Sometimes people say that water is removed from *dm2q 8r2dfkvclothes in a spin dryer by centrifugal force throwing the watdd22q8*mrv k fer outward. What is wrong with this statement?

Will the acceleration of a cq6 nlfun )k/4qar be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same kq)nq4l6fnu /speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whbf,n9ch/ oba5ere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dipo95b fh/anb ,c between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a wusw-1smezl-k4c0i krw;3 eehyk+4a-8e ut4child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratiouetky3+-lewiem1u44 k s-h- 0e kw4zs;wr8acn of the child?

A bucket of water can be whirled in a vertical circl(cuhu5 6 co:swe without the water spilling out, even at the top of the circle when the w5s6uhc :( uocbucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at le;*r, hqo*el t3 ;,n2y tf (mswkjma0uqast three controls in the car which can be used to cause the car to accelerate. What ar t ythfa* *s,nuo 0q;;mrjq(eklw,23m e they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small 7rsi/ty(.n oyhill, as shown in Fig. 5–31. His sled does not leave t.y os7i/nr(y 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 inward when rounding a curvj uphxs/3, iaj/u59 mve at high speed?

Why do airplanes bank when they turn? How would you compute the banking*,h03u w l1sltc; iaah 315tmn9cvwkp angle gi i1h*h;tnc p33,cwml 1lv5u9a 0wtak sven its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plan0x j o-jep92oee. 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. Whenjxo p 2e9e0jo- should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how j*ktwf9, kn n/large a force? Conf/9nj k*ktn w,sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbitnah3p*a1g/wpg qq23 m be p g32 *mnqqgpa/w1a3h different?

Which pulls harder gravitationally, the Earth os om.xds-3rl7 n the Moon, or the Moon on the Eart.l-37 xmdssro h? Which accelerates more?

The Sun's gravitational pull on the Earth is vqwsir)y4) vj3g:7t5rr 1t0 dqmdzudi3 xo-) much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hidir 3tq:yi5w)gv1ru0 4- mjqdx)d)3zosvt7r nt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the*;w pscj2ki) f equator or at the poles? What two effects are at work? Do they oppose each oth;)csp fk2 ijw*er?

The gravitational force on the Moon due to the Earth is only aboutiw-qkx)a8z* t half the force on the Moon due to the Sun. Why isn’t the Moon zk8 xi-*waq)t pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the x.4abbqszt:; Sun larger or smaller than the centripetal acceleration o xa:q.; bs4btzf the Earth?

Would it require less speed to launch l-yrtf/ n,hv;y4i i0va satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotatio0 yvylr,tfhni 4i -v/;n direction.

When will your apparent weight be ttbyia4 b9 z6n4he 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)9b 64bt4yzia n moves 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 long peq2ame.z9 i (auriods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship m(.uz eq i92aalike 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 expec s5c2 psi1,bbriences “free fall” or “apparent weightlessness” between step bcc5sspb21i,s.

The Earth moves faster in its orbit around the Sun in 24gh9hl.p n0alzs) t dJanuary than in July. Is the Earth closer to the Sun 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.]ldz). 0tsg4pha 9lh2n

The mass of Pluto was not x -w9ir (p .2yt td482rofxlntknown until it was discovered to have a moon. Explain how this discovery enabled an es (2i2nty4wp8d9r .or-f xlttxtimate of Pluto’s mass.

