Sometimes people say that water is r(ai+;nj1- : f ynh62pp u 5lkcvgmsl2eemoved from clothes in a spin dryer by centrifugal force throwinm- 16cv;2u gpsn(+2h:j pnyia 5llefkg the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels /fur2 fm(u2nacr0 glqrnc ;l6s (7wz8 around a sharp curve at a constant 60 km/7 nc s2gn0r(f 6c/uzm a2rfwq( lul8r;h 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 carjid 8/axql9ng,g / v)wmmk3w1zee .z7txp/t6 exert the greatest and least forces on the road: (a) at th/d3 qivgpx/ zwla,zg/jtwkt8e6 . m1)x7 9neme top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-7 )xtp rw(/fvdround. Which of these forces provides the centripetal accelerationw r/x(tfd7p )v of the child?

A bucket of water can bel )n .b-v9ovwf+y/ukf whirled in a vertical circle without the water spilling out, even at the top of the circle when thefu + wob/kfn9v)y.l-v bucket is upside down. Explain.

How many “accelerators” do you have in your cc)s/,um i+gb xar? There are at least three controls in the car which can be used to )xu ms+/b,icg cause 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 shown in(8 13gjoscs2l dp6e gl tnk87w Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal for7dp (31c8gwe lk 6 sjtgsnl8o2ce 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 spefa-4y 3. ; h/ajqwwjbjed?

Why do airplanes bank when they turn? Hop 6qlohhrz3r *z-ol /:w would you compute the banking angle given its speed and radius of th:qo3r phl *ho-/zl6z re turn?

A girl is whirling a ball on a ekjab x /brl6k7/6kl3string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targee6r3/kl7l/ ak jxb 6bkt on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? g5 5so;vizk41qj mn5bIf so, how large a force? Consider amqgnkvb 5145i ;sjz o5n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what waydvg8 44 pch.70;n4esyyt myts s would the Moon’s orbit be ss4yynmg7 .et48pvc0d;y 4 htdifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mo d n0-/qqhk64a nlfxo)on on the Earth? Which /f-naolx4qq6 d)hn 0kaccelerates more?

The Sun's gravitational pull on the Earth is much larger rq y8ob(6wnw 1ds)hx*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 r)1(nh qww*dy8o6 xbs of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What tig2+bph;p 4px wo effects are at work? Do they oppose each o2;hi+ ppgb4px ther?

The gravitational force on thg 3i * g)c* qi+lr2 f;rauip,hho:r:xb-r4fede Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Md i42, fi*fpcohru -*r:eaq)l+gr b:gx3;i hroon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su2eg h :isvoy+w()5nkd/ p9x-6xy9s o)weytjon larger or smaller than theyd5 x:xpvo9h-eo/n 9 i+s(ywk wsog)6 t2)yj e centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towggo(2c3 gpd h5hc ggod pg3(25ard the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as me0r ;)8vmuck pwasured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves 0 uwc krp8)mv;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 could be adversely agk t/xpvs97;-h/r l l/lhsc e2ffected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell te2 x-9gcl/ r s;tp7h/v/kslhlhat rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightleb7ol3qr- c1q.i8zn wu ssness” betweenc w qo3brz81-7 u.qiln steps.

The Earth moves faster in its orbit around thejzk9c1g4d q5(7y pzu r Sun in January than in July. Is the Earth closer to the Sun in January, o rjp(4z79ud51c gq kzyr 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 it was l ey7m2eg2*l)e;30 f wgr dubtdiscovered to have a moon. Explain how this discove;ltbl gyewur7*0e me) 3 22dgfry enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mo7as aurqubw4 1l8qnsc0o /+wug7rr.4on's. Yet the Moon's is mainly responsible for the tides. Explain. [Hb uaur0q48q.1os4 nwlrw /u 7+s7r cagint: 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 jys7.w tt2cq+ 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 centripe 1yb 0qybgf2dus +8j2xtal acceleration of the Earth in its orbit around the Sun,uf xq jdb1y8b2sg+y2 0 and the net 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 tp 1( rah+3aysexerted 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 of the disctpy1 3h+a(arsus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sucbe*q 2l6e sw(rface, and circles the Earth abouqec( 2lesw* b6t once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spi.28:rc bdnt;ji v 2voeck of clay on the edge of a potter’s wheel turni:o 2n. ticibv2;8rjvd ng at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolf,;b9m yxtxz;ved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spm,;fy 9;z btxxeed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a tu 85) /eudaypkvjfoe: ,rn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of tpof :e/5,k)deyvja8 uhe mass of the car?   

