Sometimes people say that water is remove)/ae . yyp5 qr c+ix*ou7e1niwd from clothes in a spin dryer by centrifugal force throwing the water outward. What is wro naeoy e7yi w+.rc15)ipu/*xqng with this statement?

Will the acceleration of a car be the same when +0g fw.n fi3if(wcve, the car travels around a sharp curve at a constant 60 km/h fcf,.f3g wei0+ i(wvnas when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly roadnli* l/rg2bwf3v).q p. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottomgriv w2. b3* fqpln/)l of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round4xx/ qoi5c5egm)g t k4t+7mso . Wht57gs +mmig tq)o/45x xoe kc4ich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water lxle7-9k;o9 ggs5wv9 iz,hvo spilling out, even at the l o vxv,k-95h9ig7ewl;osg9ztop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you o ;fotpptm5 esca/wi,l3-m)8have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? i3)8 cp5ot,of ;wp- emal/tmsWhat accelerations do they produce?

A child on a sled comes flying over the c83:ff7j grh mcrest 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 between83hrj7:m f cgf 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 hight)h s( 4 n,z (yzirwig7rhev., speed?

Why do airplanes bank whene sy+wwi2f it+-d1f. p they turn? How would you compute the banking angle given its speed and radius oi. wds-e+ twy2i+fp f1f the turn?

A girl is whirling a ball on a string around her head in a3 24qnpiw z50g*oquupd 8mbn . 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 q8 opz d0bi3m.*u45n2unwgpqshould she let go of the string?

Does an apple exert a . a3uh5sqdnt;gravitational force on the Earth? If so, how large a force? Constd.h5 u;sa n3qider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dtespgiwn9 -9- ouble what it is, in what ways would the Moon’s orbit be differ-g 9wtp-e9i nsent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E/sr+d nw6 vj(u ih4c8marth? Wh +hci8d muj4( /nr6wsvich accelerates more?

The Sun's gravitational pu2fgb u9.)k mxall on the Earth is much larger than the Moon's. Yet the29ab fk x.)mug 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.]

Will an object weigh m1xqa*qte zy n /ov +i)mw9k u:kbz*52hn5lu e)ore at the equator or at the poles? What two effects are at work? Do t1 u n)2+me9w*v)ukz/i5kqn*xzo5q et h :ybal hey oppose each other?

The gravitational force on the Moon due to the Earth is only about h) 5m0xfynmtf0 alf the force on the Moon dxn00ft)5fy m mue to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acc,7(2bk j/p0zaw9wyz g/pw 0 n(itvihseleration of Mars in its orbit around the Sun larger or smaller than the centripetal a thavi0w20k( bwwgiszj7zy,(p9/pn / cceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or ppc81h2k+f ya af3*yy(b) toward the west? Consider the Earth’s rotat2 fcfy*+8k3ya a p1pyhion direction.

When will your apparent weight be the greatest, as measuredqnt3mjj(q qelz2 8; n7 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 nm ;zqnq7q3(l2jtje 8constant 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 j/m)/ ul,lxcsx xk78z rfv32m(vx5tobe adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objjm )5x s //k8(covvzl2rx xfu,l7tm3 xects 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 weight sip4pyru6e;m; rx (x94(nigz lessness” betwee z4( 6pgrspimy;;uir ( nex94xn steps.

The Earth moves faster in its orbit around the Sun in Jje /4q)hvg8xcon +:bzanuary than in July. Is th8qz hcgx: +vjnob 4e)/e Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not know:a2cbwt,1.ls q y5sixw0picf ;alc 80n until it was discovered to have a moon. Explain x5aqf10t 20cayp :,biw l8w cssci l;.how this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eawtvaw06b4uarz)rr0- i w 0uoqe/;a3drth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hin06 0dq-ab ru 0/o;ew4auzt3v)wwa irrt: 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 e s31o:mf ,y-7qkpcuz2zx bc* 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 the Earth in its orbit around the S/sj;xj 9hyjd.r4f f.gun, 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 d 9; jjh gxfj.ry/4f.sradius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a ,f5vj,s(ymdm7vw 9 fioihnvyb6(23w 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the spwifs fmy6w5 7v 2((n ,ojimyd39b ,vhveed of the discus.   

