Sometimes people say that water is removektd3g6-k 6dn kd from clothes in a spin dryer by centrifugal force throwing the wad6tn6 g-kkk3 dter outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels arounl c -psy g(v8cwds+o:*kzms67d a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? E8g7s 6c vws*opzm(k s-yc+l:dxplain.

Suppose a car moves at constant speed along au ,y, e,me.zq)k12bqqu; d v/bnfp;g; guxn 2k hilly road. Where does the car exert the greatest and least forces on the y; kd, 12qpkb );ug,bu/2.mne xqe ;ngqz vfu,road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merg0f xb99nm( xvry-go-round. Which of these forces provides the centripetal acceleration m0b( 9 xvgxfn9of the child?

A bucket of water can be whirled in a vertical circle without the water spillh82n. g9gqz 1ndmjotk6+ dy* uing out, even at the top of the circle when the bucket is upsd z+h 2k y9not. jg1umndg68q*ide down. Explain.

How many “accelerators” do you have in your car? There are at least 4 bvg1zv)ha+ uto + -fiym;2hbthree controls in the car which can be used to cause the car to accelerg+b1+;a4yhoi vbhz) -2t uf mvate. What are they? What accelerations do they produce?

A child on a sled comes flying over ;4* cdlx zomy,the crest of a small hill, as shown in Fig. 5–31. His sled does not leave tocd* y;z m4l,xhe ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundi 3u/uf+6vu.0i ict :lvvh2seing a curve at high speed?

Why do airplanes bank when they turn? How would you co65hooew9;4*z plkowb mpute the banking angle given its spee wp54*wol bo96;o kezhd and radius of the turn?

A girl is whirling a ball on a string arounm f+i-yiq j3 8k;k9dhxd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball+i d; jiym- hk9fxq8k3 will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a1hrlr + k2c2wg force?k+rg lc2wh 12r Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways )/hd;sun h gcoj09g3gwould the Moon’s orbit be diffe;dj 9 ohhs/g0ncg)g3u rent?

Which pulls harder gravitationally, the Earth ( ue alkabfs d,i)8/3bon the Moon, or the Moon on the Earth? Which acceleratela3abd ,kfib )ue8 s(/s more?

The Sun's gravitational0 :0e4qs.emwmvrzsw 4 wl+q/d pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [/w0 s+wl 4s q4r:0wmmede vz.qHint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more atnj-j2)g5qdn z ysgo8+b(bp7 w the equator or at the poles? What two effects are at work? Do t( p)qnj ys-nbz7j ogd w+2bg85hey oppose each other?

The gravitational force on the Mv5bk;3-o;sz cbfzb q y )m :m)2nxn khv;cc2;noon due to the Earth is only about half the force x)nszf;zbc mm ;c22qn k;v bobny h;):5-ck3v on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accelgr) m; q0h2arh -dte0xeration of Mars in its orbit around the Sun larger or smallexrr)0 mh2 0ah;qt de-gr than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towk6*8h46 :k ;y bnuisnjqyw,f oard the east or (b) toward the west? Consider the Earth’s rotation hyf *kb6nnw:6,y 4k8 ou;qjisdirection.

When will your apparent weight be the greatest, as measured by a scale in bx*/me;v x)rd)n k2d ea moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as we *)xvdm nr/ x2kb)de;hen you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space p4-h6 -toxt iz(8bv4:rf:fzxs *vwms could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astront -4v-ftsbfzo:hx(r im*6 s8 zx:4pvwauts 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 fm0zm xja +u+r8all” or “apparent weightlessness” between ste+zr0j 8u mm+axps.

The Earth moves faster in its orbit around pofc24u/tjb q/p *l s4the 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 plabqo*p/jfusp2l t44c / ne of its orbit.]

The mass of Pluto was not known until it 6yoce.d7a *ff ) 9bdmqf7sf0mwas discovered to have a moon. Explain how this discover. m0 d7fqsc9fo)y6*bmd7fefa y enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is md jjt ad*-+r6guch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difd 6 tjdr+-gj*aference 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 traveling7tsof 5ey ix1 uo3n7f5 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 th56k knidn9a( fe Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this forcknnda9 5(k 6ife 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-kg d tk4nejnrd 9h/ ;8ky2/zcyo6f iscus as it rotates uniformly in a horizontal circle (at arm’s length) of ry8zyeod6;cnr2f /hk4jt kn9/ adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, andr, 3d2l8ixwcr a 2iqm( circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shut2 xr 2dwiac8,il 3(qrmtle 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 acceltzyc5os3y /w6pr2 bd 9i 4q-sneration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel2w-yry bo i sc54p/69ndqs z3t’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifohrzma* 7*jd tba/f,;n rm rate in a vertical circle of radius 72.0 cm , as shown in Fi *jh7 ntzdfba*rm/;,a g. 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 can round a.amr q :2yngud3r;no ; 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 car?rq3a dn;my :.2n gou;r   

