Sometimes people say that watef6js clromi+( 41*lxar is removed from clothes in a spin dryer by centrifugal force throwing the water outward. Who4rl *a1 j+(smfxc6ilat is wrong with this statement?

Will the acceleration of a car be the same when the carx3t3 f;7v 1cizfs8nitct6.fe travels around a sharp curve at a constant 60 km/h as when it travels ntfx 7;c.83f sz6ev3 ic tift1around a gentle curve at the same speed? Explain.

Suppose a car moves at constanh/n djmygphii/f:q07(0 px: et speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at fyn:he pim i7gdjxh:0/ 0/(qp 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 horse fq.; 3ei- lhwok-:q5)rjq y+6aqm,z/enxw v xon a merry-go-round. Which of these aql)h oe xzkqq+/,;-5.q:wny 3evxr6jfm w-iforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sty 9a)fnw2 29pv5mpoq pilling out, e5pq29 2o9tfmpna yv) wven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at mx1.mqvf u.x r tkr5pz)6ch*25fx;tq least three controls in the car wk v hfx*m5q1 ux.tcz.5qxpmr2 ;fr) t6hich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as y;lj,4u+phah3f lti9bk 2 jjv*0v,wv 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 l+jku hp, v4*b9t2h v,wj aj; ily3vf0the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lvsq4 jn6cyx845s9uz*zx hxe ) ean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the b ud,wkh, agc;d w0j;3hanking angle given its speed and,a wg,kd3;d0cjhuw;h radius of the turn?

A girl is whirling a ball on a string around her head in a horikll)w(3 l *7+rfhfutx zontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shw kf3 llr+t7ux l)f(*hould she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, cgge;fypn//7 how large a force? Consider an fepgc/yg;n/ 7 apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s zb0gy 4su /mo cm/m;2sorbit be diff/z yb/2s4gmmsm uo0 ;cerent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon tbi paot/s/,w u y)ufq,-b/0 yon the Eary fbiatuwy/u/ t0/)q,osb- p,th? Which accelerates more?

The Sun's gravitational z 6/9q89agniw; ql rshu*ha.dpull on the Earth is much larger than the Moon's. Yet the Moon's is maiilqa*s ad9 quwh./nhrg;z 689nly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at trtu3xtd r bdj(c80q p83f:b)h he equator or at the poles? What two effects are at work? Do thdp3qjbd r3( txc bf)r8hu 08:tey oppose each other?

The gravitational force on the Moon due to the Earth is only about ha)q*8wyhi v/3h ;ph j7x6wrheklf the force onh/q*3 evph8h) w7yxhjikr;w 6 the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal ajqo ,-nx-jme(cceleration of Mars in its orbit around the Sun larger or smaller than the centripetajejxo (-,-nqm l acceleration of the Earth?

Would it require less speed to launch a satellite (a) tow(hbu i6hg; 0ypard the east or (b) toward the west? Consider the Earth’s rotation direction0b6p hyh(iu g;.

When will your apparent weight be the greatest, as measu1,/q2 6 doib+zq qjc7 h4lt:ov)bvl rured 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 speed4tvv ro2j6db:+ q /q q1lzolh,ub)7ic? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected 6klmr 7o;mjy ;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 objecm6rjk 7o m;l;yts 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 weightlessness” beioxf0(tl7 soo 3 k.y+er.p1m ltween l0r+.o otsy7o 1xel(i p. 3mfksteps.

