Sometimes people say that water is removed from clothes in a spin dryer by centi8h/4 jmj,wui sx7ji0 v 5+qydrifugal force throwing the water outward. What is wrws8yj, 0i4 7xj/u5+mdvjh qiiong with this statement?

Will the acceleration of a car be the same when the car travels arou ciatj2w1w6*pffn0 x7nd a sharp curve at a constant 60 km/h as when it travels around a gentle curvecp0ff7wwi* ta21xj n6 at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doesamk q2focu6tce hk . 8y pdcs8i7zz00q v:((r7 the car exert the greatest and least forck2m( zcqpaoyveuc7fq:0hsitdzr(6 c87 k 08. es on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a chilcbqmsdy au5b5b0vjm 76fx0-2o)cu 5 y d riding a horse on a merry-go-round. Which of these f ucmb6syy jbm 7q5) o uvf52bxa50-d0corces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withou 4w- qm w/ixz7uy4)zeut the water spilling out, even at the top of the circle when the bucket isuew7 i)q4 /w-xy zumz4 upside down. Explain.

How many “accelerators” do you have in your car? There are at least three nxe0ap / h0e;eqkuh 64controls in the car which can be used to cause the car to accelerate. What are they? What accelerpax 04; /0heu6eqe knhations do they produce?

A child on a sled comes flying over the crest of a small.j fs5 t+7p4u+ussdpv19rp t w 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 betwee7ut5fs+s1 u . dwv9tj+r4 spppn 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 cctnx)6 cy *s w(yhpgsmu )8f8 ey75i:ourve at high speed?

Why do airplanes bank when they turn? How would you comp.ulw;f.7px 6waiw(mr f 7ba ad*s+-a03o za rpute the banking angle given its speed and radius owb(pa pa.f0wuoara lf-a 7 wm.;6+dxis z7*3rf the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. She7 v5 u(k8hokf)6nzpu9(b tuu47i t zyu wants to let go at precisely the right time so that the ball will hit a target on the otherot6 uf p bnytzu75i 8( ku7kuh)(uvz49 side of the yard. When should she let go of the string?

Does an apple exert a gravifh*lq.l 4 6bkrtational force on the Earth? If so, how large a force? Clk*rf.4lh6 q bonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways m 2j enc -gp9.wa89aslwould the Moon’s orbit be diff2a9ce9 .p l8n sa-mjwgerent?

Which pulls harder gr30 i lef xn qkgtyeeu4+w+d0:/avitationally, the Earth on the Moon, or the Moon on the Ear xt04l nid 0/ewgueq fyek+3+:th? Which accelerates more?

The Sun's gravitational pull on the Earth is much l8xmqn9a,w qn u82xj6targer 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 o6 ma9xn, 8qx2t8qnjuwf the Earth to the other.]

Will an object weigh more at the equator or at the poi3kxz2uja.+ 4okv jw- les? What two effects are at work? Do theyx-2.oaiuv+j3kw z4j k oppose each other?

The gravitational force on the Moon due to the Earth is only abu6zz 6p0kf uy/1)nsxvout half the force on the Moon due to the Sun. Why isn’t the Mo01u nz / pvku)6sfyzx6on pulled away from the Earth?

Is the centripetal a/ wo(bu-ka h:ycceleration of Mars in its orbit around the Sun larger or smaller than the ceo-(u yahw:b/ kntripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east od9cr5 t-8ibnjr (b) toward the west? Consider the Earth’s rotationjr 5i n9c-8tdb direction.

When will your apparent weight be the greatest, as measured c84dm 2z ;abav(,r gpwby 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 m,c;r 4v8( ab apdgz2wyour 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 spendib 5py 0j (+vcu(bs7pa long 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 ho+v 0cu5b7(jpp(b aiysw 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 exjp,o s0;)ud g3lq(fvvperiences “free fall” or “apparent weightlessness” betweeng uv3pjl; qso(vd)f0, steps.

The Earth moves faster in its orbit arou1yyvvh7hs x am--1- mhnd the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This mhhvmv-1s x 7-a1y-hyis 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 until62)v/4 bteaq dysdgd( it was discovered to have a moon. Explain how this discovery enabled an estimate of Plu4 st2q( bge d6vy/add)to’s mass.