  How large must the coefficien6g nebnok-q:- t of static friction be between the tires and the road if agnq- - n:boek6 car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to *rw2n,rep gs:p k 4wz;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 weighz 2rp4s *:;wew,nrg pkt, 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 o)crm*c6wtfdj4 fa,9 g kcwe.abe698z f 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 is reached and the coin slides off. What is the coefficient of static friction between thect d a cgfbw8 4eak6z9rm69j,*ec).wf coin and the turntable?   

  At what minimum speed must a ropmwxgw:o83/ h* )(k nvs ar(kuy(a9zzller coaster be traveling when upside down at the to(ngm/a9w)y8z hkax v3zospk:*r ((uwp of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the d rw0ywgkl 3dl s5n5/f*ub9+oxriver) crosses the rounded top of a h30o *blulg5w5 wd/nfr y+kxs9ill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel neuz,hiwjz k m+32a/w -ged to make for thk,gm2zjhwuw-/ 3ai+z e passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in abavlq9,ub p 6sy g6 tf7z8,t:g vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2l:f zq67ap,,9tu svb8tb g6y g5.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 91 r(- )9bsr/,t eufzm 6mrtrz1ozyov2.00 cm from the axis of rotation is to experience an acceleration or1m/rz st b9-tr(vy)2ezr 1fmz,oou 6 f 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cak u,cy whf(o-duqi)5 xkl69 e9rnival, people are rotated in a cylindrically walled "room." (Siuouk5hw )y qdekc699xl f (-,ee 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 ) is rotated in a circle on a fricti 6nehjn(fdx-1 onless air-hockey tabletop, and is held in this orbit by a light cord connected toj61(e-nfd xh n 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 thi /zojwxyjs0 v1s gw0w31a;a) is time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magni;0wvwws11x j/)ygi3a 0sj a oztude 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 az 8n0r 8hpzcsol-gx ( mz.6gy: 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 masse ycaxs.kz8m 5w- ,fmx+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 m459:xqo wie wuaneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and umfcmjgo.bl 2 2w0/)acentripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speedob macwug/.l) 20j m2f is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit areakzp7t-umj1sf d,cn;/ , going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radi/zf p1u-m;7tdn k,js cal acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.9t p8pu/ ltr46o0 m . At a particular instpu /o46l8rt tpant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,80(2ai0(z)xd)ip m0 yo tgslq,n0 km (2 Earth radii) above tq y2)g(x)mil00 psio(ad, tzn he Earth’s surface if its mass is 1350 kg.   

  At the surface of a certainj .r9i oam+;il;wgzm5.scze: planet, the gravitational acceleration g has a magnituwja;mo;+ :.leg5zi.z9rc m side 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 Mnoz6a b)vo vu -s9v83noon. The Moon's radius is 1.74 u3v9-z ) oon6n svbva8$\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 that of Enze6dg1p. ,fn i* u(dgarth, but has the same mass. What is the acceleration due to gravityi6nfnzpg.d*u g, d e1( near its surface?   

  A hypothetical planet has a mass 1.66 times pc fbg1d 46jx9that of Earth, but the same radius. What is g near ijbxp 9d16g c4fts surface?   

