112t9+moy 0g 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 dt0yfq1 k+py19g t 2ombata 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 Tam ,q;ql/rvy zu )(c/relescope deduced the presence 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 ofr/mr ,lqqyv;az u)/c( 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 valley sk4q0ije6dilk. h/ey: hown 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? L64 .ke ldyj/hiqk e0:iightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a w g;+opov.iu3group 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 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 ooi ;w.v+p uog3f each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEe( 4,iztcdb 0gAR), after traveling 2.1 billion km, is meant to orbit the asterotb4 (cd,eg z0iid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a sateljaa.qf 0u)c t3lite 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 behind iatc aqj0 .)uf3t.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distancet/ 27zjvmi;pji3ira7c-0k p f from the t kjc7jp07zi3/i- i;mf2v parSun?   
(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 .b:qm* yf+iyf G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasq.yb: mfiy*f+ onable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gafee;edxp66 4olaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center f6; xeed64 oep$ \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. 5 hmo.mz+jl0fFind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom0oh 5zjmml+.f side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the/b +yu3 k) i7u;qxbhb;vgbef 9 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 t7crab l:001ed 8phu:qu4 gpuc ip of the 1.5-cm-long sweep second hand on your wrist watch? 04:h8 u1 p7u0e:cpqruad gbl c   $\times 10^{-4}$

  While fishing, you get bored an:k*e (;x90xvuqf elrsr1hlu-d start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.e x9h0*v l;u esr(u f1qxkl-:r]    $^{\circ}$

A circular curve of radius R in a new 2)e1 d5gwj;2by.tbx qytvv0 j highway is designed so that a car traveling at speej v25y1jqg.b tdx) 0tybvw2e;d $ 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 6j;enqrq/;bi cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an ;q i/r6q;bjen 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.$\approx$    $\times 10^2$