Sometimes people say thb p+*yk);b6wzg )vhcwat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. Whaw)p c)wy6g+b vb;*zkht is wrong with this statement?

Will the acceleration of a car bm0,.on3bs k* *u chrrse the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? m .,hks b*urcr*sn30 oExplain.

Suppose a car moves at constant speed along a hilly ry2rszt:b)9 t b)9dqpwoad. Where does the car exert the greatest and least forces on the road: (a) at)sbpqz2tbrt : w9d)9y 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 child riding a 2qbvn0 qs 5qouaw/ 1q702ck2 pw vz(lphorse on a merry-go-round. Whichwvk2qpq lp1qqa v2o2s5 /z 7b wnc(00u of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wwv3q 8jn0c)ub+u. r9ja,yamxithout the water spilling out, even at the top of the circle when tha w xqaj+,m98n30uy )cu.brvje bucket is upside down. Explain.

How many “acceleratoq* b. f3sjijm4rs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accf m4j qjbsi3*.elerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cre 5 43puy dtl sdjczd7a:g.:s;ist of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decyi;.jdsus pd :dlt7z5 :3gac 4rease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle rider;ucl5g6/qy)t) mqlv as lean inward when rounding a curve at high speed?

Why do airplanes bank when cni7b5ojjo 0qa;j8 fyobc7e 6)i o9w5they turn? How would you compute the banking angle given its speed and radius 0obn ioaj7q9efcy )67ci8j 55; obo jwof the turn?

A girl is whirling a ball on a string around her head in a ho bsg)hsz5dbr -)pf2 x2rizontal plane. She wants to let go at precisely the right )5srhbx2gps bd2)-zf time 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 f;)dz6l /m0 5u vyz0ru qfyj7skorce on the Earth? If so, how large a force? Consider k f6rs qmdy0 vu50zy7 j)luz;/an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wh m4gzd3 jdbf;wy /qc*7wm-96zhtjgc- at ways would the Moon’s orbit be 6 3t /mq-zbmzgg49j* h;7djy c-w wdcfdifferent?

Which pulls harder gravitationall( vhwdbb n 3:t6xt+ jfpv;)z(nu8thc e p1.)bhy, the Earth on the Moon, or the Moon on the Earth? Which acceleratebuc)3tphe+btwxfnt;d(hbv6v8z 1(. )h p: j ns more?

The Sun's gravitational pull on the8m4dx-c 8ing w Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one s-84xmdw n gci8ide of the Earth to the other.]

Will an object weigh more mu 7zdt;(rzi* at the equator or at the poles? What two effects are at work? Do they oppose ezdmu;riz7 t(*ach other?

The gravitational force on the Moon due to the Ef398a n;f wniw4tsvh7m8g h 0k20tlh uarth is only about half the force on the Moon due to the a hw tk 70fn24li s0g3;8muvnf 9hthw8Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or smj,q8bj e)0lqoll2b(q ds ,d1aaller than the centripetal accele lol)1, jdeqj l2b0qq,d(sb8 aration of the Earth?

Would it require less speed :01 q zleu,8c ebro-7fkdwm/ pto launch a satellite (a) toward the east or (b) toward the west? Consider t1zl:,/8 f m0ceuordqb p w-7kehe Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a m*zrlm41/ mr0s .jfjv voving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c.rslf *m1/r0 mj 4vvjz) 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 as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodss*0,q pmzm: vn 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 howsn* :mmvzpq,0 this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnefmey 9t790bvbss” between stepsmbf 0e9t7v9by .

The Earth moves faster in v5afcmm(.uu c0 21mcnits orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not5 .uccam mun mf0(v21c 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 dvr;).gxfg1g) e6psw uiscovered to have a moon. Explain how thisr.epu1g));g6gw f vxs discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mu( 2bz yllzia;8rhmdz7no0*/*afy qzv(x) 5 anch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differaoqnf()0/2z7amrn*; zhil8zd x z5l*yy b(v aence 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 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 travelineen n,-dve1 5d -4gvskg 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 centripj-j(z +qvmcus911: wxz1 jg qretal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts tqj1wx cj(juzz9qs1:r m-+ v1ghis 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 szm98oipd7b, 210 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 the discus.8m ,b97odzsp i   

