Sometimes people say that water is removed from clothes ebafd .inba6p46: x3z in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemenf aba z6:34xnd pib.e6t?

Will the acceleration of a car be the same g*fa1ulg97 o.meeq d- when the car travels around a sharp curve at a constant 60 mqeg-7lgue 9o1 *.dfa km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do.czix, :9ye ; uht gpp6 1vq6no(mlz)kx+e5ywes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a le h z+ );xyt p1:x,9wlmee uqzip(o6y5gcv6nk .vel stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse a1i ;0.jjrfbi on a merry-go-round. Which o1j ijibrf a0.;f these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle 1pu gds1+)y* )jkr vbkf6cmi4without the water spilling out, even a 4 pdk+ ) vm*sk6fci1)1yubrjgt the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have ii wi3ff5 7 43npqeq+d0x g8nztn your car? There are at least three controls in the car which can be used to cause the car to ac+xiw8 feqn dtni334 7g0fpqz 5celerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, asl b96 aqdpvhfbx.1 k41 shown in Fig. 5–31. His sled does not leavl91x dhb .b46f a1pqkve the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inw4szz-x8ddfq/ ard when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you/f820m+dm yzo2u fuw i compute the banking angle given its speed and radius 2fmufy+8 0w/ iuzdom2 of the turn?

A girl is whirling a ball on a string around her head ine5ib*y8 ksg c; 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 shouldscige yk*b8 ;5 she let go of the string?

Does an apple exert a gravitqpc)vfvu nml 1/7h9; qational force on the Earth? If so, how large a force? Consider an ap9v1) pq7 m lhnq/c;uvfple
(a) attached to a tree, and (b) falling.

If the Earth’s mass we( *h +okowv1tdre double what it is, in what ways would the Moon’s orbit b *1tohkov(+ dwe different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon otg hw *3nue583k jm*wdn the Eartk*t hm5*8gj3w wendu 3h? Which accelerates more?

The Sun's gravitational pull on the Earth bc*ygne .xlg r yli-(;b9)jc/is much larger than the Moon's. Yet the Moon's is mainly respons-j.lye*(g9cnb y;lxi )rc/bgible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mo gd a8g(zptt 94jpm-z3re at the equator or at the poles? What two effects are at work? Do they oppose each ot( gg3-9dzjzpp4 a8m tther?

The gravitational force on the Moon due to the Earth is only i evud3qvp7si8*mh ,:about half the forceq7v hevsi id3upm*, 8: on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its osrlsfp33;j wby/2l e/ rbit around the Sun larger or smaller than the centripetal acceleration of the Earth?b/y j e2;w3rlp3l s/sf

Would it require lessjw)7haqs5a3n. i+s2 jpic t ,h speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dire+i2 , ahnha57)jq3p.ti sj swcction.

When will your apparent weight be the greatest, as measured by n v q1nuo8/i6tuzyzwhv4 3m73m r*e6ta scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cas6q*v6nm334w hi v1rtm/yn e8ozt7uzue would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely a*yh)1 pwc( dwx9t/-zgrz7qzi ffected 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. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any ri(* )/7z9dcp1xtg -hwz yqzwother aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “app g1oeyw86wt-,y. hyb4 2xhjl harent weightlessness” between steps6lhhjgy w ,21 y.b4tyhoew 8-x.

The Earth moves faster in its orbit around the Sun in Jan 2pdu)-mok6r iuary than in July. Is the Earth closer to the Sun in January, or in July? Explair)2mku6o dip- n. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a b wcs15 b.9pfzmoon. Explain how this discovery enabled as5z9w1bb.pf cn estimate of Pluto’s mass.

