Sometimes people say that water is removed from cmgva-1.o5 of.)uycn d2dxz ;c lothes in a spin dryer by centrifugal force throwing the water ad).x- mu1.cdo cv25ongyf; zoutward. What is wrong with this statement?

Will the acceleration of a car be the mtk5o4yw kf*e7z yv,5same when the car travels around a sharp curve7ktw 4 e yok,v*5y5mfz at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at conwx( 6, cp wtj(w +byel3(kh1mfstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between twol 1xfy+hj et6(,mb wcwk((w3p hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse onmkec9x e0x;l- wm *+ss a merry-go-round. Which of these foms* cxxe; kel9ms-+w0rces provides the centripetal acceleration of the child?

A bucket of water can be wh36r+ a xljz xomeuuh/hh9k620irled in a vertical circle without the water spilling out, even at the top of the circle when the x oejh+0u/hr9 m 3l2k66hxua zbucket is upside down. Explain.

How many “accelerators” do you have:i7o0h-jydlz,km (ea/vi zt, in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What arev o0i-ze:ij(d klyaz7,/ ,h tm they? What accelerations do they produce?

A child on a sled comey k;9hp) -dlm324nl xsd+yahhs flying over the crest 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 decrease as he goes ohlph4m s; y3na h 9)lkxdy2-d+ver the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders w6h5 .iut;icyy;h lq8lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How wouln0qap o pk/3 s az/4ew1sx-w9t(a. wdcd you compute the banking angle given its spew9sp /(kaw4 p0tq3s ze.wa/- xcdn a1oed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal p( t1vjmq eld((*nc6zzao.j 5 glane. She wants to let go at preciaglvmq*5 jojd( zt1c(n z 6(.esely the right 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 force on the Earth? If so, how l (ukm, eqaow.6arge a force? Consider an appleuewo6a.kq ( ,m
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, 3w 6(,l(fqqgcooxe0lin what ways would the Moon’s orbit be differ, eq(lfo gc 0qwox(3l6ent?

Which pulls harder gravitationally, th2 hm to6fvfd42.lho q1 *b9pyde Earth on the Moon, or the Moon on the Earth? Which accelerates plm.d *fftq6dvyho24h b9o2 1more?

The Sun's gravitational pull on the Earth is much lar yt((;y k4utbdc,kcpj5.t8 m nger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side ojt4 cbp5 ((yt;,udmcn.8k tk yf the Earth to the other.]

Will an object weigh mork98izj4pey i7zp4cuil g73 s7e at the equator or at the poles? What two effects are at work? Do they pkpzi3 y g7sulci 74zji489e 7oppose each other?

The gravitational force on the Moon due to the Earth is only about half the /d*ce vi;3l ,g;wja1twx w85gni*trs force on the Moon due r;t*1wx * s c3jgwa,g vie/i;8nlt5dwto the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars) .;ru3bu1x f -hvhvew in its orbit around the Sun larger or smaller thane)uvxhh3v r. w1 u-b;f the centripetal acceleration of the Earth?

Would it require less sc k )fch3b;6hvtionj rvja* 56 1yf22wpeed to launch a satellite (a) toward the east or (b) toward the west? Consider the Ehok*h3c6w ib f)2tjj;1 v 2n5ar6yfvcarth’s rotation direction.

When will your apparent weight be the g5sf,, kamd4)zn (8uydmtw: kgreatest, 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 spey:(4 d zsgdk5tf8)nwkmuam,, ed? 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 ryl /ava0 e8ag-7k zr4 cdx;;+emk5tabe adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Conside4- /z0lkdv aer;+ y5ama ;a xkrt87gcer (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 fal6f7l bu j/ki0fy5 8hmvl” or “apparent weightlessness” betweek l /7i8hy0fu6jmf5bv n steps.

