Sometimes people say that water is removed from clor5: oai rspq2xnz hc 2lk)1(k9thes in a spin dryer by centrifugal force throwing the water ou22si q rzk:o)5a1h( cnxrp9kltward. What is wrong with this statement?

Will the acceleration of a car be the same when 05+ -qyl xbb:()y/wa dhojzlh f*q.g qthe car travels around a sharp curve at a constant 60 km/h as when it travels around a geqh: .o)q-b0*qg+wahyly x/5ldfz(bj ntle curve at the same speed? Explain.

Suppose a car moves at constjvykz.m5:k7tsw z;f /a-c* dlant speed 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) on a level stretch near the bottom of a hil:yf/z; tw5.slakd z 7jmvc-k* l?

Describe all the forces acting on a child riding a hn*l; vh7 qqh)jtfc *k7 jg;0pmorse on a merry-go-round. Which of0m7*qj)kh jf; cl7;*ntghvpq these forces provides the centripetal acceleration of the child?

A bucket of water can eutc *xj()(n+ct q7k wbe whirled in a vertical circle without the water spilling out, even at the top of the circle when the ktc) j(twe7( q cxn*+ubucket is upside down. Explain.

How many “accelerators” do you have in xxb3swb z2++fyour car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerazfbxsb+ +3w x2tions do they produce?

A child on a sled comes flying over the crest of a,s2tb1lvska1x2gz e7 small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the nb x, l11szv t7kga22esormal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whej:fl2kigow ,0 n rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang 2.k8pa0mf oh0uhm7-t ak7mt gle given its speed and radius of the turaktf mo g-.2ak0mh7mu t h780pn?

A girl is whirling a ball on a string arounnig*vb6b:;fed qw+* o d 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 the yard. Wh: *;6feow b*qd +gbvnien should she let go of the string?

Does an apple exert a gravitationamay-u . 2 d*vaplaof0/l force on the Earth? If so, how large a force? Consifva.0moy ad a-2/pl*u der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thqipb5+sq)7 g g gpgh)8e Moon’s orbit be differenq7q)si)5b+gp hpgg 8g t?

Which pulls harder gravitationally, the Earth w2zsh8m7 0,ep l/llgl alf 4u4on the Moon, or the Moon on the Earth? Which accelera,e/lall4s8mw lplfg7 42zh 0 utes more?

The Sun's gravitationaldx- /h4-tl 4tfrcam6)nzkv 4l pull on the Earth is much larger than the Moon's. Yet the Moon)4 rc tvzxl n6/-th m4f4-lkda's is mainly responsible for the tides. 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 effects uko ht,he *zn6y 6k(+ef7hb9rare at work? Dh 6(+*z 7e n,to9kh6ruey bhkfo they oppose each other?

The gravitational force on the Moon i e5x56gwr/ )pvpn7 tbdue to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pvb7g 5tx5 rnp)6e/ piwulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun vx q9;n+ *:j7 gd(m5yu asys-m4n hmmqlarger or smaller nnj s:q xyy+( mm5d79h4us* mqm-;vag than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east ot3 +3 dl(k/snvoe+jqw nh.hj 7r (b) toward the west? Consider the Eart.q7njs n/3vhw+ kehdo3+tl j(h’s rotation direction.

When will your apparent weight b(cqqi705cpc * yo8f j zzn09qpewa5v7 e 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 be the least? When would it be the same as87 c0qp 5j0wvqo7n5qci z9a* zycp( ef when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend loniq 1t)1b./7i barfer eg 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 on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b)b er.ie1b 1ifar7/t)q 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 weightwbsh5xvs)dc0j ;h7pk5/m .ua lessness” between stepssd0p)h c. ;hsvm/5x5aukb j7 w.

The Earth moves faster in its orbit around the Sun in Januaryme5i :yr.qb 03coy8 uj u+ts(j than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much t:m(3 ybyji 58jru.+qesu0 ocof a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known untilqxt0vbb2dkico:i.+ 0nyli 8j,s8w2 h it was discovered to have a moon. Explain how this discoveti b lhkd0n yqx8o i0 wb2i+c2,.:sj8vry enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is m nz,kr f6(m/9gha:pne uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Exp n(rmp/f e:,hk agn96zlain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19qebdn*a v /89;p6 *y)dwyargb 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 i42 owc0hra;qa/rxhov ,0k8 otex/metiu 2d;0ts orbit around the Sun, and the net force exerted on a;ik 2/h,e20r8/mxexcwtva00out o4hr dqo ;the Earth. What exerts 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 uniformo ojfo5 lff2(3ek+ l0cly in a horizontal circle (at arm’s length) of radjll3ecffok 2 f(+ 5oo0ius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuw1om:h f(6-mmw -zyk sttle is in orbit 400 km from the Earth's surface, and circles the Earth 6ymw-wfom m:1( -shzk about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude ol0,s3 oe d2tvyf the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cydtso2v 0l3 ,em?   

