Sometimes people say that water is removed from clothes in a spiw2t 6)tfqhi(p n dryer by centrifugal force throwing the water outward. What is wrong with this)twt(p6qi h f2 statement?

Will the acceleration of a car be the same when the car travels around a shara (y.:e29a,ogkydln je. b34vi:lrltp curve at a constant 60 km/h as when it travels around a gentle curve at the same spee(v 2yakllni .l g yore 3d4::ja,9b.etd? Explain.

Suppose a car moves at constant speed along a hilly road. Where does thmn3+qq)u z7gi 3p/.l/f rpaboe 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 nearqa/gl p7 o+nf3br/ umi.)zq p3 the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go- 5l+ 9thpgncqsq*n0u 4round. Which of these forces provides the centripetal acce05ns *hcu 94 gltqn+pqleration of the child?

A bucket of water can be whirled in a vertical circle without the w5zug*8r3x lbx ater spilling out, even at the top of the circle when th r5* g3zxlub8xe bucket is upside down. Explain.

How many “accelerators”j08 n4kgy7p bo do you have in your car? There are at least three controls in the car wjy7kbogp4n 08 hich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled co ,5j 2t8)2sxyvdhzwu dmes flying 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 his chest and the sled decrease as he goes over the dw22 h8,yvzudj5xt)s hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean in25hmgt,bj nu+0(s r0wx hgan +ward when rounding a curve at high speed?

Why do airplanes bank when they tup,ow;4 m b kkq)2b)qrfrn? How would you compute the banking angle given its speed and rad ), q4b2ro)pw;mf bkkqius of the turn?

A girl is whirling a ball on a string around her head in a horizontalg iyro+y)kg. 7crog-a4pnb* x 6gs c.6 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 b 6 ay k.ogc. ggro6rc)ng7s-py*xi+4should she let go of the string?

Does an apple exert l.n q/ive7fdy5ymm c8v+o v)* a gravitational force on the Earth? If so, how large a force? Considv+7odi)m veq8yf*nl c .5my/ver an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thrba )h18*4wr l1r n6ynn xhq4me Moon’s orbit be differeq*h4rl1yar614 wxh bnnn m8) rnt?

Which pulls harder gravitationally, the Earmc)t-s8. t t:xx)jf uuth on the Moon, or the Moon on the Earthx8.u)x cjmt: ft)s-t u? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Mooih4kugr /u( q3n's. Yet the Moon's is mainly responsible for the tides. Explain. [uq u /hir4(kg3Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects rgsrhm*v 2.x5are at work? Do they oppose eachs .5hmgxv* r2r other?

The gravitational force on the Moon due to thz/mrc*4 9mp obe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Mo9r 4p*mcbz/moon pulled away from the Earth?

Is the centripetal acceleratiovodjt )p)3s 2+xsu qb9ijb**v n.wj q:n of Mars in its orbit around the Sun larger or smaller than vp* :vn.9b3) q uj 2)i s*j+dxqbsojwtthe centripetal acceleration of the Earth?

Would it require lesh2le i5-:ya 7mbkv s:os speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directiok va 52i-yl7s: obh:emn.

When will your apparent weight be the greatecnkqz,po4 +:f8j6.u 0btza xjst, as measured by a scale in a moving elevator: when the elevator (ajpuc8tb6:faj.x 0 nqz kz+o4 ,) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affect xww5hc6u/lvz93 jol )ed by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with thulzx w j) 63vl/wh5o9ce 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 jbdo ydyct5 04h ;7tf8o+ 2bz0u5cdonweightlessness” between steps.o 5yd2nhcz obc0o ujd +8ftt07y d4b;5

The Earth moves faster if( km l5hnf 4d/etf7wp )*y2myn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of lk4y2*)wed5 /7pft f fmnmhy (its orbit.]