The Earth moves faster in its orbit around the Sumy9f)9. )-pymxb km fkn 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 the tilt of the Earth’s axis relmfkpkby9m)).myf x- 9ative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. fb1 jz7 nsjuuzsw9 -7*Explain howsjsz w *u1977z-njufb this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth a0knuy.aqf8z0f )+u 0i a evd,rr6k 2his much larger 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 of the Earth to the other.]A child sitting 1.10 m from,a .e2iufza6va80fq 0n0hrr y+kk d u) 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 2 1xdh4puj7v h$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 it9l5uhcwvf,5 3n1 08 xbo yf/z*igga 0qs1waacceleration of the Earth in its orbit around the Sun, and wqt5l/*a08,nufa 91o f5gx0w gziy1bshi3 cvthe net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotatmslf*ry:45d x wk; 4soes uniformly d;l4 f5x4:kywr *msosin a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in sx5rpaq .)k :uh38xl norbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleratpk3snq)r8u ax.:5 x lhion of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude o9 kt(gjn ,n;vsaz3z)bdwiw.y j+z9 .ff the acceleration of a speck of clay on the edge of a potter’kjzd 9w.s);39t(b+ azngiyv. fn, wjzs 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 rate du +hshi adsl4g. (21d(erpc, in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. Ia2ghd,cd r1h(e. p +(diu4slsf 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 1s)j2o+4fsz eg 050-kg car can round a turn of radius 77 m on a flfg2z+e) js o4sat 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 static friction dwmqr23p ec6yh -,bt6 be between the tires and the road if a car is to round a level curve of radius 85p 2hcb, q636ted- wrmy m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to ro; ;ljm wf0j5xetate a tf;;wxml je5j0rainee 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, 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 t0bl,r8a698jen wbnm a he axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and thej lrwb0 8 68na,9nmabe turntable?   

  At what minimum speed must a roller coaster be traveyn9zyygpmzd8;b ( ki/mj9 l 38ling when upside down at thejm ( 9gpmby8z;iy3kyn l/8dz9 top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top 3jii gnk9b0 q8of a hill b89 k qg3nii0j(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 wheel need tgo0amf ny740:d 0df12 wmsmyio make for the ms 02:ydn gam1 dfm40o0wfy7ipassengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled pavkzl. .zjx/ ,um*:vin a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in th,zu xvmvljkp/* .a.: ze 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 wed/lt) ) 5vftrotate if a particle 9.00 cm from the axis of rotation is to ev)) dtft/ew 5lxperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a khvm+ e yfiq)u(eq9;;carnival, people are rotated in a cylindrically walled "room." (See Fig. 5-eeq;q u f);+vi9(yhmk 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 3p0kq.4( rzkcv/yv y r) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connecckrrq y4k/.( yp0 3zvvted to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the bana9k ;y n)zy bl7yr.:tll which revolves on a string 0.600 m long. In particular z9nnay.;ybry7)k:tl, 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 for a car traveo-nc6(f llq *uling 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 massesrdomp +e(d:,ald +)m)ldkr/b $ 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 maneuve6p 9jjo6i: ztsr 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 exerted 9-d s7kjjq (ftuf2r-g on the car (by the ground) in Example 5-8 whju-k(g2 rsj-97dftfq en its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolise u-lc5wcfeds4*o 1soi +2e:g 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static fr+escood - 5glecwfsi1e *u :42iction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in ae 4rac(gqker ys2w el(/0p77v9i ktp- horizontal circle of radius 2.90 m . At a particular instant,2/r i(av7gwqs7rce e4pl-p(0 9ytekk 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 Earth3sj8h4j8* v: budg qju bm2h-o’s gravity on a spacecraft 12,800 km (2 Earth radii) above the E4* gbmu8hju-qv jd83osj: b2 harth’s surface if its mass is 1350 kg.   

  At the surface of a certain planed31dsj9l d-fw1o l8oet, the gravitational acceleration g has a magnitude of 12 13ewl9d- ds1 jo8flodm/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 Moyv5 -orty9 nk1zp0w w7on's radius is 1.70ry-5v n9oyz71 pww kt4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1 -oruc+ g7:d2dn.ainm.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its s.o7un2r cid:- dg +anmurface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiu8m41:qseunao 5 m ;l doyk p65ms78lhss. What is g near its surs 6 n7 51ep5alsk4hqdso m8l y:u;mmo8face?   