  Two objects attract each other gravitationally with a fkne t34 dqt/i,orce 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 , th:ctz1bjfmpc( k.o):fx ;rpy1a5rt r1 e acceleration of gravity, at (a) 3200 m mf(f1ryr at1.z:c)5c;rb:jk px1 top   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eavx hl j)hu8c(9rth’s center to a point outside the Earth where thv98h ujcx h)l(egravitational 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 p16nl kna)77/ rw u52gbtwdbzz acked into a sphere about 10 km in radius. Ez1 kwb6tdglnzr/5)n2 ua7w b7stimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averageknu 5ou -ojo xs3l6d82 star like our Sun but is now in the last stage o jn-od 5los u28ux6o3kf its evolution, is the size of our Moon but has the 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 8t5aj;e5j6hbo 0 loevj 0lew0space shuttle. Your friends respond that they thought gravity o5v hje60ebt w j805le0ljoa;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 located at the corners of a /q7s22hk6 irkm4x lxe square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other threeslxki 4h r2e2qx7/km 6.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on t.2a x2titz7 cthe 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. 5- tt22 act.izx738). 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 acceleratio ss0*9c0ujp zg:1i isnn of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mar0n zj s0 1*ig9icsp:sus’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of t09to x (+q,n4hje1vvle gne/yhe Earth and its distance from the Sun. [Note: Compare youl,n0e jveny hvtoeq4g/x+19(r answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a s 4uky:l-gl ;retable circular orbit about the E4;lryu:-l ekg arth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circz7iqj p6i mh.2ular orbit 650 km above the Earth. Hjzi. 6mi qp27how fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occti:u8 dqo:; fvt g-fxaf5+v f3upants are to experience simulated gravity of 0.60 g? Assume the spacequ 5;vf:gfto- f+8fv d txi:a3ship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circu7jv+q5h f+heklar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to hj7v qk+ 5+fhethe radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the to) :+ks2;zy y tzparri2p of Mt. Everest to be placed in a circular orbi)rtkrypai 2 s;z+ :2zyt around the Earth?   

  During an Apollo lunar landing mission, the command modultzgnkuu1 rhq(o 7 8j-.3knm+ne continued to orbit the Moon at an altitude of about 100 kmn18- k(+ r jh7umqu go3kz.nnt. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.-ag udgv lpte+1vv4u(b1pt;0 The inner radius of the rings; vpe tpb14t v-(ugvdau0g +1l 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 once every 15.5 s (see Fig. 5–9). 7;e3np01 ;o8ejtmni rl*hvtvWhat is the ratio of a person’s apparent weight to her real weight (a) at th;o*tet7mvlj; h0vpnri3e81 n e top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg1etuabm p8) bo +mm*-p astronaut 4200 km from the center of the Earth's Moon+m- m8poat*ubb )epm1 in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mas (y.nwmdar); *rd d+ 7v-hpyhus. They are observed to be separated by 360 milliyd r*uhh+7a;)vd.(d pwm n-ryon 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 - scl6jn-) 3nrbr,hu;j.bm ga read for the weight of a 55-kg woman in an elevator that rnsb-l3j,-m.b ac6 j)rngh ;umoves
(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 pm dsv2vo1o /fi4 0hf,zkv)a3a cord suspended 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 minim df12p k,fvv3i)/om vah s4z0oum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planetq.t606v8 k7riwwfn (h 3cb jqp with period T , the density (mass/volume) of the planet t0hvq6bpnc (kw7ijq 8r3.f6wis $\rho=m / V=3 \pi / G T^{2}$ .
(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 perixhm7 17 b,c65ujvau *cqbc (mhod of a76 jh5c uxb ccuha1qb*,7vmm( n artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a f c/ g6;r 98p dz.ewhgby76omfkew hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mkh eg7/ y.wmpzf6drobc9 g;68ean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan*-d-k m free bh:c4rm- /hinh1 60wmxkce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It vl1iaqg m) cn:t9tliog1 gut1k5;-r 0comes 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 distance s in Kepler’s third law is half the sum of ttu:li 5tqg9l;vg1c 1orak -i1 g t0)mnhe nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gala b zes .qq.10do.bum/qxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 ys;lp 8t,z.im mean distance for the four largest moons of Jupiter (those discovei zlpsmyt8;,.red 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 t 7(+kcy nkgw.xpu3q: mhe known period and distance of the Moon. cqwyg+ (k73:n.kmpxu    $\times 10^{24}$

  Determine the mean distance from Jupiter for w 5izcnz67:ky each of Jupiter’s moons, using Kepler’s third law. Use the dis5ck zn6iwz 7y:tance 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 bec*7uqfod mxx(d(l(xo5x l )/dtween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that(dux5( ox (*dd)/qm 7lxlxocf 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 desck+q7); esv) q/wgydw qribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). Th)yw vgdqw; sk)+qq7/e e 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 crosh z55.-lul ztfs a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N -u5fhl5t .lzzon 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 acceleo ubmmu86ln)y yiz0qd98(e/exk . .ugration of gravity be half what it is on the surface9e8.u6e.i q8yl/0dyu( m ob kg)u xzmn?    $\times 10^6$

