Sometimes people say that water is removed from clothes(x9scn7scnso+j 4 kv6 in a spin dryer by centrifugal force throwing the water outwav+7c9sjn6ckx(on s4s rd. What is wrong with this statement?

Will the acceleration (,l rsg/t8muloa3o,q of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speer,u/ 8s o,o3ltlmqg(ad? Explain.

Suppose a car moves at constant speed along a hilly road. Whbe;xn1ltek*9w l5t uj( g9-rrere does the car exert the greatest and least forces on r*enl1bwtg;tr j5 eku( lx -99the 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 oxyu:uoh3s 7 .wn a child riding a horse on a merry-go-round. Which of these forces provix uu.:w 7yh3osdes the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cirkwi(f8zis7 * 6kgi kq(cle without the water spilling out, even at the top of the circle when the bucket is upside6fgkks(i* ziik(q 8w7 down. Explain.

How many “accelerators” do you have in your car? There are px0yb/2t yl4yat least three controls in the car which can be used to cause the car to accbt lx40/y2yp yelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over s 1d+k91sn3rq02nek, hr vpfithe crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does noesr+i01r,sk f13n 9dn q2vhp kt 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 jz a0pgt fv-m 73w6v7nat high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gi 9l/*3nvc1oync gkzu +ven 9k+v3/o c1uynncz*l gits speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shef*j b3 e0uvm0f -0piyznnfj7( wants to let go at precisely the right time so that the ball will hit a target on the other side of0m7ze-v*0p f(n0yubj fn j3if the yard. When should she let go of the string?

Does an apple exert a grave q ko4wjt 56+i1c-umtitational force on the Earth? If so, how large a force? 1ekiw+ o -t4cqtu jm65Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wo5g ;rti;qq6tx89a*.o kpzbm kuld the Moon’s orbit be dizbpm* qtr8x.k;;g tkoa65 9iqfferent?

Which pulls harder gravitationally, the Earth on the Moon,3e6 )uqh.fvhmf2x1 us or the Moon on the Earth? Which aum h12e.fs3qu hxf)6v ccelerates more?

The Sun's gravitational pull on the Earth is mdby; 4sibs*.h uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in yds b*;hib4s.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 u2wkw (tiqrgbv4o-r2z y h6 n.2xu./jeffects are at work? Do they opy.(xub2t rrhjq.4 /vi62zgn w-k 2o wupose each other?

The gravitational force on the Moon due to the Earth is only about half the forc4/6vyage ;1vi(ko zs ne on the Moon due to the Sun. Why isn’t the Moon pulled awek v 61zigy4n(ov a/;say from the Earth?

Is the centripetal acceleration of Mars in its orbit 8h77gsxl;k n ut8q p7qaround the Sun larger or smaller than the centripetal accelerati nx7 sgtuk8p87qlq;7 hon of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (ys9 rq unlc14 qtqc5v :k846ogb) toward the west? Consider the Earthvg44q8 1 sc nykqu:o96cq5rtl’s rotation direction.

When will your apparent weight gg+sult 0pvemar 3+ ut77tk2iw1+g3lbe 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 would it be the same as when youli gk1rgtltus+3 tp+7 wv0+e7ug3 m2a are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer sp6wmw3zm+2a5t cy ;lluace 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 insiduy;5z23cw+ l wla6mmt e surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnes./ rpbl45.p4nq ir89ngunmv hs” between step.i84 .r/nrunlhg nmp 5pvqb4 9s.

The Earth moves fastiehnj /0*fspp. pq ud 0:n5-aper in its orbit around the Sun in January than in July. Is the Earth closer to the Su 0-njpd.i fape*u/:0 q5p phsnn in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was di/s.tickr ;wr iey/ u2.d hv1von87y6xscovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mas ki /.dvi/nu6c e.w7;81sy2th rxoyvr s.

