Sometimes people say that water is removed from clothes in a (:z 8 xpc6r6jznfddw ;spin dryer by centrifugald rz df6 6x(p8jzwn;:c force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when thew ypp:/5fum )ud px/c4;e1rnr car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the ruf;) 145 xmywcuppern ://p dsame speed? Explain.

Suppose a car moves at constant smf w(sbd 0x o9(n4af(wpeed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between(fna9 bw0mo( s4( dfwx two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forcesjcs7v w/ki -5h acting on a child riding a horse on a merry-go-round. Which of these forcvs -kic7h/jw5 es provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wnl,kpwnhm km bq155 +i5v 53ecithout the water spilling out, even at thep3bh ,5w kem55l nv icq51k+mn top of the circle when the bucket is upside down. Explain.

How many “acceleratoz bpja j0-6kd w4ve0a8rs” 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 8-v4e60bpjjk wa0 adz they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill,t*jwltv+ f,m(w4z(z)1t p wlj as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force btv1l)* jz+ w(p(w f w,4ztlmjtetween 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 rouncu/b1nkci8f, ding a curve at high speed?

Why do airplanes bank when they p b zb97lg;ao tk7rc58turn? How would you compute the banking angle givenk;tb co7blz9pr7 58ga its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane432kwu4t em5v9zx s hx. She wants to let go at precisely the kz4swu mve2x3t4h59 x right time so that the ball will 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 so, hcbby;2ay,b z 8ow large a force? Consider y yb,8z2bbca; an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whf42be2tilh0i:* qt g opixf+7at ways would the Moon’s orbit be dp4if l xge+i tbti*0: fq2oh27ifferent?

Which pulls harder gravitationally, the Earth on the Moon, o*k.e2c 8 l.vpdiuk fxq h*6.cvr the Moon on the Earth? Which a*uq*ch 8lfdv6ckp ex2..ik .vccelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moondak6) e/ii:p g'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 to6) gi/eaid k:p the other.]

Will an object weigh more at the equator or at the poles? What two e3; +dgso5;rud z2je jzffects are at work? Do thee;j3gu ; d2 jdor5+zzsy oppose each other?

The gravitational force on np5p+z 9x2h(cm xjg rfywr9+ p6/.k pxthe Moon due to the Earth is only about half the force on the Moon due to +/ zrx.5j9xp6yg p xmr k(c +p9npfhw2the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around ta6+.i dzki; ev.t-ca she Sun larger or smaller than the ce-s;ia+c.etikzd6 a v. ntripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b)1q+ig 2 kmefo2dm60 sn+g ukj ee4ol6) toward the west? Consider the Earth’s rotation gkje ef+ue olk0imo2m)s6nq+1246dgdirection.

When will your apparent weight be the greatest, as measured by a scalerp9+m r: l vlckk)ab)7ipqs)u;vn ;u; 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 wesviqb;lm ;nl urckk )v+7a )u pr;p9):ight 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 adversk5n.fl luso/a ; 9+*-lnrmll sely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cyl;ls.o k+na5lml u sn/9-l *rflindrical 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 fal. *df/-u 1 1idzfchsarl” or “apparent weightlessness” between steps.1cr fh*f.ziu-1ddas/

The Earth moves faster in its orbit around the Sun in January than i+ed iq+ ifu 46,bp2esd5wjz,b n July. Is the Earth closer to the Sun in January, or in 5qb+6psw+4jb eiz,2e u,d dif 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 diheiw4j)i tzr u1p 5z 1.;jmlkl 8g sy+9+dd5ugscovered to have a moon. Explain how this disj d+i 9j m5ldrg+y1 sg5; e lzptu8hi41kzw).ucovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet hl g-t(gk1d*h5z u hh3the Moon's is mainly responsible for the tides. Explain. [Hint: Con5dh-uhh(h1l* 3tg g kzsider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling ,97x 3ujsuska 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth i* 6g egvh3l2vfs)l 6xtn its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth vx2t6gv )g3l6h s*elf'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 2+ 1u.f4vjyovq 10 N is exerted on a 2.0-kg discus as it rotates uniformly in a horvo.+1u4 fjqvyizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in spc 76s2,uue0c 7xs wzorbit 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 ucp, zxcs 02e wu7ss67orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceler)vs3pds 2m r.xation of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolution dps32vs)r.xms per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is rev5.6ycr 1m hxsoolved at a uniform rate in a vertical circle of radius 72.0 cm , as shownohry56ms 1cx. 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 aqe6mb-y f;w8which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static eyfw 8mba6 ;-qfriction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefflhq.r c tu00;iicient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a sr; uith .0ql0cpeed of 95km/h ?   

