Sometimes people say that water is removed from clothes in a spin dryer by ces-djoho7rkr x, au ic);62rsdl 1t/b2ntrifugal force trsb -ld2j7 c ho,;td 1)2kuoxisrr6 a/hrowing the water outward. What is wrong with this statement?

Will the acceleration of a carm0dbd3qmcy +0wkgyr 54j9 g;i be the same when the car travels around a sharp curve at a constant 60 km/h as when it travem d3dq;i4 gy0r9 byc+gk jm50wls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alxx;- +:0+1zy-oms2b v ozvuwd/ caj byong a hilly road. Where does the car exert the greatest and leav-y1 o2ya-:ubzjzbvwx+ c/o dms x;0+ st forces 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 ch9 ix a1e rk.r(k09ovyfild riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration off vk10 yeiaork9x r.9( the child?

A bucket of water can be whirled in a verti.0m0putqdk2t: * y5vj ,qkmp;gcl, t ycal circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaimmq,tv ; dt0qy 2*pl,0yu:.c5jkkg tpn.

How many “accelerators” do you hal1rfyy :0q1z ave in your car? There are at least three controls in the car which can be used to cause :lr1q1 a0fyyzthe car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, ask+tm ;l:v74gsdzr n ,k shown in Fig. 5–31. His sled does not leave the ground (he doesmksn g,z +7lkrt; 4:vd 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 curve at high speed?ew 5;wi+,c -jl zp8ryv

Why do airplanes bank wh:rizzp0v iwn* hl d:/:1pumf(en they turn? How would you compute the banking angle given0znwml1 iiz:r/p:hvu:pf*( d its speed and radius of the turn?

A girl is whirling a ball on a stri50i-ax(9 fjo tq p5qbvng around her head in a horizontal plane. She wants to let go at precisely the right ox(q0 af v55bj-9q itptime so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force 61 p 09te,v md7ospifvem0tt,on the Earth? If so, how large a force? Consider an appv,0s0ett ti 6v9pm,f7p do1mele
(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 orbit jokbsc79dg: ;ea9cx , be dcs;b7 9e9x j,:kda gocifferent?

Which pulls harder gravi8 gskbgtj f71ybf; )u.tationally, the Earth on the Moon, or the Moon on the Eay1;fug7 jkt8.g )bfsbrth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yexh8vmg nu 8 s2aph bih(x )s().mc+0hgt the Moon's is mainly responsible for the tides. Explain. [Hintunmx2bcvh8m (gpxh)s h8(.ah0 gis )+: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effect wswpc*nva g9 2;5c6fts are at work ;*5cv2sw9pctanfg 6w? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the for;7 h9xomh ic* /sgt)nice on the Moonm/gct niix7;)oh h 9s* due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the (w1vxc9uo ,uzm a,5i vSun larger or smaller than the centripetal avx,wvu 1(9uc ,m5zoiacceleration of the Earth?

Would it require less speed to launchpi4:v74:db 7hcx p/s iun:vyo a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotao7y: h4p n/vub7:c4: isi pvxdtion direction.

When will your apparent weightvv :. z(r210e muu xoa9xn7czk be the 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) moves upward at constant speed? In which case would your weight be the least? When zue.2rv xvk(n71moua z :xc09would 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 periods in outer space gqj*r0ij9 r n9could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objeiqnr 99j0r jg*cts fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” f4- db)j u +xfw0dt2vvor “apparent weightlessness” between st2ftwd bf )- jvxv+d0u4eps.

The Earth moves faster in its orbid,swp ;u5 +7c:prvk*su:ejzet around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: Thissu 7kcr5 veue;wz:*+jp pds,: is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to h( kw6z5m0 bh v;kptilwaf5lmv14t; x5ave a moon. Explain how this discovery enabled a5 (5lx ;ktpmbkw vh;1azwml645iv f0 tn estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.(h 9rbc3pdp8 o bao2218jt btf Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of b28aj3cbtth(8dpo 2f9o r b1p1.25 $\mathrm{~m} / \mathrm{s}$ . 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 travelintw+(xz+eu,u h ex4wy3 *koi1ig 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal accel9g yt)z q;e*dqeration of the Earth in its orbit around the Sun, and the net force exerted on the Eart*qez) q9gd;ty h. 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 2 /8 j+tt (.csetc:wij r9wx12fzo9 ult10 N is exerted on a 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 sxzj( i+ uol92tew:.tc t1c/tf 8wrj9 the discus.   

