Sometimes people say that water is removed from clothes in:, 7sa+ nzupbn a spin dryer by centrifugal force throwing the water outward. What is wro:p bz7,+ns unang with this statement?

Will the acceleration of a car be the same when the car travels around a sharp cmm,7 3 ogfai 7elt9(2d)gk.vt/ wmtgturve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expla7 eg)(gkmo lt./iw9 dt3t,7gm fmvt a2in.

Suppose a car moves at constant speed along a hilly road. Where dou (4kevv;pr i/es the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between tw/(r ui4k vvep;o hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting p um4n6il; -w)4dvka5l (hjip on a child riding a horse on a merry-go-round. Which of these fodwh kjvi;5nu 6 m(4 l4ipalp-)rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in axs497:y+c xugzg7p ni vertical circle without the water spilling out, even at the top of7+g7: x49 iuynxgs zcp the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three vm;bxu bi17l2controls in the car x;7muvb i12 lbwhich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying overm95hocbiv . l)p5kbt, the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sli bl)h.b55c9pto v km,ed decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when ul4hl/ +5gvhyr k+j.d.b(jzt rounding a curve at high speed?

Why do airplanes bank when they turn? Hupy p-c;*+tr6m ds 2pofnz9 3row would you compute the banking angle given its speeuf9+p nrr-tc*dp6o;2 p 3szymd and radius of the turn?

A girl is whirling a ball on a string around her head in a horizont jl; wxl(aulis/5s, 6tal plane. She wants to let go at precisely the right time so that the ball will hit a targslj 6t ll a(/uw,5ix;set 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+c jh5q.kb 9-klde w+d, how large a force? Consider-b+ .hqk+ 95jw ekcdld an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what way8orv c/m m*sw6s would the Moon’s orbit be o smm6 wrv/c8*different?

Which pulls harder gravitationally, the Eaxzan s- ehd bo-l:;awa; 22krq;lr :g-rth on the Moon, or the Moon on the Earth? Which 2s2nkrh;lx :oe;a-w:ga r l- bqaz-d; accelerates more?

The Sun's gravitational pull on the Earth is much larger than the ylw+8c051kimtel9 asfs /4w k Moon's. Yet the Moon's is mainly responsible for the t8f0t 9il kkm4sy w/elw51+sacides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are 6/t+ l slac4ft(v42l r;foa soat work? Do they opposv;f 4ora (ll+scsol t46t/2 fae each other?

The gravitational force on the Moon due to thekzlt; f8-rl9 a Earth is only about half the force on the Moon dula t9lz8kr f-;e to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratih:*y 8w2cwhd m h:2yhg* 4ruenon of Mars in its orbit around the Sun larger or smaller than t82e h4*ywdr: wncg*yum hhh:2he centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward ;cc:ysx1 fel6 the east or (b) toward the xcf:; es61ycl west? Consider the Earth’s rotation direction.

When will your apparent weavqay, f;,nd,ight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cfn, v,aaqy;, dase 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 adv x,8nq1p8e ugp0d8mauersely affected by weightlessness. One way to simulate gravity is to shapu8 18ppdu,e 0a8xgqnme the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free y7cq z6y/hvva+j7r7* sbhl7 xfall” or “apparent weightlessness” between steps.7 +hv7yzx7ybqa7*6jrv/ sch l

The Earth moves faster in its orbit around the Sun in January than in Junti2bf l8tq o8:ee 8*wly. 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 8eo8te wft q lib2n:8*axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was disco -1vab j l51mce)4beshvered to have a moon. Explain how this discovery enabled an estimate of Pluto’she1b 1ecsj4lamb v5-) mass.

  The Sun's gravitational pull on the Earth is much largertcp/31hb8e ori 4d,fk 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 fromrk3hoectb/4df 1pi, 8 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 traveliniknoijga a ap+.00* sy2528t2 zx chbdg 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 accel4wk3up9 kn5p:6usrq h fg6 s;veration 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 circlfknh634vu9 p: 6rp;5gqss ku we 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 di 2z-ktsqnc ;e*scus as it rotates uniformly in a horizontal circle (at aecq- *k;tszn2rm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km frv l(+8ak9fhbpom the Earth's surface, and circles the Earth about once every 90 minutes. Find the cenv9b+pa8 khfl (tripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on f phw;.qla) ourh ;-0 d;mx;dqthe edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cwh)lrmp 0-u;dqh;o;fd .a ;qxm?   