  A device for training astronauts and jet 1 g gxzcyq/b*7k0p1zofighter 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,cgg py*/b 7x011qozzk 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 froxq9t-xp f/b7.v1c imyax bx53m the axis of a rotating turntable of variable speed. When the speed of the turntable is. cxif y19xqxx- v5b3/ta7mpb 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 the turntable?   

  At what minimum speed must a roller coaster be traveling when upsvf/ u/1ht d d3cdf,qw sp j5w,/d21qgkide down at the top of a csdj d3w,, f ufk1t/q d/hgp51qvdc/2wircle
(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 driverqtknkr(0 cr7ht)h k.v*.op;g) crosses the rounded top of a)0rt.gqp ;c v.hnhktkkr*(o7 hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-dia.e cmp *ov+catj.1h. g2l2ryw jl6y(i meter Ferris wheel need to make for the pa jvol y*pcrh(61gjicw.elt y +a..m22ssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiuoyq0nu8d +*ossh5 hg8s 1.10 m. At the lowest point of its motion the tension in the rg+ s8u*h8sn5hood y q0ope 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 axis mmg; f28-nfqhd2coo ;o2d cn8fm;2gqh o;f-omf rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyl+kkbk b;(be f2indrically walled "room." (See e(kbf2b+b kk; 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 rotated in a circle on a frictionless air-hockeyvz kc/fy( ah 2h/74jpm tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throughp2mh hvc7k/j(y /a4 fz a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weighqy q-jf4wiw77gj d +o(t of the ball which revolves on a string 0.600 m long. In particular, find yj47qj(+ gwoid7 - qfwthe 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 radix-9 hf2iwkjwr/y u*;.b* m .jjwth/jk us of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masseswrg) ni9+, .jl3ovdn-syi :w u $ 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 dedzf 5qh+x 7u7iving 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 an2k.1h mfddog0,zfza2 d centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed isfkzdg0, 1ah22d zf om. 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, going frf s 462g lycnm*y;cp/-* fpkjoom rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? lfcjm-*nfko;gpyc s642/yp* $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pac+bb5fb my8b/ rticular instant, its acceleratiomb y+b8fbc5 /bn is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Eaze8fz6i 9hochq:1 i jd::no jb(px,ac .n.+mfrth radii) above the Earth’s :jeia 6jb qo 8:n(,h1c.zof: 9ndih .pcx zm+fsurface if its mass is 1350 kg.   

  At the surface of a cf cl/(cg8;federtain planet, the gravitational acceleration g has a magnitud(;e/fcfg ld 8ce of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radiu o)q.)pf2cqkfs is 1.7.q fkqpco) 2)f4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the s-x kwrp9.1 yikf5x. 7cw v8ybcame mass. What is the accelerati 8.xbyykp17i-x95.wrvfwckcon due to gravity near its surface?   

  A hypothetical planet h 4 s ia*l35;/ichzmy8ae+eqo ias a mass 1.66 times that of Earth, but the same radius. What is g 5ecoh zeqaa4*3+liiy mis ;8/ near its surface?   

