Sometimes people say lc(wxmrzu tzp)0 +90 sthat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. Wl9tzxc zsp(+0m r wu)0hat is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp 72v g .s buso)k1gc*yfvyc02ncurve at a constant 60 km/h as when it trave17ynv v 22f0kg.gyu*s)bsoc cls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hillth -u0v 58vw jugna;(-lrzx pv4-je5qy road. Where does the 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 stretch near the-xv4rh5a j;elt-g-v0 q5 pnuj z(v8wu bottom of a hill?

Describe all the forces acting on a .7* c: tbt:rlyobvr;y child riding a horse on a merry-go-round. Which of these forces provides the centripetalrl7yr::ytvo;* cb. b t acceleration of the child?

A bucket of water can be whirled in a vertical circle without th(sx 4:ay f/yyne water spilling out, even at the top of the circle wh(s fx y/a4nyy:en the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Txmp, b;(d-5w zsgnx8fhere are at least three controls in the car which can be used to cause the car to accelerate.8- 5;pxmg,zfw (dxs bn What are they? What accelerations do they produce?

A child on a sled comes flying ovwfm(tc )b8k))e dm p4ser the crest of a small hill, as shown in Fig. 5–31. His sled does not leave 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. Ex)m)s(bwdm4e fp )k8ct plain this decrease using Newton’s second law.

Why do bicycle riders;y 9 fl hr(qf;r)8b0plwqtn3d lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? Hod7c*4dp w po1ow would you compute the banking angle givdop41d wpco7* en its speed and radius of the turn?

A girl is whirling a ball on a string around her hea,ozh f4: ibn: ,gis7a uz*:ugrd1jf l2d in a horizontal plane. She wants to let go at preciai,,4j7nlgz r* :d2 u1ffhu: sizgo:bsely the right time 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 4h x w,aiu19 ltr48romlybjz*4*z.g bul;ny (the Earth? If so, how large a force? Consider an apple bbmn9xiz1*,otwr; u(*u yl4lyg.aj4 4 8hrzl
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouewzrv-/ k) :orld the Moon’s orbit be differew-ke rvro/:)znt?

Which pulls harder gravitationally, wn cu84qp kwf. it+6;pgpj23e/ *agfzthe Earth on the Moon, or the Moon on the Earth? Which accelg*t; +p waq 6pc.j8wg knf3z/2p uief4erates more?

The Sun's gravitational pull on the Earth is much larger than tkp ;.ax2h2m z1 i,umeihe 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 Earthi m ,ma;u2 hxke.21ipz to the other.]

Will an object weigh r0viu( s6er 9a 4urjocoo1.( hmore at the equator or at the poles? What two effects are at ur(6hj 9ov eio40a c. usro(r1work? Do they oppose each other?

The gravitational force on the Moon due to the E ty:g49 rmz,ubarth is only about half the force ong9 t4,b :umyzr the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars rtbv( ;7imqbq.i(gm: in its orbit around the Sun larger or smaller thgi.v :rb(bm mqq;(it7an the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east 1 8b cse7pymgxh h+:nj6ga6k-or (b) toward the west? Consider the Earth’s rotatj :8 a6+6xsnb1 -c hhgymp7gkeion direction.

When will your apparent weight be the greatest,0d7m blkw1p3a.)e(aoyt tj6qql 2 )tl as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, ) yabl31l( q).7jwkl 2oma6 qetp0dtt(c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in oute5j czbr)9 ty8t5 qu5 z18gs,zgk1s,iotcj1 zjr space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical s z yjgqit5 8jb tsz1 58c5rz,,c)zkg19sj uot1hell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” f3vum7;p. x (fowk:gy or “apparent weightlessness” between(kf3m gp .;7vxfyo:uw steps.

