Sometimes people say that water is removed from clothes in a spin dryer by ce2wflr 1a3h vs(ntrifugal force trlfsh(v2 1w 3ahrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travelssce 94 d68.hboka;2fcpikb;;yo(ljq around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expla ekikyc f ;a4bq 8c;ldhs2b(o6 po;j9.in.

Suppose a car moves at constant speed along a hilly road. Where does thy77bjyw *mze* g++ 0iwauca.s e car exert the gywus7+.7maj iwy*0 gz+c* beareatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces (yez0dikiu*7 9a o ,yuacting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the ci u *z9u0(7ykdy,o aeihild?

A bucket of water can be whirled in a verticalxc+3vdw ( 1 u7o*jfyzn circle without the water spilling out, even at the to+*df713 wvjnz cy(xoup of the circle when the bucket is upside down. Explain.

How many “accelerators”ewe386u( )(kvtnbw mn do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are thee 8uk3n)nwtev6mb w((y? What accelerations do they produce?

A child on a sled comes flying over t)lm)z px09vcwhe crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “awzcp90vml) )xir”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rt8mpjvyb pa(c:p)0k 06ck 2u 8 4kultmounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the b *rotw+8nb4thbqu5e8ogp/0(: oejjaanking angle given its speed and radius of the owjabt*o: gju40hbe q8 /+nr58pte o(turn?

A girl is whirling a ball on a string around her tj; vlah0n ;(z6stha-x. tdx0head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she lhd-sa(ltx0; tj 6av t0nh z.;xet go of the string?

Does an apple exert a gravitational force on the Earth? If so, hordkma9;vq.)u9de xzs 4 c-j(k:el tl:w large a force? Con4 vstck( k:ard mu9 qljd.x:e -9zle);sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what way 5 (19 l9izgctaew q67u0ed;kbw l;fzds would the Moon’s orbit be differ1qwlea dtg69 l(kc5b;wdz90f7 z;eui ent?

Which pulls harder gravi 3dhj-v5j 0;jfrbgd d5( bnjq6tationally, the Earth on the Moon, or the Moon on the Earth? Which accel - n3d5j rgvj b65qdjfd;h(0bjerates more?

The Sun's gravitational pull on the Ear)/do)f -jbid0c/ h ceu8b j9lwth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatioc/ jj) boldeh9w-08/ifu cbd) nal pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effect 4x/lp 8vvx+f8zbw0 nzs are at work? Do they oppose each ot+8/pvxzx8fn4 vzl0b wher?

The gravitational force on the Moon due to the 7fof -: m spf8,aq:/omhkd(vaEarth is only about half the force on the Moon due to the Sun. Why isn’t the Mosvahp(k fd:8mf ,:m fq7o-ao /on pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around 0y 5z iv7,1q)varugvg the Sun larger or smaller than the centripetal acceleratio)r 7gqz yv5u vg,i1va0n of the Earth?

Would it require leswp;cea;q wi :ee+x,a ,s speed to launch a satellite (a) toward the east or (b) toward the west? Consider t,wie cw;+,a :xepeaq ;he Earth’s rotation direction.

When will your apparent weight be the greatest, as measuhlc/vh219fpbkkdoqw 2 n-f3h-:w6ey red by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, c2y bfo qn3-hhd29wk:wlk /f6pev1 h-(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 perio-zj b) twnt0o121gnfwds in outer space could be adversely affected by weightlessness. One 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. Contt1ww0-)n1go bn 2fjz sider (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” betwee9vixu5 esx -8dn steps 8uvx9xid- 5es.

The Earth moves faster in its orbit around the Sun in January than in July. Is jc8 znagj;dq/x uw+e hm,u(,)0ttb/ wthe 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 xuwq e hz0n(a) 8mutcb /gd;,jw/ tj,+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.56+ kpst.rb,n3rp hmi Explain how this discovery enabled an estimate of Pluto’b5+.,pi tnr3 6 pskmhrs mass.

