Sometimes people say that water is removed from clothes in a spin dryi 0paye ar,lo r;y-* 9tmq5tg3er by centrifugal force throwing the wateramot0i q erpl59gr-y* t ,a;3y outward. What is wrong with this statement?

Will the acceleration of a car be the same wh6 )*ham3xiyl g+hq;fuen the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? h6f* auiy;3)x q lmhg+Explain.

Suppose a car moves at consta 6ymi5b ,yd-fjnt speed along a hilly road. Where does the car exert the greatest and least f5d, b-6yiyjfmorces 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 acting vn(*k1k5. mtd rbu7xnon a child riding a horse on a merry-go-round. Which of t. 7dr(k5n*t1mxbnvuk hese forces provides the centripetal acceleration of the child?

A bucket of water can be whirw5-et3ybvux fnfyt jo d* 369(led in a vertical circle without the water spilling out, 6y3 nbuwf j5*fv-3d(yx ett9oeven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you ha rg5s2ptv9j 5d njhbg2pm*zd09 .um endn,-h4ve in your car? There are at least three controls in the car which can be used to cause nubzedh,24mng . d*pd-mjn9 grtsv9p 2j55h0the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smal; e)) lqkej / g1kny5faajy3nr;9d kz0l hill, as shown in Fig. 5–31. His sled does not leave the grounz)aqky j);en3yed 5n/k jla f1g0k9 ;rd (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding alyan0/zi1;h *e +gnq z curve at high speed?

Why do airplanes bank when rrtp7 .ypum0i42q0tk they turn? How would you compute the banking angle given its speed and radius of the ptr rui2k04 q0. mtyp7turn?

A girl is whirling a ball on a string ,a zsa6zbcsz1;mb cq*d, ii/+around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a tar16z s ,bb,;+ *zcscm i/iaadqzget on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitatskf*w7*8puco/ctj .w ional force on the Earth? If so, how large a force?s*t .7c wjckp/fuw8o * Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s or s)gg xtu18e2k8g bz4fbit be differ88 2t1 g4ge)zbs gxfkuent?

Which pulls harder gravitationally, the Earth onf3wnu lw*4 qd2 the Moon, or the Moon on the Earth? Which accelerate4fwdnlqw 3u* 2s more?

The Sun's gravitational pull on the Earth . reqqp-9o9.8lufyfzrsjmj 3wa9-+x(zn6 ycis much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in grq9.zs 9l9xr-+ 3ar c jy-qy.ouzn(6ef p jm8wfavitational pull from one side of the Earth to the other.]

Will an object weigh more at thea 9aizd j92)rr equator or at the poles? What two effects are at work? Do they j2 idr9)9raza oppose each other?

The gravitational force on the Moon due to the Earth is only about half the ff2puc m:j-so*qn rbn4w 19pl 2orce onn sjlbppqw2m*o ru1f -c :2n94 the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger 6zl bhthw6m(w/i e2d+or smaller than the centripetal acceleration o+6(e wlwbtdhm6i h2z /f the Earth?

Would it require less4at 9jc-a-yuj speed to launch a satellite (a) toward the east or (b) toward the wes4jt- yju9 ac-at? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scaleq:71tqls ee (k in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would q(e es1tk:7qlit 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 adverselvk3 qt8ty+jd 3y affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on3+ v tqjyt83kd 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 experksnk48k*re9lp yc-s mh1g 8qrdtc8.4 iences “free fall” or “apparent weightlessness” between strtq91c 84m*kk4-8 lg. rckdyph8se nseps.

The Earth moves faster in its orbit around the Sun in January than in Julyiuh w:8+* c6xsfcgj4y. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in produchc +xgcj yi6w:4 8s*fuing 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 discoveredh mq nb3bumnu1whcml +*.-, ca4ri1s- to have a moon. Explain how this discovery enablm-*hn lqu+ wsmn 4-b,mbhrci1a1 . u3ced an estimate of Pluto’s mass.

