Sometimes people say t- 0rb li(v9oarq qz4k bv09ua2hat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. la z(rqobqk vi90492urv a0 b-What is wrong with this statement?

Will the acceleration of a car be the same when the car travelsn)c4gnfmg a0n0. y8)ac 8xzus around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the sam)c.z8fgn0)xag am8c n4 y 0usne speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whegjj( *souc( v2re does the car exert the greatest and least forces on the road: (a) at the top of a (jg ( v*2suojchill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting:imhj :qc- wr f)5)*f j.gklx3 xzq-my on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the mm-j3 -y:clq).*kjxrw z5:fgfhiqx) child?

A bucket of water can be whirled in a vertical circle without the water dr+6*l. n gounspilling out, even at the top of the circle when+.gludnn *r6 o the bucket is upside down. Explain.

How many “accelerators” do 1lgo9e k-xhhzz4 d91ydd22nl-ht p 6gyou have in your car? There are at least three controls in the car which can be used to cause the cahl26g9 - d n oxpyhzzhd-dke114tg29l r to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hi8g2xek p1up 7yll, as shown in Fig. 5–31. His sled does not leave the groun7p1gyxe8u k2p d (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 riderf- 3+e 1girqyngb9oe:s lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute thnpyen,evp 7t r2w4:n,e banking angle given its speed ane2nptp w,ne,4n rv y7:d radius of the turn?

A girl is whirling a ball on a string anm8 -w9 odqi/15fi 3mfsu7gx bround 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 t9um1disog/ifm5- x8 b 73n fwqhe yard. When should she let go of the string?

Does an apple exert a gravitational force s8yayyge*9l* on the Earth? If so, how large a force? Consider an gsa89yy *ye* lapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what w3-c,x n6njhi .k5j erjays would the Moon’s orbit be diic-e53n jx nrh,jkj.6 fferent?

Which pulls harder gravitationa27m 2fpq3+ 9 b74d9tmims6pjphtg efqlly, the Earth on the Moon, or the Moon on the Earth? Which ac 2qm92pp7qpm 4fth 3f9itdems g6 +7jbcelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th.d.(bwi3i bdnz/v b z.e Moon's is mainly responsible for the tides. Explain.zbnivb.w.z( idd/b 3. [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 ez:57 8zkm,dtmm * o v2rd(wglare at work? Do they oppose eacel 8m*7mk:mtv,g2zzw ( d5or dh other?

The gravitational force on the Moon due to the Earth is only about half the forcxmkqybdz;.7+ o 0vw*. ehh7z/l-wu w te on the Mol+ wmtz.u/qx 770- bhkzhv w.d oywe*;on due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its o,q.ht;et:i ry rbit around the Sun larger or smaller than the centripetal acceleration of the Earq:;,t.hiy et rth?

Would it require less speed to launch a satellite (a) toward the east or (bi,-4nhso y.r t) toward the west? Consider the Earth’s,y4o-t .hs nri rotation direction.

When will your apparent s/egh:-hx0 j6iv wm5 3pnrrz)weight be the 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 which case would your weight bnsze 0ij h)v-3g:m5xrphw r /6e 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 perio36 ec.rd nmqlhfq58 ,te8pg85dpxy-mds 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 tq8m,n65fph de pq.yelgx-m8rc358dsurface (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 “appa.a1 sj8 uat9.gp n4xutrent weightlessness” betweenspxua8 9. a4utgjt.1n steps.

The Earth moves faster in its orbit aro5 l w5(2s2q 375mvoj dnzzeworund the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relatis z25me3vw7 (2d5rwq noo5l jzve to the plane of its orbit.]

The mass of Pluto was not knowy0rcq n(8.e pon until it was discovered to have a moon. Explain how this di(cy 0nor8qe .pscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitatio( ;wivfao0x *cza6wlt+ q/ fk+q. -gannal 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 Earth to the other.]A child sitting 1.10 m from the center of a merry-go-roq q (zaavoixf+c;60 nk+wg-.*law f/ tund 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 1980o u2p fh43le43mb:cw s $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 jluz,cn9 -t7,uhh/ rk the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that theu,c7k ,rtj9zn / lh-uh 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 exer+,vx+kd9zbj c5 gh5jcted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcz +jcj+dg5hbcx 9k,v5ulate the speed of the discus.   

