Sometimes people say thatx n - gc9v*l9vkke0+cu water is removed from clothes in a spin dryer by centrifugal force throwin cxlg9c-vu0+n 9v*kekg the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a shpl8:268,gfztw ltp dnarp curve at a constant 60 km/h as when it travels around a gentle curve at t:g86f8plp,dwz2 tln the same speed? Explain.

Suppose a car moves at co -ig6grun,s ( h.+ urcjd7v)zknstant speed along a hilly road. Where does the car exert the greatest and least rusr , n6uhgki -c)+v7j.gz(d forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-n7 i(0c;,1 bix knva88min yi-gceq 1qround. Which of these forces prqi x1 yg0i nn cq7va8eb8;1i-cnk(,imovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withm7 z8:9uy+w* gbjgtvfx p( v5gtcp :,pout the water spilling out, even at the top of the circle when th u9gb,p*mt+ :twv5pc7zxj(gg yp f:v8e bucket is upside down. Explain.

How many “accelerators” do you havkyko*l/7f m )i d0zr9be in your car? There are at least three controls in the car which can be used to cause the car to accelera)9yd*lrik0m7/ozf b kte. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smu y yc+btx m-tx6l;.j0all hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using t j-xb+y.mux; 6l0tc yNewton’s second law.

Why do bicycle riders lean inward when roundcj q28. msqr d.qeep8l4k 7v0y3jr a-ding a curve at high speed?

Why do airplanes bank when they h)+qez/uul9; vv7hod)v fi1i1;kou o turn? How would you compute the banking angle given its speed an o19ei+h;1) oukuu/f7dvhi z)vvql;o d radius of the turn?

A girl is whirling a ball on a string around herup6(ok ex45xem 7 4vuk e81csg head in a horizontal plane. She wants to l1v u4ek6xec54 e7gok8 sp xmu(et go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravz2) 7 (/v(griays8u4incm cp 8jl t+geitational force on the Earth? If so, how large a forcetv2 i(g7g+/n4) ysp(8zjmerca cu i8l? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were do t+r3+gdq1 nyguble what it is, in what ways would the Moon’s orbit be differenqyn+3tr gg1d +t?

Which pulls harder gravitationally, the Earth iaa3f, /e: efion the Moon, or the Moon on the Earth? Which acaf:a,ie 3efi/ celerates more?

The Sun's gravitational pull on the Earth is much larger than the Mo 5toh+x7) lgl cl)t+hlon's. Yet the Moon'sg ll +l +)xh)o57hltct is mainly 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 the equator or at the pole4 tknz5q36hqoo/i:e jkr o6.as? What two effects are at work? Do they opt46ih5n.a kezq3/:o 6rojoq k pose each other?

The gravitational force on the Moon due to the Earth is only about half the fo p( tue mg2l1r)v0l.cnrce on the Moon due to the Sun. Why isn’t the Moon pulled away from tmver( 012u.ngtl lcp )he Earth?

Is the centripetal acceleration of Mars in its orbit ari1ar /0omq 4iy rcb,8lound the Sun larger or smaller than the centripetal acceleratbi caio 8q41,/ rmryl0ion of the Earth?

Would it require less speedfza :dij1n (l7y8t ik6 to launch a satellite (a) toward the east or (b) toward the west? Consider the Earthtak d(6 zyliji1nf87 :’s rotation direction.

When will your apparent weight be the greatest, as measured by a, , ms)lugp6tb scale in a moving elevator: when the elevator (a) accelerates down,tg psblm, 6)uward, (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 periods in outedr,w:acijk/ ::bdhp 8r space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface : ,:/8idjd kra b:chwp(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 fall” or “apparent weightlessness” bew6gjwkm5 m,;ztween5jzkmw, wm;g6 steps.

The Earth moves faster in its orbit around the Sun in Janu lb;7/ys+sb yo6 dgxx.ary 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 proxxbs.s/y6+gblod 7y; ducing 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 knofv16-ev o1+5n . bakcna66l tgxi; kaown until it was discovered to have a moon. Explain how this discovery enabled an estimate of+ba6166.nkaf;1x n 5ktvao ig-vecol Pluto’s mass.