  The Sun's gravitational pull 1kls/ .tzwrd,2 gzv7ion the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain.vi1 72ztld,z/r kws g. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling n5:e; lcf)qb q*nse :aa,bz/md62hfl e (;vjt1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 its orbit around the ; gt+n t6nrmc;r +0je )z0xl a/dfsjqma2mn81 Sun, and the net force exerted on the Earth. What6t+xa0zjn;ln+/ s)t;rq 2 mfa cemm 8nrjd1g0 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 v)v5yddfx 2d9 exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the disv25xd fdyv) 9dcus.   

  Suppose the space shuttle is in orbit 400 km from thes 975bhamaa ;e Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the 7;5ah9ebs ma aspace shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the 8jbtx7e: fd7r edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diam7tr7f8exd jb:eter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ra0 gnx,j2afyuj534koax vs+0bte in a vertical circle of radius 72.0bj5 f3gajnsu0 20xk+ ya,o4 vx 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 w w/ea+nin 2wu7t v-r-)8hymc mith which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tivrytcmw) h/+we iu-8a2m7n n-res and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coef3pkwsu3cl 51zq(ni3 w0v: nwz ficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 l0wwz 3u5v(ni: pzkc 1s3n3wq m at a speed of 95km/h ?   

  A device for training astronauts anuo5mmrger)/saf 334 ir* 1rlg d jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . Im*rl g)5mo 3rau1 /fgrsir 4e3f 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 axisr-f5f i 0cl 3,gdbe(ox of a rotating turntable of variable speed. When the speed of the turntable is slowly increased r0,b3f-ldfc(5xigoe, 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 travelingqq ev* us4:1wnwez ap;94 bk:o when upside down at the top of a c19k sw ea4* o4ezbpw;:q:uv nqircle
(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 gs3:m7j 1j* esk3l+w dkp8hzttop of +e l:h szdj7g *8 pkwjsm133tka 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-diametetw(g3/a eoak:km+r 48ywxn2 r r Ferris wheel need to make for the passengers to feel “weightless”a8ra :kxkw 4o(mnw /y2gt 3e+r at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Atsya;l,p xclm ;kh 8g*0 the lowest point of its motion the tmayl s;hk xg8c, l*0p;ension 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 z tyljp7j)+y* a centrifuge rotate if a particle 9.00 cm from the axis of rotationy 7tl*)jjy+ zp is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricallk t032qtwuz,41e:1plqzxubo a3no 8 ey walled "room." (See Figtl0k2qpqbu14oaxz,8 e 3 nuoetz 3w: 1. 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 frictio0mcf9hpm wd0 rh+)ix3 nless air-hockey tabletop, and is held in this orbit by a mphd x0)f03 mwr+9 cihlight cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the baw:hejbi .u 9,mll which revolves on a string 0.600 m lo,ui j eb.9:wmhng. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectlykks 1n2)q z7f x7, z)vh8snlcq 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 massesu 8rup/ar4.8r vu:eiw $ 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 kva ; .) (;jdxpc gsb;2c8,wokmuf+civertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal componenvw b4xw vu) q/l )q;jgq+ak*:zts of the net force exerted on th+ :uqv)k/;wgwjq*qzb4 xl v )ae car (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 500 accelerates uniformly from the z10suzmqq s- t::yy /hpr,uv (pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway 0u rq-y,upszs/hzq 1:tm(: vy 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 ino n41-b,9b fxxkld(q:d a7; dh*mh bgb a horizontal circle of radius 2.90 m . At a particular instan7hd 1 nak(dd:4qhbblm x-bo *9,; xgbft, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraa. ;xg- yh+bq7-wq,o bog,su8a m 2fkyft 12,800 km (2 Earth radii) above the Earth’s suqo7sg b,hyaw-abf;qg8,2 x+.mk o u-yrface if its mass is 1350 kg.   

  At the surface of a chx )ike9 j*rd4 en7sq2ab.6djertain planet, the gravitational acceleration g has a magnitud e )axi d4j*2b7nd6j.qse9r khe 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 7eh9, / gw+xs ug2qjkxgravity on the Moon. The Moon's radius is 1.7whxg+,u27jeqsk9/g x4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1 p2d(/ao7okxn.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near it/72 npxao o(kds surface?   

  A hypothetical planet has a mass 1.66 times that of Earttt6ghj9 un3n)h, but the same radius. What is g near its surfacu3h )jtg6 9tnne?   