  A ball on the end of a string is7w9m0lbk w)lz (ev,i q revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0e ibz70wml, lw() 9vkq0 $\mathrm{~m} / \mathrm{s}$ 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 sp*g7; x eg-, 5l/ iocm1vqmbq6l8bijh ueed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction b6x lmqbljeg7 ,qc- */mhgib iuv;851o etween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of lqj7qxwdw)5d6oden 37u, x1fly9,ydstatic friction be between the tires and the road if a car is to round a level curve of radiw71nwoqy) lf,q 3d5dyxue6j d7d 9l,xus 85 m at a speed of 95km/h ?   

  A device for training astrona 6lw(cz ob xaa074qjl:uts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by thjxza70q 6( lc:lbowa4e 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 ab2-o vzvd )894zvmxyg rotating turntable of variable speed. When the speed of the turntable is slowly8g )zoy mv2zvd4b9x -v increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaste(uvxp6w;bk fx)0:at g r be traveling when upside down at the to6x txvw af)(kupb:;0g p 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 i0 u*t g2-icjm)j iwlj(7dg a8ncv:5edriver) crosses the rounded top of a hiait:vi(gej 2 jmjuwd) g0c li*5n7c -8ll (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+das,j,y8sise+u, zb -m-diameter Ferris wheel need to make for the passengers to feel “weightljd +ebs, s+a,,y8szuiess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wh9a x;gwikoz(hne+/ru 4uv l)h : tu2j)irled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting therhz;/n 4(+)u)a9l oxu:kguj ei2vwth 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 partb 0 j,b0v (cc,uowxig6icle 9.00 cm from the axis of rotation is to experience an acceleration o0,io6wb jgvc c0xu(, bf 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrw ykvy),vf ,7gically walled "room." (Sevyvw,)kgy , f7e 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 ) io/ 4bjupo 5;yms rotated 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 centoj / mob4u;5pyral 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 , prew9r(. ie. o:6 iw -dj lvrnoo:t4ayb7ocisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partiir oo9ar .:to .:74o-( wlwnyvejbid 6cular, 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 8 h zjjs;x4hq;38 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: *; ,zyhflynp b*cg-w $ 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 evasive8wk 28qztox9cww *9a 8zv 4eah 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 componihw.-/xugj+i r so2hw2 zaj 93ents of the net force exerted on the car (by the ground) in Example 5s jwh9w/3+ao 2uizh-jrxg.i 2-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goingc+: y4 2v6*y lep*sz sotj5qqi from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and j*+4z6v*qtci2: yo5 ylqe sspthe road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a hornm/dqr0 d s. f.: b1ipaz0cic5izontal circle of radius 2.90 m . At a particular insd /ic05.mqisc1nadf0bzr .p: tant, 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 17+cfj)wx6rih 2,800 km (2 Earth radii) above the Earthcr6)+h7 wixj f’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, t4+b,c42xqmk mkzl /ndhe gravitational acceleration g has a magnit4 cn x mdq42+kk,m/zlbude 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. The-8kpptx sca;cf/m :x((:rwk u Moon's radius is 1.74 px(t k;kfs:c:c ap/m8xr(uw- $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timyh4cuwe/iur a1 61s6mmw mq.;es that of Earth, but has the same mass. What is the acceleration due to gravity near its surfacu6u;.4 1m1aw iqhycme6sr wm/ e?   

  A hypothetical planet has a mass 1.66 times that of Ear5(jjebo3( xq amvwc. .th, but the same radius. What is g near its surfa53j. cb .m e((voqajwxce?   

  Two objects attract each other gravitat:o5 zb (52:eymoaxrqcionally 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 accelt6ysm r 7v8v: ,yqf.m5rpo *rferation of gravity, at (a) 3200 m fmr,yqrrm*5p: f. y 6vsov8t7   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside mbgkva7/ 2wsq) n0,aythe Earth where thegravitational ac ak /,awvqsbygn27 )m0celeration 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 mas,8onyvg6ckxo *ftc8 )s of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsx,v* kyc8 togc fn6)8oter.    $\times10^12$

  A typical white-dwarf star, which once was an average star like pna .g:u(wej)xsf ,5w)a:in your Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surj:u)(w ny,a ag5s. npxw):fieface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while o)b x.*za9 jgevrbiting 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 surf.avg9)ezbx *jace in terms of g.   