  Two objects attract each other gravitationally with a force of.llsip+nj u wr8*cx () 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 of gravity,j2r -t- 0h*- ihfoyxkw;we+ibcg qg9) at (a) 3200 mgr h-wy- hgx9-;t i*wjfo2ic)k ebq 0+    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eart;uc-+b4i.f 5wuad ve jh where thegravitational acceleration due to the Earthc e-+i4a;w u bdufv5.j is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the jma/ xv97i 1 4abizllob8bujxu5 2(8qmass of our Sun packed into a sphere about 10 km in radius. Estimate t9j8a48bv l7uu 2l(m/zboiqx1x jiab5he surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sunlq)ulsby o; /4)tvue*9*wgckn/13 dhz n o 9yx but is now in the last stage of its evolution, is the size of our Moon but has the ;zbykcd *h1 3l/nul*s)) 99ox wt4vq/eguno ymass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel we veuokdn99*8;,)usqqqo.r 1faig,b nightless while orbiting in the space shuttle. Your friends respond that they thought gravita9un evoq1r.db,oi,* n; s89 g)k qqufy was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60f -l5g pz6 )lz2)otmyo m. Calculate the magnitude and direction of the total gravitational forc2)f tgp6l lzo )ymzo5-e exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred ye ptlf0dst kz8l)2a(z;ars most of the planets line up on the same side of the Sun. Calculate the to;2kzlz(pft sl 80 ta)dtal 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 acceleratiexe(1 vu-dglt57 m7pk on of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mapdkmxle g1vet7-5 7u(ss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the :v 4b;kao+)gd,ifm f ic qyi,0known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawsfm+k,f04 ;agcvyii:)bdiq ,o , Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ci ed( z,;o,a cwl1xgr :+vnwmb*rcular orbit about the Earth at a v d,1n+l* g,(caex:wwzobm;r height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abov;lkzmj*/q+c: :x ddtwzvua7 /xx * 7yme the Earth. How fast must thej7lc/zmu+atm:*d x/ d kx7vwqx:z*;y shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to exp*;,*pj4u+r2fs4tpo blzpj ip erience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your p2ij ofzp*ut+ s4rl*,bp ;jp4 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 ik 2ebuw,kgf4(e uf2z; n a circular “near-Earth” orbit. A “near-Eart z2u2k ;,kube(4wef gfh” 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 8 wayzdo00 /nzlaunched from the top of Mt. /o8d0 zy0nwza Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the9e2o,id0ql rg2dhwt *h5 ixe f221ccw command module continued to orbit the Moon at an altitude of about 100 km. Hor2ilw2 ctd1c0 oe,2h i hq 9gw*de25xfw long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice :)+cxrr bji/5zvyfdr h:f id 6; rx5g1that orbit the planet. The inner radib h1ri)/r ;rffx6yd i vcx+d5gz:5j r:us of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whuad7uk-ilz/ .bwl r 0/at is the ratio of a person’s apparent weight to her real weighzuwd k.uai/ l/br -0l7t (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronautytj -zkj9*p0nw d1sm8 4200 km from the center of the Earth's Moon in a space vehicle (a) movingj w8pj9tm 1dk0ysnz* - 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 sux(a38vzc8fh .3b lm +r1fegwystem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a poi 8l+fm(.3gr13h xue cab wv8zfnt midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an enhl* 0sc(2e*ym voh(elevator that movesem(no0y(* lc*vsh2h e
(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 ;rrbyczm(2g p0lj4p uuj01huzv 9 d/+ of an elevator. The co1cv z /(0; hum+p jlupd9yr4 jzu2gbr0rd can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periodcop li)u3 :hf6u88 odaz n2m2e T , the density (mass/volume)pfu8)ao26ced8 nm3lz:ho 2iu of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 kd, jm1o-er; kq:(b npd) to determine the period of an artificial satellite orbitinomj1pek q k; -b,r:nd(g very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik2zkybifjyg0/) :vfu zn7sp3 ,e the planets. I yu07 bf/ yvz,i:)fz3jpsg 2nkts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4df8 dteg v9.xd* :lhf5.5 $\times 10^{9} \mathrm{~km}$ 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 onmj5 z/xo-u k/oy2;a;p ik 4l1uquns/tce every 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 in Kepler’s third law is/ -2/ nm 5u;xaokt/ lsi4 zkouj1puyq; half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galax8v a 7d km*i6c1f-h/ltzego(oy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 mod4ixc 5hdx51dons of Juddc5 4dhi x5x1piter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth m +2mi-kb-gjp(awv a,from the known period and distance of the Moon. a- (g vibmkpj -2wm+a,   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moe h61t 5bh q+o.ambiv6ons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. C ebvoih6 a1 6m.q+bh5tompare 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 (whillz iob bk(d m:)g6v:1ch some space scientists think c:o m(v6 ldbg:)bi k1lzame 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 5irr+b76e,g nrafb9fk+ ; 5nzdnacxw8*mh *m"planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our o+fe ih7ar5xna+bc8*k96fgdr rb; nz5m*mw n,wn, 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 bpl4r0 b bbbubd+w7.6.j)) p adbq dc4ny 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 pob4p )dnp7 bbbbcdu 6. b r+q0.dlw)ja4int 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 acceleratms3cm/ zwb pz5kqo n,sk71.z (ion of gravity be half what it is on theps1k( kzczzmmb.5 qsnow3/ , 7 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and . eayh+h7 6ejhspin in a mutual circle once every 2.5 s. If we asseh. j+h a7h6eyume 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 acceleration of grgbs q4d,v-lv 3skpw1. avity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractl14 vp sq gswk3dv-.b,ion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a so x7v1w8yq yts*d0ef *pacecraft traveling directly from the Earth to the Moon experience zero net forqvx8ey1* 7y odftws0*ce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when ymz k+ :j*xbl;sou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration;lmxb :kz+j*s of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular 1 +g+v ,5feiyrqskgf3tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day)vyfe+s3fr 5+g kigq,1 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 v kc;xli d3fkx*/l c:ylv ./u*aople), ertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its rada0):zmgo8wc jz:. nfwius r, the accelerationzjfc8:)w wnamg.0 oz: due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vedw*d 0,c0 ;.uabmcbobrtical by an *obbucm;c,b 0 d.a0wdangle $\theta$ 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 If7,wm qkye-t9 i/tz y0(v;as. nxyz.au the coefficient of st ,-9is( ;a q/yu tzaemkz.vw7y.nt0yxatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectu,mvlub(7 ,sjxm+rmppt l 3, 0s at the equator we3v,u7r mx,busmj l(0m+t plp, re apparently weightless?    $\times 10^3$s