  Two objects attract each other gravitational* ys2b 0yivjaov )ryjui);, ,xly 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 vbouyg49v c vi s9 ak.cg3,2mo/alue of g , the acceleration of gravity, at (a) 3200 m g m3byvv.,g socc929ou/a4ki   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ,socqn4: ysf f4o py ew;:/wl1outside the Earth where th f/ p;lywqo:y fewsc4s:,o14n egravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has f58fu1xzg n. mz fmra:9ive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsterfnaf zgu r1zmx .9m85:.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b5xo z 4pbhx 5adiwb:88ut is nowdapzh4bi55ox8 x 8: bw in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spac k64+dca.2-e iyydk fye shuttle. Your friends respond that they thought gravity was just a lot weaker uyd ycyf.da+ 4i26e- kkp there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at j6*3kiuk .ti(g5pb dh the corners of a square of side 0.60 m. Calculate the magnitude and direction of th3b 6* g5iuikjk dp.h(te total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mossbpk*3qr*uj)fp0 j nnse0p/)t of the planets line up on the same side of the Sun. Calculaekrbnpps * *p jnfsu0 q))3j/0te the total force on the Earth due to Venus, Jupiter, and Saturn, 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 acceleration of gravity at the surface of Mars is 0.38 of wh4fqam 6uk0ay, at it is on Earth, and that Mars’ radi6m f,qa y4a0ukus is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value foys 3tru b;wu/ vhw3;d4i.rgh 0r the period of the Earth and its distance from the Sun. [Nots 0wbdruw4vh 3;it ;hyr3gu /.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 circulqq; /jxze1,gaj 2x.pwar orbit about the Earth at a height j.qqgazj2 pw, ;1 x/exof 3600 km.    $\times 10^3$

  The space shuttle re :tw)3 vnuguarn5 4w8vleases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be 4nnu5) gurw83w:t av vmoving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan8 y 71wamzk2knts are 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 Question ayn1m k z2kw8721, Fig 5–32.)   

  Determine the time it takes for a satellite to orbi rckma3+ 97q p3hjue0nt the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the sure q3 cnpa3ku7+ jrh09mface 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 satelo-wwv 83. n4c tqjo)kblite have to be launched from the top of Mt. Everest to be o v8c) bwqj3w tnk.4-oplaced in a circular orbit around the Earth?   

  During an Apollo lunar landpeudpx 8a+pr4i8j-7y ing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How pp p4-dxa8y 8 eij+ur7long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks *, ztcxd qgpwy3cwhi2vx(2 ,k( xu 3,yof ice that orbit the planet. The inner radius ogixh y2kxcu,y 3c d (pw*,32twxv (,qzf 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 wsr9q201f5 b*jig ho bin diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a perso 5gjiq91 bh02wrb*f son’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of avct(/esx o9tzxzk-+2l,lqp5d jd, +y 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving jq /d,xtvt,pl(o k+ dsz5y xe+zl-9c2at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They a 7ljxf)k8lr3u re observed to be separated by 360 j7xll rk)uf38 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 of a 55-kg woman in an elevatqh.rbw7w25lmk 7b s *lor that mokrbw .lw 7lbm5q *7hs2ves
(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 um;*y7..html. g wcbd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as theyc w mhgu*dtm. .b.7l; elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surf+ riuezih483gace of a planet with period T r heu4izi8g3 +, the 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 the Moon (27.4 d) to determine the perinil 0e 4f.ia7nod of an artificial satellite orbitingn l4fe0i7. ani very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrov 2) y;8 fpx/pcx2+abrf7f b7u8gnkdoss, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fromn7fg 2 cuv/f2ryf8 pdb xkaxp)o7b8+; the Sun?    $\times 10^{11}$

  Neptune is an average diu do( g0)-kvpu3gty* fstance 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 b39qsfy5ta 1i Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest apb3qi1s5f ty a9proach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center8 4adw;s- i9jufo jq,c 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, periln8txwe1f ;7y)r f 1vbod, and mean distance for the four largest moons of Jul f8n)1bxyt7e; r1vw fpiter (those 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 the known period andddaj: e.w6 ve:)n8y-fay -hs 3:tvqii distance of the Moon. sth ei.yvv3::dfa-)6n j 8wqde -yia:    $\times 10^{24}$

  Determine the mean distance from Jupiter for wzu, blehtpd-y5 p 53:each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valt5 3,d-hepzb:pl uw5yues 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 (whse273mvu 8*s9qlu m4+mjh dm gich some space scientists um s4g*+j em37m9s2mql ud8hv think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the fkwbm;.:4w rmqorm 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 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 ywb m4k;w .:mrqear, in Earth days?   