  The Sun's gravitational pull on the Earth is much larkrx +ikf8b; ccq oud93hli6x)/ e1gz ;ger 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 othlxcx3 rfbkz +u;;o8h k gd q61)ci/9eier.]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 1*bb-brtarj0a- .jbx3980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbig4 asxj+xv 3y)t around the Sun, and the net force exerted on the Earth. What exerts this forcsav)y3g +jxx4e 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:hhi; vpn e6 /npd1+fq 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of n/6v i +ep1h:qh d;fpnthe discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's ae 4e7k l z/klp77 cmr59(dvtdsurface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in klce57dlka( zrev9/tmd 7p47its 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 ouqo4:4 nu khs 66rro 3sya;t:tf a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s d4u tk6:r;qoht 6:su aoyns3r4iameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rated3(h,r3q etg. kjzsb6 in a vertical circle of radius 72.0 cm , as shown ihjbd3.q ,kge6s3( t zrn 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 whic 1h 46rfz6)bx7i7oq+ow p slbuh a 1050-kg car can round a 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 independents ri+o61bhfzu 77lqw)pxb4o 6 of the mass of the car?   

  How large must the coefficient of static friction be b g/ltk ts6 ,,el fkn+b)(djaj8etween the tires and the road if a car t8)+ stjbjfgl6kld,e , k a/n(is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training a8 (1tzc 6qaogdstronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on he( 8gc adot16qzr 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 turntabyzj7*6xuja:p w)b 1 anfoa1 t-le of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of stat)6x 1 7j:*ta 1jbfwpaazuy-noic friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be trave 3t)5 p1g:dbkw- kfjyiling when upside down at the tok 3i5jwf:1-)gypt bkdp of a 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) 8i)w:k lk 6x8+qjfesrcrosses the rounded top es jrw68 kkl)+i8q xf:of a 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-diask 3ac,uqf wf2 ;s (ov3wz6ho-meter Ferris wheel need to make for the uf;wosca36v2o-3 kfq(z shw, passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vp9g7fpy)f n1w -wzpr 7ertical circle of radius 1.10 m. At the lowest point of its m 1 )f-9grpp7p7 wwzfnyotion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate ijdsrui56 fd :,f a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115sd6:iru 5f jd,,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotateafukwp 3r0tv x/mp+t+8 x( 5n: vr,dbwd in a cylindrically walled "room." rt xxmkbu p t85vw,v r:pa+wfdn +3(0/(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-hgre:7pm d(q i*a3xp:4ieeek; ockey tabletop, and is held in this orbit by a light cord connectedpreq3k:a;xp * e7ge(i4: ie md 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 wei*l i;avb (tuzd qbn)te3j2c02 ght of the ball which revolves on a zvc2bu i)jt(n0 d3btq*ael; 2string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly hvsjax;2e13evy 9+j9s )ib ywbanked 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 masses -j,2c4w epb jw$ 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 divilv m;a+na: /f+q/nk alng 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 centripva*cv dfv dmgwktrq-6a,4)f 5(a 8n 0fetal components of the net force exerted on the car (byf arn6dck*5gq f4w- )dvtam ,8af(vv0 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 xy 9 .fylmv10p+0 .5e7fnvguxf:jcd sfrom the pit area, going from re.mf 0f.d 07 c s95jl:neg pyvxvux+y1fst 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 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 particular s q,:,d(phr fk;b(zd0bwa5dg g2qn -linstant, its a:l rbk2q0q,h5sg (,fpz ;a(d b-nd wdgcceleration 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 sa-flkl h np;:/pacecraft 12,800 km (2 Earth radii) above the Eart l-/:;pl hnfkah’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hjw,mh:-i pfd 7sj+4 zgas a magnitude of 12+pjmd-f4j ,z 7: wgshi 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 gravizqncxdy5p rg :972 ,raty on the Moon. The Moon's radius is 1.74 d2pc,yzq7 rn 9a:r g5x$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiumq6 :)s6tbj usdm hv*5s 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravitybtm6su)dq 5vm 6:hj*s near its surface?   

  A hypothetical planet has if s0jj b+,q*ta mass 1.66 times that of Earth, but the same radius. What is g neas*j t+bqi,0fjr its surface?   

