Sometimes people say that water is removed from clothes in a spin dryer by c7(nr8 yd+l fye( ;0jx9bi6 jw:rxznpp entrifugal forcnnj8pbei(fr +:(j w9l0 yrx7xzp 6;yde throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car n;bv 0+*9nmb o7s/rjme) feh ytravels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? frn7m0; svb)+bhomee9j /y* n Explain.

Suppose a car moves at constant speei ;hi1tef4drj /r+ f6od along a hilly 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) fe ohjr6ii/1;+dtf4 ron a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a me2,i 0b4bewiqrjgxj .:rry-go-round. Which of these forces provides the centripetal accelerab4jg.,0 x eqi2 w:ijbrtion of the child?

A bucket of water can be whirledymw3ak31kg69g6w 9 kpkyb tu. in a vertical circle without the water spilling out, even at the top of the circle when the bucket is 6wgw3ytk y6.k 9g91 mkpb3 uakupside down. Explain.

How many “accelerators” do you have in your car? Tw-wxsd7a o4a 9here are at least three controls in the car which can be used to cause the car 4-9xwsda oa7w to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying 7sqz: ;(tyqlkjpp x14ii a9c-over 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. Explain this decrease -qxtp1lkpis9az; jqc47yi(:using Newton’s second law.

Why do bicycle riders k :otdzc1i 7y/lean inward when rounding a curve at high speed?

Why do airplanes bank z0:mi3w l /bcywhen they turn? How would you compute the banking angle given its spewcz0b:m l i/3yed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal p16kgvx:,j** f43 fayibu24r b,dw gkzdxw;bhlane. She wants to ,bkw4 b 1vr*gwf,6x42 : bfy*h3zaxj uki dg;dlet go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how larg p v3 :y mw6dci+b,t,o-f1ud)yrg fe32)iwhkle a force? oe w:if w kfr1 3)6ui dypt,+dgv)l2h-cy,bm3Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wou0vt3s3q mb0sald the Moon’s orbit be different? 3s0va3bs mq0t

Which pulls harder gra34puq5qu z-4g+uo oitvitationally, the Earth on the Moon, or the Moon on the Earth? Which acceu p uoi4 o4z+3q5-qtgulerates more?

The Sun's gravitational pull on the Earth is much larger than thec1ugq26uh5y6* ljfmy p-2hnj Moon's. Yet the Moon's is mainly responsible for the t ynu-5j p2 6u ghy*jlfmqc61h2ides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two efff3 (.le2iw+npuo )aa uects are at work? Do they oppose eac+i3a)un wp (u2l.aofeh other?

The gravitational force on the Moon d- owusp01uyk;b28wt iue to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled aw82 w-itswu b01op;kyu ay from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suqhb*k (i5g8 mrz d g zflx1x6o1-gw52zn larger or smaller than the centripetal acceleration*(1x 5 qg6gzg dwzbxmi2-85klrzofh1 of the Earth?

Would it require less speed to launch a satellite (a) toward the ze5lu61uz5v ceast or (b) toward the west? Consider the uzzvl5615ce u Earth’s rotation direction.

When will your apparent weight be the greates;dywr 1k8ysv(uim4f32y*ey bt, 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 be the least? Wr;dy4e1 bi28y 3 my(ysu*kw vfhen 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 lon1ln v*4l1qg wag periods 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 o vn41wl1l ga*qn the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightle( sd(gs. h0hkubo( p gyyb))q .ok5y9rssness” between stepshpgs.k yhogb (9bd0)(5uy.r sqk )(yo.

The Earth moves faster in its orbit around the Sun in Janun2sal- p5yvy2 xg3cw1 ary than in July. Is the Earth closer 13gvya5c 2-spnxl w2y 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 relative to the plane of its orbit.]