The Earth moves faster in its orbit around the Sun in January than in July.d.lpy, ocpptniser-g9n o(0ao; ) +x+ Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of e) 0cs ;n(9ar+nlotiyp+ -., goppo dxa 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 nqi bzf36kd5v..0w sqlot known until it was discovered to have a moon. Explain zf lkq.w. qdi 3b50vs6how this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mjf j17r ryqc 7f6/l7jmuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenc71qrf/lryc j7 6 7mjjfe 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 travelindi),pzpi1,+jnkn5sg1 t5fcrm83 u te g 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 )woc8q xmj0k6x e0(rharound the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radixj) ko q6 mexwch0(08rus 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force oflhx;t-k 8sxb(g -3l8ftjx d ;i 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radiu (d kl8jbi8-s3; x-xhtl;f xgts 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttlef7 kyv5.yalg -/cw9 g kl55jhm is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the g5g9 5myk. hjg5/w7lvc lakyf-ravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration 7tahelp/0b7)g4r p hwof a speck of clay on the edge of a potter’s wheel thepa0r )lb77 hgw/p 4turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stvz h7b(w;vay3q p7baz0e+ + og+n3 sxgring is revolved at a uniform rate in a vertical circle of rave+qb(w +7+yo3avpn7x; szg3 0 bgzhadius 72.0 cm , 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 c4eq- 2xsgri,(ilf,goi s3v3q. jf ej 9an round a turn of radius 77 m on a fo-3.sgjii3 ,igl9 er2 qfqsv ,f (4jxelat 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 p f )qr*2,tukdstatic friction be between the tires and the road if a car is to round a2tqfdr,)* upk level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilot+pg96e-t q b0gg+.c t;klgkxts is designed to rotate a trainee in a horizonta . g+p9tl06e +gtxgtgck kq-b;l circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable 4m5 l z(/guyibb (dbv,speed. When the speegi /bdl,u zb(5bm4y (vd of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling wxz9tcb dw2,b.hen upside down at the top o ,tbc2bd.xz w9f 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 mas7.l;0x t d+exz)fxhbcs 950 kg (including the driver) crosses the rounded top of a hil;d+ xe. hzxlb0fx)t c7l (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per min,lzc7j,;w6 d2+ 6gxnf csnnenute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “w,cwes j d,fnx;gnn 6n7czl 2+6eightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rannvip d )p:xw qb5-/jmm14w+ t /c1ebxdius 1.10 m. At the lowest point-px/)v w m51iqben tc 1wbm:pjx/+nd4 of 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 pa bm.rr4 aek6e b5i,gp8rticle 9.00 cm from the axis of rotation is to experience an acceleration o,rke5 a8bre m.i4bp6gf 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindtz9e :h(oa :hld. pd/k22oymurically walled "room." (Sed.mp yzoo 2 l:9(k/ dh2:uhatee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey w5/srn2q6f y*(sko7 r xvey0 stabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through aq2ys*svfeyrow7(r nk/ 6sx05 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 weight of the bartt yd a1as7r4f*knl t1.-4 bfll which revoltydlt fas1 -4b f.tr1r nk47a*ves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fyzwy3e.u )cebb k)fnm56:wk- u e/ ne5or 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 bgj3is 9h3 z wc-o0fk:-wky-ns $ 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 vertically as lu8bfp b34 s18i;osibu.8e7+wcj -w e,gvj it 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 force exerted ce-np3qtq* ;q on the car (bpnt 3*qq;cqe-y the ground) 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 uniforma f.wd+d-az94b d sv*nly 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 accele-v 4adsbndwfd*9+ z.a ration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Aoh.7; rzwa. ny tm,(dit a particular instant, itsrat .dmniz;y,7. oh( w 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 Earth1irbq. (b oa7j-bvox4 ’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kgaobob.7b 4-xriqv (1j.   

  At the surface of a certain planet, the gravitational acceleration g has a ml (nq9 /pw:y)f2gljzw agnitude of 12g(/)l:2 jwq9pzw nyfl 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 M +*yutkwbmg +n:u5d0 9 gi,hzooon's radius is 1.74 b9g *+ wmtuk0,5nhoyz+udg:i $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 bu.49t6cq, c bqeatqav8h,h7times that of Earth, but has the same mass. What is 6,7qca9. ahh bet, 8b4 tvcqquthe acceleration due to gravity near its surface?   

  A hypothetical planet has a * g k*;q6g rhsnw:l 2kyfwk-fa0j ec93mass 1.66 times that of Earth, but the same radius. What is g near its surfaceky j6g; 0k29:wrfqe3fcg-*k* n aswlh?   