  The Sun's gravitational pull on thedubewhfu* .-9 ,i-9/ katyjd q Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from u9.aiuy-ted b9*w/h- dq,j kf 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 1d;nf),+(w w;9 j *dvxdeufrry980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Ea:9fao q 1/ftjurth in its orbit around the Sun, and the net force exerf uaq/f1j9:t oted on the 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 w. ;b(ful g 5ie4pmq+wis exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lengiqwl(.peb;wf 4g5u+mth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttl 7x a-t,h gga2xz)we*we is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational w* -ez) gat7xa2gxh,wacceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of aqj dt3iow 18o: speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter ioqtwod:13j 8is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verira0n(xhr .kng 7 9i5dtical circle of radiunir9krn.0 adhig 57(x s 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a x+12if5cxe1l( 2ijx lm8n zebmh n02oh5jh9i 1050-kg car can round a turn of radius 77 m on a flat road if thejhn ni f8bozm h902 1 l25xe2jchixl i5+ex(1m coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefj3 h+go 07swfo4uueu1 ficient of static friction be between the tires and the road if a car is to round a level uo7hs10ewuj+gu4 f3ocurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed t(1rz2( 0untvtu qc t4oo rotate a trainee ino(uzr12t0nctu(qt 4 v a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turnt3rvs6xhyso+7 j ii*m*gv-fud+1:ju 0m dc dv)able of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the tu+6vsm10: iv fiyhsj3 c+vg doxud-)djmu*r*7rntable 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 roll- ov.e58katxf.1rv zn er coaster be traveling when upside down at the top of a civn -..kf t a1zovr8e5xrcle
(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 roundq5vuj7qnh 8 9hed top of j98 5q huqnvh7a 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-mw aemonusy, ofph0 r0bmfs .;nn 5r2. 5h+).fdiameter Ferris wheel need to make for the passengers to feel “weightles .+.o;fyn5w,)uo52sfhs. nr h fmm0merpa0bns” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticakr4 degycbrm - .1fg./l circle of radius 1.10 m. At the lomk rgcd41. r/eb.yfg-west point 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 ce6ra8n;tcu z e+a e9g/gntrifuge rotate if a particle 9.00 cm from the axis of g+;urzt8gc an9e /ea6rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrica. ;k tmzh1cz-x9o:fmt lly walled "room." (See Fig. 5-35 hxcm;t1fz.z:-mk t9o.)
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 uyxz1 lamz u4(1+( awaa circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danyz1(aawu xmulz(+14 a gling 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 *)e yovtnb)x3h-jyu d ( w(:zutime, by not ignoring the weight of the ball which revolves on a string 0.600 ) w*d3- hy:ouu (xn(bte)yzvjm long. 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 perfectly banked for a c3yx8rcl wc1t9 rv d689d inje-ku t78aar 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 massev:4igjx2 ) wv+p 8jppns $ 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 verticati(4 wic/ ri*w;jz/ ymlly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of thea v50jvwl b(/b net force exerted on the car (by the ground) in Example 5-8 when its speed isjla5bb (w /0vv 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 ato un0hnw;y( )ccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the cunu wh nyt0;o()rve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At 4)snk+n4im (nal8/kbycji9h a particular instant, its acceleration is i nb l4nmiyh(jck /8a k+4sn9) 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 spacecr-e c jaddfump(in:9(cf (ul/* aft 12,800 km (2 Earth radii) above the Earth’s s/ iau ((mfd(9e-fn uj:d *ccplurface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelet:)l2nxookkw)+ 3 lxhfv p dp0p(5hi( ration g has a magnitudx(fx doh3wn(kol p02 t5)vipp ) h+:lke 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 radius is v8k ij qa+(2bwhhrx/ m-s 1edbivr3.61.74 b3hxve2 8( mws-r6.ridk/v q+ijha1b $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a 46 wxcpmr4zg7 radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near izmg7p r w46x4cts surface?   

  A hypothetical planet has a mass 1.66 timeyvvu82h,y9uqn s . b*xs that of Earth, but the same radius. What 9 *hqy8un svxu,2bvy.is g near its surface?   