The mass of Pluto wa q.o bvuw+j8uf i1id1:s not known until it was discovered to have a moon. Explain how thi+:duf.q1 18bujiovwi s discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger 4dmf(- l,jfym 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 centf ydm,jm4 fl-(er of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling qx2ok fp x,.0g1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ozn*n2*4l hhl arbit around the Sun, and the net force exerted on the Earth. What ehz n 2ln4*alh*xerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uni:9pn(ss 5;3tk-pdd-ddurcslt k8q 6 vformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. 5cqk3ddvp-(n; 9sk 6tutpd-l8 sd:rs  

  Suppose the space shuttle is in orbit 400 z h4mo, hvi,+bkm 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 ai4mo vbh ,+h,zcceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on tdnnl/;si1cr y:q 6-: tgjjfa9he edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter n rfl9n;1-tciq/ d:g j:6ayjs is 32 cm?   

  A ball on the end of a string is revolved at a uniform *iht c hrdu-;zp(74hmrate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3h4 h7m rt(-*dcphi z;u3. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg t) zhvvd20(cs b bk .8rrix17kcar can round a turn of radius 77 m on a flas zbi.0 rhrbvk8 txk1c( v7)2dt road if the 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 the tires and tmos8fw e g;5n /:j3zguhe road if a car is to round a level curv8on jzu:5 g;egws3m/ fe of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots i3gt0xl52m2p1w hmr c b-grw:qs designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she5 1tmg2rc0wbgwxl-m q23pr: h 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 turnta5 g(w,e. nb2dvxsr,qc ble of variable speed. When the speed of the turntable is slowly increased, thn(,2qs g dxw5, rvbe.ce 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 coaster be traveling when ,u9y*b-epd p zupside down at the top of a c-,bp9u*p yz deircle
(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 t:oa b4kuy3j,-g ; dqlihe driver) crosses the rounded top of a hill jlayg:-ibd,; 3qkuo 4(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 minute would a 17w4-d iwcc9nj5-m-diameter Ferris wheel need to make for the passengers to feel “weightlessc-4 ij w9cwnd7” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticalr gfs9ep tu6)86e oba. circle of radius 1.10 m. At the lowest point of 8.) satu6p ee6br9go fits motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axis p*99v 9g2u*xp ecp mohof rotatvg9pmc*x99 ohpe* up2ion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peg,.2aev4cbf +fo zh k0ople are rotated in a cylindrically walled "rocz+ eok v0f .fh4a2,bgom." (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 cic77a-wg;rzu- fqzk.iox e,6z rcle on a frictionless air-hockey tabletop, and is hewxf g6qa7 z-ie,; -.zkczr ou7ld in this orbit by a light cord 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, by not ignoring the weighte g w,zlk;0t9q0 vg p+w1bbxi1 of the ball which revolves on a string 0.600 mw,p 1b vx;ie1g9lwt0z0qbk+g 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 rad8z c8wbv4tcm7 ius 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 massevt13nc l+ u;t:y vza.ws $ 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 tbswrv/hg.(/ 2 5aig)(igz 7wr o kl8kat 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 net5mpo:)uuz9n w (5pzl v force exerted on the car (by the ground) in Example 5-8 when its spemnlu)5u zpzpv:59w( o ed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 5w m2,wyknn9+jclj2 n 900 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway wc2kn jw nymj+9l29,n through the turn, assuming 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 homp2 hhc3hw(p5r+e, lgrizontal circle of radius 2.90 m . At a particular instant, its accel ghh+p cp(l r,me3h25weration 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 Edakn)tzntt:5kw-b ;r m.4 17 fl4cvzharth radii) above the Earth’s surface if its massw7m4 ;ltnb1k.4zta)kdc: fz5rv tnh - is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratio)30o +)p ctxph psae.en g has a magnitude op0e xac +th ).)pes3pof 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon'7oh4 tit/j-g 6;i lnkls radius is 1.74l6ih 7kt;gl/nt ij4o - $\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 tg4+*kfmzj ze0g /k.,hu; wmta z2or)e uv-q p*he same mass. What is the acctp aw um-qvk *uerz)jg,02.ozzk 4gh/e ;f*m+eleration due to gravity near its surface?   

  A hypothetical planetk) i -wcgw*hl9 has a mass 1.66 times that of Earth, but the same radius. What is g near i)c -l9kwigw*h ts surface?   

