Sometimes people say that water is removed from clothej-+p;qk 4nadxs in a spin dryer by centrifugal forceaxn-qj+d4k ; p throwing the water outward. What is wrong with this statement?

Will the acceleration of tr0 0p71xy lnt6 9swz8msf)r1x(aagj a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle c0lpa ajyg wxt17szm9s1nr60(xrtf) 8 urve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exelguiq;l24 +su) xmz9p 9 2)gu4lxq+mui psz ;lrt 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 bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-royxs1s3i pq6b1e) p 6yhund. Which of these forces pbs1eix 3)hp61yy p 6qsrovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillink,uqd9nt w) k6g out, even at the top of the c)w 9k,qkdn6 utircle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leatyw6oj /-; szwe/ 6mo( jdhwz(st three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations d jyowzm6zt/(6 hwd/e-w;s ( joo they produce?

A child on a sled comes flying over the crest of a small hi kuov37,09f)u:c8e awmwsotm: es5apll, as shown in Fig. 5–31. His sled does not leave the ground (he does 8asom3:uwt osmvp)a 75e e, k:9cf0wunot 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 rounding a curve at highjqce m(tf8.tp d/5 k.t speed?

Why do airplanes bank when-76yha7eh;d tfv k /mu.3ai5, qmdjdf they turn? How would you compute the banking angle given its speed and rada hma75jut67,q; 3m-/k.dfv iddefyh ius of the turn?

A girl is whirling a ball on a jzm;(f44tqx g string around her head in a 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 should shxjz(mg t;f44qe let go of the string?

Does an apple exert a gravitational force on the Earth? If s fokwn a9/pul :e1t7w io5xh5o8 -hba6o, how large a force? Consider annph/ -69uoo5hk17ta5w8axf ei wb:o l apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would t)v-6o - igm,pq :6o2npscc mjj*hmr5zhe Moon’s orbit be differentm crzv pm,i s66j n*:jpo-5o2cg)hm-q?

Which pulls harder gravitao 1(( rb ofvyfz4dg e.(q6;jzztionally, the Earth on the Moon, or the Moon on the Ea r 1(dfvoz4.(fj g;oeqyzz(6b rth? Which accelerates more?

The Sun's gravitational pukm5kwnv+ j2)i ll on the Earth is much larger than the Moon's. Yet the Mmnw5jik+)v k 2oon'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 more at the equator or at the poles? What two efub.2yhf9 hag)q;1u 9hmm7p vwfects are at work? Do they opp;hyb. hv2 m9gw pu)fh qa71um9ose each other?

The gravitational force on the Moon due to the Earth is only abou2 xuso *lz.w;hmtohw - l3/rw(t half the force on the Moon due to the Suwoxwsu2 .lz(r -wt/;h*h3lm on. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in it jzd4rwf- ymcif32 .2o:ho vq5s orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?hrz5-qomf2jfoy2 :w3.d4v ic

Would it require less speed to launch a satellite (a) towlt: wy+ilf 29s9m8j atard the east or (b) toward the west? Consider the Earth’s rotation 8ljw m+l tas:29t9if ydirection.

When will your apparent weight be ts2wp:(r61dvy *h5 mkvspkn kf w6j))n7gno1d he greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In wv7sn5)w(d : m* g6 korfk wnkvphp2js1 d)yn16hich 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 1z t4, 7-kzorn hvf un.u64xphadversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrixf647o.-kz,r tuzu4n1pvh hn cal shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnessyu e3 zg714vme” between ste ueezv4y7g1 m3ps.

The Earth moves faster in its orbit around the Sun in January thag7h po+6v 8zmi7 l3qnln 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 th 6pzvhin + ql3m7ol7g8e tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until i o8*a tfl)wjq3q 3ze,xm(a9eht was discovered to have a moon. Explain how this discxotfa ,8eemj9()hql z 3wa3q*overy enabled an estimate of Pluto’s mass.

