Sometimes people say that water is removed from clothes in a spin dryer by centrgjnt)m .0p*n e5kx4hjifugal force throwing the w 5gn jmeh*)4nt.jx0 pkater outward. What is wrong with this statement?

Will the acceleration of a car b lbhr (,thz7sd7vzz4z6cs0j g1 h);wqe the same when the car travels around a sharp curve at a consds ,zc(r47 6z 7vqh;sg j)0tz1h hbwzltant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do.t4 (sonf 2jlid ja-okqfr44x45 jl 1xes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dipfxil1o4 2l4n-jd4 .st4q r5kfjoj(x a between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on angwu-y ,8 a3( xmpxpe l6z 3m/s8lmw/g merry-go-round. Which of these forces p g3 l-w 8x/wes3lz6ym p/ (m,ugm8npxarovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circl1bbryuj)*h q blp1g90y4qm /-haj5gme without the water spilling out, even at the top of the circle when the bucket is upside down. uhlb*1 my4 0)j gbqgjbprhya/5m-q19Explain.

How many “accelerators” do you havem:*yqm(+gt n5o -lf)3 y cscjs in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What arlnso )j qc3+g*m5ys fcymt-:(e they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown i:m.0c-/9b-h ye njpmwpw( udqn 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 t./e qbp-wjy n mc-:( 0wh9udmphe sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean c i)yiu3fu6d ,dmd05g inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anuf0 l xd6jrw5,cc3fs +gle given its speed and radius of the jc ,f0 53swf+ludcxr6 turn?

A girl is whirling a ball on a str qes-:i39lncboz ff; 1jv6preg/8 ep:ing around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targe:beo9e6 /3fzv: elpjrq cipgs8 ;-fn1t on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitatia . bew)60vd* i:r0,mdwq yldrb:g i/eonal force on the Earth? If so, how large a force0:ybw dlq0 idd,i mg.ew)evr 6br*/a:? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would t iaeelz.4wye nub .z4pidru8tc 8,. 13he Moon’s orbit be differen84riu8 iu,zznd3 bpea e.y.e4wc.lt1t?

Which pulls harder gravitationally, the Earth forp.u a*-1+ 96hk4thx/om bbh c0ak b5 lr3ooon the Moon, or the Moon on the Earth? Which acceoor16.r3* m4 t -ubh5xb9bkh/olph0c + ofak alerates more?

The Sun's gravitational pull on theffna7k f7d- tv xm3l16 Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference 63l f fdfkt71- xv7nmain gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wr)28)4* pozwb4v pcn+ kkdkethat two effects are at work? Do they opbotcn r +44w )8p)*2ek pdvzkkpose each other?

The gravitational force on the Moon due to the ij*ob26 2 fa 5zkc6fpnEarth is only about half the force on the Moon due to the Sun. Whyjo b* ckiafz2n6f 25p6 isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun laxfi.:9nr; iax rger or smaller than the centripetal acceleration of the Eartii.9f;:a xr nxh?

Would it require less speed to launch a satelliv df f,9x-qo 7pwr7xw+4u/s1+t cmn41 buvcgvte (a) toward the east or (b) toward thewug7dbx1,wft /1or mcucvsn4 fp+vq4vx -+ 97 west? Consider the Earth’s rotation direction.

When will your apparent weight be th.ss tgtnx 71 zdrk1rfc6iy(sn3,ea*8 e greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acceles .1(n63asg71c*se, 8tirnykdt xzfr rates 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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectedw.o92k:y -*my g t38ylgxdr*x dd -pxp by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can tr *y8:x9 g l opm32-xtgy.pd-wdk yx*dhink of.

Explain how a runner experiences “free fall” or “apparent weightlesslts:;d2:,kc 0u je c+elmrxsv/f 0y. nness” between steps.clnmj xd,rlf20 y+ .k;/0ctve u: se:s

The Earth moves faster in its orbit around the Sun in January thcqwp4 v etkn+k h55**q 1wowa/an in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axh w no+ /1tk5aq*wq*v 45wpcekis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon.k7ds6nv+vl3z) hki ( u Explain how this discovery enabled an e h(v7)k6vuzdnk+ils 3 stimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger t) ) )gqf36 za 2okgmtfkvecy1s i(h/0whan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to ts fg 01/)k3yfvimk)hq2oz a)(6e cwgthe other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1v09wvi s6ar i/980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelks6oi5 if6h+i2 8lks. vsrjcpi. .f3v eration of the Earth in its orbit around the Sun, and the jfc psisi.s+ o5irf62h3 k6 .viv.lk8net force exerted 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 r(xqv9cl)kki +nyvvs m/)w r1 :otates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the x1w k )kv(v )nqsyl+/mvc9ri:discus.   