The mass of Pluto was not known unti3*iv0.bjclt1q5 xbzr.f o8eole3z +z l it was discovered to have a moon. Explain how this ejeiloz3zq.v50.or*fcb zx b+1l83tdiscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than th l a:bod*zr;m4*m- 1fdmmlm(ae Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull f:*m-4lbr(1dam a; o fd*mmzlmrom 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 +)1 9,tsmbr*t1ogws ae vm jw6 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 orbi6y qvk l8/tygp-dxrm9pr0/: ; olbgl 4t around the Sun, and the net force exerted on the Earth. Wh-vrl0y /l9rb4pq/yx8m o;dkl6:p t ggat 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 exerted on a 2.0-kga0a n.aj w, xftt,vk6z x*z49w discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calctn,*w,x9zwj z64k t a.aav0xfulate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfjawu4yu, ox:bsm q 170ace, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface.moxu0b:wsqajy 71,4 u $\approx$    g

  What is the magnitude of the acceleration of a speck of clay wk8rq ourm r0;9h 93xzon the edge of a potter’s wheel turning at 45 rpm (re30x9 hr ;kur zwmqr98ovolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verd f- oa2)sa ))fngt8lztical circle of radius 72.0 cm , as shown in Fig. 5-33. If its stf)al)fogn 2d)8za - 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 whicg4*zq / 0 wjmp,*ayhdhh a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the/ ,zw4pgja q*m*hy0h d car?   

  How large must the coe155ru i.f zxx7 vtdjc,fficient of static friction be between the tires and the road 5,.1z7iucx dv5t x jrfif a 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 qlkat d47:lw9o 1wl-- hi4tfxto rotate a trainee in a hor4 1ild: qwato9xlh-k- f4 w7tlizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the lb4xunyw hk:h-3 (s7l axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefflks-(bx h7h uy34 nlw:icient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be :vt*t,6*/s ksz+egxk -v uo untraveling when upside down at the:,z-ekk*/ oxvn s+ttus* v6gu 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 (including the driv)96zq uvscn19dy o-cjer) crosses the rounded top of a hill (r9cy cju o9)qvn z6s-d1adius =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 ky i)aih1t19 j15-m-diameter Ferris wheel need to make for the passengers to feel “wjtik1ay )hi19 eightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. h3ug q;9quq g;At the lowest point of ituqggq3u;; qh9 s motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.lutiwnbal 0vk8 /j46uun-c /, 00 cm from the axis of rotation is to experiencevl0/nw/8u,aj- i 6tn lbuc u4k an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricavs/ )y0gsqle 77 4zsoflly walled "room." (See Fis v /s ofq)lgs4ey707zg. 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 frictionless air-hockey ta:;pb2tywsp 8qpsa:p vb.3/k wbletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central holeyba 2:/p pvs8;k spbwt.wq:3p 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 t nws, xy e s*ea7eg6h5b4lj08shis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude osygw5, aeel6b 84x ne7hs* 0sjf $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 ord-*t)c.it)s,rq u ct;7 tcsperfectly 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 masses2r;mxhk h. b 66mfa)aa $ 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 evwx,c1.m 6x f1rye8cvae j4vw 0asive maneuver 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 centripet +/i ip7xegq0xv*iyi* al components of the net force exerted on the car (by the ground) in Example 5-8 when its speed* yxii *ve pqg+ii70/x is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500(qq he /154knkno2 bbpg ez18v accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, whatehnep1kbg8vqo4 n2/(b qz 5k1 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 2.90 m . At a particulabon,b q)x tz-3 ,z3uzyr in qz nutb)x,z3,z3-ob ystant, 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 12,800 x kc.k*v;j ovrzpe;o j8j+/pj0:pk :t km (2 Earth radii) above the Earth’s surface if its mass is 1350ke tp:vo pxj*vo08;jj +pzk/crk.j; : kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnd-f.ugq6 hn j,itude of 12 m gh6,.-qn fudj/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. Thev7 -eqg6jwdgl/; (dkb Moon's radius is 1.74 7-l;q /g j6vgb (dwekd$\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 Ea2yrfa-y/ab.onp n 7a*rth, but has the same mass. What is the acceleration due to gravity neaf/* nan-o2ray. ba7py r its surface?   

  A hypothetical planet has a mass 1.66 times that oflq/;o 82 qspwq Earth, but the same radius. What is g near it q/owp s2qq;l8s surface?   