  A ball on the end of a string is revolved at a uniform rate in a vertical ci7ruhtb: 6t1iq rcle of radius 72.0 cm , as shown in Fig. hb 1 rt76iu:qt5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 105+q*) aq:)zjfoo6 cbiv 0-kg car can round a turn of radius 77 m on a flat road if the coefficient q6) ocfa+)*i :jzvoqb 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 betw gqg;s,q ly0o9een the tires and the ro o9gs,qqg0 ;lyad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighk+:mss m-nwk 7ter pilots is designed to rotate a trainee in a horizontal circle o mm:7+ksnw-ksf 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 rotat03ovglf ;r5hu(z(s xuing turntable of variable speed. When the speed of the turntabllv (zsx o fu0hr5(u;g3e 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 coaster be traveling when upsfu-8bmi qwvh u 119i(aide down at the top ofbia9vhmw 1 qu1 iu(f8- a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the round98yr 7tg5n;xaz 8spf red top of a hill (radius zyp r7589;fxn rt8asg =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 15-m-diameter Ferrisc8iz g) n ha9 akjr/(qp:;ad(g wheel need to make for the passengers to f japhc;iaqrk :gn8/ (zd(9ga) eel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of ri ;q*w g:r(h lojc,q7vadius 1.10 m. At the lowest point of its motion the tension incv7i(q;: ,lrwh*jo gq 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 )vtxuj8z ,x v*3p w;jzaxis of rotation 8x*z puj3wjx vz;t v),is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walledhh8dyq l:uhyrd326*2 v bf/a m "room." r6f h uy8bhd *m32ld/ya:qh2v(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 rot;s e-89zyl9i,vqlyugated in a circle on a frictionless air-hockey tabletop, anlv, 9 l;uyiegq -9s8yzd is held 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 ;0xu2mf.w)enpn9y ey(rgwts5gz(3t cz;d k; not ignoring the weight of the ball which revolves on a wgsgwc; e(ny.e2fzut;tm 0(p 5y );nd9rzk3 x string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a c q*v(b yay1lz0ar 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 massej ghwd, :j *tml0l/kc 5xx+sw,s $ 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 w /.wg.u0y5psae.v cq evasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of tlb;wz9: 9)prxtc 4kezaeuz9 1 he net force exerted on the car (by the ground) lb919rt9zz)awc x;:e pek4z uin 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, going fc yh5:ru( /yawrom rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car wa:r ywu(yc/5h hen it is halfway 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 horizontal circle of radiuddszr 5 -q)aw a 6y3zj,06rat3 v6smlts 2.90 m . At a particular instant, its acceleration is 1.05wtrjz)a ar a dyzt,6 3dlm03v5s6- 6sq $\mathrm{~m} / \mathrm{s}^{2}$ , 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 Earth radij lrs4p9um:vqm.pe/7 i) above the p q9se/rj m:mvpu7.4lEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravit65ryp3xht/ g v/ :vuuiational acceleration g has a magnitude of 12 m/r3/ u:vh gp6yivtu/5xs$^2$ 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 tog,mulk x, .yh0p+;nx;z.yu dp gravity on the Moon. The Moon's radius is 1.74l 0,muzx ng;p.k, h+x;p.yydu $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timeo(k v .ej.,xyekoi0c .t 0hx(as that of Earth, but has the same mass. What is the acceleration due to g a.( .0vxjckoheti(,0xe oky.ravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tdfe yc*/wld/4pk 8z/ahe same radius. What is g near its surface? dfdac/yke p8zw */l 4/  

  Two objects attract each othzraixo(0rjo 7*w02 um er 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,trj8 )f xh9(ze at (a) 3200 m )j8(rhxf e9 tz   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance frrch2bohw x;((pgoj7h5;y m 1oom the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth i h1wy((xr5oo c;mjgpho7 ;2hb s $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five ltw 40f)jwj;l times the mass of our Sun packed into a sphere about 10 km in radius. Estimate ;wt lf40)jw jlthe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once w /q - /(bt;rmohgucyh2as an average star like our Sun but is now in the last stage of its e trhohq/- (/;2mcyg buvolution, is the 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 weightless while orbiting in t,:3kmj edy.n;rzo xv 1he space shuttle. 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; krd,z ej3n1v oym.x: terms of g.   

