Sometimes people say that water is removed from clothes in a spin dryer by centt,mxta-0 3nt frifugal ttmx3-0nt, af force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car b(cppg7o18h ipe the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve atp8oc pi( 1gp7h the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wh5baix)oldw;u4/ mca *fq 1du 5ere does the car exert the g5abqdwx 5 lmu) ;4 *dcfaoi/u1reatest 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 chi2i(5f ltw1rxd8 .ilda ld riding a horse on a merry-go-round. Which ofdw.(iiatxf l2 51 8ldr these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertic/ zx)myl8 fk63;bhkqsal circle without the water spilling out, even at the t f kbxls3/zqm;h6y8k )op of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contb0 8wjts)jk-g :x3u fwrols in the car which can be used to c 8bsg3w jxwtj)0k-: ufause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over,zz 7wa2ap 1uo ,m8xmd(b xaycj; g96h 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 betwe (zj769g 1,upoyw8xmaaa ,z md2hxbc;en his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward rlh/:ose7 ut,v )mxg4 ;no,qo when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you computetvol:0.mq ac ; the banking angle given its speed and radia;:cq l o.0tmvus of the turn?

A girl is whirling a ba1*hl6 tcydxm .btb r +ffs*.t-ll on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of1b* tmy stbdf*.cf+ -l6tx.h r the yard. When should she let go of the string?

Does an apple exert a grap; k asg45 ndh-h,e*wlvitational force on the Earth? If so, how large a force? Considea;-epn g5hh kw,sdl 4*r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doum.+xz zi1nz r1vkl4e) 76jxxable what it is, in what ways would the Moon’s orbit bnrxxzi7 xlj1k )1az4zm 6.ve+ e different?

Which pulls harder graxr w c nk4/o*:ig2/xyvao ybuhwu;954vitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates kowxuucw4 * gyh/:/; 9iay52nrvxob4more?

The Sun's gravitational pull on the Earth is much larger than the vfu; x ++mpadbkzszv0,;55ov Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in+avfx+ou5vp k0 ;s, 5;dzmzb v gravitational pull from one side of the Earth to the other.]

Will an object weigh mog;y ccvw se* c,o(6m7ere at the equator or at the poles? What two effects are at work? Do they oppose each ots7 (ymoc cee;vw*c,g6her?

The gravitational force on the Moon due to the Earth is only about half th(5gjewmv i3l1 3ynp9 w5ukle/uo s3o(e force on the Moon due to the Sun. Why isn’t the Moon pulled away fromnj1(kus3yi9mup w3eo( 5 lw o/35 vgel the Earth?

Is the centripetal acceleratlgv ;u5ih:f/o r gf+s.ion of Mars in its orbit around the Sun larger or smaller tha uog;f/h.:5gs lrv+ fin the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) g) mfrj tizk4*7f.)ux toward the east or (b) toward the west? Consider the Earth’s rotation directfmig) *7 4.r)jkxzfution.

When will your apparent we dew-c +/ir7ktight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) ae-wd k/t r+ic7ccelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long perioc2t5rtmq6f)ni*jy-g (j/ nvads in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that ry(*fn/qja2 grt )t56nvc m-j iotates, 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 think of.

Explain how a runner e4im(m/ey d(h mwkaz 37xperiences “free fall” or “apparent weightlessness” between3 k(/dz(7e4mawyh mim steps.

The Earth moves faster in its orbit arouhx5u/xuv9 ce*vg0 * q:q8 ujmind the Sun in January than in July. Is the Earth closer to the Sun in January, or in0ui mvcv 8*x uujqhg*:9qe5/ x July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known unty)e0;s ow2* cdde mc.nil it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s e m0.;s2)con c dywe*dmass.

  The Sun's gravitational pull on ml1ti8f;1pl pc x fc18ko.l(i q 0sho9the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffq c1m pk.l i8p;flt81(9chi 1 fol0osxerence 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 traveling 1980 z3fouamb lagb,i.)(2 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelcx)58rxb*31h:oqq kz p qepd,our4y7eration of the Earth in its orbit around 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 radius 1.5yqhp)kp4 :5rox,qr7 8ob z*3uqd1cxe0$ \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 i0 nz9,r ekwq(d0 - +qoyfiqx0dt rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. C(,-zd0 0yfn +we0 iqxo 9kdqqralculate the speed of the discus.   