  Two objects attract each other gravita-7.u ps1rau,u irlcv0w56m yj tionally 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 ofpd -1iv1;mow f gravity, at (a) 3200 m pfi 1-mwvo d;1   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frb-lcb ,vx kl88om the Earth’s center to a point outside the Earth where t8vbb ck-l8 x,lhegravitational acceleration 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 mass of our Sun pack5t bi20aa fgxxu3 u6q/ed into a sphere about 10 km in radius. Estimate the surface gravi2a5 u 3iax0xg quf/tb6ty on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star li8-(3-ixq2-gr hvp szb pne ;ga(rzo9vke our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is tqv;v -2ap8 pgih-zo(x3 9 snrb( e-rgzhe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space s8(b647e r phtu2zpobwhuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s suuprb4oe8h7 2z(pwtb6rface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calc 9nfqr3ed.z ag 24vf:)*lptk hulate the magnitude and direction of the totav :zflp.fk4)9q dtgeh2nr * 3al 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 plac1vkkuo / +fd6nets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line ( c1d+kvufk/6o 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 accele, +mu)7ate/ h*cdgywpration of gravity at the surface of Mars is 0.38 of what it is on E* wyamgd,utp )e c7h+/arth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using t7b(oy 7 m:cgdfhe known value for the period of the Earth and its distance from the Sun. [Note: Compare your7fdc:( ym o7gb answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite momyv.4m;vs0pe e/ 8h5qloaw1 oving in a stable circular orbit about the Earth ath4/se m p.1oqvlamo5 w0y8e;v a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abp qghrbf a (m4*).n,t1w /k2vdugsij:4v si:pove the Ea:r(/p2qf, tjsivb.an4m *1 g i ku)h sdwvpg4:rth. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if ohbf d7p-f 5tr-ccupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for off57p-d rb t-hne revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbithh4+ xu y e jxxl;xm(kl)p(+2g the Earth in a circular “near-Earth” orbit. A “near (u+4x)+ph(m glehxx lx;2ykj -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 mass of the satellite?    s ~    min

  At what horizontal velocity wvg fkn4b 377: r6nt) vwjvkkl:ould a satellite have to be launched from the top of Mt. Everest to be placed in a circular o nwr::vb)n gk7lk3k4jtfv76 vrbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbitu oj5 th,6- ys.mf-gfv the Moon at an altitude of about 100 km. How long did it take to go around the Mm ov jf ,h-t.uy-s6g5foon once?    s

  The rings of Saturn aw 56y/dknvnyl2dcs1d) s0 w j9re composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,0kl9cwn) /s 6d2v5wdny 0yd1sj00 $\mathrm{~km}$ , 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 da mtz 9rn j4+o2)v3bb15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weightr9bjt2omdz vb+4a)n 3 to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weigb5)2jbc af l eu90(qwsht of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vj5(ecqsf2wb0 9b)al u ehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-f3 0+n1 g5 zumb (sjkgtw;mm gw)kj he5)9vb(sstar system consists of two stars of equal mass. They are obsbw3m()su0g+k j(tmggh;e)1vz 5 nw mksbj95f erved 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 scale read for the t03tf6on e0bz weight of a 55-kg woman in an elevator that m0t6tfeb0n o3 zoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. T9xven5tji /tjvu2,tmv0*; nmms7i )l he cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directiom7)0lt;nmv*tu inj2sxv v / jtemi9, 5n)? a =   

Show that if a satellite orbits very near the surface oy*cwg8hw((9ki- t lpnf a planet with period T , the dk-pnlg( 8(wh*c9 i twyensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the perio+,7d 2sp9rt2f+ wdgmppd,thud of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Ea,d2d+wpd9hsp 2m t7pgt+ ,ruf rth’s surface.    s

  The asteroid Icarus, though b h 2/q,r4u/gh qeax0ko1vhhepf/m.;mup: j0 only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean 0h4. moppx hq g /1u,e2/ej;r:v/khumfqah 0bdistance from the Sun?    $\times 10^{11}$

  Neptune is an averagff +zu0/3+gfy+vw0d jhn-wuu e distance 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 once every 76 years. It comes very close dp,pms9q+) te to the surface of the Sun on its closest approach (Fig. 5,q)+st med p9p–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy(sq rqjx,-p 1dncb)jp 7bi; d3 $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, peri;q dw5+qj(t p nhx(e(dod, and mean distance for the four largest moons of Jupiter (those( (dwj; nhx q5q(dept+ discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distanc)qe)yb j-joux8yx n(2e of the Moon. bn2j e j- q(yux8)y)xo   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons y0(bd3kj4x ue m,djh9, using Kepler’s third law. Use the distance of Io and the periods given iny (ukb,9h 0 d3jdmex4j 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 Julx6l51fla +, gqfm/ gspiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed). q1x f5lagl6g mls/ ,f+
(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 "planetcp1f13 w ecjo;plh zy3 c2-(xt" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, thip3e1oytwz1;x c(f 3hcj2 c lp-s planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc fromlgx/ rnue v )i5vw62fpzs+q*, 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 v )2zv+ pr fls*n6 xgv,eu5qw/iine is 5.5 m long.   