  The Sun's gravitatioz g1t 2c)jkbs t/xyjumc)7f.; nal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Eart7bz )t 1sfj)x/ckcgj 2y.u;mth 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 19800rh yo;v pyqhi8 +(o6f8xe2xw $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aczz)y*fqi/g j;vcg4h+ celeration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on t/i *fh qz+cjv)g4gyz;he 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 ansg qmih h 3ro590x9m7fwrv:( 2.0-kg discus as it rotates uniformly in a horizontal cir(mh37m9vw grr fnhi:o x09 5qscle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and,; k pvyugn*4;cg6phy circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your ans*py 6,hg4v ;ycnpku;gwer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitud1ssrwhcd ec ;-) ;ta9pq j x-))k*vhrze of the acceleration of a speck of clay on the edge of a potter’s wheel turnin;;ecvr) hc kxjas-p z)wq 9h 1)-*tsdrg at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved i 75n18, 1t sdblueeytat a uniform rate in a vertical circle of radius 72.0 cm , as shown in yuttisdble e17,85 n1 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 can round a turn of qhln9p1/ qu)bradius 77 m on a flat road if the coefficient of static fri)nq9hp 1u/b qlction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and thec:lh0ma gl c,x2 hn-leo1 1n;a road1c l ae lxnl2,:oa;-0hnc1mh g 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 pilo lhx03pv cy-5.d.frpa ts is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weigv. yxlpd.5-0rh acf p3ht, 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 rotatingfjop8 67v unvs wb5z3zq/93qd turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 3357fws v zzqnpu6 8v/bdojq936 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at theshems:r:;b-j4c/ykre 3tq v t +pr71 a top of a circle rbq ;1pyh/r+csamte e:str7k:4 - 3vj
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundem nh4i;muo7nm8 68q eamz 9h.xd top of a hill (radius 84nqhn6o.m97 ahiu8x;mzmme =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 nup74mwuq tjv ::sz,615-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmonqw : ps,z7m64u v:jutst point?    rpm

  A bucket of mass 2.00 f ip0artn+2 eq-6 yptwmz9 1g*kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the b*t + 209mgr-pazytnepif6 1w qucket 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 rotatdf8+mlw4jve)3lwku )ze .cqy82h f f:e if a particle 9.00 cm from the axis of rotation is to experience a h.cud zwy+:k )3me)v8f8jlf 2 wfel4qn acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cy-18b. d6 ajvysq0utwu lindrically walled "r1u adqu-8b6 ws tvj0.yoom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-htjkec 00oy 4va)rg7(mockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a caem)v tg74jy(o 00 krcentral 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 thct t koudva:59,y4 ;alis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magku;d a ty9,ol:cv4a5 tnitude 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 cfq nndj634z5agm+k x9 rgj::uhm;vb+ar 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 masses9iytl kls/6 qp;:sgg fqj4/,x $ 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 diving vertically at;n turqy*q*e -tru 9swcui)i3ij9;: o 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 xk* azfhuy02 .*x.2 xfywn(qt net force exerted on the car (by the ground) inz2fq*. 2nx(tyaw *fyx.h0x ku 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 the pit area, goingivy1go/)tz)h 9q0b9 yuxpo.z d b(y3i iq.dg0 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 .y gxibouqzy1/it3qd yoi09 0 d(z h).vb9p)gthe 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 cir71v t*uavq099j*km n)lvgfg rcle of radius 2.90 m . At a particular instant, its an9rga9u 7lq01j*)mv vk v*fg tcceleration 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 s1 u)urw773dn vucy *nkpacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 135wduk*vucn 17ru7yn 3 )0 kg.   

  At the surface of a certain plan jxxwlqm0e5fwke2luc8 9d44 / et, the gravitational acceleration g has a magnitude of 12 m/sk5e l2q40lj x/4mdc9ewu8 wfx$^2$ 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. The Moonowe al20 d-jx6u +jr2.pylv(j's radius is 1.74 v6e+0(oxpu2.jj l y -a2rdjwl$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hxa 6h72;as gy ecjhn..as a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surf;ny .7ah2cea jsx6.g hace?   

  A hypothetical planet has a 8hix 4ykl z1 dcj(,n+lmass 1.66 times that of Earth, but the same radius. What is g near itsd 8c+ix,zy k(hl n1jl4 surface?   