  Four 9.5-kg spheres are loca q5j(a5gj1qi bted at the corners of a square of side 0.60 m. Calcujq5 q(bi1 agj5late the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on tp t/; j.z07 hd7t pmoli.9utiqaki9)fhe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a lin t il7q9);z k9 /.pojdf0t7muhit.i ape (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of gl; 7x6 l4zjnfwhat it is on Earth, and that Mars’ radius is 3400 km, dete6l7gnlj4 x fz;rmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of thd ;pj9knmoq6hiw (+ j3e Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws,+j( d qk hpj96nim3o;w Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abouheb. z+2ykq q5qi6gx5t the Ea 6ye q.5+qxgkz25 qibhrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km a; a4k 31x0l1uuswe8wp qz y,mqv yx*p5bove the Earth. How fast must the shuttle be moving (relative topeksuww;x15qq,lx1vm u ap z 3 y*y084 Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience (0a8bc mnq7 uzsimulated gravity of 0.60 g? Assume the spaceship’s diameteu qa8m z(nb07cr 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 sv+ w *v1apf/fl75 sy sjf58d3fjub m4latellite to orbit the Earth in a circular “near-E 85uwldv7p 4fff3vmbj *f/ays 1l5js+ arth” 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 satellite?    s ~    min

  At what horizontal velocity wo5tu5e/s7 *j zjub: ciruld a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earthrjjiz5u:u*cb 5/ tse7?   

  During an Apollo lunar landing mission, the command module continued to orbit th j(v. wa2qf:hle Moon at an altitude of about 100 km. How long did it take to go around the h(2:fwjaqv .l Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The innvru/6/ r3::/mlw kkcj ndn/zuer radius of the rings is wmr3j6vcnk:nr //u /:ld/kz u73,000 $\mathrm{~km}$ , 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 o9k,s.iuyabtq h7 -lpr2t nm)9d8p 1yence every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weir7tkpe- 1a,u 2 qm.pn)l9hsy8tb9dyight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a bntv bv,a,/-n75-kg astronaut 4200 km from the center of the Eartbtba,n/,v- nv h's Moon 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 ejcmr .d(f0 elcwe 734aqual mass. They are observed to be se.m ac3j(e4rld ewc07fparated 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 readpv rb+f:g uf(, for the weight of a 55-kg woman in an elevator that move,fr: bpug (vf+s
(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 hang6ee gw;68y hnpw*c d.qs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks a8ge*ww.cyn;6q he p6d s the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbp5m ngx0aw59:q irf-bits very near the surface of a planet with period T , the density (mass/volume) of the p9ipf nb:0qa5rg 5w-xmlanet 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 gxuh4v 8kiuqy,l4-;r period of the Moon (27.4 d) to determine the period of an artificial satellite orbitrv-lkxyq,8 ih4uu;g4 ing very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acro) ob6j+f*wx rsss, orbits the Sun like thej6 )w*s+bxof r planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance h;l1 nrxb ga4,l* p0vlmj n)g+of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun rw hvp(ddmtoet/4:cm g7( h75c oughly once every 76 years. It comes very close to the surface of the Sun on its cloet t :m(dmp57/hc4 wg(dhv7c osest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of tht894 0 3grjhp.cda3rr0dlu fve 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 largest moonsn 0lgv*0 fb pv 2d f,cji2d7uc8mmf)9u of Jupiter (those discov2 ufucgp79v li dvn8,mc f0f0bd2)mj* ered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth nok ;)qnt+dpwwjsbec ky0/h u*5i359 from the known period and distance of the Moon. yhcw);b ej/kn9 okw 3u0 * qst55pi+dn   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinb xpa07v6 cut6g Kepler’s third la v0 6bua67pctxw. Use 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 Jupit 7fsfkex 43a .-i(77fbfkipyrer consists of many fragments (which some space scientists think came from a planet that once orbited the Su.pi 7y 7afbxiks rff (74k-3efn 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 ae ;bw1ddcvl/p8; s,q fn artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). 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 Elep d,s;c/vbqd1 8;w farth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 2h/5fa 0dql1qh6 eocw 5–41). If his arms are capable of exertin5 6ao hcflh0/qe1 qw2dg a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accel -sucq fnn 6;9+3c9z g35bamt-wndz fteration of gravity be half what itsan;z+f9nn--mwc zf5 dbucq t3tg39 6 is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equ d83ic fh-mws.al mass grab hands and spin in a mutual circle once every 2.5s i-3mdw8. hfc s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration f jj67i e-fbagf 3g;-)b hz9kuof gravity at the equaf);j36fae- uhg-b7kfg9 iz jbtor is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trave ad-bo/km7 j t,i3h9ypvy8;q tling directly from the Earth to the Moon exp, k yvd-jtp8 aiq37;y/9 hotbmerience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on xpj5yy9l9 b-x a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the el 9xxy-p jly9b5evator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a c+ged0* zfa;o1dqqp5se :ait*ircular 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 perpo*qa+ q;:*dtf 0sie1edz5ag 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 aircri t-8imlg9 wad6m,xg- bhy( s5aft 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 in terms of its radius r, the acceler40hm 8-x /h mp5pfntu*vuyp*jati58uh p-jtnhm4 *up pxy/m0* fvon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m o9p c o;v1 ss4gh7gxh1hanging on a string) is deflected from the vertical by an angl hp1coh x9;sggs 1vo47e $\theta$ 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 ban;iln nai k g,qgi 1l,0lg,w)yard,y/5ked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handl,d,/)g;rlggalw01liy i y ai,,nq5 nke the curve?