  Suppose the space shuttle is in orbit 400sx v7kxn m9h.s; lu0m9 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' 9uxmkn9m .l7h s0s;vxs surface. $\approx$    g

  What is the magnitude of the acceleration of a siqbo t6x5 ox91 us2addx4((ftatl 4-speck of clay on the edge of a potter’s wheel turning at 45 rpm (rev(o6(dtastx-u atsb5i1 q94xd x24lf oolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvedi0-cbcaq fzhw0u e,(7 at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. z, (ucq- fwabeh0ci07 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 g6 1efxoq8k b2my7i9d(m. pfaad2ya0ztxj +7speed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires ab.a1ajkx6+z xep2 92my qg fyat0o7f( 87 ddimnd 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 the gcgae3x7nx k1(mx j8)road if a car is to round a level curve of radius 85 m at3 )geg m7ax1ncx(xjk8 a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots , kdw)9mma/cp j;)m7yfqv1 h zis designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee phy/ jdmv)z,c) 9;7 akfm1qmwon 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 rotating turntable of variable spe *j,grzka8dk,k+rmi0n 83 zhred. 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 slidesn8k zak,mj,i +8hd0g3krr r*z off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tzditi ypz4.hx2a4j( f-3 psr: raveling when upside down at the d4 4p2jai.yf t( pzs z:3hi-xrtop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) cross n 2dvwq7m-e:4da3d b,mh6i/renyz; o es the rounded top of a 6n,/vdz qr-3de7hned i4o2wybma;: mhill (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 revolutionsu k+pq 9 )+0 -mipz1cet 2:npfbi5sffy per minute would a 15-m-diameter Ferris wheel need to make for the pan p2fus pfbi1i p 0zfmctk9)+-:yq 5e+ssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kgx ,9g d+7m ntev0qs*6ql5mzi j is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tensio vme*6lx0q 5+d jns z9i7tgmq,n 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 cenvi+ydb 781w;ssid u y: 0bkga n*4+rdetrifuge rotate if a particle 9.00 cm from the axis of rotationy:isu0bnge87 ; yi+kd w*1 4rs ddvab+ is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindv7tb d6 5ok9kerically walled "room." (See Fig. 6deko7tb v 59k5-35.)
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-hockeyb ec4,om ( jl)w;pjgu2 tabletop, and is held in this orbit by a light cordjm bc4)olew,;jup2g ( connected to 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, cgahbv0, ef+yan2k 3)by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partg,a3knc)avf 20bey h+icular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked glx 68l+rqgefz/an* 7ub)z 89wru- bd 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 masses8gfkwscb;f*w8wlf0bw e 2265 5lb, kxcch 1 yb $ 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 ve fsyyvw)3yk:,0ha6txrtically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force e1; 76unx aaiolmvt)f3 xerted on the car (by the tfm7v6) la3n uxo1ai; ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area,v-g 5b-yj :y p*m/x8 sc8xxzsc/kyd* s 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,j8s- ydpxxm /8 zb/-cv*yg:sk c5*yxs 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 circlemjhy2 7v3qtf: of radius 2.90 m . At a particular instant, its acceleratio tq72fmhj3v :yn 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 12,8:r/ )zlzr hyg /:4;kbn2unmto00 km (2 Earth radii) above the Ear tb;n2z hlg)mko/yu /r:n z4r:th’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a maz,x.cn,85vk p :v8ut / 1wr; eapukqcfgnitude of 12p . ,8 ,z uketfpqra;vwxcc 5/1:kv8un 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 Moon's ra4yxjoa y2i/ny+qjq5s h3o(2 fdius is 1.7 xi2o4ysfaq nj3 h52o/jq(+yy4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same v3t -wnb8.,uaoxs* (l-o n uqxmass. What is ths8 l- (nuxux 3o ,onv*bwatq-.e acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bup s:wir6vk 7*i-il6gjt the same radius. What iviigps wlk*j6-:67 r is g near its surface?   