  Tarzan plans to cross 4azl7vypme:yj1;s 2 k a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms py y:z7vj2l1s km4 ;eaare capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the +6f zagowh71co,e c1k acceleration of gravity be half what it is on the surfw z e1ha f,g+6c1ok7coace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cifrwux85;,5dr oyh f / 0iolq+rrcle once every 2.5r rd5h8iq flfowrou+y/x5, ;0 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, p4vn :sh v-zla)a6nx) the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotateaan-)x :s vvplz4n)h6. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will -n avbm2w jjp mpm)z,kupe8 2z)03j f3a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earmf2z vj3abpuj2p)km)3m w enp jz8,-0th and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but whe1 xnj qp8s;fn1,p7tpen you stand on a bathroom scale in an elevator, it ; ptj pn78,qpfsx 1ne1says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists ofnmwe(p vnjr m81to ++0 a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about r0mp( j +mtonn+e v18w1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig(0* 3owyyk xt;sid5qm. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r +q7uiy7+ryee , the acceleration due to gravity at its surface and the gravitationaqyu7ee r+y7i+ l constant G.

A plumb bob (a mass m hanz.qb l,f s2qi)4fw.cwging on a string) is deflected from the vertical by an ang )w.2 fwz.i,ql f4cbqsle $\theta$ 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 spi9kwo9lwdg *)eed of If the coefficient of static frictionol 9dw9)igwk * is 0.30 (wet pavement), at what 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 o2z /hnzjyg9*qzw7 +q at the equator werz qywz n+h*9goj/ 7q2ze apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dista t2jqj)xp6 oc.nce 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 o,kzy0 a)1, 0k)keqgob wo:bc vf radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5kv )0e aqg1, ok):wcbbzoy,k0$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as bjv j:7f9ng5zg) /c:avo o xq-massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calcjon xb:59:f7 a) g/ozvjgvcq-ulate 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 deduced the prj v(du ;w1l4jqvwrz ica0 2t:3esence of an extremely ma;z24 0j v(arqid3ut c:wlv1j wssive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed 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 shown in tvn ;0/vgb)p6js5lbi 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) Whgv 5 i)/t;jsvbp0nb6 lere 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) utyy: p ow a +fr,;(+dbvanok/0uilizes 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 altitudofy +kdy:,ornwav (u+/ap;0 be 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 (NEAmmw6j m/:e :teR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Er:e/ mmm: 6etjwos 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 need of rjt -*s4u3gt:osd :kiy epair. You are in a circular orbit of the same radius as the satellite *jdotys-: 4:3iuskt g(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) What is its m84 8sx0o lowdxean distance from t xd8swl08oox4he 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 bexoct,)l1w0d3uxt,exv h p8y. if you could actually "feel" yourself grwxxely )8td0vux3p ,,t h.co1avitationally 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 Way Galal(bfqvom 1(*edxu 2 l0xy (Fig. 5-46) at a distance of about 30,000 lightmllf20(xbv* 1(ude qo-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 side. gv5nssjjkw jm 3268-o* c(xx pFind the magnitude and direction of the gravitational -*cw 2gs6kv mn (xjs pjo3j85xforce 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)v *vq.+ zy3 o(lx lf:jg(zelw 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 tioi*ot,0k(cq ah g2l 1vp of the 1.5-cm-long sweep second hand on your wrist i0t(hk2ga*c,o loq 1vwatch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight c)ilg,/fui zc0rz 3zad:/ (sfaround in a circle below you on a 0.25-m piece of fishinz)iu 0f /li/cgdz z3(fr:a,cs g 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 p y) al).cmx-hnew highway is designed so that a car traveling at speed c)y.mp -l) hax$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilttc9vi qrm2ndv+ax ) ;, 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 for+2,q xc9;rav)n imvdtce 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.$\approx$    $\times 10^2$