  The Sun's gravitational pull on the Earth is much larger than s3r kk,:(sownthe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the ce:osk, 3(wksn rnter 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 198gv ley v6l-4ijf7b rm n.,s,r50 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 qbtqtk96s; q9fx- 3vcits orbit around the Sun, and the net force exerted on tkqbq3 txsq9t;6fc9- vhe Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates u;t v4h,u+pgmx niformly in a horizontal circle (uv,x+ m 4;gphtat arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circlhy5seok* jj ,/es 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 ohj5/jyk,* e s, the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on th)0l.g /,bihyq dk l2qyr5qji7e edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the 0yg lyjibqqk rqhd./)5l7i,2wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cirzy4q/ 2c/aa;hpud g6l cle of radius 72.0 cm , puzya6hd/ q4cg; la2/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 round a turnnjrvev-5(p )5bvv s/ q of radius 77 m on a flat road if the coefficient of static friction between tires andjpvr e(s5vq)v/-nb 5v road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the5hlhlc hf9:2o . (ieqa road if a car is to round a level cuhah5chq2l9e io(f : .lrve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a s(ix uoa)pz m0x(5 jd1-rdz,2wke-8bpy:fq e trainee in a horizontal crwo 1fm(djq-e-s ip z au25xdbx0:k,)p ( 8eyzircle 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.. q*o,7a fudam0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static fofaqa7 *m.,duriction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dopbous 4h7(j3y rf)2mjsi ,fd/wn at the top of a cir4psdyjfh2f (7uir3)o /sb jm, cle
(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 d -u)ox/b/ wvln5be i,iriver) crosses the rounded top of a hill (radiuw/)/,uib n i-5lvxe obs =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 wour 4q zd:/x:djild a 15-m-diameter Ferris wheel need to make for the passengers :dqjxd/:i 4rz to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirlh2lz-u5j+8ysff , wd 01r uos61uweq sed in a vertical circle of radius 1.10 m. At the lowest poiy z,dsh0 s6ejs18q2u-lo1uff w5 rw +unt 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 hum/mmf pe-zd bhzk+7+(d5w+from the axis of rotation is to experience an acceleration of 115,0ez5+ +pmhw uk m7dm h+zf-/bd(00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopl0d/shndxc sb :2rz4flwk81 t8e are rotated in a cylindrically walled "room." (S8r:cdsfdnxk1 8tlz4s0/ b 2whee 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 r6q a0q( (wknieotated 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 ) throwqne06 a(i( kqugh 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,l cx+z1rl0cu8a rk-l3 by not ignoring the weight of the ball which revolves on a string 0.600 m long. In -rxr8zl1c k+ 03aluc lparticular, 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 bn3w i40ne w :0i*rkzchw 3/luz4 np2qryj0m5car 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 massesg0xja0f(wu / j $ 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 diving vxq8 x7ri: cxa:ertically 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 n3 ppn 6l)dbc,and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its sp,p nc l3bpn6d)eed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, g. wb5+ mu arsa-y1 m*xlisb0l1oing from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and ray1 +.1baix mwsl s5u -0lrbm*adial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2sn hnyb qe-)f)a 8 gghid(y,45.90 m . At a particular instant, its acceleration is 4 q)sbg8h fni5a),gedyy(nh -1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth ra* sxej0dps s ( -ri)2f7ap/tqedii) above the Earth’s surfia0j s xrsp s/qp)e2*-t7(deface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g haq4yrp yc676 lj 1gkp2ss a magnitude of 122yk6p rp1cj s7gy46q l m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. T7p*jjyeu43ekt-to6va l 4(nd8l kz5w jd/(nhhe Moon's radius is 1.74 ok 8tpnv j-wa(kejlyz(7563 hjdln*4 4t/edu $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 t5n.72-i0jcvfsmkl1w;t32z i8katbi ix t zn 6 imes that of Earth, but has the same mass. What is the accele8 it2t;n kbs6c-imn730fjkiz. tzi5x21wal vration due to gravity near its surface?   