  Suppose the space shuttle is in1z q+s1 6dd:upvbf9xi orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal accel+d9i zb1:vfd16ps xu qeration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of thefl78a(7 aqkx9cg ik .gg,; f1mx2 tcle acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cmc(7kkli9gxg;lf2 q7e 1,. c8ga xat mf?   

  A ball on the end of a string)wn +mfrs;zr 0 is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown iw +;nm)0zfrsr n 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 can round a turn8 )razhxix7 ui/zcr-(0++xdo0 x ertz of radius 77 m on a flat road if the coefficient of static xuxz) zrx i(r0/o78d htxcir- ++0e azfriction 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 bety.*,lg6twm gl ween the tires and the road lygw t m*l,g.6if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rmbruw*8pa/; -kwnv. u z3dfz 0otate a trainee in a horizontal circle of radius wz0;um 8 a3-r/v nf.zdu*wbkp12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating8ltyh2pva1 w7 turntable of variable speed. When the speed of the turntable is slowly increase7al82h pt1vw yd, 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 static friction between the coin and the turntable?   

  At what minimum speed muz6 v-.,cbym( w pjzu8: r xqp7i1hh9uhst a roller coaster be traveling when upside down at the top ,iry-9x 7puuh6vwb.m:qcjz hh(z1p8 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 (5zkl;ctzt ebx/p/) cu f95 gq-including the driver) crosses the rounded top of cq; tzxpczkt9)/f- u55egbl /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-diameter Ferpvq( +ghl- p)z, id;f 6 ufhf(,oe8iwsris wheel need to make for the passengers to feel “weightless” at th-6 pfs)+,d8 hh,i(;vo (pwegz filuqfe topmost point?    rpm

  A bucket of mass 2.00 q-v m4 (cm0e4fyjr*bqqa: c8wkg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tensi rqjeavym -0q c mf*q48b(c4:won 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 roxo s fr.oeq3 -3raeb9/;f5kkutate if a particle 9.00 cm from the axis of rotation is to experience an acckb; qfsu ae/3 o.rok-3efx r95eleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a car+g(ldyn 947wvs)o /qt c1dchi nival, people are rotated in a cylindrically walled "room." (See Figgv 9(ol nqc+tc7y4/ d1 )dihsw. 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 zrkqa :rck*i1yf s3bw4)u4 0d air-hockey tabletop, and i03isc4k41 fqkuywa :r*z )rdb s held in this orbit by a light 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 n5rnhe3 pac /,chtj+) :ii.nelot ignoring the weight of the ball which e+:nrc3cah) t5e i/j ,i.hnpl revolves on a string 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 banked for a car traveling j(:,rpsv76hgfz zm .c75 $\mathrm{~km} / \mathrm{h}$ , 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 massesui703 o6haiuogm. i+h $ 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 verti2x5 deck dd:7c-q:bpncally at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the3t0fw1mhdgrq1c.18 js+ 5jl 9u wzlbt net force exerted on the car (by the groundr s019huqg ll b.jw1z3m+ tfj5 1c8twd) 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 uniforuj*qju et+ a10mly 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 cuueu+0*1a jtqjrve 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 51a/ 4d* a5ruwye8tqeo4asj qradius 2.90 m . At a particular instant, its acceleration is 1.seqq w o*d5u5ja/aey41 84rat05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 *u6:2 di.;j b/80j phmd tef5edtosrd km (2 Earth radii) above the Earth’s surfac0tj bj dd .tdip*umr/52 f; e86eoshd:e if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationali ruepv9 (,z7z acceleration g has a magnitude ofe vr(i z7uzp,9 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 2r*6 scpka3xb to gravity on the Moon. The Moon's radius is 1.74 ab3 rk6c* pxs2$\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 Earj4*vxdhuf 4gotkw97 4th, but has the same mass. What is the acceleration due to gravity near itxk*9gfdh44jo uwv 47ts surface?   

  A hypothetical planet has a maozmwv5 t+y8fhrc 7q1d++:xcik *3o ckss 1.66 times that of Earth, but the same radius. +vc7m1fi5x w czc kqo+8hk3 t+yd r:*oWhat is g near its surface?   

