Sometimes people say that water is removed from clothn)kep hufvd :,) (j2mjes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statementenj )d,2 :(umvfkp) hj?

Will the acceleration of a caflz9:0(18 gp;) aeef btlutf lr be the same when the car travels around a sharp curve at a constant 60 ke;: gut lft9z)1 8ba( ell0fpfm/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constantx2,p s)b7kdu:m4oss:a yg3dl speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a leve dua ,:oy:s27msxk4 dlpgbs)3l stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-g:4ik) k6jy5 vemaau)po-round. Which of these forces provides the centripetal accej m4):yv6ik5k)ue paaleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillingc5 t5btk:w:(2ut:vb b5 0oeti7e y dbf out, even at the top of ic5(tbwfk2 d5bto:te eu:vby 05 :b7t the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leastxur5 :b1diuk .gpa1k8 three controls in the car which can be used to cause the car to ac5u11kgui .:8drb axpkcelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of t kexj8ina8 ((-2 bviea small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “aikbx8e -(v8(tnjii e2ar”), 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 rider (yz w(;dis6gh 1uiz4bs lean inward when rounding a curve at high speed?

Why do airplanes bank whendaf5 n5 zch/i ;db0:k-y /hjur they turn? How would you compute the banking angle given its speed and rad/d- y;0b:kh 5cdzr/f n5ujahiius of the turn?

A girl is whirling a ball on a string around her head in a hokn(tgu+ a5m9 e e0ri5qrizontal plane. She wants to let go at precisely the right time so that the ball will hit a tarqke natu05gre(9 5+mi get on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the fu ev)3n 9 atetu;k-joynl4;4 Earth? If so, how large a force? Consider an applt t eyn43kfe4oau nuvl);9 -;je
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what ie+1w k;ni5r5m kih65y7+s inkjbt eg,t is, in what ways would the Moon’s orbit gwie;+t +k,51 ishkk je6r5niyn5b 7mbe different?

Which pulls harder gravitationally, the Earth on the Moon, or thti9u jyg05 j5ye Moon on the Earth? Which acceler59ij5u0j g yytates more?

The Sun's gravitational pulyax m30ywg5 n8l on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides.wya 85g3x ymn0 Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more ak gg2adpqkc(c/g2 dng1 /kgcx8a(1 4 zt the equator or at the poles? What two effects are at work? Do they oppose each/gcx1qkg8( dkga 1n c (p4 /zcd2g2kag other?

The gravitational force on the Moon due to the )a maepy aeks147b 6j c1,ucl;Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon a1y4, u lej7ap6 a)escb1cm k;pulled away from the Earth?

Is the centripetal acceleration of Mars in cw:tb8vaz.ja(z l d. a( ym27n(y8 mrcits orbit around the Sun larger or smaller than tvrayz dl7 nm8.z(ay( (8acm:w.c btj2 he centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bvlmgpi/jn. i;)8fs*n,ww1q o ) toward the west? Consider the Earth’s rotation directiw so./ wqm8)1n n;fjp ii*glv,on.

When will your apparent weight be the greatest, as measured by a scale in auqatvqm6d:r *d/ .7d v;tbov6 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 it be the same :;btr*m.q76q6aotv ud /dv vdas when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be advers+v q* jm9mhy-mely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (bh-+9 *vy mmmqj) 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 w4 6p ni8,zgepwr9xyp+eightlessness” between sy6pxgwz 84p9+ i,repn teps.

The Earth moves faster in its orbit around the Sun in January than in Juu+0v oa3ks1w;z f o:nhly. 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 — t :1aus oko3znvw0f;h+he 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 dhxri,26ki q q,iscovered to have a moon. Explain how this discovery e q2x6rh,iik, qnabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lk pg(,d,-g*u;;gy t oqm6yefgyv: u v,arger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gra6y g(u;*eq:p ,dv,oyg ,m fyuggkvt-;vitational 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 1980 qz1krw 9x5c,d.ni--t nv1dtnd2/fo x$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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:j kd 0fkxev+-7 bmeef3gw --315b c +uifutrj its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on themx:jk7 ej +--rgbifcb3f- 5udut1 3k0w+evfe 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 Nr c ,2kzij1u- yqdj5t1 is exerted on a 2.0-kg discus as it rotates uniformly in a horizoku1 tc dj,z5 -ijq1y2rntal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cw i.hkf+-iadgm03e; uircles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration afu a;hi.+0 d3kg-emiwt the Earth's surface. $\approx$    g

