Sometimes people say that water is removed from clothes in a spin dryer bpccjn9 ;bh c5.y centrifugal force throwing.nc;5hpj9c bc the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels arou oj-0o .njy7ji a)za(p3*aolend a sharp curve at a coi .jj3n oa-)0ylop7o*jza(eanstant 60 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 does the car exel7tiez 67 (o,(gc chwkrt the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hill7gztoe( 7c (w6,kl ichs, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a ho ax4s lloh:iis76 *;mpkms5 8grse on a merry-go-round. Which of these forces provides the centripetal acce5g i:8pkllimxsh m 4o;6sas*7leration of the child?

A bucket of water can be whirled in a vertical circle without the water spillinb4fiikwx( h/1cw .e+tg out, even at the top of the circle when the bucket is upwiwei/.x h+f kbtc4 1(side down. Explain.

How many “accelerators” do you6votgh*4u hpsx-;)o o 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 they? What accelerations do they prox4 ot)po;v*soh-g6h u duce?

A child on a sled comes flying over the crest of a smare o(v77 q/syhll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease usin7(vr/ ysqheo7g Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speelb-z cm8t o(2l5i/coizzo n zw. 22j(rd?

Why do airplanes bank when they turn? How would you comny 7r wxg4 omzw*w/77vpute the banking angle given its sp4x gyr/w *77omvzw 7nweed and radius of the turn?

A girl is whirling a ball on a string arouncxxll5( eycxshj z.mq( ../h .d her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. e(chs.zm.cxq .l5h(lxj.xy / When should she let go of the string?

Does an apple exert a gcarig/:,b1q ;gbm jr-ravitational force on the Earth? If so, how large a force? Consider an aq/mgrab : c;gbi,j1 r-pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wereme n;k)vzpipao o3c7m68)gt- double what it is, in what ways would the Moon’s orbit b68g7k3zpoviptom; an m-) )c ee different?

Which pulls harder gravitationally, the Earth on th;o4mx7md wk+vkwcv r (0u )es5e Moon, or the Moon on the Earthkdv kwver )5o0xsm +uwcm( 47;? Which accelerates more?

The Sun's gravitational pulluuhq(rk6sk, 9z xn8 g5 on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatioq5 ,8kkz6u(gs h9unxr nal pull from one side of the Earth to the other.]

Will an object weigh more at the equator or atby,2g7ic e9 . 2c zj1i:biezan the poles? What two effects are at work? Do they oppos7 e9:.g 2yb ib cea,ijz2zc1nie each other?

The gravitational force o./5ni;ybn z axn the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?iz nx.; ny/b5a

Is the centripetal acceleration of Mars in its orbit around the Sun 7y8 sxw*g xsh7)m 3xptlarger or smaller than the centripetal acceleration of the Ea hxxw*83xsy p7m7tsg) rth?

Would it require less speed 9n nv +; 6o1kjpkt3inyto launch a satellite (a) toward the east or (b) toward the west? Coitn o+pknvn31y96k; j nsider the Earth’s rotation direction.

When will your apparent weight be oiw.bngsi/ *2the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) mo/2.wgboi*s n ives upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lo7+mqwp - e-ps,oae4mx ng periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think o-oa,psq 7e4 xmw+p-mef.

Explain how a runner experiences “free fall” or “apparent weightlessne* d1-dfrc); hk)so hp u3/ytggss” between ssgyr1k;3)/ -)gdh*tpfhcd uoteps.

The Earth moves faster in its orbit around the Sun in January than in Jlbg :3g i5cq5kuly. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in 3bc5q il g:5gkproducing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. vfe0 1c1gbqw8Explain how this discovery enabled an estimate ofwgvfb10q8 ec1 Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largerp.mly0 ed/1s9d4fp jz than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitt pj1 d4fpm90dze.ysl/ing 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 198nq.(2e l0 xxyi0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 a*vd:+cfiua b s/r/8 yfcceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's*/ +yfu8ic:vfdbar / s orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-r)sali5 n c u7,eew 8bm3rb4n,kg discus as it rotates uniformly in a hori7i nne ab) ,rlwrb3e5u8cm4s,zontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circe1. -jrrsibp63q) yj dles 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 acceleration y dpie 3.b -r1jjs6)rqat the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a por5ko t9e+az-xf.o)ea j 1mdi; tter’s wheel turf .eo z+-5oie;m rxtada9jk)1 ning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strinrwe1a t9kl 0io:;fz 8cg is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as ;1coawref 9 :iztk80l 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*vwmhxhz,wol c k *a :nx2/ 2x+r1lax6ith which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient o2 1w*,ha:w x *h2x6o/r naxk llv+czmxf static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betw6ax6y plym 2mv(w6l 9jeen the tires and the road if a car is to round a level curve of radius 85 m at a speed of 9m x(a69l6jp2vlm yy6w5km/h ?   