  Two objects attract each other grav l po pb8mcme,:s2pv/ 7yldql-z d/+v0itationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelers)y rzx( a;z( mfxm7)tation of gravity, at (a) 3200 m mt) zsxa)( f;(my rxz7   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eart::64uw)i*binn l 9z 4ofvamjk.ibu +qh where thegravi.u:i j)6 u4nbi*f +94bwmknza:vlq io tational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star uda v, szh*em-iz(0fd 2/l1yzhas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on vfd /m2a( id e,1hzz-syzul0*this monster.    $\times10^12$

  A typical white-dwarf star, wrkgd1poxye odhr.46 * h)t:9t hich once was an average star like our Sun but is now in the last stage of its evo)kog*r1hyt tx .do 4e9pd r6h:lution, 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 weezps pyoq9p;6(k7 o;tightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s e6;s ;tp79py(oq okzp surface in terms of g.   

  Four 9.5-kg spheres are located ak-ra5 o wm6w,gt the corners of a square of side 0.60 m. Calculate the magnitude and direction om w65rwga -k,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 most of the planets line up z1l wd,s1*j zron the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assujz11dl rsw*,z ming 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 Mtud+-iwm:7 iav9wr (xars is 0.38 of what it is on Earth, and -+9(dmvu7i xiwar wt:that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using d wzejxba)17ulx-)3f the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that ofl wde1b7x au-z)3j) xbtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a s/( fbj; rtyw tgcnc;o+*3n h4ttable circular orbit about the Earth at a height(jc3*t4n fw/tn ty;gc +;brho of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the E e(ire(hdg/k*yq1n,z arth. How fast must the shuttle be moving (relihn d/y( gke, *reqz(1ative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate ifp;zr2ju: jm ut(op(1i occupants are to experience simulated gravity of 0.60 g? Apmjo 12z t:(uiu( p;jrssume 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 satellite 6fa: gnfz358z:qr hob)qqxry*j k7g.to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your resgn65fh*x :yabzgjrqq 8r:z 3q7k of).ult depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fcbgi:ee9c-. ) 1 wno b,2zgyjyi du,7grom the top of Mt. u9g ei-)w, 1zc noc7b :jyid yg,.g2beEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuedsu 62brm88h. -+v osjyacs wm9 to orbit the Moon at an altitude of about 100 km. How long did it take to go around tmsos 9cjr-bs 86yua2w+ vm8.hhe Moon once?    s

  The rings of Saturn are composed of chunks of ice th7qsfv lk:28 +dni /nahat orbit the planet. The inner radius of the rings is i8shf/ 7 dkn+:lv2nqa 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.-dxam wwhtw u:ch63 ):0wobl5 5–9). What ) 0wcua6thb d-w :xlow3w5m :his the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astron hh754ke-/cl tr6 ly44qw:ehxzqyy 6j aut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at consta:5j4qk6 76we - 4 ry q4x/zhhtyhlcleynt 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 zyf bdwvd- wg-0n6p)y48yau2v 9pm/ktwo stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbitvn k6-) ddm 0pw-9gyzbap4fv/yu2wy 8 about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scalviliry; ibt2ny1 r f/9h08jkakf1-t9e read for the weight of a 55-kg woman in an elevator that moves 9kv; ry1 kl/ i rjyfhb9i0 8t1f2ia-nt
(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: 4m3;sdby, fmmksjr3 suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and diremdsyb; frm3skm: 4j3 ,ction)? a =   

Show that if a satellite orbits very near the surface of a planet withgjw 60i,,rozn 8m 5ldb period T , the density (mass/volume) gbz oli jrd,60w85,nm 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 period o2eru qf t/-l *dexf8.l1z+dcof an artificial satellite orbiting very z8f.r/ fodc-e ll1* +qdxt2eunear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metersy69cz wlq(lee-u8rl ; across, orbits the Sun like the planets. Its perio9lw8l6; lcuy- e( rqezd is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist ypp80fyz*+e6 lot;f nance 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 orbitshpd-rpy;/ le)0xklq 2a ply 8- the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its c x2-8 qypyh/r ;0plklda)p-l elosest 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.]    $\times 10^6$

  Our Sun rotates abou2 s wzuy0-qy4wt 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 moons + w2whppy4uh:of Jupiter (t2puhw4h:p +y whose 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 Mo2 ji1 jxzjc9l5on. 1l 95jjxjc2iz   $\times 10^{24}$

