Sometimes people say that water/7 c x*gpx h(tpg3czu8 is removed from clothes in a spin dryer by centrifugal foh8g7t(u3gpz *cx /pcxrce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when vnlxful9e(ix , /lv4( the car travels around a sharp curve at a constant 60 km/h il,fv luxe9v n4(/(xl as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car jw2in 5obpn.;exert the great j.bwipon5 2n;est and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acti *q.oqm,dw tf)ng on a child riding a horse on a merry-go-round. Which of these forces provides thd)f.w* q qtm,oe centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withoul( h)s l1ugkn.go5j *g8 /lqgp)yq(wf t the water spilling out, even at the top of the circle whenpl 8og.j q5)luw ggn(*1fghk ()q ly/s the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at lfhat 3/ dsh-wj-p nu(0east three controls in the car which can be used to cause the car to accelhpu/w n-ha f -jd(03tserate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of +2rml 6uo. ask vm9q3nw5gsl2a small hill, as shown in Fig. 5–3135. mmu9wv2sl +gs6n2orq k la. 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 Newton’s second law.

Why do bicycle riders lean inward when y)j*fa//s.u7r vuz uw pdk ::nrounding a curve at high speed?

Why do airplanes bank when they turn? How would (+iisvx 3wu+ ,k0jgjuyou compute the banking angle given its speed and radius of the tusju,0ji+wv 3x ik+(ugrn?

A girl is whirling a ball on9lsz)m9 lp ae( a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a s (pela9l)m9ztarget on the other side of the yard. When should she let go of the string?

Does an apple exert atx) fx a;mx2l+ gravitational force on the Earth? If so, how large a force? Conm;l)xfa +2tx xsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what3, ,ojs tz,pz1vf q.te it is, in what ways would the Moon’s orbit bqts.3p,z1 ,zev jto, fe different?

Which pulls harder gravitationally, the Earth on t7oell xb4 f x/)f*xk/wia p.x2he Moon, or the Moon on the Earth? Which accelerates more? 2ilxa4pe //x*b.ff7xolwxk )

The Sun's gravitational pull on the Earth is much larger than then(bvsim au x t;3,lwd8*-sa t: Moon's. Yet the Moon's is mainly ram; nw,lt vt(-8 s*axsdb3i :uesponsible 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 .b/3 c:ipzuap1 kgn7f equator or at the poles? What two effects are at work? Do they oppo uf: pa3/nzi.1cgpb 7kse each other?

The gravitational force on the Moon due to the Earth is only about half tkn2l* x4u8*c kipx y0e:oc6l dhe force on the Moon due to the Sun. Why isn’t the Moon pulled away from the 6ldu8:kx2cnpc* i 4ke0lo xy*Earth?

Is the centripetal acceleration of Mars in its 41 hmt/xmzcz g*3 ge1oorbit around the Sun larger or smaller than the centrg1mg*z3 cxhem 1ot4/zipetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east okd:dz qw fj00mgx7l05r (b) toward the west? Consider th 50xj: 0w7g zldqf0mdke Earth’s rotation direction.

When will your apparent weight k0qa+,oew5mvy;:vqvc y5z6 u 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 cons,uv +5:0w m6 voqcqva5ky;yzetant 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 4tf t6 *hxhex:ori; wz b;o1j*long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Czo tbxo4xw1tf *;6 ijhr;h:*eonsider (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” be:,oks8f02q g syck.:tc s px8vtween stst8kgf:c vp, sx82.k c0: soqyeps.

The Earth moves faster in its orbit aroc bx+vk5i(;zl r+8nb yund the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is nc x+;birylz+bk5(8 vthe tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was notqkqqf7kqbc4o+i .e 7 rid5 9 ;c(swlt0 known until it was discovered to have a moon. Explain how this discovery enabled an estirotd5;kw7(7.c sfi k4q el 0bq9i+qcqmate of Pluto’s mass.