  Four 9.5-kg spheres are located ai2b8qghx wp +x7z0*jit the corners of a square of side 0.60 m. Calculate the magni *pzhg+7ib82xq0w x jitude and direction of the total gravitational force 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 same side of ths+ ,m68 /xpy dmoe:hwfj4zcq que;1:be Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are hewbe1fq +, :mys;q4j:6/ du cm8xozpin a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface ;ju34n0qo9w4c)4aui nrl fo09 ;fa nci8qpmt of Mars is 0.38 of what it is on Earth, and that Mars’ rw)tp cif98a nrcj4l;no44u30qm 0 uon ;qaf9iadius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knoyy8 e7o velm s7n2qor6 5r);pxwn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laeom )5ro7s y p;6lye2x8nvr7qws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a ssr79(u.aff0pm*cw rmwgly 3 7table circular orbit about the Earth apu*.fls f rg(yw7 w0 cmm39ar7t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650l5)c 2kp5m2p )gj9 t fbzenat- km above the Earth. How fasaj-zf )9 p)b kc 5gttnp25lem2t must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceqa kgk: s: :l4*-k* hlj*qxrg)ap,he iship rotate if occupants are 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 rk-::g )e lpijqhaqr*4k:*klgx,s* haevolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to z s2b6 :9kftu4e 93risepv0a torbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whif zu3s e426krp :bas 09tetv9ich 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 r.wcqly5/: glbe launched from the top of Mt. Everest q5.r/c:yl wlg to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbig,d87wbx am*ji :6zwbt the Moon at an altitude of about 100 km. How long did it tbjzm78b ,dw6 *xwaig:ake to go around the Moon once?    s

  The rings of Saturn are co9oxh2iz7 dt o0mposed of chunks of ice that orbit the planet. The inner radius of the rings is 73 7ot2ohz0ix d9,000 $\mathrm{~km}$ , 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 diametekz :sva y/yyz72l n4h9g:uos9r rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) kyz gy snh4 oz97a:us:9 v2/lyat the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4ehw(x,z 2 n2e6qhui.eg0 l(muh gy6/x200 km from the center of the Earth's Moon in a spacel 2q e/h .,ixguy066 n (g(zxuhwehe2m 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.9pggvr 5:.n xp They are observed to be separated by 360 million km and take 5.7 Earth years to orbit apxrgvp9 :g5n. bout a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the wef;e x /x(hwvzn65m6 m6fty/slight of a 55-kg woman in an elevator that movef mmxs;6v nef/hzwy/56 tl(x6s
(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.c-/kwq l xo)apj *9p1s The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direct*1px/)oa-kp l wjcs9 qion)? a =   

Show that if a satellite orbits very nu/;zryaq 6 q.uwob/. mear the surface of a planet with period T , the density (mab/;.z r/mwu.y uqo 6qass/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 (27.4 d) md9j(e fy0hml 7wh9/obpq 45ar9b k2b to determine the period of an a5mfy 9re d(pkbm40o/ bh9jb 2ql7wh 9artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrossuph b8s/kyq6)c23iwxsmbi 3,cx3w. u , orbits the Sun like the planets. Its period is 410 d. s,wbi 3/psy3 c xiubk3m6w hq2.c)xu8 What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dis4:eyd;x/ o 7:he xpgfk9qhs3 qtance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It p4hwl c(2 lx6acomes 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 6(c4a whl2xpl 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 of the Galeat)ir)nm ;w)a;c. wwaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 fouh3tch*f t7 m)*gxi rf0r largest moons of Jupiter (those discoverc*ritf*fx0)mh7 h gt3ed 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 lo-,mo27f zb1jz 1cl m cu q6e:pvu4c,from the known period and distance of the Moon. bp -:mu17oec241j ,z olz6ucm,q cvfl   $\times 10^{24}$