  Suppose the space shuttle is in orbit 400 km from the Ea wiv8:a3/bwe mtf p1r+rth's surface, and circles the Earth about once every 90 minutes. Find the centrif3pwr 8wtai: vb/1+mepetal 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 s952six1v5o czwlmp3jpeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wcvjl2 im5x 5o3pw9 s1zheel’s diameter is 32 cm?   

  A ball on the end of a str e+7c y44qmk8 krif9tfing is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spq9fmefytk748k+ri4 c eed 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 turn of r /x9if2*qi;6oa axbivvoy78 hadius 77 m on a flat road if the coefficio/ib7;q y8hao9x*x6v i vf2aient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficie5b p,xi4kkxg 8nt of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 9b5gxpki84,k x5km/h ?   

  A device for training astronauts and jet fighter pilots is desig7 eu9*t9buw c2fpkuo: .ydvv-ned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.8fv 9 v :d-2ueokw.p*9b7uuytc 5 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 variable cj.k.wpwtmb/pf hw9e2b3f/ *k +tm1 fspeed. When the speed of the turntable is slowly increased, f2febm jhm1k /k9t*3fwpwtc .b.wp /+ 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 beb.eq w .h3ox7t traveling when upside down at the top owo het.3q7.xbf a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roun:wv ;m+efo 8gcded top of a hill (radiueocgw: m+ fv;8s =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 Ferris7y2wxce a mm m.d,ej*, wheel need to make fo cmaexw 2d*,.y e,mmj7r the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circlexrb61 c-v// khb wpd,c of radius 1.10 m. At the lowest point of its motion the tensi-bc dhp1b6/vx,kr/w con 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 thev;e; w*3fs+sr ni, wci axis of rotatio,erwiss3v n ci +*w;;fn is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rota9d+xlv cu6ol8du2oi svd;gi0 3 s /d6sted in a cylindrically walled "room." (See ogvd+8xd/6lssv i2cd du0i3;losu96Fig. 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 1x n1+ )pmxb7 rtahc 9hu+7kle) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling x+ 7 1)1 7heutan9pcmbxlrk+h block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the wet si* u 6+-8.z2dw bbpeyr22wzul +cpgight of the ball which revolves on a stri blispp rt-.z228g+6zd c*uewwy+ bu2ng 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 :j frhjp-y7b4of 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 massez8(tt8nr ls.q 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 n3z-c2eti1 kg by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net forc/-vvp y ifi/ d/h-t;1jon;s cxe exerted on the car (by the ground) in Example 5-8 -/1vnd xi ish;f c t/yjp-o;/v when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolxym0 9x tg;u,e .lv0yvis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming 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 skiddiymvt,gex9x0 ly.v u ;0ng? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 wj+xb*,j 5 :/ec--ellz)*ofmqal fzo m . At a particular instant,f5m cz *f -* jjez-a+ x)lqowe/:ol,bl its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2c6kr 0jhk:bi vx,(m+j Earth radii) above the Earth’s surfac,j mx 6b(kkv0 :c+jrihe if its mass is 1350 kg.   

  At the surface of a ,,5aum 5phi ticertain planet, the gravitational acceleration g has a magnitude of 1i5upit,a 5, mh2 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 Moon' + 2i;a7jopmcol (fez/qf :;was radius is 1.74ff+ l e;wo 2iq/:;zam(7ocpj a $\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, buef5a 6u:ed ;2 9k)fgjvrkch *lt has the same mass. What is the acceleration due to gravity near its vle hcd9kr)fg5 aek:;ufj 26 *surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but twzls7 6nt)c;j:l4) twcp3ee g he same radius. Whalg;j4n3ws t6z twecl: )e)7pct is g near its surface?   