  Two objects attract each other gravitationally with a oc5 2eqveceo /kq c m6z()bm6,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 37a 2b0jgiosri- g6slvalue of g , the acceleration of gravity, at (a) 3200 m s-0glg2os36 a j7 biri   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where tu*a3 7tbk2coshegravitationsoc2 bkt3 *au7al acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere b(k(t kugy 2r.about 10 km ibryk( kugt2.( n radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is n:xna):,m ud pusyp7 c2ow in the last stage of its evolution, is the size of our Moon butsa:uncp d y2xup7: m), has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whileycnpf1by 8 9+eoh+ vyf.pkyf6/w,l;a kyt5w7 orbiting in the space shuttle. Yopafpy,/v1e.nyf f69yc; kb78ky+tw w5l yh+ our 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 surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sideyj l29s7ub1 3h( hrdex 0.60 m. Calculate the magnitude and directi2y9 d7(h1xrj3bshleu on of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostj .avrzn8:xj, pl2jn , of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sa jjn8,v:,.al2xnjp rzturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 2a1u) zm,7udmbtl +t /vx;wyz of what it is on m2,/dw 1m)7yt;vz aublu+ xtz Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usrqz qj5w 8e nt+3zf2f nl76m,ning the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’szr6fq2qef3 w+tzlm jnn,5 n8 7 laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about th p2r-7hwr2c5xe oas a6e Earth at a height e-r2ops a 2wh5ar 6cx7of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the -f fhnuc)u6) p:/ /qnl2vcczsEarth. How fast must the sc-sznu/:culhfq))6c p 2 f/vnhuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical sph0olu5nz4c:d9seq l0*wf g 8mt,9rrr aceship rotate if occupants are to experience simulated gravity of9 rmr *quctz:,nego0 s0 94h5wrl8lf d 0.60 g? Assume the spaceship’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 satelliteg:.qvlh.8;.bb mb vo y to orbit the Earth in a circular “near-Earth” orbi vl; .bb.ho.m:bygv 8qt. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hav 5l/o(lyxp/ ,i:ym mfse to be launched from the top of Mt. Everest to be placed in a circular orbit around the Eart:fl(xlyp,/ m/ oym5ish?   

  During an Apollo lunar landing mission, the comma m-y10ic-:e mga 7smdqnd module continued to orbit the Moon at an altitude of about 100 km. How long did it csm-m1- yqe7mda i0g: take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planetlk,cbqthb lo,5 r7)xr)b 06mntqrc 5/. The inner radius of the n0)to5bxbl mr5 c ,7htkc qlbq ,6r)/rrings 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.o9skp-g2lxq,nkj )5 5r 5.soygbm tj8 5–9). What is the ratio of a person’s apparent weight to her re5-qkk nols .org,m t8y5pj5 2x9sg)jbal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of t1f)9q(izwsw bhe Earth's Moon in a space vehicle (a) moving at consqw 9f)sb wz1i(tant 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 e -xg2wrvkpw4,qual mass. They are observed to be separated by 360 million km and take 5.7 2xvwgwp-4r,k 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 weigh/fh c *iw6bt7b,z ,gmkt of a 55-kg woman in an elevator that m7b f,t gzb*,6 m/hkciwoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elep ij+)+ rd b+*zw:bgmrvator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What brg:*z d ++i+mjp)rw bwas the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellitelsy2 x u738)qxhdk1tz orbits very near the surface of a planet with period T , the density zh8k us2yxl3) t7q1dx (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 (27.5iga3tvd, h) o:4gq fn4 d) to determine the period of an artificial satfoa :,4igtd3qgn hv)5ellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hu7cft- sqif+q -ndred meters across, orbits the Sun like the planets. Its period is 410 d. What is -qc+s-7tfi fqits mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofs c- woqjs zyh.j2*7ke -3g(xw 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 :iw9ww( )yyhv 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” 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.9yvwh)y w(w :i]    $\times 10^6$

  Our Sun rotates about the cen8 5-te ehbs; d;6lgi orjcps4o)evh-*ter 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, anaj f+8tj q p0tq/427vlgxg in5d mean distance for the four largest moons of Jupj+/4ixltqvn2fj 0p8a5 t7qggiter (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 Ewh/nz+ztk wn;,dvisi,e-hs 5 4 d4e7x arth from the known period and distance of the Moon. 5 eie h;7ns , z/z4vwd,xkh+iw -ntsd4   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiny fd0 pxd dnx ym3x)ju)23-c2vj qu5z*g Kepler’s third law. Use the distance of Io and the period ujp)2-xvnc5f*dyqzy2x dm) 03u3jxds given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragment-onzl*xs+f vsg4,*pkg7) fth s (which some space scientists think came from a planet tsk-+fvggsl*phzt o74n,)xf *hat 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 al4unxp;x4dq1b89,50coq,w igla vliw +x0h i rtificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same +g1wqo 4ua5x ,n0di 0,w lc8l4hixi ;vlxq9b pas 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 hanging vine (Fig. 5–;8 hg2(we: (zb z;zkz/dxl mwj41). 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 is 80 kg, and the vineb(z8:(2hm;j wlgz zkdx;z e w/ is 5.5 m long.   

