Sometimes people say that water is removed from clo 9u,bep q5z+rf)k gud-v*tve glpq3/*thes in a spin dryer by centrifugal force throwing the water outwarzq pqlvb regt9u5g/v*,dpk u-ef)3* + d. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around v.qt; iv9w9k ed+n.ija sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explj i;v +9i9vtn .dew.qkain.

Suppose a car moves at constant spe( wylm: 7(hhp8q8 q.tvrffoa(ed along a hilly road. Where does the car exert the greatest and least forces on the r y(qvfmfpto. h7q88l(: hw(ra oad: (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 act nf s;.oturds023wk( zing on a child riding a horse on a merry-go-round. Which of these fot.f (s0 d;ro3zks unw2rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wanbxzuywgtmb26 e::dq c+c;: .ter spilling out, even at the top of t; d::.:2xewb6ng mutq yzbcc+he circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Theyerba- ,sk-h9re are at least three controls in the car which can b-9ebyk-sa,hr e used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyingm9 vphm7n 4n/hx:+;rndgwg) n over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between ph: rhg9nm74wg)x/; m+vdnnn 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 inwa khv92h7myn2n.6lji+l ts1mc rd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking anglej lc3m1, dqs4qlv(7hx given its speedlm7 sc vj(1x3d,h qlq4 and radius of the turn?

A girl is whirling a ball on a string around her head in a horij epja: 4j w6+eemown :3lbq+8zontal plane. She wants to let go at precisely the right time so that aeqpjmee w6j+83l:: +b4wj on 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 gravitational force o3wy4shk 2c qc;n the Earth? If so, how large a force? Consider an qc43 ch;ywk2 sapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbiy)p i*uey 88d2soyb/x t be diffe8*oypye2 b /di)8xsu yrent?

Which pulls harder gravitationally, the+wu53h:dcyq k Earth on the Moon, or the Moon on the Earth? Which accelerates mor :hu+qdcw53k ye?

The Sun's gravitational pull on the Earth is much larger twmfsv0 f9:h* cx)- .foxip/ruhan 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 th-9f:*) /xw.s0 ohxmcr if puvfe Earth to the other.]

Will an object weigh more at the equator or at the2 o5zky.m7ltk( +xhgw poles? What two effects are at work? Do they oppose each otherkow k+2(y5h .mt 7lzgx?

The gravitational forcju izq8l-1*lobfw xq:*b2r y5/i lok0 e on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pullfjlu l8 5- *1 q/l*byq2io:ikwxz0b roed away from the Earth?

Is the centripetal acceleration of Mars in its;,qrw2 c-7w ;jm8ech* qtcq iq orbit around the Sun larger or smaller than the centripetal accelerq8c iww j;7,e2 qrq;mq* cc-thation of the Earth?

Would it require less speed to launch a satellite (a) toward the ea0,3v3r jbl jdnst or (b) toward the west? Consider the Earvld3j jn,3r0 bth’s rotation direction.

When will your apparent x exaywkavy.31 /ri)-weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? Whenv1yky)r- wi/.xa xae3 would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be ;t3qc.ps(vc x 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 thv c;. qx(st3cpe inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent wdsg) nka73- bceightlessness” between steps.c 3n ga)-dkb7s

The Earth moves faster in its orn+ hfrgf,2fz7t o6m3 9ky*gx sbit around the Sun in January than in July. Is the Earth closer to t o7g3 fz m*kgn f+fxt6syhr29,he Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until itgw 1adblm4 ;-j was discovered to have a moon. Explain how this discoveryjbwa4m1-l; d g enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger t /xt:*rd,t yskhan the Moon's. Yet the * xdtrsk/:ty, 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 $\mathrm{~m} / \mathrm{s}$ . 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 19gnslg:0usto)9 gxss pv 43)l/ 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 t7:0zmjf)gu q its orbit around the Sun, and the :t 0q)7ufzjgmnet force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exertfw .-8gpl (dieed on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculgp(i.8 l fde-wate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, a4 *3qcgg/abepciyl9+ 8ay)w ns gv r+-ryt9z/nd circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle n b8 yg4 gc+pci/*ar y9)wylgrevz/-+t9 a3 qsin its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck dp ;j6 lk,:gonaab1m5of clay on the edge of a potter’s 1g ;ma o ln5djabp6k:,wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at pi6epmyg sb/9oalw)o gq3 843a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp/yi gq l34b9s6mwgea)o3p8 poeed 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 1050x kclu-la3horuz8+e cg/kyr-6 * a;(:xu2w jv-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result in ohcw2 g(z;larr*xk -:6-u kjvcyx/3+ 8uuealdependent of the mass of the car?   

