Sometimes people say+ rvr8g kejle(,l:k;j azc22a that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong c:vllag+a ;8j,jr2 z( 2eekkrwith this statement?

Will the acceleration o3 o6ujnmwl5z,f a car be the same when the car travels around a sharp curve at a constant 60 km/wo 36u5 j,nzmlh as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does ghx- ty7mdm0m: 4o 8vdthe car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level sytm7m0hgd:d- v 4 8xomtretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a mbmm 6 w1i31cklc*+( sqe6p53zobdocv erry-go-round. Which of 53c6w(cm11*i 6zm3 qb +dpbv sk oleocthese forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillrat-vjd,;i b he .q3 j.aaa0ni0rt80zh y*h ,aing out, even 3ytj hd0aa e0.*.0ai8a v,a,zt- ;hhrnqjibrat the top of the circle when the bucket is upside down. Explain.

How many “accelerators t/g vtli swq/lt3d:o2ax*+b/ ” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerq+d lxltb va/witt2/g 3*os:/ations do they produce?

A child on a sled comes flying over the crest 4,u3h2u83 vr wa4ppxnzrdt. t of a small hill, as shown in Fig. 5–31. His sled does not leave the grou.43 2nup zthpwvu 84a3,tdrrx nd (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 wh ok7y3 v,v pu+t*g oi72ts5nlnzg( /rvhg 1l3ben rounding a curve at high speed?

Why do airplanes bank when they shj:rcx3vzl52z g 0pn ( h0(kyturn? How would you compute the banking angle given its speed and radius of the t3 (00(vzhsy2jzhrgcnl pxk :5urn?

A girl is whirling a balt/ximar)q fe8 r*o4 mj0lgo8:l on a string around her head in a horizontal plane. She wants to let go at precisely the right time te80jl o rr)fqxmag*:4moi/8 so that the ball 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, -e-xrq6fnv (t how large a force? Consider an appq vetfxnr--( 6le
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what i+*pj;joacj ,br(+vd *h*ewvmt is, in what ways would the Moon’s orbit be differenj(m*+cr j,v*we d+ p*o;avjb ht?

Which pulls harder gravitationally, the Earth on the Moon, owhse*(wd u5h 8llfz,1sr- o) pr the Moon on the Earth? Which accelerates more?s su(51*d)ohh rl wef,-lw8zp

The Sun's gravitational pulh svp59mww4f 41v1s 8wtk6no zl on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Exo9m6khn8v w1 t4s1w4vsfw5 pzplain. [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 effects a 0nfbx,cbv+18jywo0 cre at work? Do they opc y+vw1b08,fo0njbx c pose each other?

The gravitational force on the Moon due to the Earth is;nt v+z+hv p.l only about half the force on the Moon due to the Sun. Why isn’t +.vnl;t+pvzh the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larq4: r)f3*rkzf rrsd f7ger or smaller than the centripetal acceleration of the Earz*r:)r3rkf4d sff7 rqth?

Would it require less speed to launch a satelj,)p+gnfmtedbj 9 ez2mbx9 9; lite (a) toward the east or (b) toward the west? Consider the Earth’s rota9)fz29d+p ,jmtg;m nx9eebbj tion direction.

When will your apparent weight be the greatesth8(c:wvw6 ezc, 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 constw w ez8:c6(hcvant 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 xswfrwj+c7hj6+ (,w /rp qt+speriods in 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 astronauts walking on the inside surface (Fig. 5–32). Explain how this simulaf+ w6 j+p7x+ sqt(/wrcswj,hrtes 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 weightles,2b x(dh :qaun0+ qbvrsness” between stepsh(x,qdb u2n+ 0rba:vq.

The Earth moves faster in its orbit around thnf0 vx.j:cql,lrxbqi2 sn 2 (/e Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain.0bx cqv(s ixrjnll2:f 2. ,qn/ [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 no1m)pi.p6hi pkdk;t*o1shq9 ;j+pag-n bgli 6t known until it was discovered to have a moon. Explain how this discovery enabled an estimate of 1p*q.po9jni-is hp 1; ml+akk6phtd i)6gbg; Pluto’s mass.

