Sometimes people say that water is removed from clothes in a spin dryer by 3i s7sj,4h *g( r0qpznuli kcyi63v5lcentrifugal force throwing the water outward. What is wrong with this yipr0 s5 (il ku7vjzql3gc63,ni s*4hstatement?

Will the accelerationnd3z08by h qo r/dmpqgz;w*65 of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroh35p;b * q/qzddzw8nygm6 o0 rund a gentle curve at the same speed? Explain.

Suppose a car moves p6ek l4yxf1 8g.pemk/at constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top e/6m .xl18fpkgkpe y 4of 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 merrbsd /5rnw9j -./: c jojf-bixoe,tl6sy-go-round. Which of these forces provides the centripetal xfl/-o65jor.j s c-,bbj :/siwnetd 9acceleration of the child?

A bucket of water caoqoyrddf4o(5,8sk . (qa5aopx6: qkjn be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside doqkq5 o 6qjsfo8 ,ox54o. dp aady:(r(kwn. Explain.

How many “accelerators” do you have j( je;u;hmf/k t fwdpr0b ( phei:86a.in your car? There are at least three controls in the car which can be used to cae8 k/r dm0;((w6 faptjj ;ph:u .hfebiuse the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as showt r0m+cd6 eo*te3dnrb+y e*2 fnejl0+n in Fig. 5–31drl*0m*ee2 dryeo+j e+fnt 0 6+bctn3 . 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 rounding a curve at high bw;ob 4,aiidb k;2pl ex.+4uw speed?

Why do airplanes bank when they turnlm2tmwy( zq 71a n jaf8:xkz mv57i1q7? How would you compute the banking angle given its speed a 7 m( kji172a78yzlqwt1 5 mvfq:mxnzand radius of the turn?

A girl is whirling a ball on a string around her hea) n ig,jxac.g9/8y. irbuskhb8 34zkwd in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?u8z)x sbkij, a94wn3kg8c/h r.igyb.

Does an apple exert a gravitational force on the Eartrmein2cro5*1 h? If so, how large a force? Consider an applo*miner5cr 1 2e
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wa /jgxh ;p(m.ziys would the Moon’s orbit be dip/hz;( gmij .xfferent?

Which pulls harder gravitationally, the Earth on the Moon, or p3u/z3b k,kfqthe Moon on the Earth? Which accelerates kbpk uq ,33fz/more?

The Sun's gravitational pull on the Earth is hfcu nc1q*3 l,much larger than the Moon's. Yet the Moon's is mainly responsible for the3lq,f cc1n* uh tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at thya :7 v wj7djtd8pg++ae equator or at the poles? What two effects are at work? Dod+ajvwdp ay+8t:77gj they oppose each other?

The gravitational force on the Moon due to the Earth is only about half th 4z. 5cd/-,-+etlm wgvdigqs2io auc7 e force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eartdg4 aev ml-2+dc/i.wo 7q-gz5 sic, tuh?

Is the centripetal acceleration of Mars in its orbit around the Sun largeoel: s*u*)n mwr or smal:s nem)u*w* oller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) to (7wg9.glc hmf33nw4ix 8ftrdward the west? Consider the Earth m(ngdx3rlc7f38.fgwi w4 h9t’s rotation direction.

When will your apparent weight be the greatest, as measupmlekwk (tw4s,o7laba43se 8cb,)y/red by a scale in a moving elevator: when the elevator eoa bm,t/pa l(e ks4l8kw43sy, 7b)wc(a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space cocdku2 gg93 9uhuld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts w2ku9gd9u3 gc halking 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 experiqgy1p70i misy;8)tbm9ej oe 2 ences “free fall” or “apparent weightlessness” between steps. 2y0y1gj) 8pt;mi q7es9ombei

The Earth moves faster in its orbit around the Sun in January than in July. :p+ybsn (rcdk9e 5r*g Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not mnbg sp*k:cr5 9dy e+(ruch of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knownx. fe2f2ez7.sxqq 4nokd4c ;)enfi+b until it was discovered to have a moon. Explain how this discezcfe o ne 22s q744.d.f)fn+ik ;xqbxovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pulvzwuw xi ;bj g6orzzs1m):1,) l 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 1.1 vuzzwzwgr ,m;1b 6os )jx1:)i0 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling sh b ju/.j)e)1cyq655fifvwv 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 of:dgle-xmz inci /o, hw9hh11/t;( g iq 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 Eaxqn/ i:o 9h h1gd/mchltw (1,izige ;-rth'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 ishse: :4:zl .ltnjv;7l/xi gqd exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of4vll:x:i :elszg.;hnq t/ dj7 the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earthcbd;anirdf-b/njmq q. f;6/ .'s surface, and circles the Earth about once every 90 minutes. Find the q .n/a;6cdjr. if bbn/dfm-q; centripetal 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 acceleratio zev7 s .kbi8)huzo;37zzgje )ao.i*yn b1 (fmn of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm? ; 1f zzjebu.)(esyi 77)vn3gkzozh omb 8 ai*.  