  The Sun's gravitational pull on ts,g* /e lcrvv.he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitgsc*,v/ lrve .ational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 18h nc/wk 7+i1aia/ bjt980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Sufhcfgo y.e0ph702ma z x2ae); n, a fpoahm xhyfce07ga22ez) .0; nd the net force exerted 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 h quq,i5251h/ 2 yelueww:whtcr/e 3p is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lengthptu5 i wee/:h/q3ql15c 22 wrh ,ehyuw) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is ina:utp r5qo(k/b 6tb*v orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spacer5tb bptqvo6*(k u:a / shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge sf.gp1 v sbzr0x/qq+8 of a potter’s wheel turning at 45f+0x1 8pvqsz qb.srg/ rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved atjlmg6*x.zj,wfcl y8 d+ym-1 x a uniform rate in a vertical circle of radius 72xl*y-j8,+6m.l x fmj zy1wd cg.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 1050-kg car sxz4v4 :0l byocan round a turn of radius 77 m on a flat road if t 40yv obsz:x4lhe 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 coefficient of static friction be between the tires anny2 idna.i/too)-m np yp9e, 20hwr2d d the road if a car is to round a le, ynyp n2a9ohdrmno/ i-i022 petw d.)vel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronad)b8y/ 4ictnm uts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12y)dm/cb 48nti .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 t3 0+wodqoxgk b6a m.)t*k ku,uhe axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable k*6xkwg 30m tuoa+,b.ok d)uquntil 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 up 9 8bfv4,*khqocdxl g,side down at the top of 8bc ,d9v4gok hf ,*qxla 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 the ro 0x7llz0wd80myu x4tgunded top of y d0tx7u4z0wxl l0g8ma 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-diameter Ferris wheel need tovr)a9bjzat5*/e/nf n 9ksl;w make for the passengers to feel “weightless” at the topmost poin jnk9r;e*/9 /tanswa5lzv b )ft?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Aaht2va73xf;mx hp(h3t the lowest point of its motion the ten 3(hx73 ;m paxvfahh2tsion 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 rotate if a particle 9.00 cm from txv yx1 0n)*(h+ htqtvct*jtk-he axis of rotation is to experience an acceleration of 115j0(x*tqk *-ht)vcv+y 1xhntt ,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically waz3c1 ;ul)eck qlled "room." (See Fig. 5-35.z3 cc;)ul1 qke)
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 frictiq8hpf +bnz e7s*+p+ptlz0a- ponless air-hockey tabletop, and is held in this orbit by a lig0n7ptpfe+hz -pb+p* slq+ 8zaht cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the ba)hshyr6r* 4uuka q2-wll which revolves on a string 0.600 m long. In particular, find the magnitude of ra6h uk2s4 h*ywu-rq) $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 pe*x*5s9.el gvp ;vcqrsrfectly 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 massexu. 76;dfp9h8n,qa ufvsc, hfs $ 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 vertically aii56e v/if p()m)i syxt 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 componn .56e,f cvhink* 1 n9uof9ek6el9czlents of the net force exerted on the ca6ku9evnc, 9lzc lf6hk f 95n .1nei*eor (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 uniforml )0z;,swrfa xpy 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 frictionrfp ;a,s0w )zx 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 on1 1valp0v32t1 ixra yf radius 2.90 m . At a particular instant1p0iavlt11r 2vx3ay n, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’syen*xqx;, o l*tgx: )f gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth* y; l*q)xoxx:etgn,f’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the 4t8udf d85h bcgravitational acceleration g has a magnitude odtc488b ufd5h f 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 M--5wi ddnkg6moon. The Moon's radius is 1.7 gn-6dm k-w5id4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has mpo,:k8l0 hlkthe same mass. What is the acceleration duel 0,hkp:lk om8 to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tim q+si6n ob w4fakd-a(gg;-q3 xes that of Earth, but the same radius. What is g near it+dax;qki (n4ggba3wo-qsf -6 s surface?   

  Two objects attract each other gravitationally with a force of)0y5l9 dwv wjetyu )/o 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 effectiv1iv1e zjif : )2swa3broxk9s.e value of g , the acceleration of gravity, at (a) 3200 mo2 v3iair1e kxwjz19sb). :sf    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wccnskmv -1.:7t v *zntrh ,o0khere thegravitational acceleration due to t:-0n. z*stkcnvhm,ko7c1vtr he Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five r4 yv.5-vb1ho9bho be times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on 1h-o.e5 rovybb9b v4hthis monster.    $\times10^12$