  A device for training astronaut:b.aodi yb qlu+(b-.ys and jet fighter pilots is designed to rotate a trainee in a horizontal circle ofqb(oi -u.a: l+ybdyb. 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 turntablegtlapgsnz(1 vd5ty3p+ d(f egd+ bo(q .+11mr of variable speed. When the speed of the turntable is slowly increased, the coin remains fixfsg1l53+gdd+1t ((gz. (ot +1premd vqb npayed 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 upp 4 4+qje+dttv8g6 gvqlxki 78gc+cz/side down at the top of a txck egp6 i8gq d4/+v84jc+gq7zl vt+circle
(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 thf (th v- lq)j1w2(ucdoe rounded top of a hill (radv-(q1h ( tojcd2wuf l)ius =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-diameter Ferris wheel need to mak. 5uutb7tcvc ejj5p ; jpdo-:*e for the passengers to u7pct:- jbcjej 5.*; d5opvut feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cdh )zgb8* x4v;vczibu ;)qkg hg.rw. -ircle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buck4h gi8qdb-u ;g*..zxzvbgc ; w)rvk)het 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 teai 2x2u1ne4b 2d1 ( b:iqhpsohe axis of rotation is exq1d 2beb ih: 2a1 uspi4(no2to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carr k aes+; ;bklpz*5sbtj6v9)ynival, people are rotated in a cylindrically walled "room." (Sk;rb)s6jvze bk;y*a lpts9+5 ee 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 ina:mauwhzfpy 5n5g 82 . a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) thr 8 wa.y pag52fhuzm5n:ough 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 weigh//;5mr bmmlxun- e 2uct of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of el/um xun2r-mmc/ ;b5 $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 fossp*(kn-e0m) qw s*1ma8l hhvr 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 massesx:- (f rzf //m)tea jqa edgn6qn(h4g/ $ 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 divingbs s07nys r-n4 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 and centripethhmdm9pzhhsv 52*ip 2oe73(zal components of the net force exerted on the car (by the ground5e9p* (zizhh odm7 mh p32sh2v) 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 accelerate9al-xb5ba9 n,/zcohb k w6ke.s 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 curve were flat, what would the coefficient of static fricti x/kkleb9hwb5az- .b,6nc 9aoon 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 a partidza 4l (few4j3cular instant, its accelerat lj4e(4a dzfw3ion 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 Ea(fquwh 8 wyri1s071xt) :vm pwrth radii) above hmi78xfv(w: 0w uqsp1w tr)1y the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, thq. l 7bw.k0zaleg: 5ua.z 4upue gravitational acceleration g has a magnitude of 12 .z7qukegub.u aa :.5lz 0p 4lwm/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 0 o0l 9e. yoyo4yt2w* ml,lmbion the Moon. The Moon's radius is 1.744o.o *o9ti y,m yby0lelml02w $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 +-ij/iqt rfl1;e) h tltimes that of Earth, but has the same mass. What is the acceleration due to grav-/ tij)h1efl tqir +l;ity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same r05w+-fdiz cz jadius. What is g nearic d-z0fw z5+j its surface?   