  How large must the coefficient of static friction be betweens ow2 q7o8,bzj the tires and the ro,wq j z8so2b7oad if 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 3 ixf q4 m2tx2x+chwv7designed to rotate a trainee in a horizonw4x32xtqc+hx 2ivf m7tal 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 axis of a rotatb9q;o ocik w+2ing turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36ibkoc9w 2+ oq; rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mush:amf3k22, -hthl 8c1pq odlh t a roller coaster be traveling when upside down at the top of a c-chq2lao1p tmh 2hfkh3d:l , 8ircle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses thr m y5ra2qut+8e rounded top of a hill (radius =9ru+a2q8rt ym 55$ \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 Fs;eny8c x1;fm71pz wierris wheel need to make for the passengers to feel “weightless” at then ezc;wym7x8 1psi 1;f topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ra ev1e6ndyj64o dius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buck6ye 1od6nv 4jeet 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 particlefb .5 224cq )eog/ zkhjgqain0 9.00 cm from the axis of rotation is to experience an acceleration of )0 4. 2oqhgg5ie kjqbzac2/fn 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically iptomn,)/ )ziug 6f2 dd6a u7 ohdn;)xwalled "room." (See Fig. 5-35.) o dzgd662ihnmx))ptu d7,u oa)/fn;i
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 ) ist3 fb(:l+ef5u7cb1 q z gl1avt rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as show5bl: 1fqtb f1a l(tzvueg3c 7+n 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, b7-zj+ ph9xptf0:jincy not ignoring the weight of the ball wh -txj:0pn+hi 9zfc7 jpich 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 of 88 m is perfectly banked for a car txscb2ksxk bd;nd,t /ra3*3kw31i*ul ;l-l karaveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses )bib+k*t8hukx75m 1an)qdv g $ 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 evasivv6rcwb nxqnd;hrt/( (o;tyj +d /--rle 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 centripetal components of the nu2q 02zz mqh3yet force exerted on the car (by the ghz2m 0 3q2yzuqround) 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 acce 9+z u5tcdv0rmlerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slippim 5crv +9zdt0ung or skidding? $\approx$   

  A particle revolves in a horbiwt2 ;d3 xi +ge;xd-oizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05;w iigto2;d-e+x3x db $\mathrm{~m} / \mathrm{s}^{2}$ , 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 i; gm0n1e*e2 yux5jfqEarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kgeng12m 5ei0j x ;fuqy*.   

  At the surface of a certain planet, the gravitational acceleratio/ lkq2n373w; lj7lfnfd9 +ng zsvzn+xn g has a magnitude ofl7 +2qn+3l jng7wk;fzds nz/x3 nvf9l 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 :5krncc.noww+w :8jad ry8u;9 *c a lbto gravity on the Moon. The Moon's radius is 1.74a .+n:u8r5jo:wcr aw;dcc byk wnl*8 9 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiu3 fl)d,6w r uj1u3gbafs 1.5 times that of Earth, but has the same mass. What is the acceleration due to 3,g rdwlf31 uf6a) jubgravity near its surface?   

  A hypothetical planet hbe r8fxy4e 8+ras a mass 1.66 times that of Earth, but the same radius. What is g near its sure+ryx4 8e8br fface?   

