Sometimes people say that water is removed from clothes in a spin dryer l+8o,f;kz15g8s roqy ykcc7e by centrifugal force throwing the water outw7cgo1s el5k ;ofcq8zyykr8,+ ard. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around6;y.y2r /hashs hr d ae2o05qw a sharp curve at a constant 6/o 5hs2eh wr2ys dh6aqa.0;ry0 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along u d jqjp 3mo5dv(,,9sia hilly road. Where does the car exer (m io9s,u5pvd,djqj3t the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a ho goyel+s4iys ;an 1bf1o -d;)krse on a merry-go-round. Which of these forces provides the centripetal acceleration of td1sgbon4+fs;y) iyk1 ;eo la- he child?

A bucket of water can be whirled in a ve9 ,vc u8oeo6pzrtical circle without the water spilling out, even at the top of the circle when the bucket is upside ,o6u98cvo pez down. Explain.

How many “accelerators” do you have in zg ksp6+:ji7n-g*xl gyour car? There are at least three controls in the car which can be used to cause the car to accelerate: k-+li gngx76sgzj p*. What are they? What accelerations do they produce?

A child on a sled comestkexdbn :o i8jo)k j-+d2u q3,.fcs)l flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave tl.e kkuj)d83 sf j 2+tn)oqi coxd,b-:he ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwsi cy5za 2y*t6 /zym3aard when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compuzt1kzsgs,()1q-4qtoq s uv) ite the banking angle given i4 s1)o 1zq(-)kqtivsgzs ,tquts speed and radius of the turn?

A girl is whirling a ball on a string around her hen2rqun9( qt 9f kbs),lad in a horizontal plane. She wants to let go at precisely the right timn q 9bn9(tr,kq) s2ulfe 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 large a fo)v aq c9wfn.lq9 .r2g/rb lob.rce9owg2a.b.r. nl9c/q f) rqlv b? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what iq -lb-er8defmy v 93j1t is, in what ways would the Moon’s orbit be differenm38eb-9rlv 1qjfeyd -t?

Which pulls harder gravitationally, the Earth on the Moon,tvqf6k .o:3:y 4sh iex or the Moon on the Earth? W f: hi to4vsx.ye:6q3khich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. )b4 bls,uqdwlcl :s3 *1wms7.vpbk)w Yet the Moon's is mainly responsible for the t*4qlcw uw 3l sb) l)bmp7sds1.wbk,v:ides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more agb.xm. c9g*b rt the equator or at the poles? What two effects are at work? Do they o* g .b.grb9mcxppose each other?

The gravitational force on the Mufqu a6xjz ,/2oon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away f ju/xza6u, fq2rom the Earth?

Is the centripetal acceleration of Mars in its orbit .vxvff5wq 7 ib,a-e4czjrp 9)around the Sun larger or smalle5izx e4r c9qb-ffp a7 ,vjw)v.r than the centripetal acceleration of the Earth?

Would it require less speed to launch a satepuj4+c 8d mq5mllite (a) toward the east or (b) toward the west? Consider t cqp84 um5mjd+he Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a5ahz)u vv 8f6zhws:: n ksag6/ 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 h/f ::ahzvsg86 saz6w vuk n5)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 ou o6 7gtl27gjhv6ufo9py j *wnrt*3e*iter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how* ohuvepw6ij6rtoy7jg 7ft nl**g923 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 weibl3q08qws4xq-c;t y xv a7x,/ey(cooghtlessness” between st lq0t;vx(y7 qocy/ex3q,a 4sc xbo-w 8eps.