  Two objects attract each oth1 v*rfqn 3zoe/ )yff1xer gravitationally 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 valb *qct .bttpvg2 p3v.7ue of g , the acceleration of gravity, at (a) 3200 m t p 2ttcb73qpvv..* bg   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tond6 -tu:trizw,wwl3b; xaftuz,84/u a point outside the Earth where thegravitational acceleration dueb6wl, ,rn4z/tuu xf 3a:dut;w8izwt- to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tkuq8bhvf :k63eyjt:cjo w5 524*k pvfimes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravityko :bcf 3yp :ekku*w2jtf 84vqv5j65h on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average starw)e-s-pnmka9y (c b6j:oy a/ p like our Sun but is now in the last stage of its evolution, is the size of our :np-ma6)b(s/k -wc oaj eyp 9yMoon 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 orbitintu m)ncx yd+c;po*3qn*s2f) 7t*lg qsg in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convi)*3unpxq lsgd+tt*s*c c 7onq2m );fy nce 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 loc:n/ vsut c0/vjated at the corners of a square of side 0.60 m. Calculate the magnitude c:suj0tv /n/v and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lpejggro/ 79t;ine up on the same side of the Sun. Calculate the total force on;r9t7g/ej pg o 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 acceleratio;iyxxw9c j3d; 2hsr h3n of gravity at the surface of Mars is 0.38 of what it is on Earth, axicdsh 23 xy3h;jwr9; nd that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of thei5js8k2t w 9x bu+ebhjhb;df)9 +b3yp Earth and its distance from the Sun. [Note: Comk+b5ubh fbxithds)9 j;b 2y+pw3 9e8 jpare 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 orbit about 6s4gcg2:ujy9 7xd1s:7sra ccl /t b jvthe Earth at a heig4usy26gc jca ls:gd 7sb1tjrxv:9c7/ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km zq 7-6zrvgbl ; 2fhj-iabove the Earth. How fast must the shuttle be moving (relative to Eav -r7bhj6; q2 -zfgilzrth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants o3,nayap7 xg0rw a)ivd2 1i *iare to experience simulated gravity of 0.60 g? Assume the spa2dao av r3gai7)n px0iw1 i,*yceship’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 i ( kvkwra9b756 vbpsx4n a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result d(9k 5rk 47abvvw b6pxsepend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be lauhy5fty 8 k;;jgnched from the top of Mt. Everesthjy gfk;y5;8t to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orv 5xs fuwt+yu+z( g91fbit the Moon at an u5 y1(gfx u+fvt+w9sz altitude 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 03hclnou c -s)uo/ncp .8i(dithat orbit the planet. The inner radius )d(lup8.n0cci-scnh/oio 3u 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 gijl:(v7l 0uzf-htp es6i d ;2(see Fig. 5–9). What is the ratio of a person’s apparent :z-li 7j2dvtls0f6u( ipe;hg 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 kmaz 6lmx/n-whk7 t*,rz from the center of the Earth's Moon in a space vehicle (a) movir/hlt,z 7kzm a-nx*6 wng 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 stary p( i2r2-1fz8p ey d*fuyd8sds of equal mass. They are observed to be separated by 360 million km and take 5.yi-e( *u8 sp zyr2d2fyd1dfp87 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reaiqoowr;2a rd )( twb09d for the weight of a 55-kg woman in an elevator that moves dtiw9boq wr 0; oa()2r
(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 a3j+ cho1 )hyga cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. )ac+hgj3oy 1hWhat was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near tziv;4 a;-t qibhe surface of a planet with period T , the density (mass/volume) of the planet b4;;ia tvqiz-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 per) 8dd0 i ;-qjjaoyddn+iod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surface.y0d nd)d+jdi aoj;q8-    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lq3 b: 3uhiqcd)ike the planets. Its period isq:hi3 u3cdb q) 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan 3k-ezvkwcaj 9c7jcm .w4tn20ce 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 ona tzvn+*f2c vs* 3nu3ace every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’a *+s*cftz2nn v33auvs 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 9ex0 i+gtq/;uui 2*oe fsi.cxof 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 m ( :a fb7s;ngalubau4-oons of Jupiter (those discovered by f ua(a g sb-7u;l:anb4Galileo 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 and distance o3r3451*nhxbayw d hnpf the Moon. yr 4*xnhw3b1 n3da5 hp   $\times 10^{24}$

  Determine the mean distance from Jupiter for ea8, cc,osl (ngks)37p+ ds;hiptth 7xjch of Jupiter’s moons, using Kepler’s third law. Use dj)7 ,ghsckhtpc l;px (st38os7+in, the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whi gjh*;*2oowq 8v:ks kach some space scientists think ca q ;gkh*:8ooj* v2wksame 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 "pl cgf3s145wk szanet" 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 exactlf 3cs1gw ks54zy 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 gootz)*zbk (d) -9h0oyrma1isxrge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exertins)it)dkyxo * za0 m1h(z-b9o rg 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 acceleration d1oqqvd*nb;5 i*;tglm rs;,s of gravity be half what isiosgr1qm; td*lq; b,5* ndv;t is on the surface?    $\times 10^6$

