Sometimes people say that water is removed from clothes in a spin dryer by ce3g 4pt9zkdpt9 ntrifugal force throwing thekg9p pd93t z4t water outward. What is wrong with this statement?

Will the acceleration oz r w z+vgo0qa4 psr0qts,r-5/o1+,emy otgy *f a car be the same when the car travels around a sharp curve at a constant 60 km/h a1rwga+oq*0 /qo t5tmsgv4, rpzs,oez+r0 y- ys when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly -/1u. sif:za o3qte2z5 yum vqroad. 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 hile2 q1smvtz :yf qzuo-35/uia.ls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a j.pw q ,-sv x8.a+vlochorse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chi+ xjwloc .a,-vvsp. q8ld?

A bucket of water can be whirled i*mf, refq avt ii//r5)n a vertical circle without the water spilling out, even at the to/ritr me5*, /f favq)ip of the circle when the bucket is upside down. Explain.

How many “accelerators” do you haj08a.v)qw j,s+jsjgqhb ; qy5ve 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 accelerations do they produce qh jqjjs8a bqjy+ svw;.5)g0,?

A child on a sled co.b+-* onk6c0, qccfj l9ajhlumes flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the glq0-+o c.6 ccl *hu9,a kjbjnfround (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 leant8udz5d:b -h ra)mdu66oe 3pb inward when rounding a curve at high speed?

Why do airplanes bank when p iozn60-( hvsc01:jp3lbghc they turn? How would you compute the banking angle given its speed and radius of the tu:v hz-sio0c6p njp 03l1(bchgrn?

A girl is whirling a ball on a6/xqb)i;7ki fx 5ccc s string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball wixqc s 6bx)f7ci c5k;/ill hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If s j(xu i/i(;;z )gjrooio, how large a force? Conside) igo/iu j((zjr;; ioxr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wour38pv e(cv fk8 zixo8;ld the Moon’s orbit be dik pvvio(x; 8f8zc3r 8efferent?

Which pulls harder gravitationally, the Eart3+kxrq.h a9 a:jtg e,xh on the Moon, or the Moon on the Earth? 9 rgehtx.jk:a x,3 +aqWhich accelerates more?

The Sun's gravitational pul. bs w*(cu+wuy h-5vs4nuy 5oll 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 f- 5* uwuowucl y.5+n(sv4sbhyrom one side of the Earth to the other.]

Will an object weigh more at the equator od7t y5z gokd orlt te+:+*6ppc*2nn1pr at the poles? What two effects are atng2yc*np5 zl 7+trt1k:pod*+to6 pd e work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the fork;mvhsqnqveq1w0p4e; 9 (.p 9, puh hace on the Moon due to the Sun. Wp (; qhqhuhn4eq9 k0 ,9vw evap;.spm1hy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger ort42pjqad q 1l9 smaller than thedj 2lq pt1q49a centripetal acceleration of the Earth?

Would it require less speed to launarqsy-o ly) dl16vi6*fj 47 jrch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s ra-iy j lo r764sf1q* 6ldjy)rvotation direction.

When will your apparent weight be o haymotomw8l- 2w;i bi+g.8, the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When wobimwtw -.y+8l 2a;8g ooh mi,ould 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 ;zzg :pj 6m0uiweightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates:z 0;im6zgpuj, 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 “freed z.3+okoor6d4)yvsrat gt)3 fall” or “apparent weightlessness” between stepdsg z.4 t+ ktooy3o6)drra)v 3s.

The Earth moves faster in its o,3 f hl, p)q8-jombtlxrbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This i3 hq8t, ,flxl -bmpo)js 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 until it was discovered to haveo98o,8 dw2e7zliv frl a moon. Explain how this discovery enabled an estimate of Pluto’v o2zwiro98 lde,l7f8s mass.

  The Sun's gravitatiou/8 he) cbsl8onal 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 chilb8 ulsh/)oe8 cd 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 198t:.ny zw(2 gfzf3pd 1s0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 th3h zkepj9p):ne Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the :znp) kh9j e3pEarth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as v0;sc9gk)fj d it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of c;)v kjgsd9f0 the discus.   