  Two objects attract efw k,n/vl5xmsybq -mw*4u 6j -ach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effectivnyr3zw: il e)+:o ja8ne value of g , the acceleration of gravity, at (a) 3200 m zwy8)i +ranj l:eo:n3   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’sbo ,vcxt6* 7 t5iqtlan0:sg3a center to a point outside the Earth where thegravita57tvs at:ing6*a 03tob, cx qltional 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 into a sph, ,4:h9hzaj f0/qp 0ebafkl zrere about 10 km in radius. Estimate the surface gravity 9zbrq khhj4alzffe a,0: /,p0 on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average staxdjuz*my4s1hrd )0 2rr like our Sun but is now in the last stage of its xrd*y2mju4 sz d h)r10evolution, 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 orbilv-olybm64 m :ting in the space shuttle. Your frie-:4b mvl mly6onds 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 thenvae8c fv3ke o ;5oc0+;/)ad:u r*wujzv xj a. corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by . av8e5cw3*fx)o;ze +vc; 0n:jdvujraak/ uothe other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yeai:1+;(b 8jws*cj2ggly;qp nk)q mzgm rs most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). T *iq1gb)jc2 ;g w 8ymzmnq;jgpskl(+:he 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 tdm,cwr3m t-g2he surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 kmc23mrtdg- ,wm , determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of th8(vbl; uy 4nsqe Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtainedbyn4l8 u ;(svq using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed ofc xy4.0t)bx+jk yu2et a satellite moving in a stable circular orbit about the Earth at a height of 3600 t02eutk)y.+ 4x cxbjy km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above, 7o5sme+tc:s d8fcl x the Earth. How fast must the shuttle be moving (re xde5mscco :+7 8tf,sllative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are r:0g+bj1sh7)uqfv qty j 0*h vqh*,gzto 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 * s q)tg,z71fv* uhjjyb0qhr+h:0vg qrevolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ea,myiva3m 4 i0prth in a circular “near-Earth” orbit. A “near-Earth”m,i i m3v4ap0y 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 veloci w9 h0pci) rp8q,9 rjf0eqh/qzty would a satellite have to be launched from the top of Mt. Everest topwqip8 j0qr qhh)e9cfr/,z90 be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to org8vfu6 is.in7 bit the Msiiv 7fu86 gn.oon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chu.wi;mkd3w 5 jonks of ice that orbit the planet. The inner radius of the rings iw5m;wkoi.j d3s 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 diameteiwimepud ul(3 (,0z 5zr rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a personi3zdi(5el w0(u m zpu,’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cen,2sacee- * x(goj4pxip4nn 7kter of the Earth's Moon in a space vehicle (a) movixnxia 2j-p e7* s44n(egcokp,ng 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 co1y zyd jg- 0oi7:l0vhgnsists of two stars of equal mass. They are observed to be separated7jh 0o0l:iyv 1dyz-gg by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a hswp lg(i+ (3gswbj;/55-kg woman in an elevator that movebwsg ih3jw(l(+s ;/pg s
(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 elev-1 6*k gy 9rh:5yiupu-dbcuby)(zgs.fsd-u yator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directionb*zugry -5uyg :-dsuyu6ds1ipf cy9- (b).hk)? a =   

Show that if a satelli;g74sk 97k3 nqpge spote orbits very near the surface of a planet with period T , the ;93 4 7sq7snppggkeok 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 Moonrp0 yj3c2q-uu (27.4 d) to determine the period of an artip 0 ryju2uc3-qficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,lkd0959.uqk v1 bkoql orbits the Sun like the planets. Its period oldu vklk9bk95 1.0 qqis 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of txuh0wu a4,q+ueza. k) 1-vc o4.5 $\times 10^{9} \mathrm{~km}$ 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 close tkned-2i-7xd:q1qp2it tod6t o the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the od6t -1de xk2-dti 72 :qntpiqSun.]    $\times 10^6$

  Our Sun rotates about t/62mgw.n w9wz jfsx x0he 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 distanx3iw6j m+b: hhce for the four largest moons of Jupiter (thos6 jmiw:h+3 xhbe 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 o yzxy6* zlh/3rr:0 ooklng5h7f the Moon. r5kly oo:03 *hrx/ lzn6hz7gy   $\times 10^{24}$

