Sometimes people say that water is remov p5 urpg 2l:snvdm+0gog:: /bfed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemv0gpdf5rm:p sg l:u+ o2 :nb/gent?

Will the acceleration of a car be the same when the car travel5kfye( /,g2 le:vfat+cjkf; os around a sharp curve at a constant 60 km/h as when it travels around j ekc:5 f2f;+, flevogaty/k( a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hil3d +c+ q;p0dggdq 1atrly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b d0 p1dq+3ggac+tdq r;) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child *zrfjfr+lwi622 v 82bow rc 5xriding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the chilxb r* lr262vzi o8jc+fwr f52wd?

A bucket of water can be -o h5bc jr s2c e71t9c+n 4;tjvzhi*pfwhirled in a vertical circle without the water spilling o ec-t f+24 c19c*obr5sit7;jzh h jpnvut, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at le vuc- 00lwec0/kn3ep kast three controls in the car which can be used to cause the car to accelerate. What are they? What accp03/k0ueel -vcn kcw0elerations do they produce?

A child on a sled comes flying over the 1f-ijv62t5kyzki,f mq4 g k0r crest of a small 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 decrkz6y ,j10kifk gmqif2v- 5r 4tease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inw6khrxpx(7an1: fv . *p*y ebsqard when rounding a curve at high speed?

Why do airplanes bank when theou z k:9vm8i 7o9mrnz.y turn? How would you compute the banking angle given its speed and radius of the turzimur. 97mov89kzn: on?

A girl is whirling a ball on a string around her head in rrw,0m w7ei4rmu3v2oa horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the st02wm347,ror i mrw vuering?

Does an apple exert a gravitational 9 chk i:bz/ ijgkj0ai* 2.-uzhforce on the Earth? If so, how large a force? Cou9ji i hkgz.k -bca2*h0 j/zi:nsider 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’smtj :ni 4bvqy3,n+x2m orbit benbymx:q+v4 j3t ,m2i n different?

Which pulls harder gravitationally, the Earth o cur2y2d,0rton the Moon, or the Moon on the Ear22u ,r rdo0ctyth? Which accelerates more?

The Sun's gravitationaletszax sg(d r46s*4x) pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsibleaxsg* 6 zxt4re)ssd4( for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh morfa;gv -nt 3jtu6ix:4 ye at the equator or at the poles? What two effects are at work? ;a6 jyi4-f utxv3g :ntDo they oppose each other?

The gravitational force on the Moon d- ge uq;6rp/ewi6kb ,/atrmt*ue to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled /r;tk-areu/qi6,mb* pg6ewt away from the Earth?

Is the centripetal acceleration of Mars in its orbit arouum9 v0 4 oxs)z7o3oghknd the Sun larger or smaller than the centripetal accelerato09ovsz x ogk)h37u4 mion of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b7azydq pi-1y-b8 - 2vbal;iisp 2xm3u) toward the west? Consider the Earth’s r2iiq-p dl73 m8x2;b-aayiuyz1b sp-votation direction.

When will your apparent weight be the greatestywq xnr q;9ma0r:m* 8g, as measured by a 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 case would your weight be the least? When would a* ;yn xr0q9rmmgq:8w it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend longx al51vfsuq0 + periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape thl1vu0+fqa s 5xe 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 of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betw3chx0t0 p. ;b r/+nhmjtz:vhw een steps.hh3t .z/;nrt v0w 0cmjh:xb+p

The Earth moves faster in its orbit around the Sun in January than in Jub4yz7r qg zw6q7 5vwy/ly. Is the Earth closer to the Sun 7vyb zrw47w6qz /5yqg in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Expla ozisy. a; gx j;ej-8lrox/68nin how this discovery enabled an er.j8/on ;ayj xz6xo8i;g -elsstimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much la *o 9j0z/2l/ u r:dtet.xfnspbrger 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 sitting 1.10 m from the center of a merry-go-roxo /9rj .l :znte fbu*/dps02tund 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 travelingbzl1bza8d0 : r 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbt;2 wpt3zs66ham:l e bit around the Sun, and the net force exertedwh2 :3ettsz p6a6 b;lm 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 is exerted on a 2.0-kw -et f1h2j1ocg discus as it rotates uniformly in a horizontal circle (at arm’s length)h12etfo-w1 c j of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfach*py0u8ess 4)s ei/vit /-ap je, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of t 48phsp/-i yiae/jstsv) 0ue *he space 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 of7:z+ixzjj9 dh the acceleration of a speck of clay on the edge of a potteh97jj+x: zd izr’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate iwnj - dx7 lda8bqjf230n a vertical circle of radius 72.0 cm , as shown in Fig. 5-w j dq3nl 2dj-8fab7x033. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a nmoom- 9szs1/turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car? sz9omm/-sn 1o  