  Two objects attract each other gravitationally with a5x0wy. ry yb3t 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 accel :q zrny.0j/re0 8rpoqeration of gravity, at (a) 3200 m 0 ye/ro z:qjr8r0np.q   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr(qagn.wh yp9. 3ow.yaqse5 4mom the Earth’s center to a point outside the Earth where tgam9q q3n.a.yey( s wo.5p4whhegravitational 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 x,fca0l .5dscnl 9;lce w* h/sthe mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface grlslx/hc f;n9.5, ce0ca d w*slavity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an f-aj+o0fq pt uf3xxiigyh .*d /,(+un average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surf uxfa-+t( fi+f*.ix oj3d 0,guq/nhpyace gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the sput omp *zplh9r(et24 /ace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculati lrh*o4u/mett p(2p9 zng the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the couc88qh4-5vx2zftrw z 4lsg +vrners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by t48szf 8hr-c v qzwgt4x5+vu 2lhe 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 the Suns -bzt-mh/( ef. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuminghsb t-fe/z-m ( 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 isgf ftk4 txa 2fw,u49jw2sx(5t 0.38 of what it is on Ear 4t xkwf5jfas tuxfw(29 2gt4,th, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known l8ksr . rvrq9i ws7w0j+chs: 4value for the period of the Earth and its distance from th0j4w v w9 sss8rlrcqkr7+.i: he Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about .s; d -twh ydmvz75vh-the Earth at a height o5 mtdwz7v;yh-d- shv.f 3600 km.    $\times 10^3$

  The space shuttle releases a satellite in ;ezsmoajd96ksmwyyhd ;p0nx w)*;0 / to a circular orbit 650 km above the Earth. How fast must the shuttle be moving ;aps;ysxdn0w 9m 6 yok0d ;je/*wmz)h(relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate b 5ckxdozo(-f,zu 8-rif occupants are to experience simulated gravity of 0.60 g? Assume the spacesdz,(xb co5zf -o-8ukrhip’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 satellitem;/z ity(m j1i to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth.(t i/1jm;zyim Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satpp. jgq/v /n6b* 0keq+p2rcxeellite have to be launched from the top of Mt. Everest to be placed in a circular v cn/bp2 r6kxpp*0qe qjg+e/. orbit around the Earth?   

  During an Apollo lunar landing mission, the command mo8: qrv v/ ;y:h:zwirjtdule continued to orbit the Moon at an altitude of ay8: hv :vi;twrqr:z/j bout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are compobqr e /*w/k,bmsed of chunks of ice that orbit the planet. The inner radius of thbqkm/* /w,erb e 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. f66do5xk 9omz (ibe hoc3mm0g;;g5ey 5–9). What is the ratio(; e5 o59;z0mei6cmghk m3bxoo6 dg yf of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kgp txabv14h: nq1x7moo3*c yt3 astronaut 4200 km from the center of the Earth's Moon in a space veho3 th7m 1n xvpobx4a 1cq:t*y3icle (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-hylx/d zb+u8 a;en:*04x 01 pngopjfpstar system consists of two stars of equal mass. They are observed to be separated by 360z0 0xo pn1h* +/pyu; :aj8f4b edngplx million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator t( h +q14qjhtsb+gx9arhat h+q(+14at xq9hjrs bgmoves
(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 q(i0 o0 8mwzza:j.7su+qcda1m yf*nnthe ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was thyqc z d*m0.1(7o:qsnwzaa0 +fjmniu8e elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with dqogh r az,m/ kb8k/,c,m *)esperiod T , the densityk ,rm/,* k,q z/8mhgcaso )deb (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.hw :nra d)5ffwnm6 yu88m0 ll(4 d) to determine the period of)8a6lywwm ud lhrm5(n 8f f:n0 an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbit4w6l* di0yud ts the Sun like the planets. Its period is 410 d. What is its mean distance from the Sui* tydw 460dlun?    $\times 10^{11}$

  Neptune is an average 2 b/t rpt/sep1l*0zuq:hz;xedistance 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. ))el7 h5/ geh,v(oorf y8pddwjm+ u6fIt 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? 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 thhu)8,mdw erf/yv lgo6 foj5e7hp()d +e nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about+ 1ya sk u+g64hto(gne the center of 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, and mean distance for the four e4vu1 k-fagl,largest moons of Jupiter (those discak,e- ul1vfg4overed 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 an fvc+/ej2nyl* ho 3e8tyz2*d yd distance of the Moon. y/j3 *zye vd8 eo2y2+lftcnh*   $\times 10^{24}$