  The Sun's gravitational pull on theo+m9 c6wo fk9o 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 sidewfo9km c+ 96oo 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 travelingy-q mz es:p4 ,5evor.d 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 acceleratii cem;gz2+vz7on of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assuzme 2c7;igv z+me 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 discus as it rota u4maqhb f)/+yb 9nkb( ga5p/wtes uniformly in a horizontal cir bg/yb)qhp/ua5 wb fn a4m(k+9cle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit (ksn*etkf:0pohua ( 8 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surfacek aun( f8(e*t hskop0:. $\approx$    g

  What is the magnitude of the a 0 nhumjen,ml0 n3ko4f. y6e9acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter i ne.yhl603fe 9nujano0k 4,mms 32 cm?   

  A ball on the end of a string is revolved at a uniform rate i0y +e*g-e6 dp-o*ya hhk 1p)n ufas7spn a vertical circle of radius 72.0 cps sgu h7f-ea0 +dpp6** )ho- yay1nekm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 105scjr pwoi)5a /r l7)kvd5)ul 9wfvp 4/0-kg car can round a turn of radius 77 m on a flat road if the coefficiei r7awrfol)l puc / v/s wp)5)59dj4vknt of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction l*ax jsy-d 27bbe between the tires and the road iya72 x-bldj *sf 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 fight1 elhf9 3xms/ser pilots is designed to rotate a trainee in a hori1e m9hsl s/xf3zontal 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 rotati*-e1ti:lfq6w4 dhz(oyskg5z z:l4a tng 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 slid zk(q:ttwf6hz d g4za ls-y1i*5:l4eoes off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must9k/dr n5cshe4 a roller coaster be traveling when upside down at the top h/cr4sen k9d5of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the tqft ,pr ibg1)*-d:u xrounded top of a hill (p* xdiqt1gt f)b:,u r-radius =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 min0pymry km*/: 0t* zjqdute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightle0m :*rpm0 y/q*ytk zdjss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m.ggfsvq /e2*6yw 2te1c At the lowest point of its motion the tension in the rope support yg6 fv2cws*e/2eqgt1ing the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axkf3d.io 820p1wl ga mxis of rotation is to experience an acceleration of 115,00 i8w2.ld3kx1 ofamgp00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are ro cq7abhb3pd) n)sq5 b1tated in a cylindrically walled "room.pbs3) c)anqbq1d bh75" (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-hoc4;q;t4t /qgfdyg y+ d)r+twpvkey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a ce4+;rdd )yvttw/;q+ tf4g ypqg ntral 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 thisj-x z0bdpo 8d0 time, by not ignoring the weight of the ball which revolves on a string dxdpb -08zjo00.600 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 radiu awcovkea 7aof5q11 f7(o8i5b s of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses oem:urx,)-vzb *qtj9xe) g-/xv k 5xm $ 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 mane*g 5b3sb o-fpduver 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 a5(ziyrek*b9v4fd jmk.q:ug; nd centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when4gr :j q9d;u.(vbfim5yzkke * 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 th5yoc874i(voqk 5 t zpwe 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 wer(tk4 o7zyq55 8pocivwe flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of r9v (lblbii1 0yadius 2.90 m . At a particular instant, ity9bl i0(l 1bivs acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 E+fm0 pqpsi sgo-5d erag( 57.tarth radii) above the Earth’s surface if its mass57r-t(p5g. +o edsqip a 0sfgm is 1350 kg.   

  At the surface of a certainb-rf zn)j1v eh4-a65d aua3wa planet, the gravitational acceleration g has a magnitude of 63ard-az4-febh)uajwa n v 1512 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 Mo t)mtk( gwx-)1iaq(d9r yvu1a on. The Moon's radius is 1.74(g (i)kvqt1xruy a )w a-1d9tm $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hah)vas.x5 *zk,jw f ee-u*ewv07s ,mzt s a radius 1.5 times that of Earth, but has the same mass. What is the acceler)txavk wssv0 w-*z,fh57*z .eme,uejation due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but thejck*fgwh0 3k3 same radius. Wh0 *kkghw jf33cat is g near its surface?   