  A ball on the end of a string is revolved at a+vm4p3i hk)t)cc mp .j uniform rate in a vertical circle ofp4 mkjmhtc3)c +p.v)i radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum sp,b:zrfx*a20 1 aly9 5ufuy)tqom3o sf eed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road boo *f ,)flx u3ra12yy ts5am uz0q:f9is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of ./pub z/)qwixstatic friction be between the tires and the road if a p/u qwb)x/ z.icar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet)v) :i38eg 5sbzislph4b .leeq; o +zy fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.5vbz:lel h)3)ze+i i. qs 8b4y geops;0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable ot )*z n6ie5o-asb *gqq3zxyes :ys,3nf variable speed. When the speed of the turnta*-*6tqqs in5ye szyb nez3asox :,)g3ble is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whi,4vwx kq,ht ;en upside down at the top of a circw,vtih x 4;k,qle
(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 (,(rwgakt2ld/ .w +6v yie12yyslef b 3including the driver) crosses the rounded top of a hille(rse vw2byyk2f 1 y3,6a+iw. gdl/tl (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 po1 14ws4sozt rg)dosu6ek/ n:er minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “ 6r1owo 1:zu sgt44s/ndek )soweightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of vr 5dxn..z vr:radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.zv.xdn.r: vr5
(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 centrifugs ;w3-hw.9- kdhxvlx4fmjx0ve rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,0;w.vm9vxfk w-x xlh0d3s-j4h00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people areyea 2zb*z6bymx+ t(9qs7zo)z rotated in a cylindrically walled "room." y+xzt2 ( 9* yqma)e7ob b6szzz(See 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 ) /eqbgq8cg b6 )7fr.t*qjt:31s jwuxh is 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 central 7qg3.sx ebqtb8 61f:wqg ju/*jcrth)hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weig*e*d cju (o9uvpm3m.cht of the ball which revolves on a stri*om 9pe3.u( v cujm*cdng 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 8-ye* dsf5b6zb 84 wifz8 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 uqth x .w96c nwkr, k1v+jv)k3$ 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 -ue:kcvln-;b o nqp uds8go:/,* 2awaby diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exbqxlj;;zi;auv16 fi 8erted on the car (8v1;zx ;6bialfi; uj qby 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 acceleratei0v+q(io yv0kq /mh* rs 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 the road to provide this acceleration with no sl0iqh* iv vy+/rqm(o0 kipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.9yt,p(z6a kk ;eb ghzq 78i9+am0 m . At a particular instant, its accei zq ;a78ehz bmyk,9pg(tk a6+leration 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 12,800 km (2 Earto (pm(q ;tsmr+h radii) above the Earth’s surface if its mass is 1350 kpms (ot;m(qr+g.   

  At the surface of a certain plane*yn8c a: vyabw 1ms9 8c7ii:(srl3uf xt, the gravitational acceleration g has a magnitude of i:1 iaw yucnayx398sfr 7v sc*(bm:l8 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 acceleratios 4 :yp/fv3:i;vofykd n due to gravity on the Moon. The Moon's radius is 1.74 sfk4 y3i;ov:ydfp/v: $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that6/ 9k3urf1.hr r.o 5eljwuiul of Earth, but has the same mass. What 1.3u9 hlerur uwko5f. jl6i/ris the acceleration due to gravity near its surface?   

  A hypothetical planet has a mas,m rb prhhf73-s 1.66 times that of Earth, but the same radius. What is g near h m7,rpr h3b-fits surface?   