The Earth moves faster in its orbit azpbr24d5 kar0a mpkd*9kqob z8k 8(7 zround the Sun in January than 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 tdp 9mk5k8r7qr(bbdz* akpka42z o0 8z he tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not k wy91ovsdn9;6q5/ ,v yepyhvvnown until it was discovered to have a moon. Explain how thv6,9vyy19;vwh ynp e dqs5/ovis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'sj 5fy+zoen0rpq.sqb d. *lk) 4. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child byokj5*+f q0qerd zp.s.4)l nsitting 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 travelinme*e) xrp 12t4d8-bz vkj,jqp 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 inirbmoa /bvoi5cj77. 1 its orbit around the Sun, and the net force exerted on the Earth. What exer5iv bomi17/ ra 7objc.ts 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 w8 xz8 alu9;vma bj.-zfwx m.(210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius8-89b . ;lzfawmavwx(. xjmzu 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbi5)jn zq9g8eeu t 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 graviz)5ju gn 8q9eetational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a (onx vmo-:c9lpotc- n(:9vom olxter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform: o:sp tvlxdi - yv.qe-h98*hf rate in a vertical circle of radius 72.0 cm , as shy*l. qh:of ihvd sptx89e--:vown 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 rounwr./ gshc1t *xd a turn of radius 77 m on a flat road if the coefficg /c.*1tx wrhsient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeff t*9c5e.bplnficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 mlc *e9npb5 .tf at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pah t8. bpm9dlan:l*w 2ilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, a*tn.a: l8 wb92lhdpmhow 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 speed8m .tb0n0ciis tvj (8i. When the speed 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 covtit(s.8jm i cb0n 08iin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dom g+dopl;mt b9:x61 w)azh i+jwn at the top of a circle +dtb)j16:o mi l+wxpazh g;m9
(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) c1z 7qjjwi1vm0: a n3 :z oq)qxv5r(pzvrosses the rounded top on)3vr xozp q zvm(wi1qj:va :71z05jqf a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris w:mxg9mmeo 9 c5kijl 4m:2q9x wheel need to make for the passengersmm mog99imk:24: we9xql xc 5j to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirljz51 2exix 0tled in a vertical circle of radius 1.10 m. At the lowest point of its moti5e2z10xx i ltjon 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 9.00h9)zcbvadb;8 h oz04m cm from the axis of rotation is to experience an acch mzha84b0)dzv ob9; celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniidbi2 z t8g20a9o:f dnval, people are rotated in a cylindrically walled "room." (Sat2 d:9igf80ibn z od2ee 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 bwi2*0 uzel*h g) pj4trotated in a circle 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 showp*je2lu)0*4h gw tizbn 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 t t*r8zphhh,dicmapyl 73,2.iime, by not ignoring the weight of the ball which revolves on a stri*8rtaz,iiyh73pp2m c.d lhh,ng 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 .ww+a5 fd4cwa- q2xja (h sbv688 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 c/4yva9v kvt,n+ nb dnwd2nb jy4)u17 $ 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 evasi 8/0 ;p xfm(qwkda,vmvve maneuver 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 force exert.fwonapy b; (5ed on the car (by the ground) in Example 5-8 whe ;ywn5.( aobfpn 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 acceleratesnn/d alk//oo2( h w+c.l+tlys 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. ylnkllcao (+/w/hs2 +./ ntodIf 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 ixng6,ufu w-tvw(h,*7pcets pz+t a5v q r /r;,n a horizontal circle of radius 2.90 m . At a particular instant, gpw( , u-rnv,sc+5eufxv6ah7p t*tz; wq /rt,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 (2 Earth raapk- zze ,i(2(fd*jw)0n f. :xbrqqf h oxj9:ndii) above the Earth’s surfacbqx (jke2zq n) :wofpffd9,j-xhi*n: 0(.rza e if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a m(2r62 bnfhqeb.,j e(slel7l xagnitudelb,j2he(b72 xn(rqf se6lle . of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. 4j:vau(pf-i.j c )b i5ckagb,s k+,go The Moon's radius is 1.74 +iu j pa4g,k-c5jf(ska ob :,vcg .bi)$\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, b uop :f:ck9xor4z;mjpp ja((iem-)+k a 9mwi. ut has the same mass. What is the acceleration due to gravity near its surp 4 pk .jizk ciw9;fjxmma+ pe-oaru:)9o: (m(face?   

  A hypothetical planet has a mass 1.66 times that of Earth, but *oty:saw/ v. kthe same radius. What is g near its wvyko *.:/tassurface?   