  Two objects attract each other gravitso *5 1ysk ,nxcqknzxryo,). t wr4-4dationally 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 accelerati+d5yd 7e 7rsyoon of gravity, at (a) 3200 m 5dy7se o+yrd 7   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center t1zm d.or puc0i:sd2y 9o a point outside the Earth where thegravitational acceleration due 02yzdd pm:r9cs .u 1oito 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 paz; ,2i ioxa)h( l5j1iyfaw i5jcked into a sphere about 10 km in ra;hjxl2( ii,z w)jaiy 1o iaf55dius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun bj .+te .;c0bodgv mfn6ut is now in the last stage of its evolution, is the size of our Moon o0 ng;t f.e b+6vmd.jcbut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space e99.be 7lwfw pshuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calcul plwwb7 ef99.eating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locate uj/lm 2n7qr5jd at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerj75/um ql r2jnted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most 1yt 6b: o,-wt7et u2 2mrrgs;bldw,s jys*,dyof the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fobwo 6 ds*rsbwg- yl2t,:ut,srtme y2dy; 7,1jur planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars i+ ooqvgt-,9 ce;ouf f,s 0.38 of what it is on Earth, and that Mars’ radiu+oooec;g,,f quv t -9fs is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the 1n con:9cj8zfd/2boj period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Keplerz n9o /dnj18b2o:jccf’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stablw )wi q:gf0) :fhtex1de circular orbit about the Earth at a height i)wef1:w)f 0ghdtxq :of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into as,lmzv+p i*sjx2 bc( 2 circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releasm2s*lx pbz, is(+ jv2ce occurs?    $\times 10^3$

  At what rate must a cylindriumg3ab-2 j p8 vm8o,lucal spaceship rotate if occupants are to experience simulated g2mouj,883v-m albu gpravity 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 izp n4:x2 kp(zhk41whzt takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the sanp2kz (4hxphw1 z :kz4tellite?    s ~    min

  At what horizontal velocit xp8 wjxx,5xz(2qgxv0y would a satellite have to be launched from the top of Mt. Everest t(w2gxx5jx z p0qx8xv,o be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuedhbr+- 19r1thwwdg-z w to orbit the Moon at an altitude oh19 ww- hdtwb+1r-rzgf about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn armrg-: j6x0cag e composed of chunks of ice that orbit the planet. The inner radius of t-:xaggjr 0 m6che 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 io lwzv (k),z,xi5f 237owcnfonce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the toi)2 vc(i3 lxnkww oof,7z5,zf p, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of+3+)lmuu deh+ owadl( the Earth's Moon in a space vehicle (a) movin3a h+u)ldu d+e+(w lomg 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-stav8/l w*;lzt zqhb0f;bzj2 qx: r system consists of two stars of equal mass. They are observed th ;82b vz;ltj/lx0 *fqwzqzb:o be separated by 360 million 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 weigh4 phnyko8gx *,wm2n3gdl0 y8 jt of a 55-kg woman in an elevator that 3 8 ,mxyh82 *dy0gj4kwnpglon 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 cr j.2 9/zrrreb(h0v5dneyxe4jp 53x tord suspended from the ceiling of an elevator. Thy5zre rh(tv5 pe3d0x rnx rjbj/.2e94e cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet w hzug3/etef/4 ith period T , the density (mass/volume)t4gfe/uh/ ze3 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 thed) ld,p-;pm tx7r8vtr period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting vr- d 8)7 r;,vxtpplmtdery near the Earth’s surface.    s

  The asteroid Icarus, thoug8qfv iqhl9bs fy-,-7 *yc7nhwe4a-f dh only a few hundred meters across, orbits the Sun like lvfeyfniqq8 w -d b4 f,c9h-s*yah-77the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofw4m gu(,v bpcqmq)c8; 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 every 76 yeard5ze p 7hnx)/cs. 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 cexn zp7 5)/hdin Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxw wrs3ee8 .-qm mz:pa0y $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 thm-(g ahxz3j)e e four largest moons of Jupiter (those discovered by Galileo in 16xzje )g(m3h-a 09).
(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 dist 7wco33jg iu6pance of the Moon. j3cgu wp76i3 o   $\times 10^{24}$

  Determine the mean distance from Jupiter -ao(hyru) yw5qr kg gwkm6;5-for each of Jupiter’s moons, using Kepler’s third law. uk6)( kwgy-hyg aoq5-r ;rmw5Use the distance 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 fragmen/6eind -ot z-zts (which some space scientists think came from a planet thoe n/tzz6 i--dat 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 o6tab 46cc ewr.f 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 y6a6rb.4twc ecear, in Earth days?   