  The Sun's gravitational pullwm.w7,kzs0jtn 61j bc on the Earth is 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 the center of a merry-go-round moves with a speed of 1.25 c jt0 ,jn.wkb16sm zw7$\mathrm{~m} / \mathrm{s}$ . 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 0kn wc 086obv *80tyidii(hdx 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration ofv9lx7k gt8u8wtcz,d * the Earth in its orbit around the Sun, and the net force exerz9kdwtu, vx* l8tc7 8gted 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 57vikd5qpv9 *f ix,ipis exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) odfvk, qxi55i i pp97*vf radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's3 1mnl b2y ma7f-d:unz surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at udy -n2b7mn z: afm3l1the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay 2b3vnfbho2xz3 qd 91ton the edge of a potter’s wheel tur xnz3f29bq3 hd2otb1 vning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is n)s;0n73pn jqalh (kbrevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33jlan n0q;n7k()hsp3b . If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car c*. l5tgqy xo0yan round a turn of radius 77 m on a flat road if the coefficient of static friction betwqg* yo50 ylxt.een tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static+l,f-g8cfwbr (d hw0 f friction be between the tires and the road if a car is to round a leve-hwf0fl f8 b+ r,gcdw(l curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotaten pr ox0e6m. i06hqe72 o3odho a trainee in a horizontal circle of radius 12.0 m . If the forco0 h.d q3oo 0hnroepie266 x7me felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable spee:,eg3-/ i89qakpq1f yagobej d. 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,fe8/g1aiqa 3 9pyjo: q- gbke between the coin and the turntable?   

  At what minimum speed must a roll 7: zzahuxq .w nxam e1)egt,:.6c;giler coaster be traveling when upside down at thew l h6xz7tene1az:,.)acg:u; g.i xqm 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 fcyjn 1.ernw-j picn9r9) o(pjx29j(rounded top ofj9r p.(pn j9ij eo2(-1 cnjf)n9wr cyx a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions p4a65i jn*idp4a+e fkter minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “wej4pea+dfti5 k 4i* na6ightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cq bh-bgk4(gxia- )o :vircle of radius 1.10 m. At the lowest point of its motion the t bb)h -gokqa(gv -x:i4ension 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 ck0j c rb ,2whi1a3br8cm from the axis of rotation is to experience an acceleration of 11502a jrc8hkw,bb1ir 3c,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricalu:o6vd s2h ;o*)gs:o q +:wxwqybgfl( ly walled "room." (See Fig.fg*s: +ov):2bo:o wswquxg yhd q6l ;( 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a 4oev8d4p l*0 v:.wpu s+fgfkn frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fik 4v4fv .p+e80wd sop:lgf un*g. 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 notm 1l:/+5omvzoh lju,n ignoring the weight of the ball which revolves on ulvmo :1,zl5om /j+nh a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectlygvfok9nq2a:xx*o73 9+ zvla k 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 massesqc gnbe/(xvu,tc9 kl;m0/n-ixb y0 l0 $ 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 dive)1sjuu l(4 kmlx-f 6ting 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 centr2+pc0 f fgk h8svsp+/zipetal components of the net force exerted on the car hpp0 +ks2f / zg+vsc8f(by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the ph vw:(gr8 kgff-)js i*ko c4r*it area, going fromgkf8schk* *irr)4wjg(-: vf o rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rad/ 7*ye ss/tezxius 2.90 m . At a particular instant, its acceleration is z7xes/*es/ ty1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 kmv6a.e- lygng g9:vd 6l (2 Earth radii) above the Earth’s gv6dl:9e .a-glg6vyn surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g q*fb9-u3 zqze has a magnitude zf-uez3q 9bq*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 o)9enr)rl xklyt 66 ga6n the Moon. The Moon's radius is 1.7) y6r6rln 9alxe)k6tg4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5b,a28qe)(avl bw,il8f3pl il times that of Earth, but has the same mass. What is the acc,if l)8 paa2l8liwvebbl3 q(,eleration due to gravity near its surface?   

  A hypothetical planet has a massh85z u3yzgen;x1yodc5z bu y9h2k 14a 1.66 times that of Earth, but the same radius. What is g near its surfac9uynxg5e1z 4bo1c ya3 ukyz;2hd5zh 8e?   