  Two objects attract each other xa9j++)g+jp u a,c yjmgravitationally 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 d( .irg:d2u0i mql8dh value of g , the acceleration of gravity, at (a) 3200 m:0i2ld.d i udmhg8r (q    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartcj+z t6s;ndlh+ ,kbe rq/xd 9 dkj*q-9h where thegravitationaldshb jjdk-xq +e*t/c,69z+n lq d;kr9 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 o5z +p-ddeq s2fur Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster. 5e2q+spzfdd -   $\times10^12$

  A typical white-dwarf star, which once was an aveal.zc h-h0x4hd(1 zp crage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?( zh h cxlcph1ad.-4z0    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space :on w7o7nbfr pniq-6+shuttle. Your friends respond that they thoughiobpn7 :+qr wo7 f6n-nt gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0k*r1hqgnq n /*y ,4.nz v02su.wpt lkz.60 m. Calculatz1,n y* .2tw*qz/plk0qk r unghv.sn4e the magnitude and direction 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 lwd, z 8re.,qn y68d -jsyjy .qcm3gos:ine up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line 6.sy:doymne- jg, .qj8sqzdwc3,8 ry(Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what +c5p*gq-e q gdit is on Earth, and that Mars’ radius i5+qdcg-*g p qes 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period ofu mzo,myo6kd nksyv::9 -3uj 3 the Earth and itszy- ,::knoo9kydsu6uv m33mj distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in ao-v/-k l,4unc;o xbz b stable circular orbit about the Earth at vuo- 4n/ bxlokb,cz -;a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circulat 7 zwkhu1g*21fz o4oqr orbit 650 km above the Earth. How fast must the shuttle be moving (relativ*2oog uz41zw t71kqfh e to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spacesc(2rw64c/ re vs0)sj9d 2cxi nmw q0uyhip rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and givurxsrevw/42jy d 0mc0qsc6(inw)2c 9 e 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 i+ot jxgyv1 *j)ys3fbqgo 23/yn a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface ofgtqj1) v 2 b 3fgoosyy*/yx+3j the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have ahj4 i4th bzjes-6- *lsx 3-bzto be launched from the top of Mt. Evei6l*b-34z e 4jx-bs-sz hat hjrest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missiontkh1:5jp,3n;x k:jv 8 2 qzcp*yovfs l, the command module continued to orbit the Moon at an altitude of about 100 km. hyv23: o: 8,5*lvzsjn f1kp;pqjk tcxHow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks b 2wsih; 1uq zbp/1tu*of ice that orbit the planet. The inner radius of the rings is 73,000 sqh1zt1*u bb;w upi2/$\mathrm{~km}$ , 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 rot 8x4va(xcl1hiw l* w2fdp9+pxates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to ldc ha2p (vx8w i xp+w9xl*f14her 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 from the center 0m:l ljsr+z e3of the Earth's Moon in a space vehicle (a) moving at co 0lrzs:el+3j mnstant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They ar ajk+1-srcjupu /.9( eode/yx e observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is ta-9pjr.( xk+e u y1eoc /sjd/uhe mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wosrs ykb 8-*a+hman in an elevator that 8h*ay-ssbk+ r moves
(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 f6; /wtkg4h1-q b irzqan elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerationh/1firg- qwz6;qkbt 4 (magnitude and direction)? a =   

Show that if a satellidmo /4v6j:i)v+i 1llw;eesj4 eux0k qte orbits very near the surface of a planet with period T , the dxsw;ek) l/oue4 4jqed+06i:i lv jm v1ensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine7:tj/fkko l(js9k9r g the period of rtk (k /fjo7:skl9 j9gan artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbiti*b;jlyh l r+5s the Sun like the planets. Its period +y5lb;h*jilris 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of .j-yow)3: mfds3c 5tswz vp6m 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 eveh-c-+hb /f d3 4jwiv+mqsv+ksry 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 di+f s hvj +ivdk b4sm/-h-wc3+qstance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gq6lj:mlba o/0 : -ghatalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 dist/x;scop90ic -ar x 4bxance for the four largest moons of Jupiter (those discovered by Galileo in 1609).cb r ;xp49xx/0aocs i-
(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 dw8 xnijg ba4h5p 446-+d cdiiristance of the Moon. a4-xi d4i+ i gph r5jn46wbcd8   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using +3yf;ao0m( -lfejfa jo*nfi 6 Kepler’s third law. Use the distae ;oaf0f 6mfa+o jf 3ij(y-ln*nce of Io and 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 ,b9 i x wzg.v:fe2uvx8p,ile( Mars and Jupiter consists of many fragments (which some space scientist,iw(xu f2. be ,xv ipz8evg:l9s think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a)e uaj*1o80b;oo ry pn 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)1o;jabuy np oe8 or*0 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 innst,fu 29 9ywonz8nbe 42oeb;/ 7ahja an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on wa42zb7h;ub2oa ojen/e9 t 8sy 9fn,nthe 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 half what2eo rxi5+0, o crj5vigz o61sx3vgzj0 it irx05jro oi0zg+3ex jc2o ,v6 5ivgsz 1s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mus8hq-* 94yum/vqhqcw tual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are qm/8 hwc9h 4sq q*y-vuthey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accel2bqi-55plgyq ,e ei l0eration of gravity at the equ5 il,2bqi y5 qle0e-gpator is slightly less 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 a: 9t2xzw(*yikz 5jw4a)sov/5 jcyum will a spacecraft traveling directly from the Earth to the Moon experience zero net2tswvkx mi*4(w /zo )5 :5jyuz 9aajcy force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathro yoys 1bgd*r,5om scale in an elevator, it * so,g ydby1r5says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consi2m,f +cn fx8 ds35tk;r * vb/g)cdwsyhsts of a circular tube that 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 rotation speed (revolutions per day) ic v2t ),fn +s3/fs by*5hwdmgdxck8r;f 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 inbdbih5- ej( 8h a vertical 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 itwzfj-,zf60x ,zu5n ojgx u)v w6:h5lp s radius r, the acceleration due to gravity at its surface and the gravitati )5ufl5nx, jo zf g0-pz:jhxw,v66uwzonal constant G.