  The Sun's gravitational pull on7a2x023v ajcf1bdp gv the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible foja3px7gv 2 a20c1 vbfdr 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 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 travelin /8dmo:1se;u+o zjqdfg 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 acceleration of the Earth in its orbit av/co5 o ox3:boround the Sun, and the net force exeboc: 5oov x/3orted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniforme/pk2 4-hllx 5b+efsbly in a horizontal circle (at arm’s length) of radius 0.90 m.e-42bhk5sll f+ exb/p Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circly 9p 1e3vruq0p v-j0khes 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 , t v390-ku ppjhy10er qvhe gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck oaye) kk2h.1jr f clay on the edge of a potter’s wheel turning at 45 rpm (revo2hej. a)krk1 ylutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string ih/k e4giau w v5i8):ustarj,6s revolved at a uniform rate in a vertical circle of radius 72.0 cm 5ug j /e4tra,iuw :ivh)68sak , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a tur+ href*f1e l0fn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this re h *rf+0eefl1fsult independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires aalq7;w++ ze)r+gz venoxj 9a 2nd the road if a car is to round a level curve +zxne+2)eo l+raw9ja qv zg ;7of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pi m*pq+av7 6sfilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on s76*q pvmf+aiher 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 (hr x2 lr94pcycm from the 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 xcrhr9 2p l4(yreached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rollexriz q*. w.*ke;jz;emr coaster be traveling when upside down at the top of*q*kzer; ; e jzxw.mi. a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the drivecht4 rml 4 g6-1 on1udhjv;yp.r) crosses the rounded top of a hill (radius ;r ycu-jvng41mohd1t.4p 6hl =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 Feg sjzywosz, go3 a+//0rris wheel need to make for the passengers to feel “weightless” azyg / +s0os,aw3j/ozgt the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At cfl 6q33n4n s12vzjy 5lli t6athe lowest point of t2n6lzsan1i5cv36 qy3 ll4 jf its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axib1i8tq : pcf f*yzq+5m4jxo//.kji i ds of rotation ix5z ij 1pj4bktf8.*iqy+mfqid: / o c/s to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "rdu;f x7 tg 6e:nqtt2s) lr-u t3*qf6kroom." (See Fq q;6rt lxtg*2f6nutk)- :fr3de su7t ig. 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 5glu)9y0lfo w;k b x1ct-)pdi:*rdh ycircle on 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 shown in Fig0bkfth ;y 5:l 9*1wxg)d li)upyd-cor. 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 ti/(m i2wdgh1 ikme, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnidgi/ hm1w(i k2tude 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 radi z (vnqz,-zqy3c- bmo9us 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 masses ict oew.j0/:s$ 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 very -5 gzfwrovf0l3sj0 *tically 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 cfv d0cl7g 6i.5-b os8wqkno4zomponents of the net force exerted on the car (by the ground) in Example 586 lvn5-qkwd.is zc7o0o fgb4-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniforml,cy6z;8f k(-6ynl g/ n3q j tjpuiltt/vrm45gy from the pit area, going from rest to 320km/h in a semicircujyf/5j8cnln,(ky gv m /t4ugqt l6z6;-pt i 3rlar arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.9j;,5czgjjd5if kg 6 4f0 m . At a particular instant, its ac5 gc dgkfi6jz 4;fjj5,celeration 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 spx5,r/ne qvxayor,-wfrin) 2 on0n4k 4acecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 135/no rvx4 a)5 qerfwy0xni,ko n n,42-r0 kg.   

  At the surface of a certain planet, the gravitational acceleration g has be-+y8:nba h.e g*hwba magnitude of 1+:bn8g. * y b-hebwhae2 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Mooa5 x3tgram ius00(f-e n's radius is 1.74 xt3 i0agm(s-raf05ue $\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 t w)l 9+r-:qq)x/ f ;1luqkopgkfxtf5 ehat of Earth, but has the same mass. ) kgwk;:ulo1 xpf-f)t5q+rfl qq 9/exWhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 timeskv l 944(ywar eb*b(do that of Earth, but the same radius. What is g near its surfa(yd val(9o4 bw4 ek*rbce?   