  How large must the coefficient of static friction be between the tirs)ma).fp gli 4es and the road if a car is to round a level curve of rad).m gl )fpasi4ius 85 m at a speed of 95km/h ?   

  A device for training astrzz c ru4p,9qjwtys8qvav ;x 7, )f6y;ymi8* mnonauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt x, z84nyvm9j tqr)am;*z8cw ;ypy7, ius6vqfby 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.o7t s75 b-47l(i sytdqf16lg8y7hp dy cx8 aam0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the 6h8t(7 -58poxlcagq t ssfddiylyy77bma741coin 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 travelinkxtl,aqpy9 /11fbh a hmi.(o1 g when upside down at the top of a circ (fq /,1a11pkh9x ombyilat .hle
(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 fhm))028 1gq/yt ote fj s-gdnkg (including the driver) crosses the rounded top of a hill (ng8/j- )s0 hy1qt)2gdo tmfefradius =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 m+hbq jzsyy4l;6 .jfs1t- o;y t;u4jit ake for the passengers to feel “wjqy;i jz4;+6 1y bot tt .lus;sh-fjy4eightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ofvc k+(f fer;s :p9svdfo0v4 o5 radius 1.10 m. At the lowest point of its motion the teo9;5:cvvk os(sf fd+4r p0vfe nsion in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotatcxgc c0qslpl, x,w(.)n sd81(ddoa8 be if a particle 9.00 cm from the axis of rotation is to experience an acceleration o d.a bxdwcq 1cpon d,xl)c ,(g8ss8l(0f 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnit dssgu9(kl57f)1 s fqval, people are rotated in a cylindrically walled "room."(1usgl5s 7fq dt9ks)f (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air)m3dbe rr o-2v-hockey tabletop, and is held in this orbit by a light cord connected to2vebom- )rd r3 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 bava p1iweq+ lq99 zr)l. xxl7rvm)g a/vs01k3ull which revolves on a string 0.600 m long. Im)var7g va3e vxlpqir11 l.0/9qzw)k + sxl 9un 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 ofvgxor +xahm /p.bc+xi.(s) w/ 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesp3uwb6 js;bz)xhu )9s $ 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 verf /d( ivlry23jtically 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 the net force exerted on alkip1bkffcjun3(,a z:82g-the car:pk3(k 2f, 1njb la-gfcaz u8i (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 f kawrswzn 547wty ,ha,s)h;zycr 266from 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 halfw6nwswta 4y,fhazc2z,k h rys 6w) r;57ay through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a 8jb yoi3g8f0p s1u 0nue-)xsmparticular instant, its acceleration ixup0oem)0 -j1fsuy b8i 3 s8ngs 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 Eavlgn;+v36fq) hwk+o /uax u p5rth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its3o+nw x)lf vakp5u q ;+gu6/vh mass is 1350 kg.   

  At the surface of a certain planet, the gravitatioiard/ 3ta3qpp8vqe(+tf i3( hnal acceleration g has a magnituqd3+ert/a3 p3fait( h (qiv8pde 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 acceleuf9qwql/y y, (cbvp ta.+w7 d.ration due to gravity on the Moon. The Moon's radius is 1.74 pd(7t/9+uqafw. ql, c w.byvy$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius )dm q9ypp3wq: 1.5 times that of Earth, but has the same mass. What is the ac wy:d)q3 mp9pqceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the s- ywrqj iclw( /r.x1x0ame radius. What is g n.xlyrx/rq 1( w-wcij 0ear its surface?   