  How long would a day be if the Earth were rotating so,u nx jctz9nn.,e k*(*l,put p fast that objects at the eke npxnz t,tj(*ln.cuu p9, ,*quator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distat;to (y.1y mjence 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 t zgw0fpxj68* ngd1;c(dx y1 tof radius 235 m. A lamp suspended from the ceiling fx0d 16wg8ydx1 ; (*tnjpzgtcswings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as maishot9 : 2d7gassive 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 since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at tha g:i7h ts2do9e 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 Spah8g563nmb y 4m tdd3dlmu5d2e ce Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dens5em b 63 m2 yd4hn35ddgumdt8le 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 hi (oj.y; -zpk0 b-jqaeull and valley 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? Ligh-0j;pu yez ko.a-qb(j test? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a grou p kpm3qz,+u wqy:m poum5*47tp 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 satellm p:y kpw* 7pqtmuz,5oqu+43mites 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 Ren*.ep wb gyg , +xs0;eb4napehg1p 9.wldezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km g. pnhb apse+bwe;ggy*e w x.14l,p90. 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 in need of rejqr(znzbgj6p (f4g. a 9s 2,gepair. You are q6ps(z nabgf rjz,.g94 2je(g 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.fh)lnpxg6vgy ep 6-iwy 6;b *7 (a) What is its mean distance from the Sun? -7hgxbfi6nlyw6 e6 ppy *v ;)g  
(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 neeyjqrhq:c + f* 5wwrmbqw6+:l :d to be if you could actually "feel" yourself gravitationally at5 6r+:cmrj+:yf * wlqqbwwq:h tracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cente2 ejrb-bknx u9b(me)p*g m i(-r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centerm(*ein2 u b-jr)gxpb 9b em-k( $ \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 lo90 tdfmir 5vh3g8hl; pcated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side oftg9p;3ml5 h0ri8v h df the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits l1vkvswmbka1 os38e+la 3+r)the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep secnv1heuk-20 ytond hand on yt-vy2 u0 khe1nour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker o 12h+d(blpr n xr09hsweight around in a circle below you on a 0.25-m piece of fi 0x1h +( rsd2pl9bhonrshing 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,xtcn enm4m52ce:ji1j 0 n+tu in a new highway is designed so that a car traveli n,j e x4 ej5ti:2m0cncnum+1tng 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, uti46rnccd(i*ntgx n385axh.m x lizes 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 xd8n cxnm.6 hn (*t45a3 girxcexperience 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.$\approx$    $\times 10^2$