  On an ice rink, two skabp .,uwxhi 14dters of equal mass grab hands and spin in a mutual circle pbx ,h1w .4duionce 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 acceleraf c 5lux; ,2jafe ;ybgjrg;2wga q;3x.tion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is t2;y 3bl;ex gg.,5u;w ;ag f jxqfj2rcahis?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traou;v bo;ou: 04r+5q7jb iv wgvckx*w. veling directly from the Earth to the Moon experience zero net force because the Earth and Moon vog. + kuicwo4;vr x;u 5ob*j:07vw bqpull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an ev*zzzaqw,bxz3 hcjkm ) :y 0;2levator, it says your mass is 82 kg. What is the accele*0,kmwzz;)yqzx jz32b: hvc aration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cir8nf - jtp;o g3vj6z0jocular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diamen8tz;vf j 36pjoog0-jter 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 hi773r pr;c5h/ym ukjmes aircraft in a vertical loop (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 a7l3w j9rzn .mpcceleration due to gravity at its surface .rzjw7pln 9m3 and the gravitational constant G.

A plumb bob (a mass m hanginwrug4n0v- w o :eohh)3f8p5pxg on a string) is deflected from the vertical by an angle uxppre:vg80hwn o3w5 o-h4 )f$\theta$ 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 iydu; -sn p. -;sjks66b7 aoaxis banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range y;6d ijx -a7uop. sb;s6a-nksof speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at fe w/o5 k k/pewd qc,3qljl7-5dpy((q the ej5w dlkqk7 ld,qwpeeo3/5 ( c/pf(-qyquator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart r 67q*v( 6drurdln9isof 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 radius 235 m. A lamp susc3 pv yk+0u ry9lg(8 vu*mloc*pended from the ceiling swings o pv 0g(c* *mlvuuo9rylk yc38+ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas *nh4ni).q*nxdfba /zsive 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. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter bz*nhinf d4/an.x)* q: 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 Hmaa sjyod93t)/ (rq*x ubble Space Telescope deduced the presence of an extremely massive corraym*a/d oj) x3qs (9te 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 traver 19xf xqd6u +2s*fcvz2n1s mxfses 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 drivvq2nmx+6s 2u zdc1 *ffxs 9xf1er feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of n6 k491 911 )v( ijoreplf,yq pluzpom24 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 nauticajor9o q v i1eppy,(ufkp1n)9z6 1 llm4l 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),,rf0+ ct0pf(:.e y *ntbbhohp after traveling 2.1 billion km, is meant to orbit the as, .otbe:(c pnf0+r* tbh0yfh pteroid 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 sp:jr)sjwg 27l lace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite sl7g )r2l:wj j(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 petl5agqf ca go/-+ w*nlmf7p76 x;zy+i riod of 3000 years. (a) What is its mean distance from t+5az/ifxfy6 a p+g;7m 7n wtqg cl-ol*he 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 valp:-8dy8 1je(h+g aeugquvxh 5ue of G would need to be if you could actually "feel" you 8 ey:vqgx1jd+h( pgeh-5ua8u rself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a d hh 1w/62dnz/k.ffxo f. *nkpsistance of about 30,000 sp2/6 1 .n.dnk h/zo* fkhfxwflight-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 corz466t sjq-zo rners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side oqjo- zzt64s6rf the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ear36su/f a eyv:t 1kps7rth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the yh)df7 hdwr.0jlhb)g. z6 *h r1.5-cm-long sweep second hand on your gw dblfzj.06rhh.dyh r7))h *wrist watch?    $\times 10^{-4}$

  While fishing, you ge::i-gs8lo,d 9ye yewat bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece og w:ly edy9, i8se-:oaf 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 i h8yh)ch hhh:v ybe9 /wkxf;2;n a new highway is designed so that a car traveling athe ):xh bfhy c;h8hk hy2/9vw; 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, the Acela, ut9nlvqo/bm,2n a0nt fbd3h- )cilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passe20,nf9 qdo -v/ nhn)ct a3mbblnger 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.$\approx$    $\times 10^2$