  Determine the mean distanc13ax3fub 2r ohj/* ow9 lb2vwpe from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabw92/ p ojl u31h3vo*rf2x abbwle 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 fragments (womnee7k,fdx.5a/ q4y hich some space scientists think came from a planet that once or,fo75kee xnm4 a/dy.qbited 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 descge14w p7b v2l4jol hn5ribes an artificial "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 as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity ofojn vl4g4 5wlh17 peb2 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 vine0 2 y x1(og d,2bxcre81iuljz9c-ffmi (Fig. 5–41). If his arms are capable 9 icjr 2e(g -f 0yx,ibf2l1zu ox8dm1cof 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 surfacmq;7 qz,7tbhw e will the acceleration of gravity be half what it is o hq,zwtqbm77 ;n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab ha. lfb4(r e9mzvnds and spin in a mutual circle once every 2.5 s. If we assumeb (rel .f4vm9z their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accel3,y sqto/vcb,paq ngo;z 3y68eration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate thzc3 b,3ypsy goqvto, ;/6aqn8e magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the g3ce2hy o 6+ztwunnk/8w8ea7Earth to the Moon experienc u/c6eywzno 7ek8a2h8 w+tn3 ge 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 wher8m +--itisar(9*sik c)wgrsn 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 direcsm9 wri isr(- g*8)ca+ki st-rtion?     ----待选择----upwartddown 

  A projected space station consistsymtvxc 5e )r8lfk.u3: of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5 :.e8tufv)ly rxkmc3 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 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. o e,q e1pr9l3w5–43).
(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 typ g+tbi ,p jm8fgtw j25g,-)jhe mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant G.w)jp jt -8 tigf+g2,5gpy,jm b

A plumb bob (a mass m hangingqm(ght, y; z;y on a string) is deflected from the vertical by an angyt,g(h qz ;;ymle $\theta$ 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 dr6bye0b t)q qm:3 zv,,qvr bx6esign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c,bqbt0:)qbm36r 6 erqx, v vzyar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obje -m+9-fg0yrx1yqd h ehcts at the equafx9- hyqem1d-0h+ry gtor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a conj9y)k5tpuwuy 1 bvc: lun r;;:stant 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 curve of radycmxg 6l(*y,90lsovdius 235 m. A lamp suspended from the ceiling swings ydl6x9 s,ym( log*0 vcout 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, it huuh n)4mwe; 6p. dn1a6f8wdksas 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 ' k6d)w;.hsf 8wenpu6d uma1n4s 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 Spacoejq)k76m)7k0 oy j-a+phv kzsfq;.j e Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouhesf.v6k+oq m0ayj) j k;7 oq -)j7kzpds 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 spehfc-q,r f g,+ped as it traverses the hill and valley shown in Fig. 5–45gfq h pr-,,cf+. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning S7)8gk uk3vk*wi aiuh7ystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to 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 7kai)i*h u7ku8vkw3 g miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billifrv3+s )nq6kson km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros3 k f6qn)vr+ss 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 si 1 sd*d-po4gz e35k-1fqyktp1bi,k whuttle pursuing a satellite in need of repair. You are in a circular op-b,1k1yf pk o4 1k-gdz3iiqed s5*twrbit 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 of 3000 years. (a) What is itlixvr27ajk- y;bd joo5 *; 9vjs mean distance frxl;oo5 * vj ibja;r2-v9 yk7jdom 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 valuxe cx8;gdv))ff*e4e xe of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lixc)ge*v;ff8x 4d x )eeke F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Waz ;sc o4h e+sgk3uf-,x1l0ovcvf2kk(;s2zxty Galaxy (Fig. 5-46) at a distance;-t szk0+4kzf(;e l ofo3vsgxuxhv ck ,sc122 of about 30,000 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 at the corners of aiws 64 -wmbym3 square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg m4mw3bsi y6 w-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 orbit6v+ *a:w*l8 tiiikij ws the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swv21:rotgqpb+ )8d8o t hqi-wqeep second hand pob1qq 8 t8-+vdrtw:qh)2og ion your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to skk,fvd4zjwz3m 3+.ci ct1 h) rwing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight +1hk3 m4j3v),ckdz zcrwti.f makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tz(whkn c(od ;iz0-,fl raveling at s(zl ni-;( dw,czhk f0opeed $ 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 negotiatingx -;;ih7aruy*um s u9y 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 r-yx*9 u;h7s; m iuuaya 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.$\approx$    $\times 10^2$