  Suppose the space shuttle is zce+ h ,01*xoz5r he ,pamffc2in 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 , the gravitational acceleration at the Ear5 xcezfzcmp*h1,ro 2ef,a0 h +th's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on th caled x-ge18h hlymt:440g 4ze edge of a potter’s wheel turning at 45 rpm (revolut-eygzd40 hm81 4gahlltec 4:xions 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 cm* agtoe 7v. (q4kpu.vircle of(7oq amp*v4egt.uv . k radius 72.0 cm , as shown in Fig. 5-33. If its speed 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 speedg (m:bpit9o-f with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of sta:got9 (f mbpi-tic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of st9hw 7lvo58wf zu.ud1wk4mv v:atic friction be between the tires and the road if a car is to round a level curve of radh8vwdoful9 vzv4 5 mkw.u:17 wius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fi0w ob ,sk:*gu 6(kbnbjghter 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 7.85 times her own weight, how *k b,o:ujw0( ngbbs k6fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of varia:xnyq694uo fx wbbn.7 ble speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 3xy4wf6x u9qno:b b7n.6 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 v rfty(mef 9f*nw4; /ex+x1u6c5 p yftmust a roller coaster be traveling when upside down at the top of a circf/ t xf u(ffvw6*nc9e t1x+;yy 45meprle
(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 maso wb3z::j x8vos 950 kg (including the driver) crosses the rounded top of a hill (r: jwzo8:bv 3xoadius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a be(+ fk, j lh gk+rnjkr04qy(; .z;dra15-m-diameter Ferris wheel need to make for the passfbda .n+kyjrr(;,q+0gr(he;zk l j 4kengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. r./zi8y w ov v9mm2xe9At the lowest point of its motion the tension in the rope sup .v9/xem yizomw98 v2rporting 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 centrifu(/f4v1prp hwodq0i jey+8:s;set ag5 ge rotate if a particle 9.00 cm from the axis of rogs1:+/qp0ps 4v 8jw dreho tf;yaie(5tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival ev.9l0 v4 nn.ljj,7 ofrq6ahr, people are rotated in a cylindrically walled "room." (See Fig. fr .nv j 0e9ao7.h4 lr,jqvln65-35.)
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-hoh t4v xsyc(.kss4g6g5ckey tabletop, and is held in this o4 sxyg5cv6kgs ht.( s4rbit 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 n+d 4cbrbai9ny; aa8ldek p.(4 v1jiz9ot ignoring the weight of the ball which revolves on a string 0.600 m long. In9e;4va. lbia k ynb+rz91 (i4c8pd ajd 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 a y nj2a z6qv9m5ia0 .akcar 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 massessb.6gxr f, nj; $ 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 maneq9oep,p6 , 2xzxzo4 zpbza1h8aihv *7uver 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 centripetal components oazp y446lhs+z;/zz mwf the net force exerted on the car (by the grounlys w+z z4z4/6amz;ph d) 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 acceleraab3zg//ax;:w8mh( naw1 ,zxd kl xs;qtes 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 ww(m ,;/kzhq z:bxdaxgxans 3/1l ;a8through 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 radius 2.90 m . At a par8wj4 ) nm 5-t gt4mevwwi6 yx.*zgog-alxm)8qticular in tyozm t gm8-)a.l*em4)wj nw wq -ix8vgg5x64stant, 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 ofrzk+kv 6kie-9 Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Ea9ikrv+6kk-ez rth’s surface if its mass is 1350 kg.   

  At the surface of a cerxw6k)ec5;5 g w2ttoo9b :ovnvkgs+b/ tain planet, the gravitational acceleration g has a magnitude of 12 m/s/) o o;x+9:5sgbke 52 wv t6otkgwnbvc$^2$ 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 ow d2a*a odxz g-r;9 6w7fm1mien the Moon. The Moon's radius is 1.7da7wadgiw 16fr-*mo 9emxz 2;4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.bfhvy50j wi415 times that of Earth, but has the same mass. What is the acceleration due to 45jwhvyb01f igravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, buy lm+o z*pnzekm04ev6)q4jkg:ww4 j4t the same radius. What i e)gn4m pkwz kz4 +yjle4q6o4w*jm 0v:s g near its surface?   