A plumb bob (a mass m hanging on a stfv 7.:f,;8zdmj/ye -r7ubo( nymnror ;9a jxzring) is deflected from the vertical by ann(rj/ bod9u ;r , zme78m-ov.j: rnzyf 7xa;fy angle $\theta$ 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 smjm+. mube-1.rtk5+an le z r;peed of If the coefficient of static fricu+zeajmr n1- bt5m. +.mk ;rletion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that object6nl:rx dp f6w mj83i7rs at the equator were app: wl fd7xp 68m3nijrr6arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a consthb r0owdoc(u-,g84f 6.ie djlant 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 w+gmds tsr /a9w(s3r7a curve of radius 235 m. A lamp suspended from +3(d rr/wswt7 msgsa9the ceiling 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 as the Ear5 r/ fshn:z5lnth. Thus, it has been claimed that a person would be crushed br5zh lf /ns5n:y 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 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 7. q dsc f*6: 6ratk(u4q b5yrsls;woqHubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense ts uwtq6 7q kfd.*ro:4cr;bs6ylq5 (sa hat it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and sk2w 4( m9x:)efi1 9dwjfo rglvalley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest?1rif )ojwg4x99( 2fed lw:s km Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliu1n;*a7l lst9y2b rwqtes orbiting the Earth. Using “triangulation” and signals transmitted by these 2t*y;7uabw1qlr9 l nssatellites, 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 (NEAR), after tr, +,zdbch88qx md g(pgaveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . g xdg,zd8h,m8cqb+(pEros 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 satelluf9h6i.kgphijbm.uhn,w-jx- l k23 .ite in need of repair. You are in a circular orbit o bg- w-.3n.imh.9h,2xuk p6kj uhilfj f 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 1y1 m2qjg ouoh/+nphxh:/c+p its mean distance from the chhpohxp+q/+o 1 :mnu21 /gjySun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you coul/-m *r5tzdg d3o ghqh3c:h y-id actually "feel" yourself gravitationally attracted to soqt c5 yd :*/ -ggrzdh3o3-ihmhmeone 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 (Fig. 5-46) at a5yiugptp/ 7 t2t 0hzek k.z9s1 distance of about 30,t/ ph9.i172u5tzt eks0 kzpgy000 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 locavky5 4p* v ,wvpqit*7pted at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg ma*ppyp4v*,k tviw5q7 v ss placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbityo64llx .uir(( / qf5ab +q- )z cdjcn/ljceh7s 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-lonswap2q ,w2i )vg sweep second hand on your wrist wapqvaw)2w,i2 s tch?    $\times 10^{-4}$

  While fishing, you get bored ade2x o 2eoe6e+kx; (nand start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes (2e2xoe;ekna x 6+od ea 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 auh0.j ureaylz4 r f:5t+eh8)g new highway is designed so that a car traveling at seh)5.4euat+l0ur h :fjz8 gyrpeed $ 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 Ace9z-w jvnh1cqpnw 15y - c6+dbieru*:fla, 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 force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (appro f 5q-cw9przuvb16 n*j+:ie1yhncdw -ximately ). (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.$\approx$    $\times 10^2$