  Two objects attract each other gravit)tgafoca/ 9bcsg6g0 ,( i/bxv ationally 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 , the acceleration of gravity, at (a8f7 mtr9ua)fa) 3200 m turm )97 8faaf   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where ti.9 .nwleas8shegravitational accel.e9issa.w n 8leration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivbjjc0bmwyf-f 6:jf.6h 1 a4k we times the mass of our Sun packed into a sphere about 10 km in radius mhfw4 6b:.-jj a1ky wb06fjcf. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf s/tv)iopd z(fg 87 6swlm04k wetar, 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 mas 86/zptw)fmwk (4eisl o7d 0vgs of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting q5p xxmzeulq:f w80el5x9 e+8 in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the accelepq9 ee5w :mqxx f80e85lxuz+lration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side- 3 /u-mk9noofr87b6lod uymf 0.60 m. Calculate the magnitude and direction of the total gravi/u-fymkd f 3 loru8no697b om-tational 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 +uaw1h a5 brk.q,rzn*2xw* kvSun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets arkuq2 .anw* r+x,k*zbr1 hvw5a e 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 acceleration of gravity at the surface of Mars23fm7/h h ezaa:s eg6c is 0.38 of what it is on Earth, and the/7hag6c h saez2 3:fmat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of th ;n uhecfve0/6e Sun using the known value for the period of the Earth and its distance from u; 60 vnfhece/the Sun. [Note: 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 orb w*rslqowe(,8it about the Earth at a height , owe(rqslw8* of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into z-or kfqft-4ak m )(xu.d0k)sa circular orbit 650 km above the Earth. How fast must kt0rk zo fkx.)d-f(4ua)q s-mthe shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to ex71y na 3o +vd2rjj8tydb/ ht5eperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time neh5bt13+doje/ y2vydtr7n 8 j aeded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a cir 0vgvd8las6v r 5j vxij9;;2a xfvrh0(cular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth wh a(r0f rvv9 hg8jv 5 va26li;vsdj0x;xich 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 satezh2 /klli s susx-7t*.llite have to be launched from the top oftlxshk.zs/ l -s *u7i2 Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the comm*a,jo.-; q nzpe lkae7and module continued to orbit the Moon at an altitunk , ala7e*.oq p;zje-de 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 pcml9 j6xp;,1/7egr nnam+ yii lanet. The inner radiuscnjg;r97 eyl6+1mi /a mn,ip x of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s ldz nl9n0j4s5 (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real 4 9lz0l dsnj5nweight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centifcd 4ia8 sks +m)8y.)+pa l n/jb/oljer of the Earth's Moon in a space vehicle (a)cmisyol i .) /+l8+afjdksb4) p8an/j 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 oor3w6ax * f42bjv)e92 aagrb mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway e2*go 4ra6faa 2jxb)ro 93bwvbetween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for thegu0n6t4da/a lkn +f9owvul5: weight of a 55-kg woman in an elevator that move5 g ol 9dnuka :w6af/04uvl+nts
(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 froa+ xi/xh4bvuk o40f+p m a cord suspended from the ceiling of an elevator. The cord can withstand a tenk+p+afi4xu xv ob/0h4 sion 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 v kmiwzkdkh8 a -h- n*96ej-x)zery near the surface of a planet with period T , th km9znk*- ez-)jkd6-x whi8a he density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the7gs,lcfk m 9w- c.ocr4 Moon (27.4 d) to determine the period of an artificial satellite orbim7 .4,lcrcfsoc g9k-wting very near the Earth’s surface.    s

  The asteroid Icarus, t4iry 2 xj )x+jxij,3zxo-v0 cghough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean divij- zj 2o+ 4ri0y,3j)xxxxcgstance from the Sun?    $\times 10^{11}$

  Neptune is an average ;:q/ef7 t g5gn(sv/xqo ,szji.qh-lzdistance 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 ev 1q yarb7-x *a7cwhmwl/rv((tery 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 when it is out there? [Hint: The mew m 7twrqva *(xrl-/chya71b (an 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 9f2v5 bdg b.ytthe center 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 the four largest 4f+ aa.h;fym.o iiiyu 67c/ibmoons of Jupiter ( 6ohab +.u4c f.7 fiiiy;i/maythose 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 t p4 e57qcq-akuhe Earth from the known period and distance of the Moon. q45kpe-q7 uca   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, us zcjk 2 k*.kixo(f61jbing Kepler’s thirdb*2ixz.ko k j6 k1f(cj 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 consn77 bak4 -h)luhwvn fn//sa8gists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was8lwfbh/4 k)7g h/n vnua7ns-a destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a baymzbpp x2 awenn.3,g*l +idzh-cal/at: k/2;nd completeln+aph tnlb yx2z/3 2,-e;m pwgd*l/z:.ac kiay encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), 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 go; eaoq3s.di1yrge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the asoy3d ;ie1 .qvine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelp9b rpx,4tgi ,eration of gravity be half what it is on the surface gb x,t4ir9pp,?    $\times 10^6$