  On an ice rink, two skator ( hbmicm:j i,zz4d,zd-n d0j* r72cers of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are thezi* (rjhoz, cn cd4m7drdbi-2m:0 z,j y pulling on one another?    $\times 10^2$

  Because the Earth rol) f:r8*f, avvmwc5a ktates once 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 fractio5r* l:avmw )k,vcff8 an of g is this?    $\times 10^{-1}$

  At what distance from j4h0lgl0 e :uun+uy nvq i1/e* fngy4.the Earth will a spacecraft traveling directly from the Earth to the Moon experiencenl e*1n eu0u+:q.iy0hfgnu ljgy/ v 44 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 scale in an elevarn pl+u6-:j ottor, it says po 6rlj-u:+t nyour mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thawv,49stzm-to omh 0os7lz*zz:ch 0h-t 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 c zlo mh0 zm0z,s-o9zt4t:*ohvs-w h 7be 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 aircra(s(jg 7z 4cqrjlp,n 1mft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelerip y3m))a;wtpation due to gravity at its surface and the gravitationalw); t3iy )ppma constant G.

A plumb bob (a mass m hanging on a string) is defl92hf6h2ft d ewected from the vertical by an anhf2dh 2et9 6fwgle $\theta$ 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- 5blfvt: qd0 bfaob-o89o0xcknq scm k)/26 n for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a )l0 fdb-s2 ocatbqx0 omf:b98n o/vk6nc -k5qcar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obn56q+2 akst gojects at the equatonoq 6 st+52gkar were apparently weightless?    $\times 10^3$s

  Two equal-mass stars f)c9ebw1vdh y b:rab3u.3c6, ,u yow kmaintain 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 aq/0v 6yv6ghs a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swingqa h6vsy60/v gs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as ma unbg970da x(essive as the Earth. Thus, it has been claimed thxe(a9u0 7 gndbat a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for 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 Telescope6jq9bb d-xp wt)h m.d08lfhu; deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which umlwxhbpb -0 )tdq.j89 fh 6;dno light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trav -pkes 3gtbkn0yg7 m:1erses 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? Lig g tk3b0gk7:y ns-mp1ehtest? 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 24x01 sl,kdyz4 u*yv jpl4( dqe, satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determinep, yeky q,sj*dvzl (4duxl041d 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 (NEARa k:fxlei,r ) w+gd g;g. jroy(wa(*e1), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rougao; ( r,igk*jlxw+ge:d1 w. ) fyger(ahly 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 /gfr e; khis4)pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.skgrhi f); e4/
(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 years. (a) What is its meang p/o0xk9z bm ,o(s,kiizj5 :b distance from thembk0zjx : io/ k,5z sobp,gi(9 Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could avbqj scm5jvn qk /856.ctually "feel" yourself j /qkqv5n8vb6.j cm5s gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the : -r 4qgfj ;o7yg8;njx8doqfjcenter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from fr 78 j8xj;q:jg4ygfo;-nqd o 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 ji-/(hk.bwp) vil-6 mb*)f 8 +yui fputen( vion each side. Find themj i(u b) eivpfuhif8t)*y/- w+ni-lp6k.v b( 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 orbits : ;v zlzv3sxa,the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-ldno0 qs/)vtar hr ;i- 0,x9qjzong sweep second hand on your wri 9/)z 0,atr;dn -qrxhvqoj s0ist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wess,as xs2kl6/q,i;;c*u zfqcv v3 gm .ight around in a circle below you on a 0.25-m piece of fishing line. The weikvqg/zs;,u;v6as *sf cx, lq3.c2 simght 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 a cara*2fxizgzz ;,*o m/hz traveling atm,zg *za xi/ozf*;2hz speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatinn6,sh b+-(bknl.qfcuc0zb7hvv (+(m g sq1rag curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide theh0((sq+zbn6akv v-+mub(.c rh bq fg,71nlc s centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger 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.$\approx$    $\times 10^2$