  Tarzan plans to cross aok t:1ef5v 9j )vpg1v:6uay mo 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 g9 ::k5 e vjvpv11uf) yo6motahe 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 acceu64y9i64 7)khg,yjglttks y x leration of gravity be half what it is on the sgyg6 uykijts9, 464 kxyht 7l)urface?    $\times 10^6$

  On an ice rink, two skaters or .ycy, :,ict99rwst qf equal mass grab 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 are9,ty,cqs.yrr9wt ic: 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates oz+ jh(nqgd -w7nce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitunwzgh7 ( d+j-qde of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance froxr74ox t57sz*wl,wbh) y g-mym the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposi 5-rwg*sxxyh l7o,tz7 yw4 bm)te forces?    $\times 10^8$

  You know your mass is 65 kg, but whe (:s2qoxd3,rnds 6krgn you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleoqd( 36r:sk ,dx2nrgsration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station e wb,z0 yyc27d3:b7thck4ci bconsists 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) if an effect equal to gravity at thh,wct2:ce4zi0 b7 3b7cdby yke surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hism k+x:xx)vtw ; aircraft 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 p.gn 6 wcpcc-p1lanet in terms of its radius r, the acceleration due to gravity at its surface ac1p g-6ncpw. cnd the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflmkoukf 2 h.;mp,i- lr7ected from the vertical by anp. om m7kihr fluk-2,; 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 speed of 5 pu4rl7fecut83z1i-q pigi/ If the coefficient of stati/57 i ul4pi 8ctqg pirf-e1u3zc friction 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 rotatzi0,6mren uwn td:( *eing so fast that objects at the equator were app(tr*6edm z n ,w:ue0inarently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of rlg b ;i u)cyjz.j3 l0.u4a/dt 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 constan/bkp p,zi 3uy-kemy 1,t speed rounds a curve of radius 235 m. A lamp suspended from the ceil1- ykupz,kme p3,iby /ing 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.zxl 3t 5.fpq2wt5dx+rp (ye n been claimed that a person would be crushed by the force of gravity on a 5w x f2 lzt+ pqxr3etn.(5ypd.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 Hubble Space Telescope deduckb9;8w( wqnr ted the presence of an extremely massive co;8wrk9qwtbn( re 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 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 valrp7 xua 17fh c3x*x4aew 6rqe*ley 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? Li3a1 hqr *74rx6xf*uxce7aewpghtest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Systetr;12o0 z, n zdx;qbchm (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determiz2;nc; h 1d zx0tq,obrne the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, 2/w9x2cwy ex0o qo1//xmuos e jt5dl0is meant to orbit the aeljo 09u td xmw2/10o5ywc xq //so2xesteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite yk3m+*4d bkhv;w o6m pin need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 wk;pymbm34 *+ 6ovkhdkm 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 year4wi6 , fxkd.qts. (a) What is its mean distance fr64 k d,wfxtiq.om 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 kotd7p r8ml b1peb1):would need to be if you could actually "feel" yourself 8pebr t lo)m:k7b11pdgravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the m x(dgi9u0+gdMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cen 0u 9xmdi+dgg(ter $ \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 .d3tyhq,qwdw8 wz )d :on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass, qw 8d:qy3thzd.wd) w placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbfjox sp 3w:nlj wux,q*)1rv6l oh0.p6its 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 experiencem+bq*k j- y2lsd by the tip of the 1.5-cm-long sweep second hand on j+2q-k*bsl ymyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swi:goswve8)/6m r a3+ rnb gk;wkng a sinker weight around in a circle below you on a 0.25-m piece o :8gk gb/o;rse)kn m rv36aww+f fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highw)r99d)lot( x boi ja)qay is designed so that a car traveling at sr( 9o)o tbaj9)xdlqi)peed $ 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 8 vbisla-x uh. qo9a3: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 exus -.aalhq:oibx 3v98 perience 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.$\approx$    $\times 10^2$