Sometimes people say that water is removed from clothes in a spin dryeriqc-6 fpgli e+o1ze uk,u*/ *o by centrifugal force t+-uc q*gezl/6of u iep*o,1ikhrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when th+s:dujd y q6g5e car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle+ s:ydu5jd6g q curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does o(ljp:+k4 v.d rkt4nc 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 bott(k 4krnodpv+t:. cl j4om of a hill?

Describe all the forces acting on a child riding a horse on a merry-go- 8isl)t (v;pvl* l53b2yvdtevround. Which of these forces provides the centripetal acceleration of the le3vl(s85pvv2 yt ldv)b t*;ichild?

A bucket of water can be whirled in a vertical circle without the water spilling-nia1; wn7 .dijfj;np out, j n1 .i-n p;nawdjif;7even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? rgs*2np r0 *3yxxz3dfThere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What rx*xgd*yrzp 03 3s nf2accelerations do they produce?

A child on a sled comes flying over 2+z,z l:z rg2ze2w ydsip.g m)the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. zsl ,iwg2rzy.)m22dz+zg: ep Explain this decrease using Newton’s second law.

Why do bicycle riders t:em5qw.a x:qlean inward when rounding a curve at high speed?

Why do airplanes bank when they no hre tc ut60 a*ch9v(77z8hlturn? How would you compute the banking angle given ic7oh7*69e tuz r80lnt( hvcahts speed and radius of the turn?

A girl is whirling a ba c jfbm+**9)jaau3uh:uw +rdknf,tm5 ll on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the otherm*udju+:j) 9kwab+m,uftfac 53hn*r side of the yard. When should she let go of the string?

Does an apple exert a gravitational forcn5pxi h mu5(0te on the Earth? If so, how large a force? Cp(5 muxi 0htn5onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doujg6c am/am:1jtd i0 /bble what it is, in what ways would the Moon’s orbit be diffbda:jt j//a1m60i mgc erent?

Which pulls harder gravitationally,qgdv x3d5 znnj214v-j the Earth on the Moon, or the Moon on the Earth? Whicxq vn3j25nzv4d-dj g 1h accelerates more?

The Sun's gravitational pull on the Earth is much larger thesjpc+jerr-5x6 k 98gw/ c,5iheal3pan the Moon's. Yet the Moon's is mainly responsible for th8sw- e6pgj p,jr55ca/kh+eic3erx 9l e tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equatok 3nb5jux ug k7 qm2-sh-hyc/8ka8;rg r or at the poles? What two effects are at work? Do they oppose each othe8kbrnk7h -h3 j5/; ku8 -gquagsxmyc 2r?

The gravitational force on lqfqk3 4ve-c6 the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from th4-qkf l3qvce6e Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar/d :8vacca9quger or smaller than the centripetal aa/a 9c8uvq cd:cceleration of the Earth?

Would it require less speed to,k( llyxou4f-ghwj ;. launch a satellite (a) toward the east or (b) toward the west? Considhkxf uy ;jg ,ol4.lw(-er the Earth’s rotation direction.

When will your apparent weg/o.iwy q-6bmight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates d6 qi .yg-obwm/ownward, (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 adversss8 *8c5 isxv jn ptlm,6t0.xcely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylin s88sns xpi 6jcxl0t, m*ctv.5drical 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 “apparent weightlessness” bqj)a8lm;k(z*) x hkabetween step mq)(*b;ah zlakx)jk8s.

The Earth moves faster in its orbit aroun9(pyd hd9s34x9 phfv vd the Sun in January than in July. Is the Earth v9xhfy(9d v4 pp9s 3hdcloser 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 relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. odmmv* e,413ogu (pp oExplain how this discovery enabled an estimatem4 3m(*v o o,u1dppoge of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. 6su f587 o4hwo(+h*l a uopw6;n mvovsYet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 5vosnu7+ sm a; 6o4(8w*w6 hlfpou ohv1.10 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 g;wy, lnskz +0j: qst11980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerat*nid- .ug9ns 0unxd*aion 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 xd.9u usa i0nn*dn*g- 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 q) n5/f6zcdgdr ,j75anieq-q q+zwf1ld8xw8exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 08rn q7i5qad/8zzf6wnf jd+ l ,wqge-qdc5x1 ).90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the E yjpq-okwi7.q8u n3z2arth'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 i y7ki uw8qn3- 2.ozpjqn terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck 4t3i7vm e)asrhmz + )pof clay on the edge of a potteiazm)vrm s +p43h7te )r’s wheel 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 atun w 6.1r dlhunep0nj4)blo.: a uniform rate in a vertical circle of raou e :hjn )rb1w.nn.lp d6l4u0dius 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 speed with which a 1050-kg car can (m2ind t3tqxr)-xmk 7round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? I2 3mnxtd -)qitr 7xkm(s this result independent of the mass of the car?   