  Two objects attract e jk4f/7- gn(oyiflb5f ach other gravitationally 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 acceleration of gravity, at (a) z eb+6 wf i(v+kwpxp4 kabzd s7/w62j;3200 mz7(be/ w x6wp4z+ jbakspk+vd i2;w f6    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to.c*3,4th z4pc7 aykwpu ( gslt a point outside the Earth where thegravitational acceleration due to the.k h4,tl ypc3w *(sazpc7tu4g Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphe83agfll9d* to re about 10 km in radius. Estimatltl*gfa o89d3e the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whb .j- /rwa*- +xacvqz+ :igntvich once was an average star like our Sun but is now in the last stage of its evolution, is the:vaw- tzcqr-/.n*j +g ab+ vxi 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 wei-kv :px di6 qcgsgir26m;nm4.ghtless while orbiting in the space shuttle.k-vc gsmdxqi4;mi6. n:2p6gr 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 surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squaregjkdcm t: -fn6.otn 0, of side 0.60 m. Calculate the magnitudn-,j odc gkt6.n mt0:fe 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 planehup z2jp .48g(chcb b)ts line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assg z8c.)cu4j (2hpp bhbuming 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 surfach8qr ;4dsu ;rpe of Mars is 0.38 of what it is on Eartq;hr sur8d;4 ph, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the wd.y *8yapi;tSun using the known value for the period of the Earth and ydwy*. p;t8 iaits 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 movino5.ktupo: * oanlmw( cy1kdh;,bf013z pm6g mg in a stable circular orbit about the Earth at a heigh :;mobhctzm0g(uo. ,ka15wk3pyn m plof 1d6 *t of 3600 km.    $\times 10^3$

  The space shuttle releasbmpfsh +c,m ;le1gr,e5ms4* k es a satellite into a circular orbit 650 km above the Earth. How fast musrem, 1*h s;mlc b f,m+4ks5gpet the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants+llh. j entkx.6fqqsw (6ze+ 0 0hdc+kzk:0ha are to experience simulated gravity of 0.60 g? Assume the spa+ +qj lk q+0ae k6hdl060 h .ncshz(xt.fe:zkwceship’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 oj8.sz cawky, zap)c9 2rbit 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 sp w)9,csy jzz 8ck2.aamall compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would3,h sggr s,a2w a satellite have to be launched from the top of Mt. Everest to be places 3a2grsh gw,,d in a circular orbit around the Earth?   

  During an Apollo lunar landing missizjy6tjkc bz .s8(5f 1mon, the command module continued to orbit the Moon at an altitude of about 1ymz jfs.c bz65j 81(kt00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pe mot-hle ,mav 59 88z*gpt1rblanet. The inner rt8,r*v 8ga9 e-5 lto1m hezpmbadius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9).g*u hs;0ms 4k-glgy+ck( sf /k What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?gl4( 0kskg/yhuskcs -f+ g;m*
(a)    (b)   

  What is the apparent weight of a 75-kg astrsfx;;i8bh2 gfp0r owfe4dv5 6onaut 4200 km from the center of the Earth's Moon ifwed4;sr pbg85;ofh6xi2f0 vn a space vehicle (a) moving at constant 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 d5w)s wc(9 ouwmass. They are observed to be separated by 360 million km and take 5.7 Eartho d)s(w9wuc 5w 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:-u -g3pdnpwwa5gxq1.o n.a b-kg woman in an elevator thatp3gw-wngbaadpxq:5 1-.o .un 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 suspendgv d3iktt5 k65ed 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 andkgvdi5t5 3kt6 direction)? a =   

Show that if a satellite orbits very near the surface oawy;* gisf8 6 0ab)wnff a planet with period T , the density (mw fybn8;a0s fa i)*6gwass/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) 0xezpsq v) uayue+2y6 19k;yp0vlwf/ to determine the period of an artificial satellite orbiting very ne s0f0p6)z+kl y; x vq2v/wpy 9eu1yauear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters ak1.yt7 -8 coy n2bejbhcross, orbits the Sun like the planets. Its perhy7k t.b8nbe y2co1-jiod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4c cg tv7; 7**s b+p xwr6bsr-lwuqe8n5.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very closeh )nw)lnmx2j 3 to the surface of the Sun on its closest approacjn) x hn)3mlw2h (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 aboupgrum*w:9 tdz+j1 4htt 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 large)nu(x4pw tx +.wcjwa.2hx1 )npm 9nbyst moons of Jupiter (those discovered by cu +xny1)n p mwwh.2jxt9) wa4p. (xnbGalileo 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 distdq(eyf9rn;d j; k epj0i..8v dance of the Moon. qdyv0(idek edn.p8 f. j r9;j;   $\times 10^{24}$

  Determine the mean distancekkv ;v0/ma oe+w iq:mt d49v)o from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabl)/+:adkow;94evqvt0ok i vmme.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists o( mr 9-mre+sdgwml 758nl en5wf many fragments (which some space srgm r e5l 7wdnmls+(em59wn8-cientists 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 band c by8n(2ld p-v jc*wx;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 lik; ypc l2(cx8 jn*vdbw-e 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 from ai,k-9pab ea6o(rm ki; hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on them6r e,-ap;9( ka oikib 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 e)5y hk;h3hvteenz -cjt;wi :m) )yc0 acceleration of gravity be half what it is on the surfacecv;yj5ehmt ;e)h3zt)ewn 0-:h kyc )i ?    $\times 10^6$