  How far above the Earth’s surfa 4n eru7fbs63zce will the acceleration of gravity be half what 3ze6ursn7 fb4it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spfgso2 ckb;w .3 dli5/pin in a mutual circle once every 2.5 s. If we assume their arms ar5 fwpkgl b2i3d.sc/o;e 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 oncqb3 s 8u2hu, 9tqqroe0e per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estitus83q9q bhqueo 02r,mate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling di u)iikuen(,e-mw c)v 5ry(. directly from the Earth to the Moon expery) dv(ce ).kr5( eimuin i,uw-ience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when ywz.n9wn; r93ka 2uxjyou stand on a bathroom scale in an elevator, it says your mass is 82 kgza wwnjnr2k 3y9;9.ux . What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c wy z lj86f-um ep:xr:77p:wbkonsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 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 -byjm86:77 : pkeuw w:fzrlpxg) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.t3ew3wo d7g;fr-.f be5zu1tp 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 refco8s s+ll0f.s+ g i,adius r, the acceleration due to gravity at its surface and the gravitational constantlleso fc,s0 ++.sf8i g G.

A plumb bob (a mass m hanging on a string) ikd;4 q; k72dx5sl tcd7na a1mvs deflected from the vertical by an ;dvxl4ksa n c5qt2;kdm 1d7a 7angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design spb(m o*-jwpa:dyf /mh*eed of If the coefficient of static friction is 0.30 (wet pavement), at what range of spe hayp:-(*jmo /wb*f mdeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at theo)r4i0gk7 o2npa 7a h,r egx1r equator xe, n) o27rk0ghrp47 1aargiowere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant 6a so(0trbtseu8 t);j distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant sp3tl2zj ;0s-j* yrauvyeed rounds a curve of radius 235 m. A lamp suspended from the ceiling0yltv 2rz-su*j3a yj; swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timet7q * a85a9x d*rl wdij9trsm2s as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the nur9xtw9l7sa 82irqt * am*d j5dmber of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence oyc gm5y5gz.p, ngh**j f 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 njy*g 5yzc,* 5phgm g.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 traversel6 94wj4jtzrfs the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact wir4 z6twfjj l94th the road at A?

  The Navstar Global Positioning System (GPS) uti p e4fykp4 jg4/30r,q16m svs1nqvivvlizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nauticvp1erymp44,s3knqvj0 i 4q 1v/vs g6fal ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, ;:nt:h q1k3resjw k yd no,zc *4oq1.ois meant to orbit the asteroid Eros at a heio3*w4htes . n1d nkc ;roq,:qk:joz 1yght of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shut zano2c5xkf77 tle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the E2ox7zaf kn57carth), 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. ( zx*a-(rwd7ex fb(m8 ab xw(e0a) What is its mean distance from the Sunme( 7 x8(w-aez0x bxwbardf(*?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" ya(f n4fu(,jw km/; ewqourself gwnf a mq;uf/j(4(ke,w ravitationally 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 Galaxyac cz we,f*(9+: zarou (Fig. 5-46) at a distance of about 30,000 light-yearsu*:awr + ocz,9e(a zcf 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 cornersodnpjnx as v5y**++j+,u8caca5t *kd 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 th accau+kj*5yo+xasp*njt8 d5d, v+n* e midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ea: ,7z9tep tmfy..h 4lcz im)6j4ua:wh)lfzu zrth $ \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 1.5-cm-longccab1 i2k5x+09b4atby 5 bwd+lyef f5 sweep second hand on yourfbcc0b iatw+552b+d5 ya l4ekb1fyx9 wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weightsdsyv7p 6vv3c- s1 pyc*vw*m* around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cir-mvyp3vsc7 1d 6yspwsv **vc* cle 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 izw 7rkpk*+ u-highway is designed so that a car traveling at szk*- +ru7wi kppeed $ 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 nnx3(t7c4 ctp 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 tt7cn3n( p tcx4rain 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.$\approx$    $\times 10^2$