  How large must the coefficient of static friction be between 3f9q 0daec4*+xp kinz the tires and the road if a car is to round a leveld0+e*nx pqcaz3 fk 4i9 curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a 8e 4a2a 4bgpr dc*hus*trainee inaareuh 24*dpc4 b*8 gs 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 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 rot9k( nsjoq82vz ating 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 and th(98 o vqsnkz2je turntable?   

  At what minimum speed must a roller coaster be travc8rte71w1n1tqg6 xm teling when upside down at the top of a c cnx1 t1gm1w6etqr t87ircle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded towpk 7z -hcamw:h.lc.o*kvy6id 8 h0k.p of a hill (radius 8:c 07ohcwy.d*kwhi.k-zmv.6lpk ha =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 1kg3mc1ao d8qa 15-m-diameter Ferris wheel need to make for the pa3g1md8aq c1k ossengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verti 8rx .sryu09ijcal circle of radius 1.10 m. At the lowest poinxrsu 9ijy8r0.t 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 centrifuge rotate if a particle 9.00 cm from the uraatd+5 4wb2o n-8ksaxis of rotation is to experienr+ws aou2n8-tda5b4 kce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopleb ; y5vs0zz-fly yy7/l are rotated in a cylindrically walled "room." (See Fig. 5/ yyl z l7f;yzybvs50--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 alyknu((;lzdst+ 6ww o 5j f:/0 t5wgfr.ev2k k 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 ho;s+kj.dv2 uwr( ef0tw:ftg/k (ln56w 5y olkzle 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 weight of thl8 q-zx;yt rac*cpm;( e ball which revolves on a string 0.600 m long. In particular, ;*r c; amltcp y(-xz8qfind 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 bank vi,/(i-+sz+.(j qvblqvgpf u9s slf )ed for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses 3- - ro;mbmkuf*4oc vqw9 2kwv$ 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 divingrhw;7iilt6 , c 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 or.f4q or-o(oand centripetal components of the net force exerted on the car 4orqoor-(o .f (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 50; nvoaev/*u,c 0 accelerates 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 a nu/v v*,;ecoit is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 jjgx .;hac4ao4w ocj65 7*t4oui 5lwqm . At a particular instant, .jo5ow6 xg*l;a ictjuho 5 jcw4a7q 44its 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 Eartwf(-x)8bejejq bc(jqtgx n 2 y))t*-th’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if-bg)(-)eb2()ej*jj x ytfxcq wqntt8 its mass is 1350 kg.   

  At the surface of a cj; 3 6f3loif6vort * :x l1kmdcqgl)b*ertain planet, the gravitational acceleration g has a magnitude of 12 m/sfbvk3lxdrgco3*f*6q l )j :t6;1loim$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is hus7+ky* sxbgbfs(a27gj5g * 1.74 *h + 52 x7usb *bygkg(7jfsags$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius j*l3( y njm;lhx j; -k+gzqcx31.5 times that of Earth, but has the same mass. What is the acceleration due to grav3yqcxl+3jhm g ;(x jzj-*kl;nity near its surface?   

  A hypothetical planet has a mass 1.66 times that om1zg n.i-r sx;f Earth, but the same radius. What is g near its szirm.x1g-sn; urface?   