  A typical white-dwarf star, whichtxl5 uyl u (kq8fv4o 177sz)ya once was an average star like our Sun but is now in the l8ouks7ytl(4fxl uq 5a vzy)17ast stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel wpj15t iglkphhc()zn; o4 2+ ajeightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lp( k i)+2anlcpo41j htzh g5;jot 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 of a square of side 0.60 m. Czdh 40gya8iqy(-dsck z/ +u(l alculate the magnitude and direction of the total gravitational force exerted on ld z+yquiz4kyh0 /(8cg sa-d(one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostqke p- ypug )z;s9z7u: of the planets line up on the same side of the Sun. Cay:pue7gzuk9 qs zp );-lculate 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 acceleratiorql/+a xs,s f lt(u.q-n of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of q (ar -+/,sl.tsqlxfuMars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value foi ls.d fnkfp41dp8ln3damm-s 3 ;g r23r the period of the Earth and its distance from 41dmdf f2nm arp-s338g ;silkn.3pdlthe Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinop a go 8.bg d6s5j4ac2as*k0h1jik+bg in a stable circular orbit about the Ear6dks8.1kohi cjp+o a5a04j2s gb a*bgth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellit+xvl)pq f4z-6f uu 8sim(boog6x 6j5te into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative ti4- 8sjx66f qmbo6g(uz)f+x pvut 5lo o Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrbh+x8r ei)s o2ms2z o8ical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your a)o o izem82rs 28hsbx+nswer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellif6; e;isd.ef*01nrhaa vz 5rjte to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of rf; j*.a5e nred1;i sh60vzafthe 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 veloc9 d rm87i2a s,zb2pkbj+3 pjzfity would a satellite have to be launched from the top of Mt. Everest to bedib bp7z2mk,sr+8f3 jzap92 j placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mishkav4+bp(brq ozxo zxa) 0wkm)0 5s,)sion, the command module continued to orbit the Mooxxo04r,zb5(o vswakpb mkaq +z 0h) ))n at an 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 that orbit the planet. l( : bwa2gx38mlyeyq 9The inner radius of the rings is lyga9e bym :2wq3 l(x8 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 onckzv8vm/tc )c 6e every 15.5 s (see Fig. 5–9). What is tvtc/8k mv6zc)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 4xuzpju a+s)2((ieb t+ .)up kv200 km from the center of the Earth's Moon in a space vehicle (a) moving at constbz(+iu(s ))pe2pv+a xjk u u.tant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They na k5f3y0weq-/hzk8(j uec1d o-sn7g 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 mass of each?d1e fhjz7a (o83e wn /-kckusg0ny5-q    $\times 10^{29}$

  What will a spring scale read for the weight ovq g 3ru. 7iwve;qfrzq(/-ze /f a 55-kg woman in an elevator thaq r r-u/f3gzqq7z;.v vwei e(/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 hang(m 0fc:z)bt gt:ad9vbnr.4wps from 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 a b:.rgzvc0 nd9()mfaptt4 b: wnd direction)? a =   

Show that if a satellite orbits very near t11 s0s) dllnsthe surface of a planet with period T , the density (massnsll)t ds 10s1/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine th/5zxbjenk. 0s5b)q o ue period of an artificial satellite orzeo5x) kb.5jsbu nq0/biting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundrq*ts2 ji,p 8rtk(-cfsoph .n b.10bsved meters across, orbits the Sun like the planets. Its period is 410 d. p (cjkv2*nhbr ss..s8 f,bo pt01qi-t What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis:g bbxmyth :*e9 f06whtance 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 roeb,fxb5mbra g9 o l*4h2z*1e q bw7:vdughly 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 *meovqbb*z9h4xb :g laeb d7 f52 1r,wSystem? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center;t* uivt2hdg,m/c j z; of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons o-alf65tw +n xyf 6y-lwa5f+x tnJupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known uet.s48v x,ah2*fo rk period and distance of the Moon. uvoh8a *4fs ,kr 2et.x   $\times 10^{24}$

  Determine the mean distance from Jupiter for /4)nvs 3kznhh each of Jupiter’s moons, using Keplernvhkhs3z )/4n’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which 0yyz65 tjwxc:i( 0c.j6rd djtsome space scientists think came from a planet that once oydj0x .zr6i: jjw t6(0ccdy5 trbited 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" i0 qx 7(w8zsmnzn 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 enough to produce an apparent gravity of g nxzmq z7(ws 80as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swingingcni 5gv(( 5ut 2jb4b+ fwdxd,o 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, w tbjgcvb nd(2u(54dfw+i x5,ohat 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 accelerzs 0/xe, o ra7z,8 0aey8cosoo r*su1aation of gravity be half what it iz1azey/ra 8 s0o 7 ,s8*roousax,0ecos on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal8epiytb/2+z3nk9mi op1 r z ,g 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 indivp1itz2e9, 3no+ 8/kmibyrg zp idual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, tiv2z5 yan48z vhe apparent acceleration of gravity at v8 5nayivz2 z4the 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 this?    $\times 10^{-1}$