  Two objects attract each other gravitationally wiu *meww-6fte/th 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 ofl x2 n9(tzv,tfgbqd, 0xek0f. g , the acceleration of gravity, at (a) 3200 m fz0kg 2 ,,n xt ldqf0.ebx(tv9   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earkk(89am- ybmath where thegravitational accb9 (k maa8y-mkeleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha4k.m9*lpctx js five times the mass of our Sun packed into a sphere about 10 km in radiusjl*49mx p.c tk. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like o29 jvs -0c:+bvrlqdgiur Sun but is now in the last stage of its evolution, is the size +vcb92dls0-v:i q grj 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 astronaut8f7ibu*1m9gga yg1 tidgi 2x4 s feel weightless while orbiting in the space shuttle. Your friends res2x 7f14igdm gt ugba*9i81y igpond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners ouoc(5.r)tcx zf a square of side 0.60 m. Calculate the magnitude and direction of the total(.cc)5oz xr tu 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 xnws0gn : y32kyx2 + gsgqp i78-tt2jyplanets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are i23 70gp qns2tyxy gw+s2ygt -: xnjk8$M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 acceler35 ler+qkw0atq:yem( hw8 gi 5ation of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radiusqmiy(8 +3a wlkeq0r we: 5ght5 is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val; agd-9c3 zqm6ihn7e,ggsft( ue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kei(-ezands73c g;t,69 gh qgm fpler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit ab vf -h2kkw;/doout the Earth at a height w dh -/ko;kv2fof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit irt05po*c t6)cqf 459jn e cgd650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whenq 9ctic p5nc)t5frd 6je*o4 0g the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship 0 hro88 .b0cwmosttr/ rotate if occupants are to experience simulated gr8 ottr/wm0rho.sc 80bavity 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 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth 22.adqp ;wn8c6btx dfn4 y yd2in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above wd ntdb4 26a 8q.yfxndy c;2p2the 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 to be launched fr5 /vh,px83f )ijfu etrom the top of Mt. Everes3j/) rfv8xtf, eu5iph t to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orb ;lcspr4il7rd 8/*jvxkx 8qiw2 :ua (a6+jfq ait the Moon at an altitude of about 100 km. How lolx482( rkv87sx;a *jil +q: qirda6/pwauf jcng did it take to go around the Moon once?    s

  The rings of Saturn o h0 gwm027ufsare composed of chunks of ice that orbit the planet. The inner radius ugfw0s02 o7h mof 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.yg k2hbb3n 81rg:ajz 15.5 s (see Fig. 5–9). What is tgr8:y .n2zg3akjbh1 b he ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cenbpd; 4x9kpho+/9agamqy uk +:ter of the Earth's Moon in a space vehicle (a)+g:o/h9;+pm9k q k4xaaduby p 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 consistsd ) : 6mo onfjd;lt4g;bmfp-j5 of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the ml;fm ;t46b f-g p5dj):njomdoass of each?    $\times 10^{29}$

  What will a spring scale re9n ky1w l9k:q4ttc)ipad for the weight of a 55-kg woman in an elevator that mcy9w 9p4kt:ni k)q1l toves
(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 susp+c5o qt +jbv4f-yvl8a ended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude andtlv + -vfabo4+ c5qj8y direction)? a =   

Show that if a satellite orbits very near the surface of a plan31bq imu 0m8zzet with period T , the density (mass/volume) of the plq0 um8zm1b 3zianet 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 Moo5 , trrhd3k7kqp mc/0uw36pydn (27.4 d) to determine the period of an artificial satellite orbiting very nea 3/,m kyt05dp7q hp36rkrd uwcr the Earth’s surface.    s

  The asteroid Icarus, thoa0q36+ xvvgg+ 7lu.cfprsr5 u ugh only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from thergc6rvu.uvp ++ g 75a3 0fsxlq Sun?    $\times 10^{11}$

  Neptune is an average distance of vv b f ri2: pasp06+b(,dztl1y4.5 $\times 10^{9} \mathrm{~km}$ 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 on-my9 4cx ;wvblce 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? Whx lmwv9cyb ;4-at 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 center of the Galr.k o ,s etukmd6d.nwa+0:+jzaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distanc1llzjz uf5i n0 w/g3)le for the four largest moons of Jupiter (those discoverzi1njzwu 0llf5)/3lg ed 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 aqnjg yf5 7m93y 9ytwwr26r(llnd distance of the Moon. n jlq3r t 9yr(flw2m6 w97yg5y   $\times 10^{24}$

  Determine the mean distance from Jupiter fju2 58jhu t1o c9spy0sor each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Cht2s j85oyc 19u pju0sompare 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 ; z+k-f v s.yxo/msz3vJupiter consists of many fragments (which some spa;+zv.so- fv/y3xm k zsce scientists 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"093-hh4j 4 cggh pqx8f)aopuy 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 distance (to make the climate temperate), and that the ring rotates quickly enougcpoh9 38pq -yxa4gguhf)40hj h to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging i+ v4gj .b9bck;zn 7xasn an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N ck baj v4+s97xz;. ngbon 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 acceleration o0z73 2gqvb w 1orbgc;z1b n3cef gravity be half what it is bc2q33vg;nocbwe7 0bgz 11rzon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands am had2c7 ,pk(3n.i,f hxvg :ljnd spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another? cv gdahmn,(3j,kp:i2 xlh.f7    $\times 10^2$

