Sometimes people say that water is removed from clothes in a c)nsquy38 ;*jzkx be7 spin dryer by centrifugal force throwing the water out*ns)8z;cjqy uebxk 37ward. What is wrong with this statement?

Will the acceleration of a car be the same wh k+oiag2kw3x:s 2qiw dj.4aw 3*n8h nten the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curvwsqn2483kkdho*wia2 + 3 .gjnta wx:ie at the same speed? Explain.

Suppose a car moves atywg*q:: s ya*p constant 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 *ysw : *pgaq:ya level stretch near the bottom of a hill?

Describe all the forces acting on a chig+w-(c .ocshe wd k,k/ld riding a horse on a merry-go-round. Which of these forces provides the c.hc g -wk/,+e(ksco wdentripetal acceleration of the child?

A bucket of water ca.hecq,wf co/ z.7rrf)n be whirled in a vertical circle without the water spilling out, even at the top of the circle when..fw/cq r zro),hef7c the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Therguvtm3d*ksh7vfxkogrle26z +)jn3*/k b 5 (d e are at least three controls in the car which can beogh/5vg6 ks+d(73 zej*dfxtn)b3lm u kr k*2v used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the co1c r1e kt.mv -,ewqxo20fj2mrest 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 asetoe jmv. rc2mw,120x-f 1kq o he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roujxkr ;y8dfj;aon5(9i nding a curve at high speed?

Why do airplanes bank when th n+ +b 5lqmxq;1+lz0 k/affvqiey turn? How would you compute the banking angle given its speed and radiusfqk+inl+/ q l zv0;5bm +aq1xf of the turn?

A girl is whirling a ball or uyz(f7pg.v u y jndq52w51:hn a string around her head in a horizontal plane. She wants to dqu1ng 5h:z5v(rf72p .yj uwylet 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 fo u8sarw2zf-(v;.vg j xrce on the Earth? If so, how large a force? Cowrjv f;.vxzg8 as( 2-unsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were w.ufyw e,+w: 7khgc q.t ;ng9jdouble what it is, in what ways would the Moon’s orbit be differe7ghyq.w w:,f9c ;nwg.ue +jtknt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Ea:-.5rpw/tv gee,k1 x onw nyy5rth? Which a5w nn/oy g1pkrywee.x :,v-t 5ccelerates more?

The Sun's gravitational pull on the Earth is much larger than tf1y(h3x,zpf1tf+f8: mxy cur he Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint+ :1fftzcym8 xphrf31x,yf (u : 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 are aq+otk (zsho f 1,a+5 cvf;qe6zt (t;5sovhqao ++c1ffeq zk6,zwork? Do they oppose each other?

The gravitational force on the Moon due 5d;ehe9x o 6.4ajralg to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fromjaoe g6 dr.54; lxe9ah the Earth?

Is the centripetal a0hkexu +k*0pf1 9qn 0kkcx5rlcceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acfqk0rx0lehuk19 c x5 +nkk*p0celeration of the Earth?

Would it require less speed to lxr.pq, 9mm-h+y.6ef*j wq eqc aunch a satellite (a) toward the east or (b) towamqxh p,jw q+.*qy .e9em6-r fcrd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sc/kg( yumctx 51ale 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 as when you are on the g1ktxgym5c/ (u round?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coul;vn3arrq - hv6ce.;ue d 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) the force we feel on our feet, and (c) any other 6 q3au.r ec;;vehnv -raspects of gravity you can think of.

Explain how a runner experiences “free fall” o/i7 /yo*nuter)v.u clr “apparent weightlessness” between sti/ye*c )vl/tn.uor7u eps.

The Earth moves faster in i.xtp me4 b 0h(-f:fkfkts orbit around the Sun in January than in July. Is the Earth closer to the Sun in Jaf ftbx0fk:. 4hkpe m(-nuary, 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 was not :x0 d.rk:vdn2sg+m p39wnw ae *cn(xu known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mwwxmu.evx:dans(g+ 90 nc *: 2k np3drass.

  The Sun's gravitational pull on the Earth is much larger th2w 43xkety2;ctyk.mkwh s1 h4an the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fkt2yhem 4x;ys3c 14 2w wkth.krom 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 19zskta17l* xj1s: g0ol80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetefg *d -9o9ulwal acceleration of the Earth in its orbit around the Sun, and the net force exerted on thogl9 -wdf9ue *e 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 itg4.gjii 5)fm lpg1 3qd rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed gdmf)4 i qgg53.ilpj1of the discus.   