The Earth moves faster in its orbit ri8 panu59 xcuji1;q4c8bl(l 4yatt -around 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 itticy4 l(4 n8-b8i1a9 5 arpuq;jl ucxs the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known untilkhwq8h*0:c x2+qyxf u it was discovered to have a moon. Explain how this discovery enc 2h+ 0hx 8fwxy*kq:quabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yea,.6u,0blm xagb9k( h/ztivk t the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of i0akbh 9uzl ,,. mk6ga(vtx /bthe 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 travelingsfpo;rx +r8 -s.b xpq22xo(ns 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arounztxusry2n) s) ;1k;e pd the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is 2tp)u;1xzsk) esrn; ya 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 rotates uniforrsj,y zyzr q3t;(,bz- mly in a horizontal circle (at arm’s length) of radius 0.90 m. y -sb3;j,yrz z,rqt( zCalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface,-k4 a(-zcei) tpc1wt) ps soq- and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shutp4tc s ito-a-)sp ek)q-z(1wctle 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 t h8ao; eilhp.z(az,4tpww *+lhe acceleration of a speck of clay on the edge of a potter’s wheel turning at 4*8twz.aphapw ( elo4hz +i,;l5 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved aa,4bud*5lef b t a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If b4fa*u , dle5bits speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050 ;1e,,43jejwv+x,vjd5is km 3.e j qls,ou xxi-kg car can round a turn of radius 77 m on a flat road if the, xxj,lexsjw,ek jve3+d15 ms, ij4u ;.v3 qio coefficient 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 be between ,/9pav gwz-pe the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/hz p ,gae/9pw-v ?   

  A device for training astronauts anhevs f-8u 9w3wcmna, pdw(oa- 8;uu+qd jet fighter pilots is designed to rotate a tr+ 8 ;hca,eou(undqa 3-p wf m89wvswu-ainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own 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 speed94tq.dz4p3myh -5-.ybq fxzd /z kjad. Wd35/zaq tx.j4d9d p. z4b kyqz-y-f hmhen 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 between the coin and the turntable?   

  At what minimum speed must a roller*,i+y(0 afc rz:0)rrx hn1zgwfqy,jt coaster be traveling when upside down at the n,j+:farwrzy1xch(), t0 i0fgq*r z ytop 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 9o1wd -cq6vun482 epm9ch . mgn50 kg (including the driver) crosses the rounded top of a hill (radius =95g 1 6cumw9cqeh4-pv28dmno.n$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Fz +xmc z)rja29erris wheel need to make for the passengers to feel “weightless”9x ma)2czj rz+ at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiuvj6kh3 + +)kjyc+w7xz al*yko0 x va.as 1.10 m. At the lowest point of its motion the tens0cax 7vo6 xl.+k*+w+ hjyazvakk)y 3jion 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 centrifuge rotate if a particle 9.00 c9qt.+mnwf d-zm from the axis of rotation is to experience an acceleratiow. t+znfq-9dmn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c +db74jsgd 0qcylindrically walled "room." (See Fig. 57bdc0j q4g+ sd-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 xk* 7tao;3dqfrotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as sd7;3 ax otkfq*hown 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 , prqb 72pjz v9mqdifbg1),( 2 yzvecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular,,vp(dj) g9z 2vq17f m2 zbbiqy 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 bankktqn+on( +2wj4w2ie l90+)ytvyh rpi ed 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 (qqyz/ fbz8 d8wsgenl ++ *e(v$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310uadk e8 yo4n3* $\mathrm{~m} / \mathrm{s}$ . 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 ex(qh 0sjw16saoiq, qw(qw6 z81 xnx za-erted on the car (by the ground) in Example 5-8 when its spqa6nw ( qowxsah86 s z,1q-i(xzqwj10eed 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 z ;x 9s9h;rjnjthe 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, assuminrjsx9njh; z 9;g constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a par2o7rm i guzw bfr)7y2;ticular instant, f)7o2w; r rug7z2ibmy 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 ona)mji a2.x9)tp ,qirv a spacecraft 12,800 km (2 Earth radii) above thiv mq2.iapx )r9aj ,)te Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational a.bzi e2 hf,m7scceleration g has a magnitude of is,me7f .b2z h12 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 l:+:9pf xz0t0ctjai4 e9r 2uu*q5alc*z dmz b Moon's radius is 1.74ict+x u t e 2 :urm0d9:*9z4z*j5lqcaafb zl0p $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ti tm:d +a05e w9al5qda qq6*b5coy6w anmes that of Earth, but has the same mass. What is tqtnwwm+ 56 * yaclb:ode9ada650a q5qhe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the szlsu ol*0r4t +ame radius. What is g near itszs*04ltol+r u surface?   