  The Sun's gravitational pull on the Earth ispnv2 szn1vc;6 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 avc126ns vzpn; 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 19v5m7y nhzlf8a 4h c/6q -h.ama80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in i .k; xg57hydaa9sq+be ts 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+a;5ay shqk 97bedxg. 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 8vam x4bgy4-o9 pbse*as it rotates uniformly in a horiz9bv4a4 goe*8-spy bx montal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cir.0ygzw.bnas 5bdk *+ lcles 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 , thebawdlg* z+bn.0y sk5. gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accea qdu,,if*kn t0d16nrleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if ,d 60rknn,1tdi qf*uathe wheel’s diameter is 32 cm?   

  A ball on the end of a ,y 0ef;qiuq ;yxvh8 3estring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , a;; v que8qy30,ehiyx fs shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg cari(:kd) in+g4a6 uk.x -s xb4yn4n gsvh can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires an )bnu+64 n-(:ygnviig4dahk.ksxs 4xd road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient ofdq+sp7v 4 tb0b static friction be between the tires and the road if a car is to round a level curve of radius 85 m btp v4q7 +sdb0at a speed of 95km/h ?   

  A device for training f4t f un/pyr; uhxf7g393h iv3astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back istgf r 3iy x43 3fnhu9uhfp/v;7 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.*xp:i 3lpos*zs3y kq1 0 cm from the 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 ilx3** pssz 1ki3qp: yos 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 coaster be traveling when upside down at thwkc* p+o.wwmet sm:brv,ui80- ox(f ,e toxb8(keorwcfistvmw m,-+*.w: o,0 pup 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 ma q6c,l cq2z+i70du0ga li3 cywss 950 kg (including the driver) crosses the rounded top of a hill (radius =95q uz wclc+gcq i0y70i,l ad236$ \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-dibff4w8f9kh 1)x 8u l2amc moq8ameter Ferris wheel need to make for th49uaomhff8kxb w)f8q 2cm 1l8e passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical mywz:;ti++-bn:n co ucircle of radius 1.10 m. At the lowest point ofz:: y i;+btwmo un-nc+ its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a partw36 )efwv- tgxo2v-udicle 9.00 cm from the axis of rotation is to experience -- od)wwv3u62egxv tfan acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pxru l-mkr- gb2a(-bcf.+ bn 6m:hzwt) eople are rotated in a cylindrically walled "room." (See Fig-)rwcn.mzl-htx-+m6abbuf b k:r(g2. 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 fi2ago r;k).0 )(qlmfrlfsqc . rictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglin)2o; q s(a qfr0imk)ll.r. gcfg 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 th ,1dtx zg9fkd,is time, by not ignoring the weight of the ball which revolves on a string 0.600 d, x9, td1fkgzm long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly bankb.aja:*s end.,u-fc c ed 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 qn w9. a6jti0yu+omw*$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at229hyku z b-pw 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 gl5v)cqib iy5m sv(-2 centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15i5)2ygil( bm-svcq v5 $ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates b*t l6a 39yft,lb;vtq 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 friction have to be between the tires and b b l*3ya6,;qvl9 tttfthe road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular jr d( getf1wu-v rtn*,h,8k2h/g6gqk instant, its acceleratwkg* f dkr(t/ ,e-ugqvt1gr,n2h86 h jion 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 oq:ewl 57d dqx9n a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its 7dxwqelq: 9d 5mass is 1350 kg.   

  At the surface of a certain planet, the grak(m9 g1xz:(km25axfuiac-a lvitational acceleration g has a magnitudek 5:(gximkza(-a c 1flxam 92u 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 .g;hf*, 7rkrhrkhci9o: tvj6u6y pb,Moon's radius is 1.74 r.g,kt :bhr7 phfj9;cihv* r 6 uo6ky,$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 inx / 9sd*l v-)41mb/;zaj2afhtvzlz times that of Earth, but has the same masdil1*a/v z;fl49jb/-zas t)2mhnvx zs. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thedsggc5rj1 8uhaj /0h6 same radius. What is g negh6j0 ujaghr/81 d5scar its surface?   