  Suppose the space shu0 d5* 8kvnoiq-hkn a7qttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the 8*q7 viqnkk0nhdo-5a Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on h3. s/w u1+ tjrol1cowthe edge of a potter’s wheel turning at 45 rpm (revolutions per minuj3th/r o1.1+ucwo wls te) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string.7a1 d+9rkvm kb+ olst is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 lbv9d 7k+1 .ko art+ms$\mathrm{~m} / \mathrm{s}$ 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 car can round a turn ogel6ykgc0riii bs*5rh *r0.+ bz3f(cl+2sl s f radius 77 m on a flat road if the coef5b0brl6(i0s*rgf.+ck 2*ceirs lz s+ih y3 l gficient 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 tiresrbdic xs9):u d.r,wxompg876 and the road if a car is to round a level curve of radius 85 m at a speed ofp)x97u. :8brdxgcs,i6 w do rm 95km/h ?   

  A device for training astronauts and jett3h,uug gdx4 n26dg no fm4*i/ fighter pilots is designed to rotate a 2gfdo*,u /m4ghu 6t4 gnnd i3xtrainee 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 a1luj unp(ov6 . rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient uul 6o( jvn.p1of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling w ku wzw)jie*5*hen upside down at the top o5iw ukj*)*ewzf 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 rounde-3d +0or zboood top of a hill (radius =9o-03dozo rb +o5$ \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 Ferpy;twy0 uj0k 2 vb.ht(ris wheel need to make for the passengers to feel “wei. w( ;bt2k00ty upyjhvghtless” at the topmost point?    rpm

  A bucket of mass 2.0m + 0p/ nxrzdnd*q8yv8pm/wd2 0 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in therq 280dm/8*xp+md vn ynzdpw/ 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 7 c1 v wh2f*i1x f0/,axgtixdncentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experienctd fax2x ix,f* n11giwch0v7/ e an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindri zp2a+7 zx0f pdi).wpscally walled "room." (See Fig. 5-357p) ap.zxi0f pws 2dz+.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey ta+z2csh 97 .5wyg swvmnk4j/u4rn u8embletop, and is held in this orbit by a light cord conn4m4r 5 scuwhy.+negs 7k/zwnmu jv8 92ected 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 ignoriu2p+z(ysy8h kbz;9unng the weight of the ball which revzp2 ;(y k8b9zsuhu n+yolves on a 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 i ,th9z utmg6lu ,,.hvks 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 massesmbxqzo0/r* x:ji 2 4 i3aybw*l $ 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 divix rn+v3hl21vjpq 9k6 xng 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 o .5 v6aixpl2zw52pu6i2 ouv rif the net force exerted on the car (by the ground) in Example 5 wv po2xuziua65 r.5l262pi vi-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,nw6b -7 yt4ap:yb mt5m going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration b p5w-4:bmt7m6 atnyywith no slipping or skidding? $\approx$   

  A particle revolves in a/yalk0 oc3mi. ;j/qvw horizontal circle of radius 2.90 m . At a particular instant,3av;.c / ly k/jq0womi 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 gr5iyiid0x ) *ruavity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s su5xi )iruy0di *rface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelesw)v(5 0zm7,k.. 2rt kfbbctjjf c:wg)f.laqration g has a magnitude of 12 m/k0 .arg cjjb f(mf )lw.sb),.2w cfvt:5tq7zks$^2$ 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. Theky+surm37f5s 0 zeamih)y 1 s0n/n*ff Moon's radius is 1.7z)f+1mh/ys 03fsnerukyf i7 amn50s *4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same mast 9 o1vt*,drqbs. What is the acceleration due to gravity near its s tvr1btoqd, *9urface?   

  A hypothetical planet has a massw27 /e j7ejo j5vym.he 1.66 times that of Earth, but the same radius. What is g near its surfacjehe752owj/ y7j ve.me?   

