Sometimes people say that water is removed from clothes in a;o,0jqtp(/e yrd ayr 2 spin dryer by centrifugal force throwing the water outward. What is wrong with ter20rd /;pt(,yoq ja yhis statement?

Will the acceleration of a car be the same when the car trsne jb(kc.xey 83 -(rhavels around a sharp curve at a constant 60 km/h as when it travels arsy 8(er- hk(nc3j x.ebound a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly r)( pdg4z pu5yyoad. Where does the car exert the greatest and leazpup)4 yy d5g(st 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-byxbxffi z5n6q +g1(8o+ q- jago-round. Which of these forces provides the centripetal acceleration of the child? xi-gx+ z6fy qojb8fnq+5(1ba

A bucket of water can bez0n3ooyz 4uov b*5x 1q whirled in a vertical circle without the water spilling out, even at the t zquvzo0y*54b n3o 1xoop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There a2*6a 6qz;n/-cclglepf1die o re at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prodnlqo1czeg 26*;cfa - il/dp 6euce?

A child on a sled comes flying over the crest of a small hill, as shown in Fiyjct4 j;l gv 1;k4pz4eg. 5–31. His sled does not leavevpc yl41 4; e4zg;jjkt 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 hill. Explain this decrease using Newton’s second law.

Why do bicycle riders fqy+ /r *dfb1ni*dv2lw7; qlolean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you co ur1spo;k)yew:.65fxzoj2v + xn6 phimpute the banking angle given its speed and radius of tshpv.6+ xw xjpy;5k :inur1) 6e2zofohe turn?

A girl is whirling a ball on a string around her head in a horizonmcbm.e9i5h/ i tal 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 she let go of th e5mc9i h/bim.e string?

Does an apple exert a gravitational force on the Earth? If so, how large a f0 hk3fyaun)( ;um+a qzg;xw) porce? Consider3pk+)g0u zaufnm(wx y h );aq; an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’5jt6d4vnt ; n3fkvwnr / zt qjw36p)f)s orbit fvtqjnt63) dnw4tv 63;/ wk5f pj)rznbe different?

Which pulls harder gravitation 0ww g8kmplk-7ally, the Earth on the Moon, or the Moon on the Earth? Which accelerates mk 87p -g0wkwlmore?

The Sun's gravitational pull on the Earth is muchv0c-).oiq.ki okrn7uy*4 nsz 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 Earth to thkn* s4o7io0kz iy.. rquv)- nce other.]

Will an object weigh more at the equator or at the pole )y6l)j 6yr piiica :t2 p0/3pjzjte/us? What two effects are at work? Do they oppose eacpu2t3 j:jz6ayl0i ii/pte)y rc/6 pj)h other?

The gravitational force on the Moon dueiq1xl pvqk, /-+i-tswxk. dm5 to the Earth is only about half the force on the Mo+xmwv /dq-1s. l5kqkp i-,tx ion due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sm 3b;paeeoa;kr jm e9, b4pwy89aller than the centrbkb waj 8e9,mpo pa3;9y 4ree;ipetal acceleration of the Earth?

Would it require less speed to0pmx*5 dlmq 31 6 )gjf2rvrundzo98ix launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directiop 1zfg)il9jrx xm0* 6d58r3 qdnv2mo un.

When will your apparent weight be the greatest9xif3/ul3 oy)kwz ay6a wu 2*d, 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 upwdiw a yw2z6*au 3yf)/ol kux39ard 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 incnfl7u 6g ilvlq+je 6v l//9,t outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the a6 tg n/luel9q vljl+ 6i/,fc7vstronauts 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 weightl2dk1 rifx)xn/ejb9hp7 yv4w *essness” between steps.2 fx4nx9kjr) d/vih17 yeb wp*