  Two objects attract each other gravitationally with a fob ,us80ypc 9vprce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration +nbhix)dv( : pof gravity, at (a) 3200 m ) +vh( dnb:xpi   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to am)hr(1tgzwhyt 6 jh1qtu -*p 5 point outside the Earth where thegravitational acceleration due to t6thpqmh5t1-u*ry t jg ()zwh1 he Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star4vio 6n.ibcs+ j wij1lf2b r-- has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monste6ijiojlbw1r-f2+n .- ibcv s4r.    $\times10^12$

  A typical white-dwarf star, which once qz12+ bthoiw, y*ty:pwas an average star like our Sun but is now in the last stage of its evolution:i+z2q*th yty,pw o1 b, 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 astr lao2 kxcm+6k2onauts feel weightless while orbiting in the space 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 calculating the acceleration of gravity 250 km above the Earth’s surface in texc2 2kko +l6marms of g.   

  Four 9.5-kg spheres are located at the co rds4,:kg tsj5rners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational forcs ,gt5r: skjd4e 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 samuy0880uib co+ ysh m5be side of the Sun. Calculate the total force on t88+b0huu 05 ymibcsoy he Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity atjg67w m1benf2op6awnb4 nr3: the surface of Mars is 0.38 of what it is on Ear4f7 b3en :bo gnwm1 jar62pw6nth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the4 5mvrwh*yde2rnyqbp78 - a+1n)nra v known value for the period of the Earth and its distance from the Sun. [Note: Com8we pbq rnr vv-5hra2 n)1*y y4a7+dnmpare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sate.;eu l2vcu6np llite moving in a stable circular orbit about the Earth at a heigh6lv.cu e2pn; ut of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit e 5s/u dgs,y6e650 km above the Earth. How fast must the shuttle be moving (relatives/uysed 5, g6e to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occugfay 39ytut* c4.qyn5y +yb6 ntr:i/tpants are to experience simulated gravity of 0.60 g? Assume the spa +.yt6y f5b3y g4urnict t :aq9/tn*yyceship’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 Earth in a circuxo, .ur) cgqw5bl3issd4(- r ular “near-s(uxc s4 rrw,ul5bgq3-io.d ) 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. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top o3)oz jb)l h +/kh/skdgf Mt. Everest to be placed in a circular orbit aroug)hk+s)zobjh k3/d/ l nd the Earth?   

  During an Apollo lunar landing mission, the command module cbef6phpa+19e .pg l9gpxsr)+ontinued to orbit the )r1g.gpb9p p 6aef ++hs pxe9lMoon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composedzba jq1 8/o67ebj .ezs of chunks of ice that orbit the planet. The inner radius of the rings is 1j7bzzo e b.s8q6/ja e73,000 $\mathrm{~km}$ , 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 oncqz vp8x137nvc e every 15.5 s (see Fig. 5–9). What is the ratio of a person’sv xqz3c7n81vp 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 center of th83v t-efi0dmwz (m9 xye Earth's Moon in a 3t w8vm mdzi0e(fy9x-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-s3 ss.yvr ld+*egir:. htar system consists of two stars of equal mass. They are observed to belri:+s* 3r.vhyg sde. separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weightl ) r-eu*h0ftl)n pv0n of a 55-kg woman in an elevator that mof0p*vl nu ehnt-)0 l)rves
(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 a2 g+;kkp ryg7from a cord suspended from the ceiling of an elevator. The cord can withstand a tension ofgk g+a ;pk2ry7 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 g/r8zco81 hhf fdh(.p planet with period T , toh .dg88/ (h fzrpf1hche density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.46,e j.g hman4e d) to determine the period of an artificial satellite orbiting very near the Earth’s surface4h6egmae n. j,.    s

  The asteroid Icarus, though only a few hundred meters across,qlc- mb:u5jwn1, ( hqjm;,l tu orbits the Sun like the plan n,u:,h-q1j t j q5mwbcl(u;lmets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance omvix.5z )+a ezf 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 eve o czkz48b,p/33osfbvry 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s pbf4b/8,z vco3ko3 szin 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 ofch)9qpd fd b-, 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, 5 s kzdx+ze3kn;29dp vperiod, and mean distance for the four largest moons of Jupiter (those discovered k+d d3k9xe5n;pz v2zsby 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 thexhp xv w;lkus 8,-c4z9 Earth from the known period and distance of the Moon. u8-p xw4,k ;vzxlsch 9   $\times 10^{24}$