  Two objects attract each other gravitation4+fgah0mm :bw)dqi 5vally 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 acceleration of gravit5nh fd9xzl2p x1kh-m-ago:b /y, at (a) 3200 mh/ p zf2o mlxx:9g1akbdn-- h5    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinatsbp v8m8s hs9a06)8kk zlo:t outside the Earth where thegravitational acceleration dukosm8 v6a:lpszt8b9) h8ksa0 e to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivek9a6va ccjmm4mi7))a s b d44p times the mass of our Sun packed into a sphere about 10 )mjm9 v46 4ck4sa b )cmadai7pkm in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once b 7di3eu,i,pawas an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon b d7,u3iipb,ea ut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel cp e3w3*ymnn. weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculap cnwe33yn* .mting the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are l*bm74hyiopc* ocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force ex*ihmo b cy*p47erted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostkir0 bve3u5)fso o.c30o*db m of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. rf)i5.ode3bvmbso 0oku 0 *3c 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 of Mars euq*wc;v 7e +gis 0.38 of what it is on Earth, and that Mars’ radius is 3400 kv7q;uee +*gwcm, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuz0uta./vxmtwe: il x8., w8fx e for the period of the Earth and its distance from the Sun. [Note: Compare your answer to .l wm t,ft:0/ z.uexvi x88axwthat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mj0l g7+tk zph9oving in a stable circular orbit about the Earth at a he zght0k lp7j9+ight of 3600 km.    $\times 10^3$

  The space shuttle relexgqxa)7sb 8tcit- r*zfz u ;,6ases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle bet r-zqa, x6u )sf*bz78gc xt;i moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindkkht ;/.qx/uq rical spaceship 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 revqtk .k; uhq/x/olution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to om9y uqrddo )(e f1pw66rbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the masfm)o6(yq1ed r6uwp d9s of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top o +tg6gv ip j-f7+g;tvof Mt. Ev+j+gg7 tt 6gvio-fp; verest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing misstaa g71+b:lvnion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon ab gt1l: v+an7once?    s

  The rings of Saturn are composed of chyorie6epq 48rye44s -unks of ice that orbit the planet. The inner rqe8rysy e r4o4 6ei4-padius 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 ob.f 4ei ixu(5fg+xcf 50yg7xdnce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real 7xx5(c iugife gy .f0dxb4 +f5weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 420ca tqvg,kb-ehux ih*r-f6 f f ,.)nn140 km from the center of the Earth's Moon in a space vehicle (a) moving at constant ve- v,6 n,r fu4ck -i*1exgftb h.anhq)flocity,     ----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 equ ;du,9nwz,kq,5fvl dlal mass. They are observed to be separated by 360 million km and take 5.7 Earth ye,d,flw5 ud,v nzkql9; ars to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for ti9k pwl15i tma+g 9wc9he weight of a 55-kg woman in an elevator that moves gp99c+k 5m1a iitw9wl
(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 c3yjv1c9u1+ihy t 2 wdzord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator av+2 dzyij3h1uy tcw91 ccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pitif* ,0i2at rlanet with period T , ther a i*2ftii,t0 density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the pevx50zgrkmmzw 81 :d:zriod of an artificial satellite orbiting very neamw1 :d:05zvrx8zkzg mr the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metep6p 0lzfa- 1ijrs across, orbits the Sun like the planets. Its period isz1i f0lpa j6-p 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of*cmtf8: nfd8 )p*.eyw7e mo p -ck po8uel78wu 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 co jqneu)ofwd+n25e3z4 ( iekh-mes 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 di)qo(ki n4ee3 -52fu+hedzj nwstance 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 cente- uw7+sx:pz7uml83ph q xsgm+r of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largubb7/qv xg abf 6+/s:aest moons of Jupitef7b xqab /:v/bug6+as r (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 E-cak r9 +pb;+xvq4rjz 7t*h asarth from the known period and distance of the Moon. z4r kt+rqapv7 *a- 9sh bcj;x+   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, uhk9s -j :noa +;vf6rivehhgtq) 9*b2 osing Kepler’s third law. Use the distance of Io and the periods given in Tksh vg2n o+va;qejr9*h6: 9o )fibh-table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frhka8crc qcz8*(bk+c8aq g :k,agments (which some space scientists think came from a planet that once orbited the Sun but was destroyed)a8k+h ,acqzg cb8 *k:rqc8 (kc.
(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 descrill;0cig8 s(;65ckqo * v)xlno3q h xxgbes an artificial "planet" in the form of a band compl)vg;c6nioxq( ;30x l xcs lok*gh85qletely 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 planet's year, in Earth days?   