The Earth moves faster in its orbit around the Sun in January/ynr. 6 u(ysbs than in July. Is the Earth closer to the Sun is /synrb(u y.6n January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known untb8m i c4zry6l(il it was discovered to have a moon. Explain how this discoverlmic( 684rby zy enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet thkzvu7r4pl x;x)2k d 7we Moon's7vkkx uz;w 7)rdx2lp4 is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 c o*n jxq3a7x7$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 /u rd):ebx; 6cc1 xaczorbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume thataxcx zbu6c:rc);d e/1 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 dgx uqw)vg9 ; 4b4mvw0biscus as it rotates uniformly in a horizonta)mu;bb40q9 w 4ggvvwxl circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is cbfe wyho3hn/p;,8e.h ,lp4din orbit 400 km from the Earth's surface, and circles the Earth a, .bpdn8h 3wlofeye4hp, ;h c/bout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accele) c; 0xcagou0fp-;bjui wi:.rration of a speck of clay on the edge of a potter’s wheel turnr)pibo;xgu0ucc.jw;0a f-: i ing at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strinndn1p,4 -a(4:um v lsrfbq t0hx5q kp/g is revolved at a uniform rate in a vertical circle of run/,dprpq5k l-bt xf nv40:h sm14a q(adius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with whined, l /(z+n8beip0flch a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction betweenn,bflp(z+de 0li /ne8 tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fr/f up5h :1s;nddyxu 507b e j/oftph-biction be between the tires and the road if a car is to round a level curve of radius 8u7 :oh j 0dxpp5/bdfh1yu/t-fn5s ;eb 5 m at a speed of 95km/h ?   

  A device for training astronauts and 0f e: sq7m37qbkr- zac q((uwhjet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the forke-qaq3u7b7fz m( (hswr0 : qcce 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 rwcy1-0fw0x 3wm *fe a+hx 2ivymo);t eotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction betwee y v1a0ftimx3+f0w-x)ww;y m2ceh eo*n the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down a*b u7lk:xq5kk s()n r:.2f1 smpvc shat the top of a circlb2 *7k5s:usak.sk x 1p: ( vmfhqcn)rle
(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 (including5k)czv i: ts m4 o*/ yt(zj6u9oshua:u the driver) crosses the rounded top of a hill (cj s):so uak4z6 ti:hyz(u9 /tov5m*uradius =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 woufjq u- vb6ji 8*4ytdmaomg6-/ ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weigfob t /g6imv -yaqj d8j*6u-m4htless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertvrmtz( 6v9siu6+yen;u- dh0mp 4z(noical circle of radius 1.10 m. At the lowest point of its moti-nt rumey (uzm;hn9(6vpi4so +6 dvz0 on 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 6;7z hhdd:u bwcentrifuge rotate if a particle 9.00 cm from the axis of rotation is dzw h76;hu:dbto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peop1- t 1g.3ufmushwir ij /0*y8vhg;vhqle are rotated in a cylindrically walled "room." (See Fig. 5-35.) sg0vh- 1vh iwj1 m8;q*3 /rftuyuh.gi
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 rotatedcxo (qlz)bin0eh0 ya-)mumw 449zog7 in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected (omgx0w-9)lcq 0 i)b nyehz o74zaum4to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the bal ruhp.twh/vcrryaa) 0 ur8; 21u6/ yhsl which revolves on a string 0.600 m long. In particular, find theycvrsauur;phu/ ar1/t6w 8.0hh y2 r ) 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 ih v7o03/av:cs-q :q f fu4bg cy//iioperfectly 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 massesr ejp+.9ntny1+)tjb-:iv ttz $ 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 di g)p t7o+ekhcntal 3/-ving 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 tangen41r amtxq7ri t:kn,8 ftial and centripetal components of the net force exerted on the car (by the ground) in Examplt mi1xa8tnr4 qk7,fr: e 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 uniformlhvhw5ldqb4lg5 6,sxk +yx nfjkbms8 48 7i/m8y 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 coeff8745gnf8h6s b4mx,b+ ydwihk/ qs vl xmk5j8 licient 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 horizontrr+lo 4oeq g1)--fw a o (m9rdm(byp/lal circle of radius 2.90 m . At a particular instqfb--oer r o4+mgom1r)/wpad(yl 9 l(ant, 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 onj0ade;o)4p q5o(-xeh,sx vcm a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if it xo edcx4pjh 5 ),0aqv(e-mos;s mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerauni5* nwqg .e-tion g has a magnitudewiun -e .qn*g5 of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Mo*s boe r3fn;w2on's radius is 1.74wsb3f2*or n ;e $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a ra-9;u c/ obe:utuzxrk4dius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfacu-9rtb/e cokx; 4z:uue?   

  A hypothetical planet has a mass 1.66 times that of Earth, but t , rqv.9cf35d fgb/ewphe same radius. What is g w rf,p/.fgc3d v9b5qe near its surface?   