  Suppose the space shuttleb1;b8ci s0rk r is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express yr1r 0s;bbk8ciour 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 of cla s8or2l )azaz6e )bo;zy on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamete)ose6a 8bl2o r)z;zazr is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circle (yqqf; w8gywx1id 6v+ of radius8d +6qqvwwxi f(yg;1y 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 speed with which a 1050-kg car cp6 icjaa /h//rmy )t6man round a turn of radius 77 m on a flat road if6)api6 mamtyjhr // /c the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of stat 9mo2s4v*r62bsbp(kcyvrx /hic friction be between the tires and the road (9oy2rb*hs46 /m rvck x p2sbvif a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training asf4ok: 3i eene9tronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trak ien:e9fe34oinee 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+pn,y wa .y,2n gnkhb+ 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 reacwp bn.,ag hk2,yn+y n+hed 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 travelingpiqp:zn24 x7 z9 nac2cjkh/9 o qx52fv when upside down at theh9x2zvf7qi25 n2 4 j:onzp /acpkcq9x top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg ka td:k2uh+d 1(including the driver) crosses the rounded top of a hill (radius2td ku :k1dah+ =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 wheelkgnda3. s,boyv-o 4 7r need to make for the passengers to feel “weightless” at the t b rg7,os.oy4kdv- 3naopmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.j 1wyf ;)f)a-ok jlp4q10 m. At the loweaj jk;) )pyqwo-l14f fst point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rof:4h521jv3fodp:dy.e zt x bktate if a particle 9.00 cm from the axis of rotation is ttjx 4y 1:f 5v .zkbop2fedh3d:o experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically w23(v7k vwak;+bxq sgwalled "room." (See Fig. 5-35.)s( 3kb ;w +vag2vqwk7x
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 frictionless aq(*cq1 / 0gid eogd+okir-hockey tabletop, and is held in this orbit by a light cord connected to io(0 qco 1d qe+*d/kgga 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 ignoring thkbkt(+l6v pez;eo68 m e weight of the ball ;k+e6 (l tpbz8m6okevwhich revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius ogq132j 3lwi/atdxy+p 9 o3fjgf 88 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 masserm ttccy3)87j 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 :er 4zmti6: igdiving 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 t t h;ib*itx 69vxt2kke6yu2o8he net force exerted on the car (by the grounvit9* yik;6 e68xx2tkt bho2ud) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from nwm*frp07j z,the pit area, going from rest to 320km/h in am* ,7j0prnwzf semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a hovi m( 63fxe2vmj s g((2qlis 2wddh3a;rizontal circle of radius 2.90 m . At a particular instant, q2dj2(v(ism3 imw3( h;ex gavd l62s fits 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 12,800 km (2 E miz6 90z lcz.rrwb+r8arth radii) above thw rl9i.zc+ rbz 8rmz60e Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitahw kp 4d;o5om*tional acceleration g has a magnitud*; mk d4hwoo5pe 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 tsi+() jqt: umdo gravity on the Moon. The Moon's radius is 1.74itq ) ms:+dj(u $\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 Earth, but has the samv+v db g(wyjhxc1m1ba2 u .smm,b4 03ve mass. What is the accele3sgbm h v,vjmam1uy10.cb4v2dw+b (xration due to gravity near its surface?   

  A hypothetical planet h 3 wnhy;wc87gqae4 reai.i.8has a mass 1.66 times that of Earth, but the same radius. What hwee38i7rhigy 84 aq..an w c;is g near its surface?   