  How large must the coefficient of static friction be betwescqw sxu 40.i4 .z(u2ki 4d1iddfb 3peen the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/hk3. qd.e42sisxd(fi bu4 ducwz 01p4i ?   

  A device for training astronauts and jet fightf iq56ef7bwf .er 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 is 7.85 times her own weight, how fast6b we5qfi.7ff 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 ad z:g4 zvxdvho89h l+1 rotating turntable of variable speed. When the speed of the turntable is slowly increaseh ov+g189d4lzvx: h zdd, 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 23bqoa9) mdi ij;59mvwl m2hfa roller coaster be traveling when upside down at the top of a cir)md haw992i q 2bjvlmm5f;3oicle
(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 roor by 1ltk9xrjj:.+b lo 1m;564thqqgunded top of a l9bo5 j.6b+rxl1m:g4; k1q tqjht or yhill (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 pemkpveij ( i*jn(i(;j-r minute would a 15-m-diameter Ferris wheel need to make for the passengers to feeljni pjm i(;-ij*(k(e v “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ro r9,llb b1p5wadius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 1o,5wl pbr b9lN.
(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 p ilcs hy+c-8rat 0bhxo,-k i:--aw7ku article 9.00 cm from the axis of rotay0h+,ka8woa7uc:----kbl rt ch s xiition is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "ro1qld yyp/ y3bd w;z/hko ysl3 57*pb5oom." (See Fig. 5-35 5lsq l3bd/w/;d7yp bo*1poyyk 3y z5h.)
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(g 5k. 6+)xevkcpybvq circle on a frictionless air-hockey tabletop, and is held in this orbit by a light( )v ykvkqbgepc.+x5 6 cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoringx7zxvni /:q ;c the weight of the ball which revolves on a string 0.:n7x ;xviq/zc 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 perfectly banked for a car traveling 7zfm hw lhuv0n :;pgk0) h.m)f15 $\mathrm{~km} / \mathrm{h}$ , 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 massea in8v+ u5s2* psznx2)4asbcc s $ 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 diving2uxn9vkphu-+u z9 d+a 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 nwpr1 17ftnjc x qhw66+6i*rjmet force exerted on the car (by the ground) in Example 5-8 when its speedrq6 p11h 7w6mrfnjwj t+i *x6c is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates un lp29bn.yj .tyxymn1;iformly 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 tire 2 n .n9tlm;xbyjpy.y1s and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rtnn,q4g8(p 5r;l s xovadius 2.90 m . At a particular instantl r,4nn;8xv5 gp o(sqt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on (;6eqjc psm l.uu06 qza spacecraft 12,800 km (2 Earth radii) above the Earth’s q pl6u. 0cuq; zsj(6mesurface if its mass is 1350 kg.   

  At the surface of a certa9kw 2v(w- pw)w8jifc p a,wmn(in planet, the gravitational acceleration g has a magnitude of 12 m/p,i ja)w wcp fm2vw8 -w9(nwk(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. Tys9-nwfk(g 5todsber.k 7l99 he Moon's radius is 1.74 s 9wl99-r. (fb ky tkoeg5nds7$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planetdsr-ta1 p6 6fv has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravittrdfs-vp61 a6y near its surface?   

  A hypothetical planet has a mass 1.66 timestb b6r 9*nup5z that of Earth, but the same radius. What is g near its surface u9*rptnbz5b 6?   

  Two objects attract each other gravi-.2 nzil0q26ksboyp x tationally 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 gravity, a 9s7yfio:tvf pr8yif*w(xsy z//o;+pt (a) 3200 m +ffpz7fy:(iyow y its/v o9r x;8s*/p   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ef( :l9lseem6 -ydn *nnarth’s center to a point outside the Earth where thegravitational acceleration due to the Earth ys f:nn *nlde(l-9 em6is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tov5t ;cm4tg* bimes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsttbg;4 tc *o5mver.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is3kh 3 9zuy)z htf5zr0g now in the last stage of its evolution, is the size of our Moon but has thtyf g h5 k0u9)zr3zh3ze mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spacidca*)rdt (z 2(di 8zhe 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 surface8ztdadr( cz )2id *hi( in terms of g.   