  Two objects attract each othe(/;-r b qoezpdr 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 o;ptxgpb zm *pn 3c42t3f gravity, at (a) 3200 m m33z;b *cg2tp 4tppxn   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthvsw6a s4t-l s,a r+h1n where thegravitational acceleration du-hnl4a ,wv6ssrt +s1ae to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hae cfcs*gej (w1wvc/0+n9k+dlnb 4ml.s five times the mass of our Sun packed into a sphere about 10 km in radius. Estimat* nbfe ldjw49g/. scvemc +c1nkw+(l 0e the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wav+sgh7 u r;*h-rx/, olkc(ifws an average star like our Sun but is now in the las;v(wf+hkc g* h7x,- sl oiurr/t stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless cdjz. ai -g+o-/ j8ppcn5eze8 while orbiting in the space shuttoed5 g czzp8 je -ipa/-8.+njcle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m.-(pcc u 4a(kbv2 iyk5o Calculate the magnitude and direction of the total gravitational force exerted on one upycoak2 b5ki(c4v-( sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lin,w *tu(vz*hf *qxmz2we up on the same side of the Sun. Calculate the total force on the Earth d q(twvw ,h**2fxzu*zmue 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 a;cw,iay ,nj k;t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3cj ,,wa i;k;yn400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the -mbc293y jh(..dqo: l juevce period of the Earth and u.e9jyel(bodvm 2:ccjh-3.q its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of apf(irza fdss *s:*0;v satellite moving in a stable circular orbit about the Earth at a height offfa;0z: i*sd *srvp(s 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above 02b yhof mssp9n. mk3kc9 ;7arthe Earth. Hokmr y9b 3 n7cfa0m2ps.9;kohsw fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical at3 :8rcad*qmy/+wi5ek ffxt70ens+ spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revoled 8*n0t+ 7fa:ci/qa yftwrsx+mk35eution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earthshb5u-u-3ql s 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 satu3h-sls5 -u qbellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the a6-yq +- hhv+lcb2ivf top of Mt. Everest to be placed in ab62hf - via-+q +cvlyh circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module pyy 2g u-c92:otq ldk/continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onc92y kop/l-dtq cu2yg:e?    s

  The rings of Saturn are composed of chunk9 1:(sjs uqpbp3aqv7 ks of ice that orbit the planet. The inner rads9sk1pu a:q vpqj 7(b3ius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15ysz,/ha68 cpb.5 s (see Fig. 5–9). What is the ratio aypz,c8h6bs / 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 )ol qz:f) n57p ctxb 2xcz3sn*75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocifn*7 )zc bcn:t5ql3s xzx2o)pty,     ----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 otnzu)ev 6)p6if equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbievi6puz)t 6n) t about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for theeqp; f*a,rvu6 v7 o:so weight of a 55-kg woman in an elevator that mov*;voofv,ae:s7 q up r6es
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceil6:ywh61xqu fj/)/-ou hsf/amug * vuging of an elevator. The cord can wi: 6 gus ffhw/g uy)1uvm/ha*ju/ q6o-xthstand 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 planetgd5r5d4pv8 h, ctinj-(8 cjqh with period T , the density (mad8p( 4r,i j5dhqj8nh-cc5tv gss/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to dexcwr04 1qy.56 8auuc5 sohui ctermine the period of an artificial satellite orbiting very near the Earth’s sur1cycxhwuoa6sui 8 cq u0. 554rface.    s

  The asteroid Icarus,mwjttny-,fk 9v r21q+ though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Suk q+f y-wtt,v21n j9mrn?    $\times 10^{11}$

  Neptune is an average distance of 4.5/z ;rindh(rd1 $\times 10^{9} \mathrm{~km}$ 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 roughjoq5 pg n(f 4k08ub0ealy once every 76 years. It comes very close to the surqa bk(j0p un5f8eog40face 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 Sun.]    $\times 10^6$