  Two objects attract each other gravitati/ a w;)xqdci;sonally 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 , thg3 hbu5yb4cdx*e 5 /l po2seq9e acceleration of gravity, at (a) 3200 mbq5c4sx d/l yb*ego9 5e3uph2    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center g 9i7 ot:ulrmmx ht4pu,uda4pu4+5 k2to a point outside the Earth where thegravitationdp:up,95i2t gru44akl xtuo4+7hmu m al acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed )h *ped7aikytdp x/ 4)into a sphere about 10 km in radius. Estimate the surface gehkd/ )x td*i7 )pypa4ravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our,*cysl/r),7bpbn o vh jr5ow) Sun but is now in the last stage of its evolution, is the size of our Moon but hhsj,5) wbb/*pv, l 7)cn ooryras the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronanep2,. uk 9 hmom 6z)28)amvm pqc.qvvuts feel weightless while orbiting in the space shut)q6 )omp2,mq.nvkc.hv vmm 9a2ep z u8tle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sidekz6i 83aim6 rgff/b l7 0.60 m. Calculate the magnitude and direction of the total gravitational fo38/if7z 6gfk amrbl 6irce 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 on the same side of t,lyhd+i 0wh8ii 8y4fa cs3 yho 6(vem6he Sun. Calculate the total force on the Earth due to Venus, 0 8mh+dsw3lhhy( y6iv46o e8ify, aicJupiter, 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 accel8*)ah5 s. pqyrwlkg:tr.c1 a jeration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400l1 crj.5a*hr :p qg.s wa8t)yk km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for t ye-4 1snra1kkam5r-y sz(y egg7c+;-1wokn hhe period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws,z7easohkc1r 4 mr sa5n -1 ky(g1wg-ny-k;y+e Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sat:)1tz:j3cur(n /3feer xc r niellite moving in a stable circular orbit about the Earth ati:jf):ect3r3nu r (n1 r/eczx a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satzmi+mj3o2 zuo, c/*1 midk6z aellite into a circular orbit 650 km above the Earth. cidmzi2z aozk,j+3 o*1 6u/mmHow fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to egx35-njth,saisp a l f3*(z2d xperience simulated gravity of 0.60 g? Assume2xha-sa,s 3 pig(l *5fjztnd3 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 takes for a satellite to orbit the Eartls*juap 2fy4w/8 0 sfmh in a circular “near-Earth” orbit. A “near-Eart84ps sfu l*2/jf m0wyah” 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 wouldw. wuw038 io ipf5rj3q,b/rub+lj fq) a satellite have to be launched from the top of Mt. Everest to be placed i3rpqw iowr5wub j )fq3/ul b +.f08,ijn a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contin*0sn4fsa, cdxji /1* d-zdyw2gf k mcj7s r/-aued to orbit the Moon at an altitude of about 100 km. How long did it takgsk1wajcdxrif z ca*ny*02 /md4fss ,-d-7 j/e to go around the Moon once?    s

  The rings of Saturn are composed of chunks oj9 8zhh6 o,qixswy-5af ice that orbit the planet. The inner radiz68 axh-,w 9o hyj5iqsus 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 (see Fig. 5–9). Wha1di lfkxlvagi9hkn *2.)3dw8: oy+ ik t is the ratio of a person’s apparent weight to her real weight (a) at the top, ia kyf kl l.nx:1d*i8odhki9 w+)3g v2and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from * 3xdknh9r-elthe center of the Earth -9exrdhk nl3*'s Moon 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 equ0.lcmsjw(lpb3z1 +sqal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of epj lz1(q3 w+ .sblmsc0ach?    $\times 10^{29}$

  What will a spring scale read for the weight vy fq/ +ess3c0hh1 i/sof a 55-kg woman in an elevator that moves hs 1/qh0se +f3/isvcy
(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 su 6yrwq rwr p)7*d(elx67y y1jvspended from the ceiling of an elevator. The cord can withstandv jl)7 6r*yyxy1ew76dq(prrw 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 surface of a planp h-1x1o6ks6q3r ecumet with period T , the densiusxe1mq k66-cp1 3r hoty (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) ty)m 33iqidvm xn9mz37- (eltpo determine the period of an artificial satelllz9x dmmtq)3imn-7y iv(p3 3eite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mete 8-ji ;rpea b,.ug7dn2:uhhmtrs across, orbits the Sun like the planets. Its period is 410 dah7;8-,eut mngpi jrdhb.u : 2. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan ej-t91l*skw4:xrp 1,tzk ydace of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very closeb6+dt+7wxba (n i,f ge to the surface of the Sun on its closest approach (Fig. 5–39g 76tf db,w+ne(+iabx). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galae- tjc nnbf8ngywa /n+i)2:p5xy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, perizm1t/6t0a-tyf8 bjy qr g-bu( od, and mean distance for the four largest moons oft u fybjmt0b6(a18grztq- /-y Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon. ; 4m-adu;ao nph/49wo/leijxp 9a;o4i-ho4a;exnwl //jm du   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s - 1x hhr bofr6g,kw.yjp(-bl5 moons, using Kepler’s third law. Uorwh,bx ybr1-6pk .l5hj- f(gse the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fra4enpofw)x nu+ 7g sj4+gments (which some space scientists th74+)g ofp4u snenjwx+ ink 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 jyf.zo 1zoz4 nt5 /7aus,bv(hdescribes 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), 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 dayo.zsa1tj7u5 hv/4,y(fn z obzs?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 9oit1up/lv2 hzmqvpn k :),xs/(si6r5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.hp/tivv:,xp k2snisq u1(/z 6 om9r)l   