  On an ice rink, two skaters of equal mass graby3 bec;3i49 q cl p3ncuxa2mz+ hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 u42ac9 3z licq3be+npycxm;3 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the or1u 2wfamrz*g +y -p9apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g oa 1zu+-rgmf9p*wr2y is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fro2+j;y vb bme,;zi b-xi2od+egm the Earth to the Moon experience zero net force because the Earth and Moon pull with equal byedi;+vb+ bz2-xeo2,igj;m and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroo 9vb5wluxwz -: l0c,owm scale in an elevator, it ,: lw50zlbuc9 w-wxvo says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circuh ;k7 zzn g3l,cw6ml1rlar 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) if an effect equalm7n lgl;crz3 ,w6kz h1 to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircrcilgpk 1li76 4aft in 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 icd)+k-8otspxb3,i af 5 1s bawn terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant da+s)fpwbk 1 s3xab c,t5oi8-G.

A plumb bob (a mass m haaup+eclxme- f)* j+e6r zl,2nnging on a string) is deflected from the vertical by an angle +pf ze+lec*l6e u2m,jx -)arn $\theta$ 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 fhry22o7s)zv ,x 24 desbd q)ppor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safelyo ,h4)rpq y)xsdzv 2s dpb227e handle the curve?

  How long would a day be if the Earth werynm ks8jsu/ hs 4o:j+;e rotating so fast that objects at the equator were apk;+4ns/s ho8 jy s:mjuparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of .m+ -yk -6+d6uxq brfgib(tywg9jz s28.0 $\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 zd-kk jp q7-xre*-v 1,kejg3ka curve of radius 235 m. A lamp suspended dr 1e-3g* ,ve-kxzjkjkp -k 7qfrom the 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 Earth. Thus, it has been claime:4 rfp)7rfrb-(e(s/6lvjis5 q y okyld 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 ofs:y-/ r)lp5(i46lq e (7bysfvojkfrr 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 th-zah) rcd/ lz4 rz8lkms;fy 9/e Hubble 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 light escapes). They did this by measuring the speed of gas clouds f -84 zz;9zlas//cyrmlrk d) horbiting 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 valley showgja bm 62t35k)mccp5pn in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the norm pjkg )62mpt55bcc3maal 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 Systerkuy3 )*/u qf vhv49uhm (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 nauticalfvuhqu4 *ku 9/yr3h)v 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 (NEAv g-k w*ys5vaj;o5ea/R), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 1 vso*a-;ga j/wkv5y5e5 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 shutts(cq zay / zex3j8.erl:zp9)gle pursuing a satellite in need of repair. You are in a circular o 8zpqz3(c/r: lzge)sej 9yx.arbit 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 peruat4 f.,7c a2 ; 0iv nwyfh-ysa.fwmi0(m*rkfiod of 3000 years. (a) What is its mean distance from yv;7.4fa* c wtw f2n0kr,a-0imf .myasu(hfi the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value oft3l8x ht 72hrl G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Makerx2l h t37h8tl reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center .zs32)3u ll uulz57xbdzj/v zof the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center l3b .uuzz)z sdxl2vl5j/7z3u $ \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 oni7xb m mhe0w0p1fv9n / each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square. wn0m/x 901 ehm7fvbpi   $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitsxn-6v 1olo otq(k )ps* 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 c7ojcz svy3 i4-x5eyb9n 7+92pqba ma tip of the 1.5-cm-long sweep second hand on your wrist way37 +qbabxc5a 7jme9cv-y2 n94psizo tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around 7 xut8p)2 sg;cx 6tkthhw,/huin a circle below you on a 0.25-m piece of fishing line. The weight makes a complete cirp7u g 6s xhhcwt,kt;/2hx)ut8cle 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 ae yg sezo 673upf*2yii4cj/v e -d56z 1ju3bhh new highway is designed so that a car traveling c32/ z d hiz4g6ovj 5sjhu6ye ue7 1*be-pf3iyat speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utivn,l 83e ;gmkpf.v *belizes 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 rokbv f;pvm,leg .8 *n3eunds 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.$\approx$    $\times 10^2$