  What is the magnitude of the acceler0 t4ph s(n5yuzr ljtbswd:-5; ation of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per m r5lwh(j t:y;bsz -t0upsd4n5inute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate5:ol2mp s. tgj-u12p 6chxui .dgph*i in a vertical circle of radius 72.0 cm , u. *lhp2cs.5 i:u61jgpp odixg- hm2t 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- 1duvlkkq :-89ol /tnr xcykc s:0n72fkg car can round a turn of radius 77 m on a flat road if the coefficient of:uqk:2d98n /-ynfv kr7kcclo1x 0 tsl 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 jtn v(k(n+ ta6, fd7gvstatic friction be between the tires and the road if a car is to round a lev +kd(fvv j6,7tn g(ntael curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and enkz+1s ix;3e jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m xn+3kz ;ies1e. 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 th7.ca0dxq w2a qgor,1le axis of a rotating turntable 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 iql o7g1aqr d.a,x02cws the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at erboy n59x,l)jje7hf :3vwf; the top r9n fhebej,o5:jx)37 ; yw vlfof 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 (includib2sob) zl**d mng the driver) crosses the rounded top of ao*bszl2m) d*b 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-m0pgei l(5p.gu -diameter Ferris wheel need to make for the passengers to feel “weightl .l 0p(egp5giuess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wx4 wbxlac). d+2tjn7h hirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the ten2 bc txh).4lxja7 +wdnsion 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 par*x:qo9me 8tt q2o:.uy vto c2tticle 9.00 cm from the axis of rotation is to experience an acceleration of cx.t 2eqtouov: 2 qy*9m8t:ot 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotate*/pon:/boabkny v1c z)1b.lm d in a cylindrically walled "room." (See Fig. 5-35.)lp1m.n o*ob1a):by /zk v cbn/
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 lnc040(fgc sga/oa q0 in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light coo(qag0lf00 / sagcn4c rd 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 we +ahvky0; 3fbuvaxd(7ight of the ball which revolves on a string 0.600 m long. In particular, find the fyava;hd 7(+ b3v0xu kmagnitude 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 xu+dl smfaqmb9ao4(9;;vdx; of 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 masse hq+1h kj,-vyus $ 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 ei/*oz bp2 vlm4vasive maneuver by diving 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 centripetal components tv; f2:3rqabb9 xj2aeof the net force exerted on the car (by the ground) in Example 5-8 when its e aj;2:vaq3 xt9bf2brspeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 c. jswga7 8(gds/m89*yyab zy accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming consta7yaz( *8 c byjyd/ws.9aggsm8nt 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 : yqupuq041 apinstant:uua1ppq 0q y4, 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’s gravity on a spacecraft 12,800 km (a n(0 f2c-ue un q-27fv0wcqy-f+jwbe2 Earth radii) a2wfu c7 qy-2c-nq f0fvebn j0ew +a(-ubove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gr/cqzr+ d cs0y2avitational acceleration g has a magnitude of c yqc+0dr2/z s12 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 -ay dit7 :1ecv)i1l amgravity on the Moon. The Moon's radius is 1.7 e-i1md7aa:ic)l1 v ty4 $\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,5;pd3tqymn.* uol . fq but has the same mass. What is the acceleration due to gravity near its surfac*o. .qp3u;ylfn d5qtm e?   

  A hypothetical planet has a m9r6b(q;: j 5vxzkgizdass 1.66 times that of Earth, but the same radius. What is g near its surfaxr5zv zj69 d;q:ib k(gce?   