  Our Sun rotates about36w yli1yesx 8 the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fh)bxhc5 c):ny our largest moons of Jupiter (those dis) )cbhy:xh5cncovered 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 from the known pero3wisr: e04luu a7ys,iod and distance of the Moon. w,i7r3aoesu u ys0 :4l   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of J:15)pbs4cxb wf j(+myvus d: rupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the + p)xymjfv(4srs1bdu:bcw : 5 Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betb+i9 wka)wr*/ka yim;pbbxj 2po/, (yween Mars and Jupiter consists of many fragments (which some s);(p*bkw yok iyx/b ibp j2m/ 9ra,aw+pace scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pls.**3xs/h16xgf ig b ryzw ;bpanet" 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 grav./x6bbxr f3yh1w*si*g; pzg sity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge bykt6. ;c;wvcpqtqghy: t( d. e:8tf4pb 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 tolb 84fy: (ht;cgk..d;epp t:q6vtc qtwerate 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 surfaao6ggaa 7 fp(;ce will the acceleration of gravity be half what it ia( ;g gpaa67fos on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin il(4wkw;cdv7 :4q eh*kx2 0n 9zaojkkbn a mutual circle once every 2.5 s. If we assujk:koxbcwe2;vq kw l dkn49h4 07az( *me 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 i;k 9 pdbyi8wzp al0b5ha a;rk1;84rnapparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effebay1hadn p8akz; pi r5 wr04kli;8 9b;ct. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from pprua 9k 9pa1::q bo8zthe Earth to the Moon experience zero net force because the Earth and Moon pull with popa: p819:bu zakrq9equal and opposite forces?    $\times 10^8$

  You know your mass idl a.5ct: ctl+u 5fx8us 65 kg, but when you stand on a bathroom scale in an elevator, it s: +cu.l5 ld5t8xfu ctaays 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 tube /am* g/gbz0yjthat will rotate about its centj*mg 0gz ab//yer (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 the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop ( am xw8)9abr.ic ;htl,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 itmgt( s3e p7t(ks radius r, the acceleration due to gravity at its surface and the gravitational constanetkm t37(s p(gt G.

A plumb bob (a mass m hanging on a string) is deflected from th d,2fcm(5+ez9:qp-zc( tu 5wovhry bse vertical by a5 bhc(5-9t:v, wompc 2de+z q(rz ysfun 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 2 7fnt)8sjfcdk8oi3ibanked for a design speed of If the coefficient of static fricti)f8isf32ct nkdi7 8j oon is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fhdzru,4/8 2d-ark yj 4ymth:past that objects at the equator were apparent8h4u2zr a ,4/-p:tdhrdj ymykly weightless?    $\times 10^3$s

  Two equal-mass stars maintain omp, ,7ddk1ux 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 m. As5yx0 pvep4-b2zz x3t lamp suspended from the ceiling swings out to an a5zzs3exp 2v4-y0 b pxtngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times asl6u/(t e8kx l+g g+gzq massive as the Earth. Thus, it has been claimed that a person u/k+egxq (llz+ gg8t6 would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator 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 deduced the presence of anywn5zl93l o xxv-.)y r extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measur) rolz .w-y x3vl59xyning 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 spee3 oebsx-) 7vqyx y:8rxmirsg,:ifi3 *d as it traverses the hill 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 thexx 7gq-ivs: s)b or3y,f yxim38 ie:r* driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positionieh4txtt( ,tx 0ng System (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 accurat04ett,x x h(tcy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 zpxpojlkuyy,- t.1 1 se*i-+bbillion km, is meant to orbit the asteroid Eros at a heigpk . ype --iuo+xl,*1bytz 1sjht 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 in need of repairvbjz 9 -dhz+in t.2ev6. You are in a circular orbit of the zijh-e .tb 2+9dzvvn6same 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 o9 vu z h;gwy1xgpd o2xn8/e).2t*gt taf 3000 years. (a) What is its mean distance from the Sun?thptx waggt 1*n dyge2 uxv2/).z8o9;   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feela9p tellb1wvq,+(u1vt he2jj0 f5 )pr" yourself gravitationally t j ,pa0)rlqf u +1pvelvw1t(jh2 e5b9attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a ; 1)zn5ctbrhu distance of about 30,00uc 1;bh t)rz5n0 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are locaip 2u:+0f w hz it.(+kkfi)mzvted 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 m: mwh .kz+u )if0fz2v ti+ip(kidpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ea3j* pjw bs8m,,8)cuos c5rpfli. vw7irth $ \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 bywni1:e m0grxzh f+s( 1 the tip of the 1.5-cm-long sweep second hand on your wrist watcsw + ezxgh0ifn(m :11rh?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cin,lbtm;njr o:*:j;ovrcle:v* t jrln ;:,om;nbjo below you on a 0.25-m piece of 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 highway is designed solc y( g3-hx)4 rcop9cp that a car travelic)-p4 9(gyxc prhl co3ng 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 osd( ;tsenj4v2l/x aoot8z2(wf the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 6(ss xjean;(/2vdw4t 8 l tz2oo20 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.$\approx$    $\times 10^2$