  Two objects attract each other gravitatii+j45 wdxms 4vonally 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 , theb,z yf0bvc 5 ) 70d j8qy-j5miyk)mckp acceleration of gravity, at (a) 3200 mkp,87yq0iz fj db c 0v5k)cmymyj5b -)    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pointyyfr n0ca( gw:w6gr- , outside the Earth where thegravitational acceleration due to the Earth iswagry:cn6( fywgr -0, $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed km nq9:-6 ojxdinto a sphere about 10 km in radius. Estimate the surface gravity on this mo:- n6qkmx9d jonster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like ou6,6ddb ta8a frr Sun but is now in the last stage of its evolution, is the size of our Moon bu6f,br t8aa6 ddt has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fe pcr6hla9 a0qclu(y 63d-k8hpel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince themd639lr(h lpqak8-pua cy6 hc0 and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side t d0 vsx14ry/l(t5noh0.60 m. Calculate the magnitude and direction of the total4v5 x10l h(otnyrt/ds 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 ond w rz97uw4)ooqk-3x hbi5w7j the same side of the Sun. Calculate the total force on the Earth dueo94wuw)orhkx -5i7 w3b7jz d q to Venus, Jupiter, 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 ,k5b abknb t8 nvu4-g-gravity at the surface of Mars is 0.38 of what it is on Earth, aunn5k 4 , kbg8v--abbtnd that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of*wc jg+i l+d8z9w3hqr)evr7z* ef7kd the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare yh jvr* rcd7gkl3e9 qw*d+fz)i7z e+8w our answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbd cti ov3*1dp;.ba/qlx6 7lkyit about the Earth at b76 dp;. kyaxlo3* ivtd1/ql ca height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite z yl kyh4,/(w,o*xfksinto a circular orbit 650 km above the Earth. How fast ,hky*4( wo fszlyk x/,must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical sp h/7z9: xqh tci/:8paz/btywy. k:vqraceship rotate if occupants are to experience sz/ /:.t/ tb97zpykhxyw qc:vi8a qhr:imulated 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, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “nd 1j +m1tzpm mzii9hb2.1vc,sear-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which zhv 1d9j+c.mi1btm s p2,1 izmis 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 have to be launched from th 1/zn4bc*qzhbw w8ij1e top of Mt. Everest to be placed in a 1 bj14/b wwzcqh8zi n*circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued j kkbe/1)yp0d7 rl21rufe3qd to orbit the Moon at an altitude of about 100 km. How long did it take to7pfdlq 1 d)k/bek3r1yr e0ju2 go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pq/c n*ugp.(s11 hduo;ucrt 5alanet. The inner radius of the rings is 73,s(apc1o r gtcdu1nq;u*/ .hu5000 $\mathrm{~km}$ , 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 rmf:w:- x 3)isx8nmq zin diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s app zx:i: xm3sr)wq-n8fmarent 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 astronaut 4200 km k2*/9 f jlel8i8ir ajjfrom the center of the Earth's Moon in a space vehicle (a) moving at constant velocia/8ijeil8r9 j*k2lf j ty,     ----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 systerx 02nr1j+5nosufe- zl,z *xgm consists of two stars of equal mass. They are observed to be separated by 360 million km andeuzr+gj r 501s xzx nn*lfo2-, take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevato3mtkb0o h,amhnj9 / mg8vs2z+r that move z9k /mgjv0nmats8m,ho2b3+hs
(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 y fg/40rwz sg4*js:9it) piiuan elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimumyp4riu fw9*i:sijz4/ st gg)0 acceleration (magnitude and direction)? a =   

Show that if a satelloloy.4 eol,3z+ pv :zgite orbits very near the surface of a planet with period T , the density (mass/volume) of the g3le oopl :+4yzzv.,o 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 perio y++2+j ddt2g+ddfeagws9wl*d of an artificial satellite orbiting very near the Eartdd9lgyfws++a* deg+j 2 twd2+h’s surface.    s

  The asteroid Icarus, though only a few hundred 8a6j (vkan; pameters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from tpnv; 6jaa8k a(he Sun?    $\times 10^{11}$

  Neptune is an average *lf35rrlpxp l bs(1go l6mf( 3fr)ll2distance 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 onc+y;-s.j1e1 olbaeuw me 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.] .e uoewj -;a1mys l+1b    $\times 10^6$

  Our Sun rotates about the centi n9hv 1oc+1,dh-z fh :z;mrqjer 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 b zxd uzrv:.2i)c-/wh largest moons of Jupiter (those d2w)z-x/cizrv b:.hd u iscovered 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 Earty1ozh xjk;4lx 6xd8s(hw h(*udk5fi, h from the known period and distance of the Moon. u 18dx sfd(6yozkx,l; xhh4h (*5 wkij   $\times 10^{24}$