  Two objects attract each other gravitationallyhiy(t8 jv1 *dj with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (eyws 1,,xns(um -tf9ta) 3200 m (m-w, nys ,19ufesxtt   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside +u0dj j)u; xz9r uwmhe7gjjx4 ;qb 3a:the Earth where thegravitational accumu xgr; 0 dw:7 qj)hxau+ 9e4jjbz3;jeleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the maoxqyj6w.2 -l11 ej/ 4 wpkpifiss of our Sun packed into a sphere abouy/el -6ji.p4 p1kqwijxo21 wft 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is/ /zd9mb6j gb:4zjc-0rzdmjbe wf// g now in the last stage rb/6j/ cmb dgzb:fjzg-ej04/ 9m/zwdof 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 astron aqx hb4,tk;wl-;m1ctauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by ca4cbxtaqmh t k;w -1l;,lculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locz ump ss(m2* j/.wfxw(.sm9c2bjdus 5ated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravi2.s* ( mzjw jmcb/x.5sfd us9m(spu2 wtational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.4y. z ei7z5 xo2,43hvawzjhbk Calc oezh4yw3bj2,kh z5x4 7vz. aiulate 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 whatl, wd/ x al f:lq1*8qrstysm.*glrl32 it is on Earth, and that Mars’ radius8r*t 2sam lxl sq1,frg3d:l wlly.* q/ is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the per)i:lxuew,jy/yj ( n7jiod of the Earth and its distance from the Sun. [Note: Compare your answ , u(jyx/) wn7e:ijljyer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satr4j n k0+i1px 0-muodnellite moving in a stable circular orbit about the Earth at a height of 36kxin dj-p4r1n o+0 um000 km.    $\times 10^3$

  The space shuttle releases a satellite into a cp7h luz38)qvl fqr* q0ircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releap*08 qlqqvr zuh f)37lse occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotam 8p z/ 0y,aae045xp x tv8aeqli/z.rzte if occupants are to experience simulated gravr 5tzzi8/pav xa,/q4ex apm8z0yl0 e.ity 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 i q)q)qun)vwqv7o g;7pt takes for a satellite to orbit the Earth in 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 depend on the ;u7q)vq vg q7q )w)onpmass of the satellite?    s ~    min

  At what horizontal velocihi/lx8crwz4,9 ecc 0 xir z0tmd0an;3ty would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around t catz40c0 ld8 cirex/0 imrw;,39xhn zhe Earth?   

  During an Apollo lunar landing m, ;( su-gsltboission, the command module continued to orbit the Moon at an altitude of about 100 km. How lont-g ;(buls,sog did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of iceb6:x/h yzh0jif.v 2d x that orbit the planet. The inner radius of th2y 0zj xh6 :bdv/ixf.he 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 rotater 502g)z ) 4x(pjd8se iywfgo .p4jzees once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, an wz pejxg.ydi40)gjse28prf45o()z ed (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4209 o1kwp ec;u b1mgp34f0 km from the center of the Earth's Moon in a space vehicle (a) mov94o1bgp fe;wpm3 kc u1ing 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 cxzbt,/sn 8f.ng x6 ev*onsists of two stars of equal mass. They are obs.fsgt6enxb/ x v8z,*nerved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring sca6c9 6jzewl:fr le read for the weight of a 55-kg woman in an elevator tha9l 6fc6rzjew:t moves
(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 mzp 2vqye4)cb4y i1mo n.k6u3from a cord suspended 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)yi14qpozy2mb 6 vk4 3.uc nme and direction)? a =   

Show that if a satellite orbits very nv*tb9l u0 n s 3ww k-eptqwqnh1z2g+-1ear the surface of a planet with period T , the density (mass9qte1 w k-uslw2zw *p +q30-bgv1t nnh/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 (vplmtn v0 eja/7 w/ 1avqph73*,rc hpthe Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earr/n/m3 tv(qjp vha77lcw*,10ap hpe vth’s surface.    s

  The asteroid Icarus, though on 91hyzonr*26hyc ldk6x f-xol88yc 1 yly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance frlc - yy 6n1x9hrx2lk 8ohyy18*co6zd fom the Sun?    $\times 10^{11}$