  Two objects attract eachurl,xt--bzjr.l(6 dx qi0 h4gh4wg1g other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, ati;jy hn*3m,sqcde;2o) fq +ot (a) 3200 m somo,3h 2*qt);+q de ni;cjyf    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outs g i(vfuc) *ju6:6ccb, khf0xaide the Earth where thegravitational acceleration dueg i)6:0cfax(uj 6kc hbc *vf,u 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 paj) p ;5zugqr4b:isxnt76t1o x cked into a sphere about 10 km in radius. Estimate the surface6q5br4t)jpt7 z is;:o1xxnu g gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star l qj;fggl qak)b8/g :4cike our Sun but is now in the last stage of its evolution, is the size of oural8 )gq/kc:qg jf;4gb Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronautbxvy qj ,*a+a5bi2bhf59ec: us feel weightless while orbiting in the space shuttle. Your fr5*y:hqf xeav+i 2,b bb9auc5 jiends 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 surface in terms of g.   

  Four 9.5-kg spheres apdg7t1s cc.bd;a 4 .6s:ns9cubxy vy2re located at the corners of a square of side 0.60 m. Calcula1sd:gpc9btssy4c. 6 cy xvu.7bn;a 2dte the magnitude 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 line up op(gyh+c0f-z z furn :*n the same side of the Sun. Calculate the total force on the Earth due to Venus, Ju : uz(fn0 fgyrhp-c*z+piter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfac mxlnuwi6z+d20bryuq891 vm ) / ams3qe of Mars is 0.38 of what it is on Earth, and that 1duqr6myzqsa)3 2 ib 80+xumw9l v/mn Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the k /; zut5q3ecirnown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 3tz/q u riec5;5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite m 8lzwslu*vk 7n 2gfb+6oving in a stable circular orbit about the Earth at a height of 360fn7s b6v2w g *zl8uk+l0 km.    $\times 10^3$

  The space shuttle releases a satelle7q0*cu( mj-h0yp 0 +hgfzfdsite into a circular orbit 650 km above the Earth. How fast must the shuttlegfy0jmh0- (s7*q h d+upez0cf be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cy(d0-dfzi u *pblindrical spaceship rotate if occupants are to experience simulated gravi*upf b -z(0ddity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it kbibm :m4n9-ftakes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-m-b ib 9k4:mfnEarth” 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 would a satellite have to 0-j -jc9v s0 akgxxwn*be launched from the top of Mt. Everest to be placed in a circular orbit9vg -nc0xk jx-w0as j* around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t +1ycwhw9l4eyw0) p9wnfxb5the Moon at an altitude of about 100 km. How long did it take to go arp l eh y50b fw)ntx9cw+49ww1yound the Moon once?    s

  The rings of Saturn are composed of chunks of ice y rem oi dzrz(**l x)o8l96g1z 8fvtt7that orbit the planet. The inner radius of the rir 8oydio*16trzm( 8fllg zvxt z e*97)ngs is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fk r9nbxxa jm gvu ((7i- 9(vcd1bcn7v;ig. 5–9). What is the ratio of a persorcnv9a1v 7-m(n(x;c( digb79 j k vbxun’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 4200 k w)jq3i:hixf-/ (samb m from the center of the Earth's Moo (xf:iqb) -3mj sw/ihan in a space vehicle (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-star system consists of two stars of equal ma( ug 6 dd/kvn ds6o-rjv ;ce4vek1f31gss. They are observevv-rjdksve6n36 kfdd c4u/1 ;(gg oe1d 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 re 6gdx 5fm; itr4h75xjzad for the weight of a 55-kg woman in an elevator that moves t65xg ;h f izj54dxrm7
(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(sslu9.qo 3musnuq:7s 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 (magnituds9qun7os l.q 3:( umuse and direction)? a =   

Show that if a satellite orbits very near the surface of a plane mzoc7 zrh2,l87f. x+8h uewlft with period T , te 8wxmu7z f2.l,rofl87hc+h zhe density (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 period of the Moon (27.4 d) to determine the pern 0f/tif45a friod of an artif f/5n4a fritf0icial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though onluw /2lqkddi3; y a few hundred meters across, orbits the Sun like the planets.2idqd3 l/;wku Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancq1:u axpee6jl2 .i sy,e of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes0ikytp w k4t (ex;p*/m very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest dista; tktyi( ep/ 04xmkpw*nce from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy 06bd k)dz1i7ofr n: yf $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 k)4 zx jyekn.+vs4,kc the four largest moons of Jupiter (those discovered by Galileo in 160v. c4k4sxke)nyk z ,j+9).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moono ghm2 8qsk2m1. sm8go21mq hk2   $\times 10^{24}$