  Two objects attract each other gravitatnj *8p:wpo4 0v flx,kxionally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valued(tdkl- m tezz43cqv;0r/le 9 of g , the acceleration of gravity, at (a) 3200 m d /e z0-;eqml 49ck ztvt(3rld   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ce, ( 7w;tqqacolr7 3lgvnter to a point outside the Earth where thegrav ql w,rg37av7q clo;(titational 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 pacryi i0eu/ p/x7ked into a sphere about 10 km in radius. Estimate the surface gravityr/ xie7 /iypu0 on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average s- bihxq m31tr7tar like our Sun but is now in the last 1bhr-t7q3x m istage of 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 space shzgbt(mys mqw3d- d8s.zvl6 )82fmm,u uttle. Your friends respond that they thought gravity was just a lot weaker uptud(83mw 2dmzs v f)6zq s8l.,ygm bm- 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 *a8vej: xwt/ br08 yzzof side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphw:8 jext/ v0ar*8zbzyere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side rtblf, )0-zr)pxixi:f /br-zof the Sun. Calculate the total force on the Earth due to Venus, Ju:if ),zl- fx0 rx-tr) z/bbirppiter, and Saturn, 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 isdwxf t pj)0mods*+2l d2e* 0yn 0.38 of what it is on Earth,eo0*ljyd2fwd 0n 2tm*ps) +dx and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valochl5kzpmfh v *j m+q65,3 5meue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws,5hqz6o*vfm3hm 55epm,l ckj+ Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circularl)1 4/xqmp/dogflj 3q orbit about the Earth at a height of 364xlqo3p/ f/)q mg1l dj00 km.    $\times 10^3$

  The space shuttle releases a satellite into a co *d8 if3c cz9h2;zgmoircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release oc2i9 o8 hg*om zdfzc3;ccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship ro ) uwh-7d;:;n5q*k i:t9vmxuvqokoshtate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fq7v 5 ;qs okhuuk;xv9nw):d *it:o-mhig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth9 ,u1so,r.l n(av abii in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the ra sn(1a9lr,,o .avi iubdius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellit0ibq7j7cdbgqeo e489d3u dx7 e have to be launched from the top of Mt. Everest to be plac3b79d c8i4x0e g qdboq7dje7ued in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbi(k)1dbyunxs :+ d/gbx t the Moon at an altitude of about 100 km. How lodxbbgd )yks+ n/(x1u: ng did it take to go around the Moon once?    s

  The rings of Saturn are composed d-is2le-0g 6,dom me.9z)axxyxu; : xksui 5rof chunks of ice that orbit the planet. The inner radius of the skd9a:)mr2,oe i -6e.ysxlm uzd xi-gx x;5u 0rings 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–ng f t-sy-rzaas7 356r9). What is the ratio of a person’s appare7sfrnt6ya- a5r -3g zsnt weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astf lu +h6jsv(zs9 nh)29 q+x/vmlah+fsronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant + l vsavuhj+92f fzmx6s()hqs+9h nl/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 star43q j,a(4 +ddq5hg zc1ogyzr ys of equal mass. They are observed to be separated by 360 million km and ta3yq4qd+z(yh j5a,ggz cr4d o 1ke 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg w u yad87ihq:qb)a54yjoman in an elevator that mobu5y7qd:a4)y a ihj8qves
(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 fromiqzdd:th* cqw ,p ,(i+ a cord suspended from the ceiling of an elevator. The cord can withstand a ten p*t,qic,w+zi :dqhd(sion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wit l42*h3 pgwmyrig)i.o5r fq/eh period T , the densi m. rih3p4leoqy2i/f)*rg5 w gty (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,)ooe lu .kp8g76 xqvl Moon (27.4 d) to determine the period of an art)u7oe pl8v6lq. g ok,xificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only at6)qczd/cv: fx.ar-f r5gm*jm 3;la f few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fromaq )t5 f rfzgvrj;d c*f6ml/-3m :a.xc the Sun?    $\times 10^{11}$

  Neptune is an averag5 ek7rr ugo3bp (l6e.ge 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 76g m7rocg))us p(,dw 9e years. It comes very close to the surface of the Sun on its closest appmocrgde7up(), )gs w9roach (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.]    $\times 10^6$

  Our Sun rotates about the center of t * f lkilj0w cl+ro+xu-q;o)m.he 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 fc.t ztc e-yq,;our largest moons of Jupiter (those discovere tyq z.cc-,t;ed 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 distml qb/x*wa:u 1ef-aaeldl,h(i6o iq t:6x 5c-ance of the Moon. f qdqel o: 6(lai w:51ia/x *-behx-cm luta6,   $\times 10^{24}$

  Determine the mean distance from Ju9 /uosyiy 7)scpiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Cosyos7) yci/ 9umpare 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 tf i;nqzvw51y zai0n+f5k8 d,and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was df0q, iy 5d 5ia+zv1w zt8;nnkfestroyed).
(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 artifir3qso(qdva-0 :(m9 xb 6gvd q.c yzyu-cial "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 sa:.6o-0 -y(9vrgdxmy( cq dbus qz3v qame as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc ffv2 ;r+ hamx4ngc yp/d/1 fpq1rom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum sp xprnhv /d4 p;2m1q1c/f+yga feed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gramgya4d/rp zym5 :2 mw0vity be half what i 5ryy 2w mapm4:/0mgdzt is on the surface?    $\times 10^6$