  Two objects attract each other gravitationally with a force of 2 c;4mkz 1chp40 (pzovg.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 , wgeyh(v fy vkpz7c3) w2 6u+*vthe acceleration of gravity, at (a) 3200 m2 z*wv6h3ceyfyp +wvuv)k ( 7g    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a p 27y;l0mh8 maiv ;rwuqz0jtuy( m71b point outside the Earth where thegravitatqy(h7yj2 awzi8rmup m 1;mv 0u;t b70lional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hvjno.9bev0 q* as five times the mass of our Sun packed into a sphere about 10 kmbevnv 0.q*9jo in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wsz.xmeb+ow : n+3 5zuuas an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. + 5um+nw3e zxob.z:su What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the s. -q8 ldaq.ujppace 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 .j l q-qa.pd8usurface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.1mm zp0d9x;xw60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by tx1xwdm0 9zm;p he other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same spbsc9 )uuu:e .ide of the Sun.)9csuupb e.u: Calculate the 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 a,cg.b9 i pai5dt the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 340c9,. gip ab5di0 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ex8+ .)w)2 x sm elr mr24gbzrqoz0z1rjebq7r /arth and its distmmexo4) r21r z0x7+zb8wsq2breqj)z .rr lg/ance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movixyx ,;m2bgk8-)ecbqh u fy 1t.ng in a stable circular orbit about the Earth at a heigyfmk.) -eq yc hub821x;btx, ght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the7xn8nan /pg h8 Earth. How7h8n/ 8p xnagn fast must the 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 lrmq5 f8l lgs/ii;)ttr n uu(k3s,/emrcl12 9 experience simulated gravity of 0.60 g? Assume9tus2 1lm c);ls3r8rifn/u(lilq m e5/grt,k the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit cmz/ ,fn ddlt;nkd9:q d: hu8,the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Ear,;ddku:c9ddq tm 8nh :lzf,/nth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the topg0 (wz m o 0voyrh96 l()ma7es1ufgl-p of Mt. Everest to be placed h(lgm1 fy o)glzso(a 6mp09v0-w e7r uin a circular orbit around the Earth?   

  During an Apollo lunar lan-;r sfr xx4gp)9h.otbkg)kq(u x 2xf+5k1 jesding mission, the command module continued to orbit the Moonfpr-k+bx2e94s1h x ktfsx x.5q(;jkgu)g o)r at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn arev5 +u(zjs b.5yirdxu 6etm:o: composed of chunks of ice that orbit the planet. The inner radius of 6(:rz+jxes55d itu:oy vb m.u 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 rotatese-5nj wdjp83 s once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a)jd s jp83-w5en at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from4n h bb(ugdve fp31k/: the center of the Earth's:duh vbe/(31fgbp n4k 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 binar*il 4k *d7ts wlko2zc0w2)i*f4 rnally-star system 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 point midway between them. What is the mass of each? )strinwakc li2* kf7lzwl40ol *4 *2d    $\times 10^{29}$

  What will a spring scale read for thuh 4tf3uxrm1 8e weight of a 55-kg woman in an elevator that moves xru h1fum43t8
(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 eler.qg xxq*5ap1vator. The cord can withstand a tension of *aqxqxp gr1 5.220 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 nem km)fny 2v7-e/smy y u.uv+)/w7pyeiar the surface of a planet with period T , the density (mass/volume) of the planesf/uki. mye wyv-+ y)nvm72/u 7)eympt 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 p 88.pskea8rcj65p qn meriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very ne8n6s aj 8ecm5p k8q.prar the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun la2b-nsol y4 l; xtpc/lp. q6+pike bpocq2- 6y4/snlx al+p lp t.;the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 5h-5j(zc- zwgdldti* 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 comes v56,iff 9df+fg9g-n9fgl d vy very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of tifd9dl6vng y g-f+ gfv99f5f,he 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 of the Ga mc(3n 9fii/fllaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 masn m;5r96s zrtns, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 15nzs n;m rr6t9609).
(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 ue 4kacz*f83jnl+quf* 6 k z/iEarth from the known period and distance of the Moon. iau u4fk3* *8nz6fckzel/+jq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mook 5u bodmp, u+l 9ek21o *fp8rpw74owins, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to t2o e pol i894r,mboku1udp7*wp5w+f khe 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 betwee/w -l 4u06utcka6jga w 2r(vwny/zm l.n Mars and Jupiter consists of many fragments (which some space scientists think.cly 4t6mwawuz g(a6 v0j/u2wrkl/n- 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(ayp :ckqh;5wx .- dnc p2o+qw 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 (to make the climate temperate), and that the ring rotates quickly enough to pxwwqc(pq2;5 n ykah+.-:cpod roduce 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 swingingtdq:5wc 8co lyvh gq v5i.2z38 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 3t5gc8h2 :d w8c5vqz. oliyqvpoint of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface w0g35tpc7q1 yiduw yhug :)rd )ill the acceleration of gravity be half what it is on the surf7 ygiuh1)g0):dyt qdcr5 p3 wuace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grabd*n9 v iw)cqb b xs(y;o+e6qw1 hands 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 aoi6y 9 wwn+1ebc b(*d)s vqx;qre they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of grav0yduuxqj:9v f+f 32ch ity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate t2hc3ju f0: qd+xf9u vyhe magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly 7e 0xc-hkcj *gxze o, 1fr,ov0from the Earth to the Moon experience zero net force because o- ze*v 1jko, r7,0exxgchcf 0the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 ku5yhl6u . efa/g, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, an 56 ulf.eyua/hd in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cir w1,g5a,k kdjmfazm5 4cular tube that will rotate about its center (like a tubuwm k j5m4,,azgkadf51lar bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vekgnkeammu )) q,9z9 4yrtical 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 termlz hq + jup ja8:.+1s p,c :x;whykc6,c+xcgmms of its radius r, the acceleration due to gravity at its surface and the gravitational constant ,;, : c+psj8hcxhmwgqc. :uk++amjzc6ylxp 1G.