  Suppose the space shuttle is in orbit 40tb/fg)s v8lco t)vsr 8s/)c6f0 km from the Earth's surface, and circles the Earthrc ) tc/b8vlv)sgto/ 6)sf8f s 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 at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a pofksz . )* 5mqr67yofyitter’s wheel turning at 45 rpm (revoluoz 7)frk .miy*65s yfqtions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate czn u 0h4+*lg6mumsi/ in a vertical circle of radius 72.0 cm , as shown in Fiunm6 +hlu*gm4z /s 0cig. 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 zdq.jvnt75qv( 6rc3 twhich a 1050-kg car can round a turn of radius 77 m on a flatrv53d.(njqv ctq6tz 7 road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the ri- n+ w-wkl ey se rbckkk+0zs/f1:4x7oad rk- w4 0ks ezbsky1w 7-n k/e:cf+xil+if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astro0zm tqk4z+cd . pxfi46nauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the for t ki6+dpxm0f4.c4qzz ce 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 rotating turntable of va4cj4t l9h a iulssn4)s,mgo8/ riable speed. When the speed of the turntable is slow4ng4s h )8t/usiloal j4csm9 ,ly 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 static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside 85v*f *rz j iyxm/wch3down at the top of a circle rz3yh*x 5vwf* c8/mji
(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 0old+d) .akh2y9 t eotmass 950 kg (including the driver) crosses the rounded top of a hill (radius =h+td2o atokly09 ). de95$ \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 abf wh7y 8q5y+f l.6 0jeellon/ 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost pqfl5hl+ 07y8j6 wbfn/o.eyl eoint?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At td4s75 xb yy +ovdvvr(0he lowest point of its motion 4 sov5(0drvv+dy7byxthe 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 centrifua1izo 8:yq xs vbzr+87qq8txxl/fl84ge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelerqzlb/io7qvq: szxfx848lx18 ray t+8ation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnit8y4o nms0.i.g( l haeval, people are rotated in a cylindrically walled "room." (See Fig(.nmhlsa 8e0i yt4. go. 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 ai0x7rhdqxtr4qc4c b pf)(1y t:b42o a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shod( ati :th4)pcqybf 4rxrbo x27 qc401wn 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 weif k d8e3d6-l-tvjee o6uk b46zght of the ball which revolves on a string 0.600 m long. In particular, find the magn8u -6bfede 3lo64 kt6v jekdz-itude 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 forc k9 .1d r+z*zkvwhfl9 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 u jyxgi/ 9 (mmhooo3isc3460gs $ 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 bvr2 4 xbl10 y4(wk anos 0;3q.fzvyiuey 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 centrey 9 cjkdk;fu1fn+b1 7ipetal components of the net force exerted on the car (by the gro f+ 9kj;yb1d7kc1fuenund) 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 from the pit area, h0sapoq,9hlhl .8gw: 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 throug0qpaw glhs:l, .h8oh 9h 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 houlv :2 (g+klqp// jkmqrizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.+ lq/2mg/lu jpv:(k qk05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 Emgk*-7w fnook. ,+n hg9brd i;arth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ik,*mg9 bfk-n h d;woogin.7+rf its mass is 1350 kg.   

  At the surface of a certain planet, thp ,p r 1ycdrz.6iqk8g.e gravitational acceleration g has a magni,q ..6dkpgr1 rzpcyi8tude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the accele:w;c rw) b,sqoration due to gravity on the Moon. The Moon's radius is 1.74;bq):rw oc w,s $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has thh 1 c7,u/6epw;m kaveme same mass,vahp;m 7m/ceu6ek w1. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66a jzn 2i5ni 8pjoi5):o times that of Earth, but the same radius. What is g near its surfacei25ap5 8jo znn)i:oij ?   