  A hypothetical planetu o:8)3jqe ajo has a mass 1.66 times that of Earth, but the same radius. What is g near its surface?u8q:joe3) oa j   

  Two objects attract each other gravitationally with a force ofv8w 1zm o.6zfx-ush9z 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accco0g4kkm-ra (*f,k xmeleration of gravity, at (a) 3200 m fr04gkomm(-a,*xk kc    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outysn nxqipuzts01k5+ck hx)y nd 1syf; :;k*.8side the Earth where thegravitational acceleration due to the1y 5+08n: *nc hydk;yus)skqz sxk xfn.pti1; Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ou/ 9n5t gxk5s qf55sdypr Sun packed into a sphere about 10 km ig5 nsd q5/xfsk p55t9yn radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butldqdn3l (,5v ip ttp*6 is now in the last stage of its evolutio* (il3t5pq d,nvldt6 pn, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why ac+e5lrgw;z 0dr(i p-pstronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Cg pc+r(0d5w ep-zir;lonvince 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 locatey em;5 8jtxc29tam c)ud at the corners of a square of side 0.60 m. Calculate the magnitude andej)uay9c2c;x tt5m 8m direction 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 samq xgjr lx.92:be side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturgq9jl.x:x r2bn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the accelvds8h-snd)8 sm* 4alg eration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine th l4an* dg8)ssh-d m8vse mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usingfa9,9 kqg)nta the known value for the period of the Earth and its distance from the Sun. [Notgf9aktna 9, q)e: Compare 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 orbiwol ,c*t2 h bpr)04vctt about the Earth at a height of 3to0vc 4*tpl)hwc2 b,r600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbizi (f.r9k gyl4t 650 km above the Earth. How fast must the shutt i9gyr .lf(4zkle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are u) lnu4hswqs60b)ou+ m ,m kk-to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Questioob hm,q0 s mlu-n suk46))+wukn 21, Fig 5–32.)   

  Determine the time it takes fo*xy-6boh zu g9r a satellite to orbit the Earth in a circular “near-Earth”6 -o*gybzux 9h orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have tb-yy5ybq6zv 1o be launched from the top of Mt. Everest to be vyb6- qb5 y1zyplaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbiem z eslaf:64.t the Moon at an altitude of about 100 km. f: msee. 64alzHow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit (2zjno:l:h+p5vgwi(e bq f6 wthe planet. The inner radius of the rings is 73,o qwv+zbf( jwe(5n: lip2g6h :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.6rkdnb +twugk3;c5 9q 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, r3qwn5ctgb u k+; k96dand (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center ofi()4qi n2qryu the Eart2)nir4qi yq u(h's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star syste ppw*4) ax-sfjm consists of two stars of equal mass. They are obse*xw)pps4f -j arved 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 read for the weight of7 pbs-inbs e gig6es- zc1ynj0vk383; a 55-kg woman in an elevator that movepv-z ge;n-0js6bk3y8c gs3i 1bs e7ins
(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 sd ojl- .k ykxpv5lis0me7 b624uspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator m.lioj e6 k4yp07b-sv d5l2xk accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near t .gj*l ryf-;t d. uktxjf2m74qhe surface of a planet with period T , the densdg;x-ljy k7t2u qrmff. j* t4.ity (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 perios/0t .y.4r5j4 ydt- uzrpong jd of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Eart o45d0-4jn/ tgysyu tzp. jr.rh’s surface.    s

  The asteroid Icarus, though only a e-+w//znhamw:0p1 prqlcw. t9 om.vrfew hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its m. +o/-e.pt1plnrm :9w w/c qahzvw0rm ean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of *e, xafr9o0d zgyi 9b .q8l8wg4.5 $\times 10^{9} \mathrm{~km}$ 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 Sy41+.ed t rrflun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest we. r41rydl+fthen it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxw 4ye (r(am4miy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, k47l aehpa9p/, hdk-by;db m ,period, and mean distance for the four largest moons of Jupiter (thoseb7;hmdpkyb epl-a,ha , d4/k9 discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from theatx wklr nb33jl*2r;; known period and distance of the Moon. ;3wx2bl*;ltr rk nja3   $\times 10^{24}$

  Determine the mean distance from0-b:z,,f xkgcjak e vovk-+(amfp47x Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–0,,kbav+xg e4 xc fop(:-k7fkvaz mj-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 many fragments (which u6d(t0 ua ier7b t(3g i9q u9ljirqb9)some space scientists think came from a plandjqibt9ru ub 0gt(69 (iu9 lqiae )r37et 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 tarwo:yo.k / pi2le describes an artificial "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 distance to the band is the same as the Earth-Sun distanc2 rkwopy io./:e (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 sw nxozs6n l*;5f)3bvx minging 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 the lowest point of his swing? His mass is *l6bm5xv;fxs3nz)on 80 kg, and the vine is 5.5 m long.   