  At what distance from trhegtjl q; +.5he Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite fe;q tjhg 5+.rlorces?    $\times 10^8$

  You know your mass is 65 kg, but when you stavzldwa, l09 iq ouw4:)nd on a bathroom scale in an elevator, it says your m9 duq4lzw a:),o wv0ilass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abopy:0 49 gvnuvmui r3g4ut 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.gnymu4v 3p : 0v9guir40 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43z,ep6 vkg 2w5svu* gd;rab cdo4-l.d 9).
(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 i :wxr; dgchp4 yohbu;)9l(m;an terms of its radius r, the acceleration due to gravity at its surface and they rmh(hcup;4wg: l)xa ;; od9b gravitational constant G.

A plumb bob (a mass m hanging on a k0 ,hr qn i-7xv).c y437a:fyztp)y:ypkybq dstring) is deflected from the vertical by any-7k a4).7:pt qy3dci:k nbyx,yyr hzq)fp 0v angle $\theta$ 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;8cmj i+8 waev banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely ha+m88j ;eiawcv ndle the curve?

  How long would a day be if the Earth were rotating,r(3bgd- slgs so fast that objects at the equator were apparently weig,lggb-d rs(3s htless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance a)z4 1qll lt7 u2t h*covu-9ylopart 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 spee 8odg4)zng9(nlc6 h mkd rounds a curve of radius 235 m. A lamp suspended from the ceililg()k 8o9c h4g n6dmznng swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as f-52ikn : vsdrp)ik e,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 pik f: n)e-p5dk 2ivrs,eople 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 usy/ ijbb4g dg)zn p2p 0o*n+li/*o:2ysawz 2Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting thbg/d*0yaiun l 22+ *yizz: 42no)owbgpj /ssp e 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 wvm(7doqq:+ylr, eiq.gd yu6++xn- pthe hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normaluev- x, q r+yn:g+io7ydl(+q .m6pdqw 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 at A?

  The Navstar Global Positioning System (GPS) utilizes a h luc n;3l,m)pizr 8j9group 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, ajlp zn8l3i h;mucr9 ,)llowing 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 (NEth*oxyqj ey8141b( i iAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40i1y4 *qo 18xbyjthe(i $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 pursuim9/1wv 5fxx(k iora f.ng a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. v5rfx1 xfami9 k o/.w(
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean ;:g-dwl :;e:hw lbz4mrtqi-bdistance from the Sun?g;d4 i-;bzw-tb h l:e:lmwrq:   
(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 y2+3 j)yyw* k ,pbw. jiv7iennw ;7csyG would need to be if you could actually "feel" yourself gravitationally attracted toi.* nwnj+ks2;c eyw7ip3 )byjy,y7 wv someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around t22jjac fo5enx*.:l zh36 moifhe center of the Milky Way Galaxy (Fig. 5-46) at a distafx23 jjh2e ncim :za.*f5ol6once of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50d h bgr2ru+e*qdk,x+c i8 0ck) 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 s,q c+kdh2bu)r eg+*c 80dx kriide of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 528f at5h6v h:gbwg8xf500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced d4 edug mw0eq*fo:2.m by the tip of the 1.5-cm-long sweep second hand on your :em f4dwqu2ge o .m0d*wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in hpm7vnq0:vf(+ 7zj mna circle below you on a 0.25-m piece of fishing line. The weight makeq +v7p:v(jh0 fnznmm7s 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 nx8 m xwwg;zid3y3,4 d6bz8eh R in a new highway is designed so that a car traveling at speed xdzx 36iedwmn8 ,z3b4g; hwy8$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotic i mopw-o3c2wl1o*) mating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripet1cm2moooc3pw)il *w -al acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$