  Determine the mean distance from Jup+r4 2)e m *exdid9ynpeiter for each of Jupiter’s moons, using Keple*ir9)nx eyep+md4d 2e r’s third law. Use 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 - a3xfyfin v;7 tcu.k;58geemmany fragments (which some space scientists -xea;yigve38m ctn u5f.7f; kthink 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 dee;v+8nk smc, oihi6 2cscribes 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 th, ;kscnc6oeh8i+ i2mve same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arezfzi9d an-ej7az6js 9g1 c;/c from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the loweaez 1i s697en-dzjjagzfc9; /st point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface w5uzzh4 k:7d:zo f,ayfill the acceleration of gravity be half what it is ozz 754ak:fdu fy,zh:on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands a 6xi;odw6w/b/ j6yklynd spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another? x6/k bw lydo6j6/yw; i   $\times 10^2$

  Because the Earth rotates onx ourh p0g)w/1ce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotaxo h0 u)1r/wpgte. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tra r533j+tpbm(h*(mi 2bxqx x caveling directly from the Earth to the Moon experienpxtji353 *(hcmxbx+2( aqm r bce zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wh2 iz+fxb7-dbeo8*lgk6 pvk bfc+2g0bnh.u 7jen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleratiof -ekn7bbj khvcgi02b8+o2z *bul .+6pfx gd 7n of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consi,;k xm-a 5.d+b xp-b loxmffe4 (lxwn+sts of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g)pnx+xw-(bmdx- ;m+ fa k5 ,4xefllo.b is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aihn,5)jh* fw)y+zi hqircraft 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 terms of its radiuj mq )-o0ilzlq 28ahb2s r, the acceleration due to gravity at its surface and the gravitational const lbj)i2z-q hm2ol 8q0aant G.

A plumb bob (a mass m hanging on a (zzt :7fxzsu6string) is deflected from the vertical by an angle z 7s tu6zzfx:($\theta$ 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 b8 lkkv+(1y2dkfqk) v yl)q:g If the coefficient of static friction is 0.30 (wetdlyk)b8g+f):y kqkk 2l(v1q v pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eartsqx6: s eo:t;/ uiqt+vh were rotating so fast that objects at the equator were appa:qt6isu/q sxo :e+;vtrently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart( p sx6,xiwcmmd8bs (/ 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 roundsdnm:twv-f;8*(l k*r upngeam4l 0 yb) a curve of radius 235 m. A lamp suspended froel ;t)kb8-n*rpdwvm f:my04ag u*l (nm the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tim9n fb1we d3+hbaxr kj6 :.mn,yes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since peopleyed+ b,a3nx.w hrkfn:j19b m6 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 deduced the presence of an exzcmn7 :wfc1iq nt.4g;tremely massive core in the distant galaxy M87, so c fm:wz.i1;tq 4cnn g7dense 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 travers h)hb089 zgnk ud19qedk: (vgres 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, g bv(1 9k9udrz8d nkh)0 :qgheand C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) u r14jn 0o0 sxkzmzkkz52j7x4gtilizes 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 satellit2z xg jk5 rxkksz0m 4417o0jnzes 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 tr /i.h97o43 pg rwfknv*/n dqkqaveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughl3rgo qd7q9k vp.4n//i fnwkh* y 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 satellivd,7ys9s 6e 06ewoh(i mi0bkste in need of repair. s,e60imkbdhwe7i 9vs 6y o0(sYou 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 a3 zk vs..:(f z jcs6st*imk4ii period of 3000 years. (a) What is its mean distance from the Sun(* tjk i3:. izsvskc6s.i fmz4?   
(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 ti p/a-71ro m7m*zhsb,zl*gk g 5 0khvof G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable *s0 mzgial,r7*57kg ohk p 1h- /ztvmbassumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way:hkkv1 o/v 2:tqrnbq 0 Galaxy (Fig. 5-46) at a distance of about 30,000 light-yeakvnhqq1/v ::k2t 0o rbrs 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 locij 8- wzvkchw8*x.f6mated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midk whzm8x. j-f *8vcw6ipoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ea c9v4c5yfsz +3ajgo;g rth $ \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 b;)o) wx mwspay3 i9rv-y the tip of the 1.5-cm-long sweep second hand ooww);9sar3x-i ) yvp mn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored4c1 jksr *271vodcd xz 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 verticalkvs7 *d1ocdrxcz2 14j? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trany0 ,dai ug3e;aeo;t 1veling at speed ; ed inyu 3et1aa0,g;o$ 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,3)ds: qsmo 4pzx,6z+rjqq xlhdp++ t, 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 frictionh4,q q6 +j,d3z) :ldztrxo+ pms+spqx 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.$\approx$    $\times 10^2$