  Four 9.5-kg spheres are located c rnbem-b6xhkf8d/9*( sy xx27m 2vza at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the totalaemk8 (2by6-ch*d7xbmsv29z x/r fnx gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sii( juddgl 78 ;phs).rd jlk *v(:3iehjde 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.k7ujli*r.:);(hpigdlv d h(ej d j8 3s 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 pup,32uqkzr;cn xo/ .at the surface of Mars is 0.38 of what it is on Earth, and that p /,ucnrku z2.;qpxo 3Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kd/p8;: vi pcixl 9qq7snown value for the period of the Earth and i78;pl i/q9cdspi : vxqts distance 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 moving in a stable circular orbit about t(* r01ip hflectb b2,the Earth at a height of 3600 km. tli0* e(rbptf2b , 1ch   $\times 10^3$

  The space shuttle releases a satel jt cwlu0juzs-k9.yvm,6.v,f lite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release o-lct .jj z v6vwyms0,.9u,fu kccurs?    $\times 10^3$

  At what rate must a cylindrical spac 4hi,dor/q0fweship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is / 40frdqw, iho32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time i d,w9jl2m+cm vuo(6sn t takes for a satellite 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 small compared to the radius of the Earth. Does yourm9uo vm,(d slj+w c26n result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite /qy tiu/:3gkc28 fmsc( /jgvbej (nx:have to be launched from the top of Mt. Everest to be placed in a circular orbit aroke jv(x2fti mn:cgc 3(/ //jgysuq8b:und the Earth?   

  During an Apollo lunar landing mission, the command ukn;wu ;.7c ;.nu zkkpmodule continued to orbit the Moon at an altitude of about 1wk;..k ucnk;;zp uu7n 00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice as pm ho2nb3sw tla 4x08hc,5).ncvc5 that orbit the planet. The inner radius of the rings it4 shlh3c , 2p w50.8va)amnxbcn 5ocss 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9).fo f,w71fkyj-dxdfi; + 6ix wx* 9uy1n What is the raff6wu xx,yxyi k iof1;w+*7nj1 d9 fd-tio of a person’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 +buov*9bl-:n d*wwme astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocinl ude -ob:mb*9wvw+*ty,     ----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 eoqv)fhl 95l7 a,7)) zt g2qx l85q)dpvkrdoahqual mass. They are observed to be separated by 360 million km qdx89 d )zh,a qklt7)q 5)vh5o2for7)p avllgand 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(m;.y)y*ui *lx6)jevun t v gc a 55-kg woman in an elevator that moves nie(lxgym)vt*.u)u; y*v6cj
(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 su;p y.iuy30dfpg g* -fqspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerationfdy0fp-ygp;*i q ug. 3 (magnitude and direction)? a =   

Show that if a satellite orbits very near2 q/)sq +jzrc5,nomib the surface of a planet with period T , the density (c 2 )zm+q rq,nobjs5i/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 ze,+rw3vbf x/ d) to determine the period of an artificial satellite e3f/bx z+r ,vworbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hunrgotey,ua qij;,. 2h 9dred meters across, orbits the Sun like the planets. Its period is 410 d. What is9 giej.uort,h q2,a; y its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of m8zbr thok212ied4c :v6a i-t4.5 $\times 10^{9} \mathrm{~km}$ 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 /qrb f 7wx/ mnsru,-h*once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in,rq/ ubr 7s/mw -f*hxn” 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 9byh l2wo-k o.ipl 7uxf.cn ;2wi)3ey the center 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 distanc/ufr*,;uu mx le for the four largest moons of Jupite rfxu;,um/ul*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 Earth from the known period and distance of the Moon7l +y,1zpv9-j fbkd2rfm gc* o. 27ormy d fzk-fl*vjc1p+b9, g    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moonoq(c0 yjz-k/8- fkygss, using Kepler’s third law. Use the distance of Io and the periods given in Table-(gsy0 -z8/yofjck kq 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 Ju4 2d7vj infz0epiter consists of many fragments (which some space scientists think came from aizevj70 d4nf2 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 arv9+ w6v 0kw3tey4orkz tificial "planet" in the form of a band completely vv ezywt wkor4k906+3 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 by swinging in an arc from a/)eu9v t6:mr ugogug6rnw1-c 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 point of his swing? His mass grru)g-6c vw169tumoen/g: u is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface wim2kgqtq u .u-cdozd)zt4 ;:hn q8rfo 2:b+0j fll the acceleration of gravity be half what it is on the sujoh0b: kztt 2d8d4q2 qumqco uz ;g+rnff -.:)rface?    $\times 10^6$