  Two equal-mass stars maa *2u.cmsm fa6 cdjkk5*am 0(ma,l5fgintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of rad 4on0o -:qyxyeius 235 m. A lamp suspended from the ceiling swi :q- o4xey0yonngs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. T /lw2t8d+tl)bvsj iq2hus, it has been claimed thats /ljbit 2dt) +lwq2v8 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 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 Teles8zrwn0 p4kk. hcope 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) p4kr0z8wh. kn. They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed a)n5vw ksulr7+ ek7(hui4jr1n s it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of cur7)7viuj n wh +(5ukekr1sln4rvature 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 Positioning System (GPS) utilizes a gr9ki ng..p1o7s;2caiedi *zg ; szdz k-oup of 24 satellites orbiting the Earth. Using “triangulation” and sigk *.edpkzazg 1s- ;i ;7ndzisoc. 29ginals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), afamng hbqp137e9 b6vt +ter traveling 2.1 billion km, is meant to orbanmq9g1 3bbvt+6h 7e pit the asteroid 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 in the space shuv2c .o nflk7l*mm5b:hxt9l4r ttle pursuing a satellite in need of repair. You are in a circular orbix9lf 4ck*mohtl lv :.nb7r5m2t 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 ou :frjx5x0/6p bczx3nf 3000 years. (a) What is its mean distance from the Sun? 3b5j xx60r xunf c:/zp  
(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 valuf oyhjgyftb58os9 ,,qv) j)np, u g+h6e of G would need to be if you could actually "feel" yourself gr u),+5ygph9 gvtj snh 6, o,f8jbfo)qyavitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around-u*; vc0jt0m8o.rs : qaybmgj the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 300csr:-gqjo *8uba yjv. ;mmt0,000 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 c)v 7e/ ia.qgy yhmm57aorners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth. ma5 7/yqhmev)7gaiy 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kh7j;:l pur7p8ks00 ngyxqnysy 3y) i2g 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 ofxw v/ d.dbs7jmt fg2/r/h2 v,f the 1.5-cm-long sweep second hand on yourd 7 mv/ b22vfxj.dgs/, htw/rf wrist watch?    $\times 10^{-4}$

  While fishing, you get borei : m4f+gsx1b5f(szved and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. e( vsif msb+:x4z1gf 55–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desi/l ,2w)9*gs vs0bzhtb/cly tjgned so that a car traveling ,yj)9ws/h 0zc/bvsg* tll2bt 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, the Acela, utilizes tilt of vwekt ohc11dwn9 i4wkp4s359mnt. o1the 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. w4pcdmt54wn oo tn9whevk13k s.11i 9Consider 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.$\approx$    $\times 10^2$