  Two objects attract each other gravitationally with a force of+gs8 fxbay(ciqo5x4khb3mm:1q 5h 48 fyw l7t 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 a4xgg j6a 2/ss6cdr)k9k5w mug , the acceleration of gravity, at (a) 3200 marcjx9 k45 ) mg2sd au6/ws6kg    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside tl2zbk+6xlk . up 3d)rthe Earth where thegravitational acceleration due to the Earth isbzt)k .xl+6 ur2lpd3k $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the masl , d)ltmitdy-3j u4y:s of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsttl iym)dj,lt y: d4-u3er.    $\times10^12$

  A typical white-dwarf pw5gmm697sjnwg0c h q/* .b/clb3tvcstar, which 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. q n /*6s57ml./j0v tbcg9gmwpwbhc3c What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astro vg3-*q (eoloknauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince toqk l3(gv-oe*hem 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 e loa c)+1uk)2lc9 uezsquare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other 9 lalc1e c ok2+uu)ze)three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the gmftpl-t2f 07c:nip( same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig27n lfp0ic( -:tpfgmt. 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 accelerationfu )6vl8xgcp1 of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determ)1c 6gl 8pxuvfine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usihrlj hxp:ddodi:q;9 c0, ra:.ng the known value for the period of the Earth and its distance from the Sun. [Note: al ,0 o:rjhci;9r: ddd. hxp:qCompare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular zbg)5uj ih bx -pn+( 4ic4w9hzorbit about the Ea)nb pw x +cg(-549b iizhhuzj4rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circul.j0a6wti n t7z5 zguv4ar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurtt0z65zg7 n.jui4avw s?    $\times 10^3$

  At what rate must a cylindrical spacezp)o 9/x n8dlxship rotate if occupants are to experience simulated gravity of 0.60 g? Aslx 9zxnp/8d)osume 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 ;vb8.gafmu *c x:ug8n to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whi ga :uv; c*bfn8m8xug.ch 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 the to isecslzb ,+o*jy8.n7 p of Mt. Evere78. o izsjce*n,sly +bst to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, thopc d4 ;t66a( opwdt*be command module continued to orbit the Moon at an ta; (pw 6tbc46o*dpdoaltitude 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. Thmig l)ykai 42 i:os6jpp543 zke inner radius of the ringsmk oj l4sizk p:p425)iygi63a 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 dia 9/zbtjq7l h5fmeter rotates once every 15.5 s (see Fig. 5–9). What is 9hj /tfl7 qbz5the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 7iwdgm+pc ib)g b2j;34200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity+2w gibm;i d cj)g7b3p,     ----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 tlovr5c4ndkd .v7ue0-2pyt y (wo stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a p7udropv(4-ytk52 d ecy.v ln0oint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg womagp d:,w fk5ghon6gnt*m85b: un in an elevator thagngk,fh55m wu d*p: 86:b notgt moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevato+,cbb/c4n xvr; f 1yykr. The cord can withstand a tension of 220 N and breaks as the c41yyv + ,xcn;kb/fbrelevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satel1(dqy4d mogq1 :i+qfqlite orbits very near the surface of a planet with period T , the density (:1io1q d+m qgq4d(yfq 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 x28 ley7l(4e r q*ikvqperiod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earthe87r4xvi ly2(k *lqq e’s surface.    s

  The asteroid Icarus, bkt4 dipzk/by1v72v5 though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun? y/v 42zb7ipb5ktv d1k    $\times 10^{11}$

  Neptune is an averagt vxwg :mbg/6/mvv9g 3eo, 4nxe 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. roa1a(fj d d:/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” to(r d f:/1ajdahe 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 ceu2oe7hxe t :kvjl-9 k0nter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for t*w a uj)s9 g yif;) 32dpb(z+lyiw,apyhe four largest moons of Jupiter (those discovered by Galileo in 1609y i)9ps u2y3w zlg;yba(jdf)piaw* ,+).
(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 /xdx ih peqrliu c5 m)/u8b.-8distance of the Moon. c-le/ i.)xpduq 8hru85 b mi/x   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepolalsc i ;(n1:ler’s :;nsoclla 1 (ithird law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of ae;b6:s f)7 lk5be 1eank8xlx many fragments (which some space scientists think came from a planet that once orbited the Sun but wb1ka 5elf8x6:s7b)nl x ea;ek as 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 artiotl6 try /06naky;u1bficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the duk1ry / t6t 6obya0ln;istance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an 5dnh59 tm qu(pwxfve7yk ,5 )+lbwn/o arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowesubv+ 5,/w 5h5k) pdynw mof t7(l9qnext 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 acd 6d3b7jf17 9xmz fvndceleration of gravity be half what it is on the surface d96fzj f nb77vdm31dx?    $\times 10^6$