  Determine the mean distance from Jupiter for eac upf 1 +7j11n4 dcxg,ncoyb(wzh of Jupiter’s moons, using Kepler’s third law. Use the distance of Io apc4w(cd yn1z+b 71 ng xuf,oj1nd the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter cont5 t iteseo;44jn++ybx ab h8:sists of many fragments (which some space scientists think came from a planet that once orbited the Sun but +:aebtj t y 5+ exh;484nibostwas destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plba p1spw8qr vd8-49zccenyp) .- kw. tanet" 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). Imagi1 wpna-4.k -ct8c)sw8deqy r9pbv.pz ne that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc frnw(wn7):-.bc1h bvssuhw v )b om a hanging vine (Fig. 5–41). If his arms are capable of exe: vn whs)b)hbw7uwc b-.sv1n(rting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be halhd5zx/p ikx 8cr4)5zm f what it is on the)k5/zhc4x5 zipdm 8 rx surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handn-l gi uni s0kj96yg;:s and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and then0-kyuiljn g 6;s :9igir individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once pe4rgm lcv ;f:b 5u7i6-n 9saknor day, the apparent acceleration of gravity at the equator is slightly l:-4cfsbvi uam;k r6 nl5on97gess than 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 Earth will a spacecraft traveling directly fromw;q,a t3k(e nj43e ji*nk q. j,ozc)si the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and ok e,je o*nan;qq3 ).k ci3tjwj4i ,zs(pposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you sdl3 mozdayzz6,a2 r-t /qj44ptand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the o/4y rta42 z-z amdplq6j3dz,acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube th5sz 5tji /gmyeq(gf 98v b9w7hat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotatzw 9t q 9gem7/5gif8yvsbjh( 5ion 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 i(iwegefldbe7 o; 3,9 loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accetbfjza -u5.4dleration due to gravity at its surface and the gravitationbt4-u.5 jd azfal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve2-ktz x yr 1vl9oa.e/irtical by an anglekv9- loezr1t/x i2y.a $\theta$ 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 banon7/n6 xplbyd8e ,,vrc1;hk dked for a design speed of If the coefficient of static friction is 0.boh 1/n;dvl kx6,de8n7pyr ,c30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at t1py 4hmjhihj8t+.- sg he equator were apparen+h -phghjm1 . st8iyj4tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constanbwy97+l6yrw rj18jqxp zep5 : t 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 cow4u9 .u j97tkbl mbyb ;u-oz8onstant speed rounds a curve of radius 235 m. A lamp suspended from the ceilb-o87kt j.b;z lw99yuou4buming swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive az+xe+gl8p jd-6t v j9qs 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 such a planet. Use the edlvxqjjt- ++p9g z 86following 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 Hubblispz)kk, w1u7 e Space 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 lig k wps7,ikuz1)ht 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* 4dvpk qo58xz speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radiuq8pv5oxd*4kz s 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 System (GPS) utilizes a grourw1f7:e*xaho 4l e5sop 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 even:e hw o7xsfe4ral*15oly 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 Rekrdc 14* ma3*ia*ome8 aoirr6 ndezvous (NEAR), after traveling 2.1 billion km, is meant to orbit thmko ** 1r8ecima4a *i63aorrd e 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 ;t.onyfgb4uc p p2 s3cb3af-9pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth)yc4uno39bgp3tp;.ba2f -fs c, 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 its me95djf4x, rtg*oe e7fwan distance from the,dt9woegfx7 fej45* r 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 /dqowf*g 5 c(j G would need to be if you could actually "feel" yourself gravitationally attracted to someodc f5/gw( qjo*ne near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the M(bnn86ivltfi* r8 l *vilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cent(l nv ir**ibv8n8l 6tfer $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sjpkyd)h;))c kide. Find the magnitude and direction of the gravitational force on a fifth 1jyp )d)kc ;)kh.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 cfu 8(nl gw277qzwyis/g *(xp 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 sweep0 6rj/glku+sa second hand on your g/u a0rk+sl6jwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a s k xpm0a/pface5v.6cvgy4(v +inker weight around in a circle below /a+4v cg(56p0. ame cfvkpxvyyou on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway/ nsvw*wm00l;fnb*8skvr45jm7a jr0 0rd uy l is designed so that a car travel7ljk 0 bfluwm58/mnr v0;rjvd wyn0 *rs4as0*ing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed a/n*: yn+*ki f-vl,3l x bowuntrain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal fn b-x l3f:nwnvi/ l* oay+*u,korce. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$