  Two objects attract each otscq9q w ,b0+fzher gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effectlkef3j2 ay9ugv1o2wv)j+6mt6 x0s ma.yc9 z o ive value of g , the acceleration of gravity, at (a) 3200 m o efg3zc.y2929m vuk6wlao0xjyj ) mv+t6sa1   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the ctk-u. )y:decEarth where th:cke.c ud)t -yegravitational 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 j-nzr-imf/ xw;o 0 *mebhed53Sun packed into a sphere about 10 km in radius. Estimate the surface gr;*i djh3b5-/xeneow0zfrm-m avity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but b,xv9xye 7 k4,c, llgnis now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is th9vbcx ,kg4e7ly, ,nx le surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlesoj3/wqja.a5ax .kzr+l4k 6qas 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 calculating the acceleratio+3 okl .5/ jazw. aqx46jaqkarn 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. Calj( miodi37:dgglt 83dculate the mag3lm tg:d8 dijgo(i7d 3nitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lindb4 s ikj:m)l+e up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are li4 jd:)s +mbk $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 gravitc x(1 ml2dceqik25p0sy at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 exl cqim 20152 pk(csdkm, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for thwff2wpv 7d srh4506vncrb97 ge period of the Earth and its distance from the Sun. [Note: Compare yo692v 7nfw0bpwsvd47fr rhgc5ur answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a s/l7o;mdlk g z*atellite moving in a stable circular orbit about the Earth akzl mog;d7l /*t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ey 3;tq5fd 4t+rxykm h5arth. How fast must the shuttle be moving (relative to Earth) when the rd k5x q+thftyr45m; y3elease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to ex3u ;ai;l 1hfn yd(m9upperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Questio y fil(;d9numa ;hp13un 21, Fig 5–32.)   

  Determine the time it takes fnt evyapx +9):or 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 thy9v xt):n e+ape Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would aqxg6o,l) os6e satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Ea,el o 6gx)6qsorth?   

  During an Apollo lunar landing misscwzt ynn+a4 n g1(;/clion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it1/ zygn 4(wcn+a; ntcl take to go around the Moon once?    s

  The rings of Saturn a:f5 0q fem he xi7esbcy3g1d*bc7b4n1re composed of chunks of ice that orbit the planet. The inner radius of the rings is 7*q7x g0f7: sbnbemh1 3ebie fy dc415c3,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once ever1e/gp, wxi rc:2u6rypy 15.5 s (see Fig. 5–9). What is the ratrxu6/1i :pg, epr2y wcio 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 weigh.1j * x6mhaa5u:w ylpz3 )rsmvld3 r,st of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at djp.m1:us*lr3r6 ,5 yvzm al)xh3wasconstant 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 equx8g hbay)8mi /al mass. They are observed to be separated by 360 million km and take 5.7 Earth years to or)gm8hyx i/b8 abit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in anxi;jwmq 5,+sq a2rax 4 elevator tha x4jw i;rqax52a,+msqt 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 from a cord s; ic.zdr nu;n.uspended from the ceiling of an elevator. Theru z..dni ;nc; cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the jlwf:;81vka (+dj:wxt+fx*7 jiujzwsurface of a planet with period T , the density (mass/vo8* ffxl jwzjvixtwa1 wkj+:;(d7: u+ jlume) 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 ander;1n*ixxp ,ac ebv7hht1n ,) the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earthxrp)bhtn1*;ee v ,1x 7ihc,a n’s surface.    s

  The asteroid Icarus, though only a few hundred ,a1 7rq (ihup-t2iya2ell .b vmeters across, orbits the Sun like the planets. Its period is 410 d. What is lqv2h-i7au tp.b2( r yie1 l,aits mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5nd e,n.. 1djdypt/ am+ $\times 10^{9} \mathrm{~km}$ 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 ve1 d vs4vvv4gk*ry 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 thv gvv4 v4*dk1sere? [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 Gal5kox, :mu pya4 vfq9k9axy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,nnm 3+caeq7s.sh x8 s mean distance for the four largest moons of Jupiter.aq8s+hes c,7n3 mnsx (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 kx h;v3j z;lb1pnown period and distance of the Moon. ;j3zlh;1xvpb   $\times 10^{24}$

  Determine the mean diq .f1 q,olhk1/k ,a.ribm9fiw55gi udstance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in th5mbq51ugd fr. hki.i k1l/ ,ia,woqf9e 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 som)qk9o xvsf(9 3ozrr7xm8 .oy xe space scientists think came from a planet that once orbited the rso okfox)89rz(9x7m 3yxvq .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 vr 1tqtr h5p;0a band completely encircling a sun (r1hq0rv5 ;tpt 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, this planet's year, in Earth days?   