  Two objects attract each othw ofc b6,yu3nj36bz4 mer gravitationally 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 , th3icxo* d0:oj i-,m hjse acceleration of gravity, at (a) 3200 m :hso- ji0ixm o3*c,jd   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the E4;o bu.uovg. lzs -wl0om )9zcarth where thegravitational acceleration due to the Earlvo-;z0 .uoo 9) .mwsu4c blzgth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has 8yx(2f wjtka) five times the mass of our Sun packed into a sphere about 10 km in radius. Est(xjfy )k8at2wimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whs ;4z)dwh(swhich once was 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 surface gravity on thhhdz4(;ws )s wis star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the ko-0 cr+n-drg space shuttle. Your friends respond that they thought r-on+d k-0cr ggravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of c m15dx5od ev95koe8lside 0.60 m. Calculate the magnitude and directio8 cvlmddo k5oe559x1en of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sunp 7svk+xrt eoyk 5582p. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The massesr ks8k57ox e v5pp2yt+ 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 surface of Mars is 0.38 of w,hv1 c5 t0e jv1bvx5ykhat it is on Earth, cb 5, x10j5vketvv1yhand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knomo y01r0q-du:ktrnln *c/a1 a wn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Keplerkmc y1 a/d oaunrr:-l0* 1ntq0’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular oroz -siubtb (/m. *4iyebit about the Earth aeo(iu.z btis/ 4 *mb-yt a height of 3600 km.    $\times 10^3$

  The space shuttle releases a saxdq:f d/7w nkw((bng7tellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relat(fx/ k7bnwn(w qg7:ddive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricyy 6xpt)ot 3w bdz:.a)p/)gwwt+ux e- al spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give yourtww 6o/xgtx3.t)ad:)byy)ez- up+ p w answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit2) qizd 8advzjp9c,f 00ht:e q 8kgkb/ 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. cjk h bd0 :0 a q)tizpv9kgd/q8e2fz,8Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a m-wdlvq qoa0u *f:* akm )7f:nsatellite have to be launched from the top of Mt. Everest to be placed in a circular orbi)fnvomd:0* ua: q aqfwkl -*m7t around the Earth?   

  During an Apollo lunar landing mission, the command module cwbdp2+a4pthw+ x..nok; il 8yontinued to orbit the Moon at an altitude of about 1bpwx d;ko4p..a2h+wl +it8ny00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are comsrpf 2i ;q1(hoposed of chunks of ice that orbit the planet. The inner radius o(ir ;2 q1sfhpof 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 l sgnx ,g/la dl1c:g+3(see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, g /a,l3gds:g+ln1 cxland (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astron/-jtpwy;0rbf3*a5kyj l 9b mdaut 4200 km from the center of the Earth's Moon in a spacerj l3p w0;/-5kb9bt* amyjdf y vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. The e xd8ysf.m10 flx5d)k mfel()y are observe)lm)kf.fxd8f 5exlyd1m0 s( ed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reak0,rq: i2fo ilw*q 2 0x)nnkob)at dr,d for the weight of a 55-kg woman in an elevator that mf,),qiooq2 rw )0a l dkibnn2t*k rx0:oves
(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 o juj*;w7g ufyec8d 4+c. jqt2xf an elevator. The cord can withst; x cu+8g.y uj2eqtd 7c4*jfjwand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very nearthl/4 vd+kxv60t3sxe (bfx2 r the surface of a planet with period T , the density (mass/volume) of ( 0+4kbv3l v f2hdt xtx6esx/rthe 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 e*qp8apzmm ry0m 5) h 5q3,fxlthe period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very ne f m3xah8z5yq,0l pq e5pmm)r*ar the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrb mx0p pw/.ez.oss, orbits the Sun like th. zwb m.pe0p/xe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of/ f.,n*t/ kftlc6 xzh . 4hbbiz;v7rm qjco7y1 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 7wpu3cane +- .mqem,xz18j4tc r+).pe 7thosj 6 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 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.] cj1w ou.r,p- e+ h4)st.t+xcaeeq7j 3zp 8mnm    $\times 10^6$

  Our Sun rotates about the center of the Galaxy/ nnoi/75fy- l9gcw zd $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distanc r5n6h+a2v psn:o2 ne2bv tm.pe for the four largest moons of Jupiter (those discovered by Galileo p:rn + a2nh2.v2ntse b 6v5mpoin 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mo-cg/ d(bpl)+i zn;h ddon. nglh d dcpb ;z/d-(+i)   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of (jfepfsw( 0 c.Jupiter’s moons, using Kepler’s third law. Use the distance of I.(p0(sw fjecf o 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 Jjqw quwvk1m9 4ub) /f6va),kf bg0qe7upiter consists of many fragments (which some space sci,1qg mak b /wq64kwuuj 90e)vffq7) bventists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form weg)rc8o ,qga n6e3592satr tof 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 a23g)wrrcq se,go5986 a tnteto 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 in an arc from a hanging vidy:5n 6i0qwqx1o w)p auzdy5, el+;k*xv8slrne (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and th,xw ea ulqqo5xd1*iy w8zkl)ns;6 p5r0 y:vd +e vine is 5.5 m long.   