  On an ice rink, two skaters o lzw8sp(/8c e9pz/d -nw glpy 5*n6gtmf equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms arep- ln 8y c*/z(5mt6/8pgnl9wsw pegzd each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of d62/*jukr db, 3lmsjz i.,jsotr/wh 2gravity at the equator is slightly less than it would be if the Earth did,dsljzjho di/,usw2 r6m2.k3j * tbr/n’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling yj q(r hjt.b,h(,g2ch directly from the Earth to the h,j,( .(rhq chytjb2gMoon experience zero net force because 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 a bathroom scn9f jl +elo1z*0.5skym ,s jzmale in an elevator, it says your mass is 82 oskn5f. zljem s*l91 mjz+,0ykg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cz3d gvstj/vi ;ps+f b n5ft215ircular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed bnd j;zsg 1bs/vfpi23v 55+ftty the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–5d.;olter 7ta +plvc.4odbx *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 planed,c u)nt;o h7tt in terms of its radius r, the acceleration due to gravity at its surface and the gtn,tcu ;doh7 )ravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fro33-ygf ntsv) jm the vertical by an a3)jngs y -f3tvngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If (.7yxozb3hlz4-ohve the coefficient of static friction is 0.30 (wet pavement), at what range of eb(vlh7o3zx -h.4 zoy speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that izc wk:w)so 1*objects at the equatkwzcws: io*)1 or were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparo; gsxo: + 3u9m3ngpast 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 235-:esqlr rrgm.d8(*e o m. A lamp suspended from the ceiling swings out to an angle of 17.q:g.-m do(ee *slrr 8r5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times aschxy *w 1 s3,mm2c/phb massive 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'y3/1*s2wmhhxpb mc ,c t survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubbr9,ri.(ttmzuv nl qf*;)u rsuca1 p ./le Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thisp9 i.mz1(/rvnuacft t*.luur, q;r) s 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 t:41,wo5y 6/lgi m78dbeydbt;dx yfo craverses the hill and valley shown in Fig. 5–45. Both the hoi:4/d xy l t,mwddb7oyb5 c1gey86 f;ill 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 Systemd1sc9 fcq8 *mq (GPS) 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 witdc9q 8*s1c mqfhin 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 ty2 wbu;bhij1cjjv*)6 raveling 2.1 billion km, is meant to orbit the asteroid Eros at a height6bwvyj *i2 u ;c)jjh1b 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 shuy m+j nyhk-tx9t5**cuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (*htyucny xt+k m5*-9j400 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,dwcg cp-lcfr(5 -q(q of 3000 years. (a) What is its mean distance from the Sun? 5cqc (f,qgp w(dr- -cl  
(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 b89 0 x yciplzw6t2w9p rcb57dqe if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonabp5879wqcpz cx96r0dty2b il wle assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gala0i+cf z)fc- n-;; jb s ib6fduakl-rr7xy (Fig. 5-46) at a distance of about 30,000 l)ic7f;b6rb uir -dcn;0f+l-jk sza-fight-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 4sr iivd me7t 0v7w9w9corners of a square 0.50 m on each side. Findiw vem07tw7r4i s99vd 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 square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg or8j 6rym**c9gs s yqwd9bits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the accelerasxt 5y acfj907g 6s*j ,.vq;wi cg.axxtion experienced by the tip of the 1.5-cm-long sweep second hand on your wrist wajxg5 tacxfac9 s6.0jwvs ;. ,iq*7gyx tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a pkigri ;9fond jq5x/x -00 tjbr g4r9*circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]pogrn5fgk*r 9jq/id jxr 0x0t4b9 ;-i    $^{\circ}$

A circular curve of radius R n df*sdl3. p8g in a new highway is designed so that a car traveling at 3gs.pn d*8fdlspeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negot lbt v+ j/yy+ik(ok22kiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accek( kjy2yvboi2 +tl/+kleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger 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.$\approx$    $\times 10^2$