  Determine the mean distance from Jup-i:+sdx qt z*aiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in T-q ai xzst*+d:able 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 fragments (whic ze+ci.0 dgymv2zt*s3 h some space scientists think came from a planet that once orbited the Sun b.03vsy + tdic*zgezm2 ut 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 descraxe ) 5lao3*km3w*p mribes 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 l3prx *a5m me 3awo*k)that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fj e gy) ynndxwp 8v78-9gkb1(vig. 5–41). If his arms are capable of exerting a for 8k(9-8xjgev vnwbypy )17gdnce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerdx9zs,lf 36 igation of gravity be half what it is on the surface?lxsdi g z,f369    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cie*ceblth/ tioi 1j ):(rcle 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 ar tcei1*t/)e h(l:bijo e they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of g8 ;rjdq )11 m x+1vko4c+ ds(jknyusvsravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. yd1 qn+j)sjxdk1;+s 8rs vk4 c1(u mvoWhat fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from)xajc++rhw)q h d0rba ih0y/) the Earth to the Moorc)dr)q x/aai0hjh b0y+ +w )hn 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, but when you sav+tml1vzzo0z x4 *2xtand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which diztzlx214*vvo 0z x +marection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will/smgof a1,h:h.on .q j rotate about its cent qjh.ag:oh1 /,om nfs.er (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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lo o5hzb xd9, r3z1pg-)8ln4nofk.psqv op (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 term.nskcdrh 2w 44kaxujm/3e 1r-s of its radius r, the acceleration due to gravity at its surface d /xch. 4rnmjka4rswe -3 uk12 and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by h.mf ,vwuvex ).q )e(ban angef).. be,x(q mwh v)uvle $\theta$ 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 If the coeffici5:r7* f z cfuue6ch3((wpdkft4yxt(a ent of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle thew tr* d:((p4zc c3fu56xa t(ky7efuhf curve?

  How long would a day be c+, auf,+wi5hpt:2y8hqkni c if the Earth were rotating so fast that objects at the equator were apparently ipfat:5y+,,8khi ncchu qw 2+weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apc2(mmr;*k l ktart 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 9bbx0 hd0(tvz bhe*i 4t4(bcka curve of radius 235 m. A lamp suspended from the ceiling swings out to ath zx(t4b49dv*be(cb i 00hkbn angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massiv3f*b:l)mj36vdg tovk)a84gq xdkpa9e 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 sinckm436)vx:vgoa t *g3 ql8bf)kddj 9pae 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 Spaczi-z3 dz6e cfi kh6j-6e Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did i6z6fec zi- z3-dh6 jkthis 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 xm )xd91d2i iq as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valx9 m2)qd di1xiley 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 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 Positioningf kt 4t/ujptlggk e0i,3s l578qi ,x.t System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1t ,lx8lf7ig,s3jk 5ikptt4qe.t / g0u nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroiymomu,1o d+ z7d Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Erom+mz7, douoy1s 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 satel9w(x svzrw8+g eq*b+olite in need of repairbw vo+e srw(zg+q9*x8. 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 hasxer,dcv3g / u; a period of 3000 years. (a) What is its mean distance from thc,g;3v/ eurdx e 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(+vm)z mlr+ bbyoo ;:s would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiobm)lm+: voo;syb (r+ zns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the 3egt4f3xn; t70snlq w center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,0x3ns0 qwnlt ;4t37feg00 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cot85j sbcy)nmc)v7if( v73jxkrners 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 midpoint of the bottoy7iv ccf)n)8 stmbx5jj3 7v(km side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi;m:m gdt /yh y*qb:mvt :-gb+vts 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-long sweep secondhl.4+w q7ct 9hn0gg f(6bciox hano0wh qh ti7b6+ fgc .(gx9cln4d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cir)txh7 ea,-bpecle below you on a 0.25-)h- 7 abpxet,em piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thatt/ o*jijb+m9amo.x, y a car travelin ob 9moij*t/.m ,ax+jyg 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 train, tt*m 8*gwzz+3t vumiv(he 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) t8mzmz *tgv+(w ivu*3Calculate 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.$\approx$    $\times 10^2$