  Two objects attract each other gravitationally with a force ofqwjo( w2wg,nr qxvyl 0/n+rm*j.x9 4f 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 valu3zyb 1eqh0zdz )5z sw0e of g , the acceleration of gravity, at (a) 3200 m zz5qdbe wh1 z)sy0z03   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E3* p6fmwgw ijp-uchr0 :lq.l2arth’s center to a point outside the Earth where thegravitation.pilr06 g-w :m2lfw q3u cjp*hal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spher-7wm+)xhptqfr w ;z9domu4l3e about 10 kmpudxwlr h3o)qm9+wm7tz-4;f in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a/1ksq4e)dk /c ud,gdpn average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the m)/ d4gs,/ckdup dq 1keass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitin 3:9p l*ittk,7 yq24c bn8d hvhskhg.og in the space shuttle. Your friends respond that they thousi8k,gt :3vh* yt b o qhlcd9nk74.2phght 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 surface in terms of g.   

  Four 9.5-kg spheres are l4z6o3k pgvg. +mp1wjjocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitatim1w.vo34 k+p6 zggjpjonal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yei t*8nqxbfk4 492izbsi2p8p g;xf(skars most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Satur9fs4i4i8spq bn2f z;x gpki8k(t*bx2 n, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the sab:wiyvp9 qk0u6- y7 n5rr5eturface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, aqky9 vtb7 rnw i:r0-5uepy56determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for3;xvd- fea0j+o xla 1d the period of the Earth and its distance from the Sun. [Note: Compare your a0f -vxx laodj+ed3;1 answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sateqiffcb:q 4o* 6llite moving in a stable circular orbit about the Earth at a heigo*q4q b:6ifcfht of 3600 km.    $\times 10^3$

  The space shuttle rele qtc ;t0wh b ua4+n4hwt,tf((zkmm: h+ases a satellite into a circular orbit 650 km above the Earth. How fasthkc+4(tb,h(0tuw m f atqm hwz+t;:4n 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 ar 4)) qr8aagd 0jlqf-iopn2xvlfkb +5*e 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 revolutiogpjx *+2lr0l) 5n aokv i)8q qb-ffd4an. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sazrxpq0 .qto3fda8(2z-6t aq9t k po z9tellite to orbit 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 s3 .t rxzat(qfzp-0 q 2odoz9 ak6tp9q8mall 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 launche7zcs3tq6b1:ab xu1 v ud from the top of Mt. Everest to be placed in a circular orbit around the Earth?z buv1s3autbx:cq167   

  During an Apollo lunar landing mission, the command module continued to orb o9wlj ky/p,4tit the Moon at an altitude of about 100ot9/yjp ,k4lw km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orsk; ;vjif 0dbxca8n t o4):ov,y-ig; tbit the planet. The inner radius of the rings is c,tb4) y aixoo 0-v;nfd ;t;gks j:vi873,000 $\mathrm{~km}$ , 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 rotah.+4h4 kfa/an i2w ,v+ gdlowxtes once every 15.5 s (see Fig. 5–9). What is the ratio of a g,4xfo /+hhd4 waikn wl2+v.aperson’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronau xt lx/ :lvu;.h.dkh2kt 4200 km from the center of the Earth's Moon inllh/uk 2.h. kdxt ;:xv a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system con8j;o*-iuwkemv ;:e ijsists of two stars of equal mass. They are observed to be separated by 360 million m i j8vjw*o;;e-e uik:km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator thaob8hq aa1 93meh8q91 a3beao mt moves
(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 thh--wds;k t7c dl j0cit7x2 u0ae ceiling of an elevator. The cord can withstandcwuh0 t7t-l-s0a;7c dk2ijdx a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits 7 nt5o/w-s1 d1vz0tdle r:pz(ta p6hs very near the surface of a planet with period T , the density (mass/volume) of the plan se0v6zh t1ddpla5s7z:wntrt- (o/1p et 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 deafj4e*3nha7 ptermine the period of an apja a hf4n73*ertificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the ne/l yh 86gwp-Sun like the planets. Its period is 410 d. What is its 6eh/pwlyn-8g mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance:dm1p :etxtk/ *6ss ez 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 76k0l4 cebxe (x) years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is )xkb xe(0c4leit 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 Galuq8x-t.wo alx1 ha./qaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 xt9l,e/ k71pkg,lpig a4shn7 for the four largest moons of Jupittnh7kae49,sg1 pl kp7g xl,i/er (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the knobt2x 2 kfrv*;fwn period and distance of the Moon. ; fvf2 k*r2tbx   $\times 10^{24}$