  On an ice rink, two kpmom 51l/a 8gf zs)2tskaters of equal mass grab hands and spin in a mutual circle once/agl fso)m2t1 5pmk8 z 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 they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration o157i f.8v+slezn* vvnu3umu nfv*5r .meh mc,f gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What frs.f7l1.c +nzuv* mhu mer,vi m5*n 5vf3vn 8euaction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft m( 6pn+b l(vjw- 3qcbn4c 5 k7fsv1zzetraveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull j c- zf7c5lsbq( +1k3envnzb(4p6vmw with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand a od e3sb3b- -;ahlek,on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dire3; -blsdkea-o,a 3eb hction?     ----待选择----upwartddown 

  A projected space station consists of a circular t3ai3itty9.w y) xs)sulx5) nu )-njpuube 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 ro xwu)tin 3 -ysuy)us5tjn .xai93) pl)tation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fi0a;l y q)kswpfi7q*h/ b- by5dg. 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 termsid wvhn() 5m:b)p71yrzfa f4r of its radius r, the acceleration due to gravity at its surface and the gzh47)fi 5f a wrv:1(mpdr)yb nravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by anr ug cny;+s)0:mur/vn angl: r+0y un n;mg)us/vcre $\theta$ 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 fo qc3:o 0l38 lxwktux(wr a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curkcuo3 qwx w8 0x3l(t:lve?

  How long would a day be if the Earth were roe9z+yf al:dxkkfpp w19g d 9di8hl-:2tating so fast that objects at the equator were apparentpa-kl +1 gd:y8 w2:9z9dfxd fh lpe9ikly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constxggcqx2etz 1k5o4+(h, th5ag ant 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 radiu3 xl xwx1ho4 bca4.g :4v,fr-rmlhwk5 s 235 m. A lamp suspended fromhkml4f,r3bwc5h xl-4:o14vr.x a wxg the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it hasi-- fb+j9k76es m, irk5orgie been claimed that a person would be crushed by the force of gravity on a planet the size of Jupit-ob,gm+ re5s-jkf i7ier6 ki9er 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 Space Telescope dedp )sx5*z ktxl-uced the presence of an extremely massive core in the distantkzl-* ) ptsx5x galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley show7drrj :s9gl ;dn 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 j;:d 9g7lrrds 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) utcx62ba n*v1hb ilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellit1bvncb6x2h * ae.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 0e 5:2evljq qrdwb61 l2.1 billion km, is meant t0qjl6 lr21edb5e :vwq o orbit 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 shuttle pursuing a satellite in needq mns77n9t x:h)odj6i of repair. You are in a circularjnxnq:oh7i )d6mt97 s orbit of the 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) Whabgo8*u x)*),(wiqt: itylmu t t is its mean distance from the Sun? o):gx tql uu8b miw,(ti) **ty  
(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 cou eg*zwx*r/p +ild actually "feel" yourself gravitationally attracted trew/zx* +gp* io someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of )0qlolc*1 qlw the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yeal1cwl) o ql*0qrs 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 cornerwltl.v6 5a04nuq d v4qs of a square 0.50 m on each side. Find tnuqt4lqlw 0. 6v4vd5a he magnitude and direction 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 5500 kg orbits the Earth q 6;w vfarobk4jo0r+yk 6,s4 q$ \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 experie0q )0o)evzjl2sfx4dt nced by the tip of the 1.5-cm-long sweep second hand on your wri40jz2)do x)ql esvft0 st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a smf)p96ih ;rt +11dye(-1j el tziy ktcinker weight around in a circle belor; z-)t(yi 1kye emtf t96 1ip+dch1ljw you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is dsxpfl+)3f6q2gwp3q designed so that a car traveling l+fpqp)sfg2 w xqd6 33at 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, blb ;)y56bk3 b mv9on/ttx:ae the Acela, utilizes tilt of the cars when negotiating curvevb) ;ob tbeny x5bk9:ta/l3m6s. 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 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.$\approx$    $\times 10^2$