  Two objects attract 7:j. sf:yxi2h nxdpmqk a -:6eeach 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 vall avbp; :6rdr3bm54w sue of g , the acceleration of gravity, at (a) 3200 m a6 4rbrvb5ms :l3;wpd    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth w,rgj5 pc7z.x uxy09h where thegravitational 7 pwxuchg0jx,9zy .5r acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spxx69e c 6g8ov1mlb2buslz6 )ahere about 10 km in raxl9)6xoa8vu1626msz bebl cgdius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf sul 0pdmb y-j2z3 6il2ntar, which once was an average 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 ylz0-bl2ip6 m3jd2 nu star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spa xp5d0fr vpu n.up8x.(ce shuttle. Your fr8.duxx 0p 5pvnp( .ufriends 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 square of side 0.60a:4h0g +8;levsmwo 9 fc ,llfr m. Calculate the magnitude and direction of the total gravitational force exerted,l 8fm:9cwal o0esgh4r;lf v+ 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 on the t, hgvcr 9:kxp5i*)lqsame side of the Sun. xcqr:,g*h 59p kti)lvCalculate the total force on the Earth due 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 gravity at tqz.hicp j (uc3uy8tty+c0e 55z 31gothe surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determin g3z 0 t5(cy o5pe3 hq1ccti+yjtuz.8ue the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val-pyp yvyv,,u:2lxe+ fue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kep yuv,e-y xvy:,pl+f p2ler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a88fajk f4z.z n satellite moving in a stable circular orbit about the Earth at aak.zzffj88n4 height of 3600 km.    $\times 10^3$

  The space shuttle releases a sa6rk5*5vawb;b w l)fj-s al6s4t 9mjah tellite into a circular orbit 650 km above the Earth. H;bwblv l5h*t)5k-wafsj 96mj4a s r 6aow fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arexdmyk-p1 z.xs7 0or s9 to experience siosd-1s0xmx. zp 9kry7mulated 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 c wsl6nqcl-uyk; 82npl l.g62 the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compa6;sy ql2g -cl plc.lu 2wkn68nred 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 jmfrx 3g;q.i7launched from the top of Mt. Everest to be placed in a circular orbit around;i rq. mgf73xj the Earth?   

  During an Apollo lunar landing mission, the command module continuewu-)1z ppopc( d to orbit the Moon at an altitude of about 100 km. How long did it take to go around theuoc (p1-wzp)p Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The )i ed0sq:dc gre (8dv;inner radius of the rings is 73ed:g)qsc8r0;(idv d e,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). What(j o-haq,dsfb: r8y2h- q:asrf j2hdh8,by(o is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4207qg)n ipj,r5cj6 g) af0 km from the center of the Earth's rpc7fjg5a ,ji )q)n 6gMoon in 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 mass.mdrt0 74h18 f8kfigp+ib ah3u They are observed to be separated by 360 millionm1b04 8 pu78kgdfa3h+i htfri km and 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-kg4j f,ep9 jev0ou7;usn woman in an elevator that moves 7,noj 9u ev4j0f;epus
(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 han/8c0c syfnjh3s+w z)b chv*2 xgs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the j)c hs8/2s wh0cz cbvy*3+xfnelevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planeo6x 8jkuoh 8u1t with period T , the density (mass/u8 uo x61o8kjhvolume) 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 dg,9o: thleie-w ),4nj b dl1 7f(zu)gy9 aizrf) to determine the period of an artificial satel 9ru,b,iaenjwg:g4fe htd )oll7z-9 yfz)i (1lite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meterzc2k8(3wb*gh e6r c dws across, orbits the Sun like the planets. Its period is 410 d. What is its mean 8z hw*ckrcw6g( ebd32distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.th9wyx :p18ojawsl6+g q;fa 75 $\times 10^{9} \mathrm{~km}$ 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 orbitaaud(kwc8y ck,cgn 13 (ua9 q4s the Sun roughly once 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 Sawkyu8 c1agad(k c c,39qun 4(un.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy wh+ezj+b55-b d) uzgj $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 hqne:5y ,srq; mass, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609,nrq ;:q sey5h).
(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 Ea t9hlhu4ss5 k8rth from the known period and distance of the Moon. 9hlt8s5kuh4 s   $\times 10^{24}$

  Determine the mean distance from Jupiter for eachw0xtbzsm6 h5o ;(7ewk0*b1i 0*c gfuzjui5 o d of Jupiter’s moons, using Kepler’s third law. Use the distanui s b75wf jhoiw*0ke5td* xz0b1 0(og6;um czce 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 Mars and Jupiter consists of many fragment *u wq8shcz44ps (which some space scientists think came from a planet t8*uwq szp4ch 4hat 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 f bs z agwrzn:jfcp/2-8i7o ,z,orm of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth daf / ,2:pn8s-i7oajb grzwzz, cys?   