  How far above the Earth’s sv2t5wn kqd.0hurface will the acceleration of gravity be half what it is on the surfkvht 2dw. q0n5ace?    $\times 10^6$

  On an ice rink, two skats(zrh d03n5zt ers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume h5(z0 dnzs 3trtheir 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, thkjt6bwu)pc ep+ q/* y,e apparent acceleration of gravity at the equator is slightly less than it would be if the Earthjt,u)kqp*b+ 6yew cp/ 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 directly from ts9 ;bhfce-mxn02: rvyhe Earth ve :9rhm -xc2;nf0sybto the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bup59jbc6 6 + tuwne)ogvt when you stand on a bathroom scale in an elevatbon 6 t9pu 6+5)jecwvgor, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a omlm/5ay,o z xh ,n))jcircular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revoh)/ 5zj ,lonxma,mo) ylutions 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. wsr,/bz; f)t /h+tjfvx xbz2,5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its rad13lcarsid b67ius r, the acceleration due to gravity at its 3l1 i7a b6csdrsurface and the gravitational constant G.

A plumb bob (a mass m*6gvakb6b un; hanging on a string) is deflected from the vertical by an angbb6n v*u6k; agle $\theta$ 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 of uv z15pe 4q:oxzv (rx8 If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car :qx85e(puv 4r 1ovzx zsafely handle the curve?

  How long would a day be if the Earth were rotating s2mof p bb/;qu0:n9o/d5 zksdrc4ty7 do fast that objects at the equator were apparently weigo/ o:zndyudm7fc;r4 5 bs bt9p dq2k/0htless?    $\times 10^3$s

  Two equal-mass stars*zgk.r ;oa e1smol00e)e3rrw maintain 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 rounds a curve of radius 235 m. oz 0 w bpj0m/7q2 36jd9aes)xoxb:br hA lamp suspended from the ceiling sw)j7bh bx ordpzb 0axqj6s /o32e 0:9mwings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has*jb+ihdn77 y7 lob1tr been claimed that a person would be crushed by the force of gravity on a planet the size of Juydlb*77b7rhjin ot1+piter 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 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 deduce2c; 5/hrsap klo4c 8jzd the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes)zralk s4h 2co5/pc8j;. 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 ;m5/vdgbfdsy :+c a8w(0 l9 arhtpyy8 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 woulg(tcd8l/s 5vmf;adr+bya:0p yhy w 98d 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 savne8 +pet. p9p0edkv69t xh+ntellites orbiting the Earth. Using “triangulation” andtp e p+ 6+0vvh.x9ned9pne tk8 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), after travelingacl6bn, f r8l7:ps- bz 2.1 billion km, is meant to orbit the asteroid Ebfb:ra-8c6lz ,nl s7p ros 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 shutwgwt6 61 bcna;vv r4r/tle pursuing a satellite in need of repair.r c v46 aw;b1tv6gwnr/ You 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. (a) 4k-l+ptco2rh*kti9 p What is its mean distance fro lk24hi-po +rttc9*pk m the 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 6v/d3iekb :cx you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable asbve3ixd:6k/c sumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cw6/k*s at+tkrkle8/ tenter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cent/+tk /6kaes8lktwtr*er $ \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 0c4 l-k36 murzwbft r15p*f+yj.50 m on each side. Find the magnitude and direction ofp1 4lb *c3fzfmk5y6t+jrr- uw 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 5500 kg orby +nlbe7ex a rnd6rj -8ph7p ym+d ap:1,bhg8;its 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 acceleratiw6jobh 1oc9xb; nc;8lon experienced by the tip of the 1.5-cm-long sweep second hand on yo ;xjnc6h bl9 81;cobwour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and stwakw q6-4 na ya+ rrx.is1n(/part 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 sq y4k.ap1r+r ianwa-wns/6x(. 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 de lszbxx 1cg* se626a9gsigned so that a car traveli6bcz9lgsxsg * xe126ang 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 tr/z- b c)pcpg/aain, 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 (approximately ). (a) Calculate the friction forcpcz/ /-b)g pace 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.$\approx$    $\times 10^2$