  Suppose the space shuttle is in orbit qo:j() nrgkn1mxuiv6u;d+q( 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 younvmj:rx 1) 6 u(d g;ukqnoiq(+r answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on tbr1:z 9il0*l,y xunx rhe edge of a potter’s wheel turning at 45 rpm (revolutxru zl*nl0:,9bi1 yrxions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is q92. eefn chi7revolved at a uniform rate in a vertical circle of radius 72.0 cm ench7. q2efi9 , 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-kgj 5f cdn3ii8+j car can round a turn of radius 77 m on a flat road if the coefficie fji 53n+cdi8jnt of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static ; og)s q 7jik eb7v7ud)ruk0m7friction be between the tires and the road if a car is to round a level curv7duikevju7o)kb ;) 7 7mgr0 sqe of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and je;k9pe3 ohnm64*p4q9 oe jxje ct fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the foh*k9o jeqx;c4o6m3en 9p j4eprce 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 rotag3 rsgo*znng( ; hfv)0ting turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction betw v* f3hg;n zg(gnr)0soeen the coin and the turntable?   

  At what minimum speed must a roller coast3m2ot1;gd qxpz 8l3deer be traveling when upside down at the top of ad p3e 3om;q8dx g2tzl1 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 s b-1mpo z6ao;the rounded top of a hill (rada m6s;op-o1bzius =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 h4jq+r4ag: kuy ) dn)wFerris wheel need to make for the passengers to feel “weightlekg):rw+ d)a4hn4qj yu ss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a m :1e1qcwr9oger.q 7t vertical circle of radius 1.10 m. At the lowest point of its motion the tensict1 gr.9q1o 7er wq:emon 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 cm41o2grkk2 s)owl 1bjk from the axis of rotation is t )o1jk rkk22wblgso14 o experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindriz5t2)nofb r 3 )qdsqu,fuo,ape:wa /:cally walled "room." (Ser):e 5t/uo :2oub), sfqqna,zp a w3fde 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 roswzy 3l:c3:1q p s53zddsd(u ktated 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 hol1zwsdkdsc3s( 35u :qd:plz y3e 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 s.p: toc6 j0krthe ball which revolves on a s :rc.0st ojkp6tring 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 ba y5 n8 ;b;9b)s bbdxjacelpj+6nked 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 h-) dv 1xkvyo ra1(1bg$ 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 a f,w12sipabsh*9 / zwpt 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 tangenti2u d5i e6+,ht1ahpw seal and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 whehu+6,dt2h pa 5sw1e ien 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 ukxm320 shvjnc: /;qrfv uvm+7niformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangentialq fkvsx:vrc/u3vh7nm 0j m 2+; and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal cs;h:w eh23k kyircle of radius 2.90 m . At a particular instant, its hhsk2e3; w yk: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 jfj i bn 476m8gxbr y2k7*y9axipn0)nEarth’s gravity on a spacecraft 12,800 km (2 Earth radii) abm7 8 p y7nb6xnxk)y2fj9giibr 4nj a0*ove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the grj- :)z:8(b8unutd l( wisq xuqavitational acceleration g has a magnitude of 12b u:q-w j8sitn() uu ld(x:8qz 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's rhh0xsax d)-u- o- pfhvm*41qjadius is 1.74 0-oxhm ph sxdvf4) -*u1qhja-$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the u14yoof y 2x6h7h0cpnsame mass. What is the acceleration due to gravity near its surfanh7yox p4ofy6 c12h u0ce?   

  A hypothetical planet has a mass 1.66 tiwdu8+u iywp9 l +4k8tomes that of Earth, but the same radius. What is g ny8ki9d8+4 pl ouwt u+wear its surface?   