  Tarzan plans to crosp - lxt-hz4v1hs a gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and th hv zxp-l1t4h-e vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be halft1ojq4 h+f)z,zh;/ 1d nhlvz t what it ih;d4j, hzt1zvql /+ft) 1znhos on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cir(mb8 9tnk1 ghpcle once every 2.5 s. If we assume their arms are each 0.80 m long and thtm ( n9gkh1bp8eir individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates oniebtu( x1e*gwm oo+o :;4f5 lzce per day, the apparent acceleration of gravity at the equator is slightly less than it woulde(+*iox m t:w4ob1eulo f ;g5z 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 u7fn1g8:acehtraveling directly from the Earth to the Moon experience zero net force becac8anef u7gh1:use the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 k ;d, p;3ereskgg, but when you stand on a bathroom scale in an elevator,pd; ;esk,eg3r it 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 circular xs yh3 sw0gsg3j 0fb pc8u(nw3.l57ur tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). Ts5p7huy8 g lw( 3xb0s30c 3.usjgwn frhe circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a m-ya+1ql9zf:hl eljax s 8zn3w 1jxh-8a 8.z cvertical 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 ( wiotn ((0cx6:igw rca planet in terms of its radius r, the acceleration due to gravity n(c6 (gw tiw(c o0:rxiat its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vev mjm2*z*d9 6vw0rsfvxtm03 lrtical by an a 69*3 svjdxwz l0vmt*2 0mrfmvngle $\theta$ 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 ,3uc+pw4qbzx5e yx 5f for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at ,x4w+5e yx3uzpq f b5cwhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objectklw (+2 o m(grwrfkylu*b:l5;mfo3x .s at the equator wer+f;5ol (mx3: ubmw.k (ly2w*rgr lfo ke apparently weightless?    $\times 10^3$s

  Two equal-mass stars magr e: 7d:h1au /nynfi98dpz3gft 3f( fao 4th7intain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235.m1 bd,c1uyl)w xcdu) m. A lamp suspended from the ceiling swings out to an mlc,uxd 11c u.b))wy dangle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tipe;gs y mtp6r3c:5 wnun12e1k mes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter e rus1 y5n1wtmpc:keg6;np32since 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 Hubble Space Telescope deducedv/-2f2kh( ;g f 1:sqr evm95knzsgpqy the presence of an extremely massive core in the distant galaxy M87, so dense that it couldmf nf(2k g 1h-sz s;pe2q q5g/rv9:kvy 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 valley shcs(ei, 93 factown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the n ecc(9t a,sf3iormal 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 groupn qc2ej1mzj- / 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 n1qe /2c- jjmzorbits 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 travb c.wx; j vss -t(7:p.zxpfio1eling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly w .zfjs.xo 7xbt-p;c:pis(v140 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in nezd/tw bl6 :vb3lm3om/ujz)h f (9 xrs+ed of repair/ o9u +lzdrsmvf wz t3h(x: lb6jb/m)3. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distanceu/0 d oomm*do8(/cq hn fromud0cndo/ o(mqh/* 8mo 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 of G would need to w0)yshh ;qlv5 z2td:dbe if you could actually "feel" yourself gravitationally attracted to someone near you. Malwdthd0y2 hqz); 5s v:ke reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fijtxz jtz /br:;9(:j h+ 5 f:sajg+zoqcg. 5-46) at a distance of about 30,000 light-years from the center+ t:jz ;:xjaz5+bjg:( tqh9sof/r cjz $ \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 the0xjwu1o 6y g: e;show3h8l,vs 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 mass placed at the midpoint of the bottom side of tyj; vuhx 0o1w3o8e,6lsws:h g he square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbikrpub9a q( ,c5ts 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 fzl.3o svpp zy8 ep p)2h/ay+o*,ght1by the tip of the 1.5-cm-long sweep second han),yh h3oe/. lsvfotaz*pp1 y gp8+p 2zd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arowb umbnhykb5,vean .)8z,: 4aund in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the a: h ab , 8)anzembw.b,5nkv4yungle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so3+p/ouw p/j2c +hqaq0kzbnyrg 9np +) that a car traveli// a 2)yurqn3hcpo9kzjn p+b q 0++wpgng 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 train, the Acela, utilizes tilt of the cars when ne di:bf* ud5 fnn(xl 0b53aty+cgotiating 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 passenget cnu0 + fy:b5b*dd3f xa5(linrs 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.$\approx$    $\times 10^2$