  Determine the mean distanceu,lf5sf8vhg p/q td3 4 from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the pe38 v 5ftgf/,s 4dplhquriods 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 Marsl,r c+ (j+eshx and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was des(,x+j+ec hrlstroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes a8x v xwdqh;)zrd+ab2 1n 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 thbvd2 axz8 +1wh)rx d;qat this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a g*8.aku gf rfr.orge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of hiaf 8rg.r.*ufks swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will thn w-gxt4h0uak8 i(kk)m py c35e acceleration of gravity be half what it is on the su -( w p4g0x)a3khintc58ykm kurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spinujd,sf5 6q z kmg8wu cn::g*c8 in a mutual circle once every 2.5 s. If we asq:j u :c5m, z*w6dsggckfn88usume 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 accele b-z5hs; hz-, 4byqv/7 u5jxuzleb8koration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this blz /;q5 vhbh oek8uj- zy4b5,uz-7xs effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will as+bgvt i -i1hiz z-6q;c8 /ytn spacecraft traveling directly from the Earth to the Moon8c zt6 z ;s ii+bh-gn-iq1ytv/ 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,kyi33:by 1its /xf;dfc 81rvke xy()l but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elev3kr;de:t x) ck1/fii f(1 v yxlysb38yator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tmwf 7,mrh 4v)1lp d)*bse+lujube 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 (revolmmp j4)+uelr )lfds1 wb* ,h7vutions 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. 9c0. ogcz b3nn5–43).
(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 radius r, the )cb8thlvzz 4 4acceleration due to gravity at its surface and the gravitational c) zzc4tlh b48vonstant G.

A plumb bob (a mass m hanging on a strvdvx.o;5a) esu8 -0*3 dy kocluv8tpl ing) is deflected from the vertical by an angl-.u 0cx a yvkdov ue;*8o lvsp)3d5tl8e $\theta$ 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 fo6qyr/nr .yz0y aqk9h8r a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safr/0h.nr6qykq9 yya 8z ely handle the curve?

  How long would a day be if the;i7 x1)fhw26 ) uar yh,7wtvrkdi9ger Earth were rotating so fast that objects at the equator were apparently rw ,);h2t7eg)rx f1ii9v k7 6wdahyurweightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ou1n pf m/gio 79/-jkk)mklml.f 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 curv t( l2kpy*hfkubhc)6 ,e of radius 235 m. A lamp suspended from the ceiling swings out to an angle of l *t k ,fybu2ph)k(6hc17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimedblwyg9rr-1 :v that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data fo 9-rlwy:r1bv gr 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 extrem7uq gqa.1kjbrd6 *jg:ely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbit67 : jbkrgdagjqqu*1. ing 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 )xat. w2e, +z+ejgvh)nzvl:7c f ;e eqtraverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) eahv) +:t.,f7 j2vlqn ezz)xce+e ;gwHow do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) uti rxw/q4e8- 5jpbgkw *mlizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmikr/xg- q*5b w4p mwej8tted 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), afthu9n;ce ;8 w4xssa )rrer traveling 2.1 billion km, is meant to orbit the asteroid Eros s)r hxacr8es9;4 wn;u 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 of repaq 79j7nvxx (a.tun/4nrfqz k(ir. You are in 7njux frkta/qxnv(( 4nz7.q9 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) Whs(u n,x0tm, fu,1o isod we)+nat is its mean distance from the d,+ux)n tso0,m i1f eusow n(,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 oee 91l(9o4p q5jl hqu u6qfk8vf G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions,ujeqe8q1p v9uql6 f9(lk h4o5 like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mil(+l ewifx e ykh*f2. ry-yv)w*ky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cenx ye*+w2elv -yyfk(hif )w. *rter $ \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 a k4oi, -z2qyepf9cg 3fcq 4x+hre located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on x 4 fcekh9yfcqz-,pgqi423+o 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 5500f9l p :rwg 4ubg76kch8 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-lontf-aeu4. pqz+ g sweep second hand on your wrat-.ezp+4fq uist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around i2itn)cec fm3nu/::vld mmn0 j(eq4u;pd b 04in a circle below you on a 0.25-m piece of fishing line. The wei2e 3pef / i :mnbn40cd)cuv0u dmlt(4n :qi;mjght makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so t8 tey5b dv-3x*) shibnhat a car traveling atb bh-nevt) 3*8dxys5 i speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of thenecjr3su-n18gsgp9+s pg12vqbdn : 4 cars when negotiating curves. The angle of tilt is adjusted so that the main force exuqns11g gp+e jcs bn9ndprs 42:38 v-gerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 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.$\approx$    $\times 10^2$