  Tarzan plans to cross a gorge bq pqe0 yuzcc0hy8(- z2y swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a fc(p82q- chy zq0uzey0orce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half wha,uk /w cwjean4p*w6kr,nrk5qf, 3f, nt it is on thw,p,jn3kf,6qkek,rc w5 r/ uf4wa n*ne surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in1hn.t*kz40ggee tzg4 +8 my4tuyt-co 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 ah0czg4t+8t zk- g44 *o myn1tuety. egre they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the ap bw7:s g:*+p rk3x,cpe bjln9fparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude s ,p +lw xp3* g:ekbcjr9f7nb:of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth k ord ) kodp-7cbzrk/)o,sa;2will a spacecraft traveling directly from the Earth to the Moon experience zero net forc)d2 d)rp7/zro oosa-b;k,ck ke because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kvlw wld *91fn7g, 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, and in f7 lwdv19*lnwwhich direction?     ----待选择----upwartddown 

  A projected space station consists of a circula9 /qs5ja4p 8t9ssbvswr tube 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) if an effect equal to gravity at the surface of the Earth (1.0 g) is8 w4 q9p5/j9tasvb sss to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a ver f 7bt*4+hher pmru6a,.5r ckhtical 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+;kqk-x r og9b a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitatiog+bq9 x;r k-oknal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verti5ggyow,05p i9q, brh fcal by an angle o9g50, qbph,wi yr 5fg$\theta$ 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 my*su,)x2me y ezr60bg adz .x4 is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c.zxa6ee z,bm 0xd*4uy g)yr2sar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectsg0n987fx h6 -yngu bon at the equator were apparehnugbno n 8906fg -yx7ntly weightless?    $\times 10^3$s

  Two equal-mass stars maa4ydg4he5 0p rintain 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 radius 7ci/ad)u h:qzo60c pi235 m. A lamp suspended ca 0cioqiz76) dpu:h/ 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 mspl4;fd9 xv.hv2: c f 1tjxbo/assive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate thfcdxp l.;sv j2hb1f :tx 9o4v/e 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 ru.rpv +)u1o4ol/rc tdeduced the presence of an extremely massil rr)v4o1+ ct/ur .oupve core in the distant galaxy 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 conslf gp sep1;1;btant 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 A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (cpeb f1;ls; 1pg) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) ut8ut f : vsg)yfar z+,lvdd6n73ilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmittedusf,r7zvd+8dg l 6y3ta:f)n v 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), after travelin, zsly3 -zing2-o tkl-g 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is ro3-- lngy z2-lzsko,i tughly 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 shuttleutpz+ 4gf in5. pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 k up +fzing5t4.m 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 anzjqh .x7 r04n. .)pr5qgmwym/xo:ut period of 3000 years. (a) What is its mean distance from themr xm:x) .u z7 wpqo.j0q/.ng5ty4rhn 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 w c6dmfv4qcm.-ould need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, vdmf . cm6-4qclike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. /jw01wj gg p 8ez1efj(7,w jng5-46) at a distan, w18eg j17(e/ nwwj0pzggjfjce of 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 ov )nc2ohle3ox8sa3 )fun:q8 o n each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the ouon8 l 32s8h3qcxavf:oe)n) square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earc cd)+*t,/ui+rcxmkc th $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-lonbhqg bq7h-n ,7g sweep second h7nqqg -bh,b7 hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wpk d3b9crm/g:+ n5 che+x 2dug3 (tyuaeight 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 angl2h c/agtgn3pduck+x+b 3uy5md r: (9ee that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R xe93 6u h,;jj:urk zhz in a new highway is designed so that a car travelinh6r;:,ux9h zuek 3 jjzg 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 tiltrfzj/ -ef(4l f 8:wnis of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thf/es ifl z-8j:(fw4nrus 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.$\approx$    $\times 10^2$