  Neptune is an average distanc0 uzqjv i6y-fx1fgd2 -e 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 tviaq e,/h6:tpuj 0u0i he Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearjhv:e0i/ui qa, 6tu0pest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cen4ljvb3( r1xjmkb fd5zdl(:7yter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largesw5j5 66 eapu38teqmpk;y hev 02wkhx 1t moons of Jupiter (those discovered bp1x02kwj6 5u85 a3ph qwv;m tey6eehky 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 +h8ht3 7nhe4(lne dkathe known period and distance of the Moon. hheakt(n4d3h e8l7n+   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using K 62o ykj8 6zvimvmx6*iepler’s third lai6 8v zj2xi*6oymk vm6w. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentsqlfk s9b62) k0n;g awdojr ;vqmf2l27 (which some space scientists think came from a plak; 0sbgnvla7q2fk ;2o 2f wq69rlmd )jnet 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 form of a band cv(ou jq w9tl+ )5c+5mxk6wja9 og j8usompletely encircling a sun (Fivl k9j j8coau+(6)su w5g x jm5qo+tw9g. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinginte8abuk 2;5 5nwjy4 jig in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5tn584b2 ji5;euwk a yj.5 m long.   

  How far above the Earth’s surface wi smw;a 7*xodb)ll the acceleration of gravity be half what it is ooam bwxs*d)7; n the surface?    $\times 10^6$

  On an ice rink, two s r-(xix .wfag-katers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are theyx-(xgf.i wra- pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravit, yki)x7u3rpj y at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractiok jp)7uy3, rixn of g is this?    $\times 10^{-1}$

  At what distance from the Ea.lpo)jfc89 8(etcmf wnch+ 8 xrth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposfex8n(c.jo l t)cf8+89pcmhw ite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stab(uhi 0(:kv/ kbv)c rand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wh 0vbvkhaub( /cr)k: i(ich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will m0cl-ogabc t / (,h2marotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 gammtb -/go2c0ach( ,l) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vof0 2d8tp) a+fdu;jju ertical 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 mv5 (famr iorop t; a8uk0.)q7uass of a planet in terms of its radius r, the acceleration due to ;apfk)v5 t. q0(iouaumr 87rogravity at its surface and the gravitational constant G.

A plumb bob (a mass m u+hb: sfj/*eg hanging on a string) is deflected from the vertical by an ab:eh+ /j*f sugngle $\theta$ 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 for5g8 xlk9f9)e bof -oeb a design speed of If the coefficient of static friction is 0.o9l-kx bofb9 g8 fe)e530 (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 at the ef2e y jvan x73w9/j0mvquator were apparently weightless?379jxef/y vjvaw m2n0    $\times 10^3$s

  Two equal-mass stars maintain a ; ia**we ,zns7h3ia ymconstant 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 a8 iicb+ 7lpkhpqxmf 6e3 *;o/q constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings hipqe*xkmif7;+8qop l/3 c6b out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been cla+zm al4 (asg0limed 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 p4z a0s+ lgmla(lanet. 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 extreerrk23 6e g+m*+ vuuhgmely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). Thk rg mu+*+ u3h2vrg6eeey 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 valle lotwj whert*mw(j (;q6 6j02iy shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on thet(;j0moi *t( jh rwlewwqj662 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 at A?

  The Navstar Global Positioning System (GPS) uti489gkvox +zv/hkm(y d+l g(i zlizes a group of 24 satellites orbiting the Earth. Us9+8 gyl o(mxzk4 /hdi +z(vvgking “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), aftsyryv .) qscw9u4)o uzu6e*l)8h1jcxer traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height s y e)89och lq.*suuj))yw6uvxrc4 z1of 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 indgq:g1g8qq,01tq af t the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the samq: tqt1 df0g1qgg 8aq,e radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a)ju2d/n;o swo7 What is its mean distance from the Su/w; ud2oon7sjn?   
(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 actualv 8fhp (ti82ualy "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, v8u(fp2h t 8ialike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the)fh2x /ch:zg c center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from th) c:zh2 hfcxg/e 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 e+0ue6yg2 yba dfyj2.gq- q:bof 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 f2abby 6y-+g ed yq:u02q j.gebottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits he3,dtd0z2wv6 nv .nmthe 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 qo ot2 0(h0r*hxrosy: experienced by the tip of the 1.5-cm-long sweep second hand on your :rh*xr0o hot yqos2 0(wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in iiy.fo0- oq*y a circle below you on a 0.25-m pi.y oyqio-0*f iece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car t kap6+hi0p a*araveling at saki0p+aph 6*apeed $ 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, utili)ga vx;j 60dy uzmfluh:ik15 ;zes 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 sm61;xk:l;ujf z0hug 5) v idaypeed 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.$\approx$    $\times 10^2$