  Two objects attract each other gravitationally with a forc2/h pk-pc jow17oy3 fpe 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, at (a) 3m6s su8(-8ki z9 h3, b:bl 7aktoqunxa200 m 6zatskox,(hs i nub78aum8l-b9:3kq    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the El4,nb0 , vhygj1j 1sqmarth’s center to a point outside the Earth where thegravitational acceleration due to the Eart0m,yg ljs1qh jn v,1b4h 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 ib 9-u ql+px4b nbmp4ma*6u. fdnto a sphere about 10 km in radius. Estimatx q9ua446.bp nf*dmb ml+-pbue the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sta)owycn;ct +;r m. ,rdzv1tf9tr like our Sun but is now in the last stage of its evolution, is the size of our Moon bd)mfttc; ;9+.nzov1,rr y tcw ut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlgo+g/kdn e4/q (ci zy+t28c nwess while orbiting in the space shuttle. Your friends respond that they thou ei+q2n dz4g/t( ccg8k/now +yght 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 located at the corners of a square of side 4 qm4pb8s(f uk0.60 m. Calculate the magnitude and direction of the total gravitational force m 4pkqubsf(48exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years m o+rfkfi6v:x; ni*f 1eost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The ef *n 6rfxii1k;ov f:+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 accelerau -t daes mhhw4;;od**tion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine;w;-hhds4toa* *u emd the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period / 14ttcwja5hojvg2d( of the Earth and its distance from the Sun. [Note: Compare your answer to tc 4oj2jwgtad1vh t5( /hat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circul o-pba93btdmlb:6j )lar orbit about the Earth at a height of 3600 j t9 m6lobldb 3:a-b)pkm.    $\times 10^3$

  The space shuttle releases a satellite in- roiwv4-/1 hbtokxgj 04-bntto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Eab t o/-r-ixng1tj v40hobk4-wrth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupant1) fdhejd .9i robq4tz8498 f3toennt s are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as th94 t 838.qtjbd9 n)1 e4hoffreozndite time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes forj*13 zbkby3mc6zv8b j 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 Eb1jjym6*zkb3c 3 z8b varth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocityq3ozqq(p r c(o 9w .:j3whoa/h would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around poq:o oh h3qq 9caw.((w/j3rz the Earth?   

  During an Apollo lunar landing mission, the evbd(x.lsd 2+bef m):command module continued to orbit the Moo.+ dv) xb:(s ebel2mdfn at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of h) h:a1e/seue chunks of ice that orbit the planet. The inner radius of the rinae :h/e) h1seugs 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. 5–7 8adpnft;uo. 9). What is the ratio of a person’s apparent weight to her real weight (a) .d7aop;u8 ntf at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astron) 1vrxbhhx0.x aut 4200 km from the center of the Earth's Moon vb0hx 1x.rx h)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 st)g5idol3(n -tgn cu3 qars of equal mass. They are observed to be se-cinqdg o5)gt un33l( parated by 360 million 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 read9/3 nv0 7tonxuetsy wg*6 7kihbtq3 .k for the weight of a 55-kg woman in an elevator that movek.t t*nh/tw0 eqs g3xi37b9oy76u nvks
(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 fi5bjnu4r3qz( aoa06hrom 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 acceleration (magnitude and (h5 z0abi j36qrua4 nodirection)? a =   