  Two objects attract each othoi i q6ah7:+)lhc:vw m cl2q*tjlg)j5er 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 tb/+,fmu yo5p)rp* o;opelw g oa0(rsf( o2f8 of g , the acceleration of gravity, at (a) 3200 mt 8/ p ( s u+erbfo;oogy)5frpf,(2w0*oolamp    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinvj:k6-2x8qs xc 7dv4kmetuv/t outside the Earth where thegravitational acceleration due to the Eq7sj e 8xvkmku:d/-cx 2vv t46arth 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 packed into xkia190bh2 h va sphere about 10 km in radius. Estimatb0i2 91axkhhve the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf sr4ursqf3j-. a zz g*0wtar, which once was an average star like our Sun but is now in the last stage of its 4 3*z-sgqr.ufja0 wr zevolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in g8 j;9zz f vp;zp4y3d-m q9ywkthe space shuttle. Your friends respond that they wj9;yppv4; dzkzzyg9q f83 m-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 are located at the cornerwwhfla0qbdj tg67*- v :cs;f 9s of a square of side 0.60 m. Calculate the magnitude and direction of the totwsd*96g ; a 7hb j-:wtfcqf0lval 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 pla9ol91wvahv ww7:m(npi q )xx08*so h inets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sapnq0*x wo7 x1imvow8v( i ha9:wsh9l)turn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what its.)i g)z-nhz a ex lg w)suhgu;k020r1 is on Earth,s)ra-.0 )lnheg)uxsg i ;2z z gu01kwh and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of cui + w09/a 2mfl9 p39 qmhaqikwc;.-j9fkm jathe Sun using the known value for the period of the Earth and q999w-9 a2muc fjqmpjl/mk.cawiah 3 0k;i+ f its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite p/q5e(yoa p2 zxo qrg+.sa /u4moving in a stable circular orbit about the Earth at a height of 3600.+qpx/p4yus(2 qo/ a5oz erag km.    $\times 10^3$

  The space shuttle releases a satellite into a c ti8 ie*ag dq7zp7-wwcdh( 3s*ircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) wqct(8-s**ddgw7 aiw h e3i7zphen the release occurs?    $\times 10^3$

  At what rate must a cylindrical s)f)klgtmv; h 6paceship rotate if occupants 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 one revolution l h6vkf)tg);m. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eart rril:hwm awf 3 mu.4szgp+ hzyz0)1:,h in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth w+3pl: rzz4 :,fz.m g10ar si hwyhwm)uhich 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 be lau a /jdvgc j5vx./*p8rhnched from the top of Mt. Everest to be placed in a circular o/pc/xv*j5h .vgjr a 8drbit around the Earth?   

  During an Apollo lunar landing mission, the command module contiz5rw)buy .k+u7k11tfmv yi t;nued to orbit the Moon at an altitude of about 100 km. How long did it take to go awy vb157+r uy.f)zm1 tk tkui;round the Moon once?    s

  The rings of Saturn are composed of7 tplu ,w aw)dbj621-klr wyr/ chunks of ice that orbit the planet. The inner radius2wt 1-u)b,ld akrw67lrjp/wy of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (n (c 2)ne86)jt hhyna 6tuibl8see Fig. 5–9). What is the ratio of a pe)bnen)hc6 hjntt2u8i6( 8l ay rson’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 asm yc7wa i5os4zp fewfg*2u(/) tronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving )p/ fc7ugoa f 25*me4s wz(wyiat 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 mass. They x8y /g9hd, -m++ /zlpvwudvcsare observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is thu msczh8lywv-v+9gpxd/ /d,+e mass of each?    $\times 10^{29}$

  What will a spring scale rea si.ty 8ksnr b*5mbe 3+ww6u1jd for the weight of a 55-kg woman in an elevator thatmibyu1ewb* w+ t.r8n5 sjs36k 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 suspended from the ceiling of an ele t2is+,;2) any;hmzvv ib4cv wvator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum a2cmvsy;; b2 +)z,ih4vwntvaicceleration (magnitude and direction)? a =   

Show that if a satellite orbits w kj5vo0p6dnsmpp22+ very near the surface of a planet with period T +jvo m6 5wndpkp0ps2 2, the 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 period o v-m 2g8rccxy6cq m9(kf an artif (vm9y6mxrc8ck2qg c -icial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbf14pg9i/ axb1 yw6 yhwits the Sun like the planets. Its period is 410 d. What i1gyp fwx yb1a649hi/ws its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average0qjtts0udi ;: 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 oncw (4 ktrref5/ee every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System?rk 4f5/e( twer 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 o6t7. sjz phmm0f the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, an6u5-lfs fkm3d v86d/hiwwio7d mean distance for the four largest moons of Jupiter (those discovere-m5v i6w8/uk s7 fidfdw3lh o6d 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 1ygy64vznqs)r )n0.c6v+g 5y uo0l 5 reckro xthe known period and distance of the Moon. uq zk6.o)y1yge6rgvnn+r0rvx s) yc0 54c5 lo   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Julescj (rj s 6e+qr*k.:piter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabjr *(qescer+jls k6.:le 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many98gc6gecr z des20k -hl u3w7d-n/ gfq fragments (which some space scientists think came from a planet that once orbited the Sun r23 eg 6/ucf--ne dz809 7cdlkghgswq 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 descri z 0l+k (fy9c;1rc2w-duku fmobes 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). 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), fokwr- 2cduk9mc ;(10+zlfuyand that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an a lih*,8y opy)mrc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a fomhylp* y,)io8rce 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 of gravity bd*g uh2bol48f e half what it is on thef b4d28olg hu* surface?    $\times 10^6$