  Determine the mean distance from Jupiter for c jos1ia.7 st8each 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 the Tab siso81ac7 t.jle.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars 4kjhrawc3 : bbfl1r2/and Jupiter consists of many fragments (which some space sbf4jr /k3 :1cab2lwr hcientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale des o)nsfc ar+o ,z5wp2hw.k7 b2ycribes an artificial "planet" 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). Imagine5) okb,fn2wacr. w+2oyspz h 7 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 crosscwb,c)4)h 6t8eat wo s a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of o ecb wc68th,t)4)wsaexerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration odojxe bs6b b4u-wn5e2-2rkh. f gravity be half what it is on w- b ehndrxsjbbk5.4u o-2 2e6the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in r adw8 9+u /sooy3qjjo (2vm7s ;4bibza mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual msr /iq v74bzd (+9j ojbosoya2 ;uwm83asses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, pz s,xl yhx u9a:jcfx7,kux0 a5*re og73m)*z the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didnzu7 )l xzxjyk,9x3sx,fag*rmoe7pc5h: a 0*u ’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 spacecrau 9 rr0lk5xtr4ft traveling directly from the Earth to the Moon experience zero net force because the Eart4u0lr x9kt r5rh and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a batr0zbjh7 i1 u4bhroom scale in an elevator, it says your mass is 82 kg. What is the achjz bbru4i 710celeration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of p*t3ir a)xu6c tjiv1z fssg*h1:+wa-a circular tube that will rotate about its center (like a 3j:*1tc fts*h + v6-)1zgi araws uixptubular 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 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hi8:j6te 8.sy*)dka ah il hp0hfs aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in (z /dbsp;6t w i2*l-1mr uivujp,cg(yterms of its radius r, the acceleration due to gravity at its surface andul2b,p 6*u 1r(wcvz/g-;ip mys (tij d the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecte(+hgp uf7ut9 gd from the vertical by an angle u97h(gtf+ gpu$\theta$ 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 desi08 *yxjdjobmc( *as; mgn speed of If the coefficient of sxjd *;mbo(csj*am8y0 tatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects atp( a/ .fo.39fxy rc7( svw(k)f owlewv the equator were apparent3wwo kcwxp sv fao( rl7 ).ef/y((f9.vly weightless?    $\times 10^3$s

  Two equal-mass stars main)r o06xct)a gp-vsp, xtain a constant 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 av,u7mcir65bfkk t/q 47 8n-;ywr jiws constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle otk7r- kn, ij4wwcrmqbu; f67y8 /5isv f 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thusovmo c ah6:1/s, 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 foro61/mvo :ah sc Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an e )lq 6buib3u,agb2 p)dxtremely massive core in the distant galaxy M87b) p lqu2b6,)aug b3id, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traversesw5rsv) c(9h rx 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?) Exsxr59r(v)c hwplain. (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 group of 24 satellitgf)skvm.33*qh 6q.t0gkm gq7r: eo loes orbiting the Earth. Using “trv: oom363 qksqh0g.)e. 7mtg qf* krgliangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), afub )my2+o fbi.ir+)ffter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height + .m)offibb i) +ufyr2of 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 shuttle dnmgx w+ .pdpz.k4b+* pursuing a satellite in need of repair. You are in a circular orbit of the same.xd*+pwmnz.p dg 4k+b radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 ( r36jnyqnv *c;qjq)oyears. (a) What is its mean distance from tjny vq orj6)qq( cn*3;he Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G z9n rgxdzl 2(c,.rp 9iwould need to be if you could actually "feel" yourself gravitationally attracted to som rz(xl.,9 rpcgi 9zn2deone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy ;d( j( ktjcf ri t/r/gk75z -kirk: 8/(jqoepn(Fig. 5-46) at a distance of about 30,000 light-y7ck8rk t5kjre :-irf (/qo;(d(/n pgktzij/jears 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 corner8jl12mgb: tdswb9 i1ts of a square 0.50 m on each side. Fi gm1bl 1jib89wd2st:tnd the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500ey15:aq0k a3vc7xk.gay,. azb wmx 1f 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 experien- vts19 .xay1 wywcj7zced by the tip of the 1.5-cm-long sweep second hand on your wrij9txzc y711ww-s.y v ast watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cirk(n:puz1n6 d uu9emx5sds ( 7qcle below you on 9u(u(dk d5:ep z msq1nsx 6n7ua 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a hgf/ ed9 .mdxe2(d2wecar traveli2(e dfdhg92eem. wdx/ng 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 trk1kd- tib;v-u(q vhh*bs +pm8ain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approx uqh *;v(tbmh1- ibpv8k-d +skimately ). (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.$\approx$    $\times 10^2$