  Two objects attract each other d qaewjpp/,99t- hi5 gu-hqf3gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelerat*dpq*tmk .zh8ion of gravity, at (a) 3200 mhkdz.mt*q*8 p    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance f u0sh oj,bvt4w1qot0n xo-o3,rom the Earth’s center to a point outside the Earth where thegravitational acceleratioqwtjuo- , ohxs00 ob34vo,n1tn 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 ofyqet2-1nvq; /8jx nnur Sun packed into a sphere about 10 km in radius. Estimate thef /2tne n v1n-qjq;8yx surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like ouei(b4+9vf( *jfqewerhq6k4 u r Sun but is now in the last stage of its evw6q(4h +uevie*fk 9f j 4er(bqolution, 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 astrq l (bnxa59bzcd;*qlag.j+3 wonauts 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 gravi9 5cb *3jb(.lwaxn;q +azdgql ty 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at6+ :ou g og.8jxnrq0immahy- / the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one syxu+jr:m-g0 n6aqi/ go .ohm8phere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sidedtstylw7 ,:eo;, ti )x of the Sun. Calculate 7o:tt ds)t,,yxi le ;wthe total force on the 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 at the surfsf/h1o 8iwzzzu q4.q -ace of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine t1w uz4hq/ zs -i.qzf8ohe mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known :dj5vj:s . h90fqllx7 au9n pnvalue for the period of the Earth and its distance from the Sun. [Note: Compare your answer .sjll 59pvf :0ndqxn9 huj7:ato that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aborrf /uarw. 9s*n*i uo ,*solut:c:a g/ut the Earth atu:*r:ot, r ca r**o/u/f9 aw.snsgilu a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65fv 6*py-a,gzq0 km above the Earth. How fast muypzgavf, -*q6 st the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants aredxz ur* tij;vf60.22 0bmlvpc to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one 2ub ;d6rmt0il* v j0.zpxc2 fvrevolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for pp .i ne3x83 nwh 4bvey1n+5dwa satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a heigh8 nwex vp4en1p3dbhwi+ 5y.3nt 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 li,t ,aivn, t5vaunched from the top of Mt. Everest to be placed in a circular orbit arounav t ,i,,vtn5id the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t:pq tl+z oeh 1hx3(y v;uhq31mhe Moon at an altitude of about 100 km. How long did it take to go around the Moon qmqh (uzvp y1 e31o;+txhl3:h once?    s

  The rings of Saturn are composed of chueg5ibrzh,yh s ti5*( 3nks of ice that orbit the planet. The inner radius of th(i5*z3bs hi, e5ytghre 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 eeky6 qyv./wv8s ,kx e-* l 9wpdv.ty-pvery 15.5 s (see Fig. 5–9). What is t89wl6v.,ey-qsxy/* vt .pkp d vey -kwhe ratio 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-kg astronaut 4200 km from theh nq1n1dnor9zv+) 8qubo6v.5 mzas5k center of the Earth's nv9b8vnr5mdzqq z1 .5suo6hn 1ka o+)Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. x9i5iw 8 5jfaeThey are observed to be separated by 360 million kif8ewxji a5 59m 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 f2qntq1 7wbqo .b 3qplw)aet8 2or the weight of a 55-kg woman in an elevator that moves27q)n qqww 8q b32l1ap. etotb
(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 elevator.x,ql zob7th2hytgo erkg)c t 5(4i 35b:h)pc+ The cord can withstand a tension of 220 N and breaks as the elevator accelerate2ohtp( g5k c)qx+by)co5z4:r7 ,tlhb the3igs. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very ne 9w2h12us:zxkgi;2rqz2mvexty6g sku 21w x4 ar the surface of a planet with period T , the density (mass/volumu x1gu2t1 xyxhs2 k26z9s v:2 2rme;q wk4izwge) 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 (as9 h1:h /rvlh/gh,w t27.4 d) to determine the period of an artifici as1 ht,/hwg :lhrv/9hal satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th+; z mh8lsfy8se Sun like the planets. Its period is 410 d. What is its mean distance from the Shmsylf+z 8; 8sun?    $\times 10^{11}$

  Neptune is an average distance of 8 j8xo-cos qj0 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 yearsite:l2q b3;ax . It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Ee:qa32xi tb;l stimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center ofntkgpkr 3aj/hlb.w8 /k9 r3ubp+ *b)0mq k.kx 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 largest moons o040yc:3b ui m fockq8sf Jupiter (those discovered by Galileo in 160qm8 4ycsf bu30ikc:o 09).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mo.an9(xtt1haacn -1 uuon. 9hu.(t ct1aa1n a-uxn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitomwu;e6 , d ttmf4pb1*)csbj)er’s moons, using Keplem6ut; 1 fodtb4*p,s)bw) mecj 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 Jup t lh+c2t;8ox ) h6dow9;ejuytiter consists of many fragments (which some space scientists think camet8 o2et+;9h;x6yjcw)d ouhl t 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 describes an artificial "planet" iw l1a tk:8 ssa1rg3bs5n the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (toa sa s8115l :3rtbskwg 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 a shtc6 futie -/3rwe9(rc 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 his swing? His mass is 80 kg, and t ece3 w6is9t/f-tu(rh he vine is 5.5 m long.   