  On an ice rink, two skatedtzm80m mzvo/ 9w1a ;9s9nkvnrs of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we asm8kv;/vm9z zan1mnsd9tow09 sume their 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 acceleration of graop28 )jk,xk7vcnkbm;f c 7 b0pvity at the equator is slightly les7kb;pnc,xoc7 k0vmf jbp)2k 8 s than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling *q*bk-xfuhn 2mb:ljjb+7 ypmq 9 3)prdirectly from the Earth to the Moon experience 7*: y*lr+xf-jbqb )2puk9 pmbnjhq3mzero 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 you stand on a bathroom scale in ak( 5: caar5ttji, d :3na9mzknn elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in z ak:m5ta(k : ijrn3a,9n5cdtwhich direction?     ----待选择----upwartddown 

  A projected space station consists o3 s-y,w 1m3y 0kclgxsif 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 ry3 lswy 0kc-ms1,3xi gotation 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 his aircraft in a vertical loop (Fig. 5–43).8glevyokrl zq1 3j,1b y610.eys: jlq
(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 radius r, the accelerkm114 qj23zdn/h7idz1rzaqts. jj q+ ation due to gravity at its surface and the gravitational constant G1 i szn . 1j41zdh/t37q2+zrjq kqamdj.

A plumb bob (a mass m hangu bpyhe:k aj6x-d622 fing on a string) is deflected from the vertical by anfb u62:2h d6-jex paky angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked foskvf.5x79 iopuz o, l3r a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle thz.9soxui 753 ,olvfkpe curve?

  How long would a day be ze4, w:h0i :vwzhj0zw if the Earth were rotating so fast that objects at the equator 04zww wvzj :,hiz:0ehwere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maio8 zai qey w833bdkr ..yby3.lko,lu1ntain 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 a constant speed rouuva dmond g3o(um;ob 7+;)r) snds a curve of radius 235 m. A lamp suspended from th;omam;d )o+ 3)srv(go nubud7e ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massi w)2zb2ortfm) ve 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 number of g 's a person would experience at the equator of such a planet. Use the following daw2zormft )2b )ta 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 Hubblew ua.ran 0dl7j.llgtq.7 vy+: Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no li7l n7. lq+ua..yjtvlard0 wg :ght 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 traverses the hill and valley showatx 74 khkg/z+n 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 x+zk47atgkh/ 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 Positioninwvqcs2lm7v +6 g 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 navigational “fixes.” The satellites orbit av7 2vlcs+w6qmt 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 travexhy6p:e9 wns nz;*n5qling 2.1 billion km, is meant to orbit;hq n 65snwe*n9z x:yp the asteroid Eros at a height 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 shuttle pursuing a satellite in need oar-av6p)q;labe v+ ta)3b937ys mmwdf repair. Yo;pq 7)baltawv9-a)v 33ydem r+m6ab s u are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. 87ra7jis uk oovu34,d(a) What is its mean distance from thek,a 3j 4r78oivdsuu o7 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 need to be if you could actually "feel" youhf;mj0acq,x nc-l0,h rself gq00cl;ncf, h,ah mjx -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 Mirb*pxw*rr 7dm:e1pcb c 0g89flky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fro7b:p9 rwgb* rccp0 med8rxf*1 m the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sidejwu (dgs1 no.3. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the (3u s.1dnjogw bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the 6k izx(s6n c8hc nbb6;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 thm 3m)l3kw6 2tiqka5kod76 fzrfh . 6cce 1.5-cm-long sweep second handork6d cfimk36. qh2mfl ) ctk 3w5za76 on your wrist watch?    $\times 10^{-4}$

  While fishing, you get boevv z wv*4ibr, b51*ixred and start to swing a sinker weight around in a circle below you on a 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.] r1* ib4wvzxe5vb , vi*   $^{\circ}$

A circular curve of radius R in a e) k-kzcg+n3q k4g;cg new highway is designed so that a car traveling at spc+-kg 43ggenk)qk c z;eed $ 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 ti9qrsi9ij;8 6x . )sjop5jy ldzlt 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 (approximately ). (a) Calculate the friction force needed o ;)yl86i9i9qd jx5 pzo.j rssjn 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.$\approx$    $\times 10^2$