  Because the Earth rotax ud35 .:fgkbq aku;q6nk6/g htes once per day, the apparent acceleration of gravity at the equator is slightly less tha.hb qf/qu5g d6gak;nk k3x:6u n it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelintmsnw;1u :sng clv5j w1wuw*)( r/ko.g directly from the Earth to the Moon experience zero net force be jvss5*: w(uo/t)n 1kwu1. rwl w;ncgmcause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yovgkkm5 qm0g61yqfn-,u stand on a bathroom scale in an elevator, it says your mavkmq, g6g1 yk5-qm fn0ss is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationebx ,+hy7 n*9dq20mfh*lxufj consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42)qfd,yxlnh u*jh+7 m20xef*9b. 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 Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lo nf g2f54vdtahmt;v52vv0 q/dop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accec1vw9phl7ng6 leration due to gravity at ivcn6h 7l gw9p1ts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) isl2x*hopyy7xhm8a- orfc+; 8n8z :hwc deflected from the vertical by an angle r oz-8lyo: h 8ha+cn8cmhw x p*7x;fy2$\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffik bj0v4ru j;q96kcmt(cient of static friction is 0.30 (wet pavement), at what range of sckj(br 40k69vjq tum;peeds can a car safely handle the curve?

  How long would a day be if the Earth *wqdosxbv5k5 a m/a9y/*i7hp cv0cb6 were rotating so fast that objects at the equator were apparently weig/ o**qyi97 6cvmsw5bha5/ dca0 b xkvphtless?    $\times 10^3$s

  Two equal-mass stars maintain a constnous.vl9( 4drwn0rmzi 0o7z9ant 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 rour yp5dysb;1qlm0k:33 bhr c*xnds a curve of radius 235 m. A lamp suspended from*30sh dymbr: b3c5k;q rpx l1y 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 5fkss9 4o y.qcd)muj.zm *)mf.x8okrjxb9 x5 massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a pf o8zfc9*x m9jy5).).o4bxsjmk.md uqrkx5s lanet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an qtm u2fu -m93mmoq8; v6+6jsi 1kfp ft ;4cqvsextremely massive core in the distant galaxy M8vq upsfimt31svq8c;o6 9m;f4m- mfqt6j2ku + 7, 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 i vkxy:+.gv2s9w4sbs r t traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road a+ vsrygbw:k 2.4 9xvsst A?

  The Navstar Global Positioning System (GPS) ,3-s4g iv-7befyigu eu x;*o wutilizes 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 ;*xo ge4-fw,e3bgv uius-i7yof 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 +753mk8sscds2un a o wtraveling 2.1 billion km, is meant to orbit the asterk7od ss cmwn2a 5+83usoid 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 need of repsne1+t ,jp0zo air. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind ino+1jpz t,0e st.
(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 isfazs-0 -mfs) v nxb23y its mean distance from the Sun?sy-v0)f anx sm zfb3-2   
(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 *ay c2e6qrcukr.2,)am o5fhk"feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lrqkak )fumh.5*ea2,yor2 c 6 cike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gahio9r8. jofyku3 +tyn du 0(i6laxy (Fig. 5-46) at a distance of about 30,000 light-years from the centf th0y(.o8d u o6y9u k+rijn3ier $ \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 4ck8(det ow;eu *q-ls square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth(t84 *co d-; klesuweq 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 k nh a7/qwz1*(pe0s tsbg 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 acceleratm8pw5 bc38s 6well8c j+ 5blbbion experienced by the tip of the 1.5-cm-long sweep second hand on yo8wb w55blpc6m +b 8cjellb8s3ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight a2 g1.sg awybt3round in a circle below 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 figab2g1 sy w3t.shing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiw4jwera.gqs78b g *ii qu53v-us R in a new highway is designed so that a car traveling at sp4j8qrv.i7ae wgg*sib-u 5q w3 eed $ 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, utilizffl+ct 8q,vw(es 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 tfq(w+,v8 t flche 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.$\approx$    $\times 10^2$