A plumb bob (a mass m hanging on a string) is deflected fr91 ys2cf /2 flp;oufu+9aj*jdun lo 1zom the vertical by an1s9fu9 ;2p/+l* yfua jnouocj21fzl d 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 spmcd) )uztsj8o.e 7n0jc9i- h xeed of If the coefficient of static friction isd7mchoz j8c9i)-. nx)u sej0t 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day:kafc5efvj . h1-hyzf h4ti72 be if the Earth were rotating so fast that objects at the equator were apparently weightles 5t-k1cz:7hh 4ivajhe .ff2yf s?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of sbzqkdd3z + 0r /rb5c18.0 $\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 curwb x 57ul,+wucwa+t )-s1v ponstant speed rounds a curve of radius 235 m. A lamp suspended from the)r uwp-b a,s1lxu++7uv wwc5t 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, it has been claimex.bfv4 ir3a +ed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupi4ia3 exfbvr+. ter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ex;4fflwjrtacua s1 (b7w :38putremely massive core in the distant galaxy M87, so djl ap(wb7 s1wa:4c3 8 ;futfurense 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 speed as it tro; 7;nn0rbv vnd dx/b+averses 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 actinv;n bndb+vnxo0 /7rd ;g 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 (*4- kka6 33e dmevor()bpxsbzGPS) 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 orbit xaem4sbdr6)o 3z(3*vk keb-ps 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 Aster-a56+j)j+)xhyq9zgq ed kkmu oid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a hhk5x z 6 um -j)kd)q9ay+q+ejgeight 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 szdtxp.r 7la(l51l( w e4 3aycuhuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25(l.rl tx3ua ywcz(a51ld74 ep km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 ye +s td5)hrg)pqars. (a) What is its mean distance from the p)gq5t+dhrs) 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 be if yn9mov fq 6.wbni(5 /;m 4dyifmou could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiymm46fin i.wnv(/ m bf5 q9;odons, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dista;mv8i4u ahk 8lnce of hi4u8;klv 8am about 30,000 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 of a square 0.50 m on )6w* a5i 8htb)eyui auvsn3:k each side. Find the magnitude and direction of the gravitational force on aku *)i6h5in ast3 b8uew:ayv ) fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the2 *wc+tmpo3my2 hr u3z 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 accelerationn,;lg 3lyr/25 wcz lto experienced by the tip of the 1.5-cm-long sweep second hand on2 nl5l;r,g/yz o3lwtc your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arounq8(gr m7dxfen wc0 -5hd in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every rh g-xfe 8qc7d0mwn5( 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highior(es3 gxo xqcv)2; ,way is designed so that a car traveling aqo vx23gisrx,)eoc;(t 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 the cars whe/y4yive.eba.*k j. en n 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 seatie*. ejyby4v. n ./ake, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$