  On an ice rink, two skaters o8o bg*k4mj4kk7q s 7qof 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 andg kk jo*q4s7bqm74k8o their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratio u7*f :jy0-i6c qy3rtyw,rhs cn of gravity at the equator is slightly less th7ywy3 urfqryj,:h 6s- ccit*0an it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Ea 6mtc o);jp0o)4/5ybnp( k4bpwtj bpgrth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Ear g)tp jwn6b4pcm )by/jp5b(o0k; opt4th and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass i ewbi ck;za.)cbf0v; a.uk, (fs 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration ofkk)c w c;uba (0 if.ve;az.,bf the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rot (pv6fb7fy(1lfn w h:qate 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 y6((qwl 7pf1: nbffvh day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verticct*ou*acidl((e 4u) x al 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 itskwl v:i s2 sx :t,2bn))4dlkgr radius r, the acceleration due to gravity at its surface and the gravitational c,ln: x) vdk42t)wg2k br:lsisonstant G.

A plumb bob (a mass m hangjz5sv19 dc8f0s+geu/of *mhj ing on a string) is deflected from the vertical by an ang8z1 jc* /s+0e9hmo fgju5 dsvfle $\theta$ 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 o; 22 y vf+be4l-hnjgc1j8z rraf If the coefficient of static friction is a8zb2j4nhlfv gcy r e+r2-j1;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 rotatin+dfsau bd eqob ::-nqowa1 c)bzi:7 +4g so fast that objects at the equator were apparently weightless? queo :1- dadc:)bw7ionsqa b+4+ fz:b   $\times 10^3$s

  Two equal-mass stars maintain a consta +92ch8fo): ) ihw(vfpvtbkynnt 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 rouir)v75b(w7 hmt8lci/: p xy xknds a curve of radius 235 m. A lamp suspended from the ceilit(p8v ycrk:h 7x 75l/)wimbixng swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tisc)gd 7 xcr9d,xgs h 58xtb9ucw208ismes 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 c 9g9 8sbus)hc,r280gc5d 7wixsxt dx 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 Teles8 j21u/l1u cbp hatcj7cope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which 1b/7uh2 a8jlj tcpu c1no 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 l;p 0j2o-6l9 gzz-qrsfv du/a as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) a -gurd0j2;s9ql-fzo 6z pv/l How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group 9rq q6t* f4u/ kw(ozhvof 24 satellites orbiting the Earth. Using “tria zw/ o(q* tfquv6krh94ngulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEte .6muzbig.4 AR), after traveling 2.1 billion km, is meant to .zeut46bi.gmorbit 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 satellite in 3xl - 6lpcn24.kqabxe need of repair. You arxxca2lp lnb64eq -3 k.e in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period ;7duhi75 ygmi4c0yak1xme;d of 3000 years. (a) What is its mean distance from the Sun?7d5x 1cd;4aiehm g0yuki7y;m   
(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 pwx *ehu)0lgw(l1 9gb, kxp0j of G would need to be if you could actually "feel" yourself gravitationally attracted to someo *xpwu j)wkg g1 llxeb0(ph,09ne near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (s2y83 . n/4qqr*nz zhdawh; tqFig. 5-46) at a distance of about 30,000 light-years from the ce 2hsz.3*zq/wy4a qdnr8 ;n htqnter $ \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 o. 7eb9g 7wa0khfc4 scsquare 0.50 m on each side. Find the masoc 770g ak4 cf.we9hbgnitude 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 Earth6-8:a a khf+qa;nyspr $ \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 j+h2t3 5vi pmd 61vzirpklh 99sweep second hand on yo5ik2hp ip 96+dv1h3 r ltzvjm9ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around ikc7ny lhcp(pru6hs-d/8 p fm:l*1fis6 wb+z- n a circle below you on a 0.25-m piece of fishing line. The weight makes a lcmhuf8c /b*ryh fi7sl -61d- k:swp+n 6zpp(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 : z+w(klmmk (t7fssx4in a new highway is designed so that a car traveling atzmwtsl k(smf4k( +x :7 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 negotir6fqg:*, gjohyvzx(l.8c q w+ q4ku,tating 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. Consideukl,:hq+v gq. (ojcqtyrxzwf6g ,8 4*r 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.$\approx$    $\times 10^2$