  Tarzan plans to cross a gorgeyig2ncp.x ;y- ;9sg 1hlfro6e by swinging 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 g ;.2xy 9s16nhiol-cgre; p yflowest 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 accelem duu1u1e 5) ),tnbcsoration of gravity be half what it is on the surfa,)u ues nmu)co 51d1tbce?    $\times 10^6$

  On an ice rink, two skatqdjpl)( ,9 0a (g5ibjj6m q +uocisxp+hu+pe6 ers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume theirlep+d + 6x(j a buhjqqo9ug)+m p0i(s56jic,p arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceler1d4 m 4m h)qsqnt.m)vvation of gravity at the equator is slightly less than it would be if the Eart4 hv qmm 1.4t)vm)qsndh didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveme* s)vv)w9++oq cupfling directly from the Earth to the Moon experience zero net force because the Earth and v+*u wo))f9p mc veqs+Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand om,k*.juy 4vvx 8 bf 4f.n3bnc*doy -gln a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevat* klvg odfyx43b*bmn 8y- 4fcjv.u., nor, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo hxvzubx;lxaj) 2a9tsb4) 1w;ut 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 equ)1 hb;2;)wj 4b astlz9 vuxaxxal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5aib o4o-0to+s –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 itsh9aryrszax,x9bio6y41 u o4fd y*z*2 radius r, the acceleration due to gravity at its surface and the gravitaix4h,adsbz*2yoz 9x rafoy6 *r1uy9 4 tional constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b iu2*df:q17syiqh 73d 2kyxn9c6aqnby an angle u3xfy 6d9y nkc:qii7 7q1ah2qn2 sbd* $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed oft;;qi x x.w6et If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a cx .x; 6e;qtwtiar safely handle the curve?

  How long would a day be if the Earth were rotating so fqv6vm8-;fp e:r.s9 1d: jl/wcdwt gsvast that objects at the equator were apparently weightlessd:s ;sm1 vfjq- /rvg wtvl8dpe :.9cw6?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of w,k 8g9iqn*plq gt2w3 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 constantegzx*+9f9hs)yx bx w. rh2 3ub speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to2.xx)3+*9rxufzyse 9 wh b gbh 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. Thicavygz0c 3 ;8 t(mld;us, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupitv80 z3;ccdlmg iy(a;ter: 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 Sphszjq* q)ik 2.ace 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 k* jqis .)2hzqescapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed le )8b:c 8d. 7 tqbyb6napwd2aas it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losin62 y n78lddbbaa bp.qt:)e w8cg contact with the road at A?

  The Navstar Global Posi7lm)7 vcqfw7 ntioning System (GPS) utilizes 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 navigq)fwnm7l7vc 7ational “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), after traveling 2.1 bilh,y3992 4p xupz gz kp hfo0b43mqm1rvlion km, is meant to orbit the asteroid Eros at a height of about 15h0k9fp r4 xg9m 4p2um 1,bq3z3pvyzoh km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuizlk xzx6(*/n2ph) kv+v pz)owng a satellite in need of repair. You are in a circular orbit of the same radius /pkx2v)vxz* +zwlpo6zk(hn ) 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 yea10tdmk rmf:t0 rs. (a) What is its mean distance from thm0fdrmk0t: t 1e Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would needn b1pr5+kll:1i1y i dd to be if you could actually "feel" yourself gravitation+ypni1il kb1r:dd5 l1ally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around 4hc55rj wstq. the center of the Milky Way Galaxy (Fig. 5-46) at a distance j4 55 sq.rtchwof 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 c7be96 +:n7urwu m jgha square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass p j umh97b6u+ew:g7 ncrlaced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5n d/3tf/ lb pc+;x.qc9u(d fbg500 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 by the tip of the 1.5-cm-long sweep secondiwj vjwjtql*7*6 9z6e hand9jvwqi*j6zlt* j76we on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in ( *a.wv.h y hgvtb3zb+a circle below you on a 0.25-m piece of fishing line. The weight makes a c.vh gabtw.y*h3 z +b(vomplete 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 pzvpnz k .3/c(45,q xg 2dekyba car travelbe/5y(xpvk3 ncq,2 dz 4 gpzk.ing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cdc56 f,- udwvgb m;)xears when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 g, x;c ubw6)d5 mf-evdkg 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.$\approx$    $\times 10^2$