  How far above the Eartt z/2gbapg9c-,kf(sh h’s surface will the acceleration of gravity be half what it is on th/9tp(2s g,cg b zha-fke surface?    $\times 10^6$

  On an ice rink, two sa-h (z+rq 56 ;yvnimmpkaters 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 an5-q yh;nm(6vz+ marp id their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravicq zi wfmj )ve79b56p5ty at the equator is slightly less than it would be if the Earth didn’t rotate.z v5ip5qjbwm7)c9 fe6 Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a 4l fg a4wxebyto/a:dg82 zd 1,spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon f 8w 2g tdoez4daglx41/ yb,a:pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroomr tis4 ogw,9,7,sdkdg scale in an elevator, it says your mass is 82 kg. What is the accele s,dgds 7 gi9k,o4wtr,ration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tuj (w)gjv n5xes ayu: .tytob8.m7y3j*yfxm..be that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Eav)gyo.t m xxm: .s*afebjyw ty8(y..j3n57 ujrth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical m n878 oz-clvn/sfv 0jgd k -pet,6tl4loop (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 rnh*fv5-4hvdabt 8 t:t , the acceleration due to4tn advbt-h8v *:fht 5 gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string):5xqxog wh y4ms(. + p:tii(zf is deflected from the vertical by an.w h(+(yzxsti 4fm5:g qpoi:x angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for t4s r5* kxy:cb frz:7la design speed of If the coefficient of static friction is 0.30 (wet pavement), at whar:sr4k*7y cxftb :l5zt range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at j0*pq i b(k n-ain:id7the equ:di *n7a 0-bjniqk(pi ator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.c. h3ja,(tz8thp-t db8h cs+x0 $\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-f d( :xvmdikmh:b:pc(u /ml0 curve of radius 235 m. A lamp suspended from the ceiling swings out k(m -d/m xf:h(pld u::v0mib cto 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 yc;vw)4t.vtjq:o gv8has 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 s)t4 ovg8 cvw;y. :tqvjuch 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 Space vriul6x; z 83nTelescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense tzv r;in3u 68lxhat it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trqm pyp0 on( x:p( b3g*hu/jz;laverses 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 dy; lzgpo3/p x0hp:qmb(*( nu jriver 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 satellites oagv k m2i e8mh)u 8/5ofmg(cpcvsb16;rbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determigv1/5fbi)2me kgvmmpa ch6 c o;su8(8ned 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 billion km577 mz3yas vec, is meant to orbiy7z s3eam5 v7ct the 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 sh 3p2 ea* sx8; m6z3,kpjasjxk 6c6nxad;cczk.uttle pursuing a satellite in need of repair. You are in a circular orbit of the8 kaz.sa3nkxsxk; mx;6*3d jc62 pjceap,c6z same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) W860* gibotahrk;yf e9 hat is its mean distance from the86ihrb* okeaft yg;90 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 "fb v1 11-5za. gu(e btataqak0reel" yourself gravitationally attracted to someone n5.kbuvz(1ba qe1 0atra -a t1gear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a 1nhdf:m,q sspm: / 8grdistance of a/h ng pfmr s1:dqs8,m:bout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corn-v i/kypc-, y -itjce9ers of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sii-c -,e9p-/t ijykvycde of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg or(zyh l/r-; .h5fuo) )sagcfwx-bph+jbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-2 9olqnq)b9x+ jw 9onklong sweep second hand on your wrist w 9oj+9l )kxonq29qbnwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in i31 6y;mfxu 9s q(jxhca circle below you on a 0.25-m piece of fishing line. The weight sq(6f31yj x9uihx; c mmakes 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 radius R in a new highway is v;xr1 kki3ij02aozn2designed so that a car travelingvzi1a x r0o32jn;i2kk at speed $ 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, t/09kv6es 6xr:ol ef2jrxm-tp he Acela, utilizes tilt of the 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 Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force nemv69xk0/xojr-ree pl :ts2 6feded 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.$\approx$    $\times 10^2$