Show that if a satellite orbits very near the surface of a plaor *;uwr6az l0net with period T ,r* ;z uarw6l0o the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the per;j ,n)q;zyhxuiod of an artificial sate;y )u q,zhnj;xllite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundrerag*3py *f(b7e29n kr4wzo d gd meters across, orbits the Sun like the planets. Its peri 9rk f*4(yb wgzgp7noad2e*3rod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag49xbbloyxo 75m+ly21g zu bk 0e distance 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 comes very closee mjd5.37kpf/pf,g n eg4yjn6 to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the p m/nng 5, fj4e63f7.j pydgkeSun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about5em7rwqy t;bpa zwm1 h+8i ;:d 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 distance for the four largest ;*iuxscs 2 ,6jk 7ivaimoons of Jupiter (thosei7 u*2sv ki6ixsca;,j 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 Moon.bar*j wtvpupw,0s24:w( *ayi j ia:wwwb*p 2tup,(r 4yv0a*s   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupittww -wj,mn. r;w-l,n ker’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table,t.-lm nwrkw-w n ,w;j.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter cte .uxus izttp54tt1cy-ii k r+*d684onsists of many fragments (which some6zu5+t. tu1 tixet psr8y44i-* itc kd space scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the foq4.4qdgctr7 old2s7u rm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates qut47 7ol42cgq d dq.usrickly 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 hanging vine (Fis.ca ql 7eod g0ikt2p1 zkx282g. 5–41). If his arms a0sg.epc8ta dx7 zlk ok22i q12re 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 is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface sdth/ 11fx1l j(qxgs 5will the acceleration of gravity be half what it is s1 l(xfh11xs /qdgj t5on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab fvat6orkmg9 -lbdsts 5jp u; +cl/7*+hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and the+lp;co /tlmkbgu 9+5 s 67frt-*v sjadir 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 6nqzg8b .jpyrf+5fd3 of gravity at the equator is slightly less than it would be if the Earth didn’g5zdqnp63.by + rfj8ft 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 travelingq 32 x510j;+no xrxpdna bqh1q directly from the Earth to the Moon experien 5xo2q b3xdhnx01q;+n p a1jqrce zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,n;4rpkcz-r2p but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which di4c-np 2r rp;zkrection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate iynu3r53 dt*g about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal*n 33 utdgy5ri 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. 5da4,. 6 d 30ri0kzhw,gvnqu fh–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 ofwfm03 ki-kho4 a planet in terms of its radius r, the acceleration due to gravity at its surface 3o 0kiwfm -kh4and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertic4sb q09-t7cll-n xzjeal by an ang7ztcl 9eqx04b--j s lnle $\theta$ 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 roi:6jz3/t euy)a vpq j+4uh) If the coefficient of statiy3hzea iv4j:6/ur j)) u+q optc friction 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 ,p0 uq-n,iqxhrotating so fast that objects at the equator were apparentlyxquq pih,-0,n weightless?    $\times 10^3$s

  Two equal-mass stars maint s+t9 q3lkk-spain 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 curven 1;xy;bq c+nw of radius 235 m. A lamp suspended from the ceiling swings oxn;cnq1by+; w ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus,; mzpogz7f )fius(:bc0-zvo) it has been claimed that a person would be crushed by the f;zfps 7(czg-uom) vofibz ):0orce 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 Telescope deduced the presence of an e .s0cpf qo.4kgy42fk lxtremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiti .gkyo. ffcps 440lkq2ng 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 676wmptqma4v v-zryk 0ke)p pvxl- -:traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b)lekvp667xmv-p -q0z mv-: ar y4p w)tk 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 (GP4wtg j29bfuc,ot(1b qS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are disbju 9t tg cbq,w4(1o2ftributed 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 Rend-l.vndtth:geme w6 0yt(qk0+ezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40en(ye.0-gqmd6l :0tvht+tw k $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 a satellite in uadj )y89ehi *9n1ya06jq qy uneed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the E8)d9 y ja96uqeyj iquyn1ah*0 arth), 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 y6c r4ao+tb:l2d5uwm bears. (a) What is its mean distance from the Surlbu4+b6dwc: a2 5otmn?   
(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 actually "feel" y* ksfegb;h h1(t1h xzsj,a.y/ourself gravitationally attracted to x jbykh.ezgha*f;,s (hs1t1 /someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal rd9.dqbk 0f+zk5bzzfulw7 aq *2 *7fwaxy (Fig. 5-46) at a distance of about 30,000 light-y f*9w. 5zlb ukd27rz7kb*aq f0w q+zfdears 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 sq,mx4z (kg lof7uare 0.50 m on each side. Find kglmx7z ,o4 (fthe 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 the Earth 9bubc6 s* bl6kgbq-4m hml 9(m$ \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-long sb,*b pko -8sgkhaq9 y+e9 kw;hweep second h8 a +w9-h9 koqb,kpybsg *h;ekand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker ;sk;a*zj : oxcweight around in a circle below you on a :a;j*zosk;cx 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.]    $^{\circ}$

A circular curve of radius R inkk 93sfk 4mlq,nz)y-g a new highway is designed so that a car travelin3smzkl kfkny- 94,q)gg 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 tiladao53a )xru8fho 3b /t of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, 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.rah3a x85/bdf )o3u oa $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$