  How far above the Earth ;1ba7 ddbqys7’s surface will the acceleration of gravity be half what it is on the surfac;7ba1 7ybqsdd e?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in af0a;bjlv zi(a, n(hp) 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, ph (nz0 a;f(bvli,ja )how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dau4 )4 pn0bj9 zoob8fujy, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect.u4p bj zf498 0joo)ubn What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Eart 5ijeyn+j9/p4i r* nvf4vay f qn,e07ohzoy7 2h will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull withiyf4v+0 5j o vzh iojn9ya,n/ ey27pn*qe7r4f equal and opposite forces?    $\times 10^8$

  You know your mass is 65i4 p 0jv1mw+2e;suedm kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleratijisv4 pm + eudmw;21e0on of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abot7dw;f5: d (uwhiu0xc ut 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 per day) if an effe ;wd itx7wucu: 5hfd(0ct 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 verti drs6g3jv)v rtb:-q*k cal 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 planet in terms of its radius r, v 95 ujuog:8ah k2+hh+deek(jthe acceleration due to gravity at its (j:akuo8 v2h e5gh e9kj h+ud+surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defle4wv/r+n6 )c otahws/xio2j j+cted from the vertical by an an+i/r twxhvj6+42 c/sa)wo jnogle $\theta$ 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 banke:qu q cy/w :4dngiqe4,d for a design speed of If the coefficient of static friction is 0.30 (wet pavement):gd q q,nuyi4e 4:qcw/, at what range of speeds can a car safely handle the curve?

  How long would a day ro;4z 0ia5 2vbl. a5nvgpwt;nbe if the Earth were rotating so fast that objects at the equator were appw;lv np0v.atn 24a5z g ob;ri5arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance2jtq8bzzly:j3+ *./i( y uvf9jes uwm 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 conscbocgk ,o -/tb (y-uy*tant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to go coy-cub-*,t/ bk(y an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. m2fra / o5*fr,f.i 4ks/cpbyn1axi) iThus, 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 forsm1*cf ia5)k/ayrbp ni4i2/ rfx,.f o 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 Telesco6w(*: j3f6z *vlmjwwj-lf l njpe 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**llvj3z n :jf(w- jwmfjl66w this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as itojwiu-00fnpn8- 3sd z 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? Explaini3usw j-op0 zf0n-d8n . (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioniny /2(, zsjowgq5ngdd 9g System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, t/ gg9sqy5j , (wddz2nohe position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billibxx/9f(av4w1fzcjy5: 8 aebe on km, is meant to orbit the:e 91 bcfvabfjw8yz(/a xxe45 asteroid 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 satellite injh+4tk44f8ebzjot-g7-t6ux d bji.m need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 2go4 tbhfj7 648uj zm- e-jxk btd+4ti.5 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (i mi13r )c- sq;pk,obcxwls0: a) What is its mean distance from thw,ksqx ir3)- l0cis ob:;pmc1e Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "-5krbcn 0i(lg:l b6ilp5 .zrwfeel" yourself gravitationally attractel wglrpb6r0 - b(lc5n5i.k:zid to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the a/kp 1 lkecxv5drl)09ez4z z7 center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fr10 r l ckl97kvz54 xeezd/zap)om 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. r5 gp6zv(*yz uFind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the * 5gyuzz p(v6rsquare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 r(sqz rf-ba +f jlt;5 gh(,*vzkg 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 experi.uj.m: 2 iu8 jut.xdwcenced by the tip of the 1.5-cm-long sweep second hand on your wrisc. iuwmu.du8 x2t.:jj t watch?    $\times 10^{-4}$

  While fishing, you get bored and s3yu.crh6yf7ggpj 1 vj :(t8j ctart 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 tg c.y7v1 rj6: 8yujcjp f3h(gevery 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 radif* 3sbeq:c da1s 99qovus R in a new highway is designed so that a car traveling at speob fe3q9v s c:91q*dased $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiak4 .7;ii4,xnj prykmx ting 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 Acela train that rounds a curve with a radius of74;rpm,ijkk4.nx y ix 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.$\approx$    $\times 10^2$