  How far above the Earth’s surv2 5iei pk8b3t2y5m va e(2gkgface will the acceleration of gravity be half what it is on the surface? gkbi8tp(g53evy a 2 i2ke5 mv2   $\times 10^6$

  On an ice rink, two skaters of equal mass grab / .c awa(u.o,2pyym s:wt;jghhands and 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 yj,c/ yhp:(suwa g2oma.. ;w tthey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the au-ndiwg+ m*k4zv 4wuw;va6 -lpparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractionw wl uia-4+v -znmd uwg;6v*4k of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Eax b6(/vs1mwx6:y z0xc z0i egfrth to the Moon experience zero net force because the Earth and Moon pull wwx f6z:(x 1xi cbeg6zsmvy00/ith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale inker3h4g(j/6t.a pk nx an elevator, it sayh kp6/ejrt.nak gx34(s your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that willti r 34-mn3yln 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) nrmi33l4 yn -tif 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 (Fi3g(0.dwnn wvsagf vz-uo+d. il6;;f x g. 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 radius r, theyqp y6 tka-zm uhr7;fk7:v9 k5 acceleration due to gravkvym 6ua5kt rfqk;-zp y77:9h ity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticav;da v d)b*x+irr,g3t v hb,,ql by an ang,dbvhq* bv dgr+3;,,)xritva le $\theta$ 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 desiwnyr1io/ce53oox* f vj )m i4uyx,/1j gn speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a ca41cj fivw,xxm3/)5on yjy/roi o1*eu r safely handle the curve?

  How long would a day be if the Earth were rotating so * xh 0(.aongn:x:dgw sfast that objects at the equat0o: xxg:an wgs.n*(h dor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant rto+giqu.14uq; nv,s riekvv o1( 8p7distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rumspj2d hy2 1;r8bht5 ounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an anglhhpyu2s2b 1rm8d 5jt;e of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive s-ndak3k+qbj (5lza4as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calcqk+zs(b ldk5 3aa n-j4ulate 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 xr)a)oz :cxf8Telescope deduced the presence of an extremely massive core in the distant ga8f:) co)zxx ralaxy 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 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 speed6)in oid2jk satb+l3/ as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at il6okbdis a+/3)tj n2A?

  The Navstar Global Positioningt 0w11owh6e 4iyw91;zhn ojxg 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 or6 x0hz 4gwt1ywi9 1h j;eoow1nbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is me v*j-hj+ xw-mb1vxjmam9mz 2) ant to orbit the aster-ab *jxmj1v)w+xmhj- mzv9 2 moid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut ings8zy n2 ana.h6 dhg51 the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the sa s2gnzy dga a165h.nh8me 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 pe6 :zeur y fjc9s-1xde)riod of 3000 years. (a) What is its mean distance from the Sunfje uy1c-e) zx6s9:r d?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if yo0*cd 0wd3vgzngif+ mh+ 7+qcwu could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like F+d gcqfwd 3+* w0hgi vc+7mnz0 $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wa25owtfw k mk;7c e+wx1q41f qey Galaxy (Fig. 5-46) at a distance of about 1t15kokw q2we;xcw +7f4feqm30,000 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 corners qt0ef yt+y q )esb;r41o6z70o 4rhtveof 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 4 tet0h0e6r+oz4es tb yqvr;)o y71qfmidpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 550xgdyg0a qny z *p0 ;:la9um8,n0 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-long sweep secondl zop 5v ryw0 l:)v q,a2gx+w.0u3jomp hand on y, m: l 2x00zo vjl.o+5pw)w aq3ygvuprour wrist watch?    $\times 10^{-4}$

  While fishing, you genl6 j/sp;gbop//84i blpnw gp, (ne:hk02sg bt bored 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 0.5:2gj/pgp lboeigs, p6n 0s;lnp/n 8 /4w bkb(h0 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 designe hcd(kp6k7ve( )r1ak fd so that a car traveling at )(kpevdfa kr(6ck 1h7speed $ 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 th:woic: ) sm(lue 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 tlm w(:cosi:u) rain 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.$\approx$    $\times 10^2$