  Determine the mean di 56l8fz/ 7,cqnmkjbybl31 vjistance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance ofvc j63z/lbn fl 75jb8qkiy1m, 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*o oyv:+kj )hl and Jupiter consists of many fragments (which somkjo+l: vh) *oye space scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of 6 oohn w:a54rha 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 (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 plan 4wo 6anho5r:het's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a-1cqoru pdl;t5q+nj* hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum s tcdqpjoq ;15un*r-+lpeed 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 surfaifb98aw a- +khce will the acceleration of gravity be half what it is on the surface? +b- if8w9hkaa   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands 2r mp*cv5dsk: :au4mqand spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one anotheuaps mm4*k2 vdc:qr5 :r?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of graz 6tg*x tj.or)s6( cyvw+mkx2t b :4vqvity at the equator is slightly less than it wtb.4vz q2r x:oy)+6(wj*c m g 6kttsxvould be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecr*geu1 d(x/m. wbm /tcpaft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and .tm1 p/d wce*mxub(g/ opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scal5- yv kp/ zczbs::z4dae in an elevator, it says yo:dz54vzp-/: aczs yk bur mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space sta,. b9 ka7xet iy.*dupption consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). T ,e udx.b.kipa *9p7tyhe 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 loop (Fig. 5– pm 2,tfo; k0dzvq+ey643).
(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 rad,gg0nk 1 wzf 0n.q7hdcius r, the acceleration due to gravity at its surface and the d0,h g .0kn7qwg zn1fcgravitational constant G.

A plumb bob (a mass m hanging on a string) is def 4xtp4)ap0h ao 6)ftjao2t *velected from the vertical by aaop a)o)x ph06t4f4v*j2 ett an angle $\theta$ 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 cogn)j3ehxgn * bk;gj+ )efficient of static friction is 0 n)n); b+ hgjegjx3*kg.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 fas50 9ch;bqf6un++p/iamcpkvhx.s ty (t that objects at the equator were appare /tcuhm(6a .;in +5pcf+0sybpqv9xhk ntly weightless?    $\times 10^3$s

  Two equal-mass stars rq3b6y )a6zj4x34biz- bot8gw n8 vrrmaintain 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 sp61utnnyznrwz ofv7zdxr376q )j 9 (i.eed rounds a curve of radius 235 m. A lamp suspendu9i1t3yznq. 7)n r6xzjdzvonf7( r6wed from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, itji:xj7ta7 n 3eco*x.z has been claimed that a person would be crushed by the force of gravity on a planet the s7 i7x:x3tjo *ajez. ncize 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 Telescope deduced the presence os 2oxn ,* ,:c-d7s(py4fuxtz nc;pcewf an extremely massive core in the distant galaxy 4cxx,;cpztdwnfuc 2p 7(,* -soysen: 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 col ojkecnvqj4d2 6qz7jg +yc)4wy9 / 9enstant speed 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 Av ejo6)j/qz cl7dkne 24cg9qy4 +w yj9, 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 Positiox1yxyqkeqvp8q*e -. 8 ning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellit v1qxye-q.k88q y*pe xes, 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 (NEA21t.2ibdjp baup *hz8 R), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rough*bja. 8ib21ptz p2dhu ly 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 spac4f+rj mde ka5 go/k28te shuttle pursuing a satellite in need of repair. You are in a circulatjeragkdm5 8+ 2f /4kor orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3h,0vhb)nxcl/u *su z (000 years. (a) What is its mean distance fr c)l /znuvbx h*0u,sh(om the 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 would need to a:p g4:89d w/mdr wq)wdhi5lybe if you could actually "feel" yourself gravitationally attracted to someone near you. Make re)5hyd8 qm /w pg49wirwld d::aasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centztjwdqw .r3w:f6 ol* +er of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ligh .*qw+zr:lwf6 3wjo dtt-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 corne f1r8b/kcrl )aijt9 v:rs 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 mc9b 18flt)rvk/i:ra jidpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitshm.ujj/w 6. 2:icurv s 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 exper4cf;o 1paunye9*u7 v3qms 4bt ienced by the tip of the 1.5-cm-long sweep second hand on your wrist watch? uqmncu493;v*fp1y so4 7 ta eb   $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in.wbe1n ua7b zv82awt+ 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 th8n te +.waw1vb2 azu7bat the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway qw98;e6a*jly l(rv jd is designed so that a car traveling at slvday8rqwe;9( 6l jj*peed $ 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 the cars when 3zii 0a5. bxjn-gwh 4hnegotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger ofniz 5ihb0xhg-.3a wj4 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.$\approx$    $\times 10^2$