  Determine the mean distance from Jupdkbz,aq4/; x witer for each of Jupiter’s moons, using Kepler’s third law. Use the distadx4b,k; qw/ zance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists o)am(rq(r/ x auf many fragments (which some space scientists think came from a planet that once orbiteqa/ m)u r((arxd 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 "k hyn669r wz38 k-caipplanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the clima3wryk 6ha 8k9n-zpic6te temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc x()2z hdfsp9yfrom a hanging vine (Fig. 5–41). If his arms are capable of exerting 9hsd(yz)fp 2 xa force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gg :7u7uhh u,earavity be half what it is og77 :huuau,h en the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cip uooha ( cb4y9l bu 1afo(3a+xh(e+h8rcle once every 2.5 s. If we assume their arms are each 0.80 m long and their indivi39 bh (uh( +yea(l1o fao h4+oaub8xcpdual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates oncr.1,w ygulg5ez1+z8fz hbq 7je per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraczq g j7b.yg,5r8zu+ f1hlw1eztion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will azqu jtg 0+w0ow:0rc 5p spacecraft traveling directly from the Earth to the Moon experience zero net force because 00o0cquwp:wr5gjzt + the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on ;k;fgjqg :tr d;+-gqkt0p,;uay r 6uea bathroom scale in an elevator, it says your mass is 82 kgtk ,0u;tg6qk yu jpf;g;qre:dg ;-a+ r. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistsdvxj: ,xenm ;nf052at of a circular tube that will rotate about its center (like e; xmn5fn x20ad, vtj: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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertic,z; iffyhfrw- v8a,m8al 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 pl-3gkky8 qx/o3r4am jv anet in terms of its radius r, the acceleration due to gravity at its surface and the gravitati4/yko3 a gxqk -m3v8jronal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve(p f:ag9a*yzirtical by an angle pg 9(fa:aziy*$\theta$ 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 y/ wajo(o3 5ab If the coefficient of static y/oao ab(wj 35friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so f. /5u gzsc -*;ij n.fhmwj14m cv xjjbnj9vz::ast that objects at the equator were vnjj:wjmmbu.1z :v;*c5 cg4 ji/s. nhf9jz-x apparently weightless?    $\times 10^3$s

  Two equal-mass stars9 /e2ank,cju b maintain 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 curvf-3e3g2)lj p nlnl 3que of radius 235 m. A lamp suspendnu-gl3f3e )3lp qln 2jed 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 Eartu 627o4u(i.bh b hfc*ewwrfc9h. 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 the number of g 's a person would experience at the equator of such a planet. Use thb wowehfbu. c2 (c79r ihf4*6ue 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 Telesuw, mq:v vv,uq2v/dw5cope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it couqmv2/:wd ,w ,vuuvq5 vld 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 sjj 3us/p) (m2l-xou ixpeed as it traverses the hill and valley shown in Fig. 5–45. Both the hill)pu3jsoj lu /(i xmx-2 and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sate.4pni;i 2f7rmhsifcmia c-;s :.0 zhxllites 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 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 ffh; 0 -nic s4m7p.h;cii.: 2aszirmx ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroidh1qg;z u zmq2c6u, s*m Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros 6;u, 2zmgqq*czu1m hsat a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing ,)o,l 4tzb1f usv:ndv a satellite in need of repair z ouslvn,v,t1)4bd:f. You are in a circular 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 3000 yea4hy3nhn2 0qj( dcla+vqkv5 eh rso6(9rs. (a) What is its mean distance from the Su+ejl2r hv(dq04 h v5syo396akh(cnn qn?   
(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 rx*)izf .e gy*you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable as)*f.g ryz* xeisumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky r vl8c+nk d0+) t6)lyveduy(cWay Galaxy (Fig. 5-46) at a distance vt+ 8u 6( +0)nkcyeryldvdc )lof 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 squa,b9npv *n jz*nx86qzp vn3.w mre 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth w ,x.q9zjvb3 z*n6vm*pnnpn81.0-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 the Eam;.u ky+wrka k )s7y*/(uplxbrth $ \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 flbnvqp( ukwkbe r/ b4j13:xvg6 30l/by the tip of the 1.5-cm-long sweep second hand on your wrist war q4l/gxp3 jun v(vk /fbw30l kb6e1b:tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a si1vg xu9j/t(;9pgjqvrnker weight around in a circle below you on a 0.25-m piece of fishing line. p (gqx;v9ujr/9 tvjg1The weight makes a complete circle every 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 highway is designed so that ayy* izwnj6k+yh/ s ,/5;mnwuz car traveli//zuywhnsk ; * z5ywn+iy,6jmng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt ofmd- o8j g-m3qnfnd 2v) 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, thus feeling more comfortable. Consider an Acela train that v g mm-f- nnj8qd3d)o2rounds 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.$\approx$    $\times 10^2$