  On an ice rink, two skaters )1wx e13th(rysoc 8pe of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are ths t(hex3)o1wer1yc8 p ey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dg l u 599llho(ysfiu8 -f n()z8nwou;tay, 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. What fraction of g is thiso8t( s; n fu )n9fu8o-iuwylzh5g(9ll?    $\times 10^{-1}$

  At what distance from the Earth will a slew0 5mjg1x 1 /pd8emgpacecraft traveling directly from the Earth to thee1 g85jm dpwgm/10xle Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when 09yc -wtapg ;yyou stand on a bathroom scale in an elevator, it says your maw pycy09gt;-a ss is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circu/0nhsd-9 v psular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speep s0u n-shv9d/d (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. 5s gl2-e4h4ar 3xt- ohj–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 ac ddfivo9mkl ) (2)/no /l*jna planet in terms of its radius r, the acceleration due to gravity at its surface and the gra*j)al mn)lfv2/ck9(/n ddi oovitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vert(2 lhf9k2c e(jr( xua+bwdk*gt9 x0cvical by an angle 0dhte( 9j x ax(f r92(kw *b+lcvuc2kg $\theta$ 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 2 2 gw8 jm5lnks ep7bjwzx521dthe coefficient of static friction is 0.30 (wet pavement), s2l2bnz72e 5wp8kxw 1 dmgj5 jat what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so f- ofkm y;4wqm8ast that objects at the equator were 8k4m -qmof; ywapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a co3vtk3 ) drn/w9zx/xwwnstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radiux+r*:a8vfl .ng ur9ahj h90uus 235 m. A lamp suspended from thhnu.gaf8* 9u0jl r9 axurh:+v e 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 the Earth. Thus, it has b9tujm wma:0d: een claimed that a pers mw90:tja:mduon 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 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 Spacepk **bfku:6ibw i/ q *p-1yais Telescope 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 meas piwi s-qfki6*b:*/b1ya* ukpuring 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 consta9 tfgx,q+sb8q g5 hp.gnt speed as it traverses the hill and valley shown in Fig. 5fhgxpsgg+ 8,.b 9 5tqq–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 s2my,)ivk: .c+vr blz aatellites 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,r z mc :vk)vl.y+ib2a the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEhcjz+( )pl ,fbx1ax*i AR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km .abf j(xcx,lh1p*iz)+ 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 pur)(aq1li)t d0ut vi,j gsuing 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 25j ,l1qtg)iivt d 0a)(u 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 yearsht dpu 2l gt4/,b:+idq. (a) What is its mean distance from4thlg ut/ +:piqdd2b, the 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 valu8( p x pdg0m8wr-6igzie of G would need to be if you could actually "feel" your6x8(rzdg0-w imp8gp i self gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky b2bhm29bigi9wy4 r,d Way Galaxy (Fig. 5-46) at a distance of about 30,by24bi gim ,2 d9hw9br000 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 vq346ujses s3b:x6z+ ;tf iet side. Find the magnitude and dir;i6tfetbss4uz:6q vj3 e+s3 xection of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass vhyt0c+a e 69 *vtu//s97gl u(v nqjrt5500 kg 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 experienced by the tip of7q kpif5y 5c/bn5wpl6 the 1.5-cm-long sweep second hand on your wrist 5 kqwpy5b6p7l /5nfci watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighbv0e y.7zm:qz x)jcs6t around in a circle below you on a 0.25-m piece of f 6:z yzbm0).7exqvsc jishing 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.]    $^{\circ}$

A circular curve of 3 g*zj q 82sde*iszsi8radius R in a new highway is designed so that a car traveling at d8i2i gsje*z 8ss*z3qspeed $ 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,8*4yjnympp: m )q. ucf utilizes tilt of the cars when negotiating curves. The anglep cm4jyu yf).pm:*q8n of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$