  How far above the Earth’s surface will thay.4vda-fm;nyhn*k j a(q,1 ye acceleration of gravity be half what it is on the sur,jy1q -;n(a.adykfa4n hymv* face?    $\times 10^6$

  On an ice rink, two skaters of equal -5a rczqvt+ zy*2kif1mass 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 hari1czk*qt- z5 2afryv+d are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratez nmx0ch 2;ma+:a2eko em ,fil*6+cdion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effecti m e2cnheao*cm, +;:l2+k dfm0 xzae6. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Ea gswyh l l+.sb*ijzqk1v-h45 )tkjj a9qcv ,*1rth will a spacecraft traveling directly from the Earth to the Moon expkqji*-svk1j cvzl .+4w9q *gbj1h)t , h5ylsaerience 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 standy -imjxam;ouzoe+7 j,v69bx9 on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration +y;iue6xx7b j9majoovz-9, mof the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abu +6h9;cqngegl+ vkbqob t+zo+h/4 d3 out 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)+4thbq+b n6l9gu+ q;+hgecdz3 o o vk/ 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 loop4c : +,9e ivu63v j(xghynqhbg (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 pa; sngjblxt3lj 6:f:0lanet in terms of its radius r, the acceleration due to g6b;snt l: :l0axjj 3fgravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging ,mi ie9td;t 3xon a string) is deflected from the vertical by an angle9te;3ximt d i, $\theta$ 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 p:0v:mtbbq+hq/ (; u: hrzv8c l ulav0of If the coefficient of stavq(:rlz;u: t/v hv +ahcb0m0 8:lbqup tic 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 nj;7h,bt 725(fvs kuvuxxzm;Earth were rotating so fast that objects at the equator were apparently weighzvt7;,ms ;b nf57uvjux(2khx tless?    $\times 10^3$s

  Two equal-mass stars maintain a / z:ig.:oegyxconstant 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 roundax)abjo z4 do( 0je2 3-u0agixs a curve of radius 235 m. A lamp suspended from the ceiling swings out to an4 aeoajbujxg0 ad2 3o0i)z(-x angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 t4m)4h-r -sc mupwr9uwimes as 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't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of suchh 4msr--pw 9)ur4ucm w 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 pre-pu cd0eom (2nq agkv(o9.)t hsence of an extremely massive co2t da.h n o(kq(ge90mp)o-cuvre in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses t thmh2ht 0-ka+he 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 heavieh+k -2ahtm0htst? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites or-xb 7l) wd3 9 7nwfmwecr+45mdakbn 1ibiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly arounk 1c9fmn5 nbd7lx mibw4e+7) 3rwwa- dd 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), aftes (v:m- iqfpg9 xmxc9 5ex4xl+r traveling 2.1 billion km, is meant to orbitms5gxx9q+x9ivf -x lcp4 (:me the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satelad.r8dp l)t vrn0od)+lite in need of repair. You are in a circular orbit of the same radius as the )da +t.d)lodrrn8vp0satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) froo 9-8 /ae eqkc5un,What is its mean distance fro/8a f,e5en-urcqoo9 km the 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 woud43f, ,uu bn1 w 4ck*aze7iqneld need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lik31f4zd7n eb nwke,uu,c*q i4ae F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center omphp; dny) ,t9f the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000ppd my9;),t hn light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located ankqc oxf.dsd06c+ mw+ q/:,ckt the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at t /c+k ,s:omw6 .fq+n0dd cqcxkhe midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5q.yi -xgfkbe 0km)h +0500 kg orbits 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 experiencep8 ie6q49ec vf tg rot/,k,,shd by the tip of the 1.5-cm-long sweep second hane,kcet ,/6t 8fhqiosv9g p ,4rd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and startzory2 l f)b52t,(lskdx-g . sus27dnz to swing a sinker weight around in a circle below you on a 0.25-m piece of fishis2t2gxu rf,sy s -bzdnld(752ko. lz)ng 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 in a new highway is design5 s9to)kaml,ih:i 5w led so that a car traveling at s5lkam ti) ow ,ihs9:5lpeed $ 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 clb al2g*e1n0.s cpx8*rew2a d8hxi2bars 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 forceair2d* ep2 8xslbh8* g.enabl1xc 20w 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.$\approx$    $\times 10^2$