Sometimes people say3o k/eelye.u+ that water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statement?o/3e +eyk. uel

Will the acceleration of a car be the same when the5pq+0-b3o lpp4 t)zija 8xkae car travels around a sharp curve at a constant 60 km/h as when it tra3t k0el-pq bop)x45pi+a a8jzvels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant shdxb21:rfpnxrvd35;/ ::s xh qxap ;hpeed along a hilly road. Where does the car exert the greatest and least forces on t:d 5nvrxs2xh:dx1bhrh; p/: f3pxa; qhe 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 hill?

Describe all the forces acting on a child riding -x hvm5mp xb3(a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the child3 p(-xvm bxhm5?

A bucket of water can be whirled in a vj32u: il5jb , is( -is9 *cdo874ryfm swvjnobertical circle without the water spilling out, even at the top of the circle when the bucket is upsideos5y*j2-4, :b s 8iljj(cbs nufv dim37woir9 down. Explain.

How many “accelerators” do you have in youi89yt,g nf d7b nkm0+pr car? There are at least three controls in the car wh+n79y d,8inbgtp m0kfich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hilzwgt7drzfr yf,0 te7mmf-0; ( l, as shown in Fig. 5–31. His sled does not leave the groun z -mwtf7g7zfyfm,tr0d0;r e( d (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounjddevvs.tj +-c 6 m;i;ding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang +dut;3.* iu sb+b(8dpmjbkid le given its speed and radiusd;du38d.u tskj( bb*b+ pmii+ of the turn?

A girl is whirling a ball on a string around her head in a horizontal pla6 x3osh cwq,,une. She wants to let go at precisely the right time so that the ball wil wcq,u63h,s oxl hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gux;afx 8q*3t8p xgcl (ravitational force on the Earth? If so, how large a force? Consiq t88xc*xp lx;a3ug f(der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what w flrur*px -)i ef.iqr+( s*a9kays would the Moon’s orbit besk r(9.) aie+i*-xrqf ru*lf p different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the )o cr(ww1q8gyEarth? Which accelerates moy8wcq1( rg) wore?

The Sun's gravitational x4- ogp,77e.) z.qjjitfynfqpull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [ny.) -7jq jpxefiq.,tz fg7 4oHint: 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 effectmp4ce*--llgza .-kliib )tggm*l :z6s are at work? Do they oppkpm)* -g te.-zc:l gil6limgla- 4zb* ose each other?

The gravitational force on 99,)mxp9xk we- e6om 7 .j,kpdcibmrrthe Moon due to the Earth is only about half the force on the Moon due to the Sun. 9pwx ee .x-6c,7mkrmjp9m,9kdob) ri Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largeh ,b pbp1 9vi4 cf9qk3gy9lf+yr or smaller than the centripetal acceleraqg9l +hc4yif,13 vb9bfp9ypk tion of the Earth?

Would it require less speed to lau ,10 c+qfid03tv zrktrnch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s ,q+rcikz d tvt0f 301rrotation direction.

When will your apparent weigr;ifv2rzuh z;*8 b .ttht be the greatest, as measured by a scale in a moving elevator: when the2.htb* z;;iruzrfvt8 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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectell 58pci gj3)td by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shelll g8 i3jc5l)pt that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or ,un/sxt5gm56hija t 9 “apparent weightlessness” between stepshxs n 6ujti5t m/95a,g.

The Earth moves faster in its orbit around the Sun in January tepwz5xm c3ktjzz s i-2b +gw5o0ph705(p xnq,han in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of oz (pbw+p-7 m0xjw2gi5h,k z3sne 5zxcp5 qt0a 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 until it (k8f)c uwk-3 hvzre f, jed12cwas discovered to have a moon. Explain how thic-1kuff(v, hzkdej3r2e8 c w)s discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largeosy+h*u .g ;a tt*)ejpr than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with se+y.ja*o*u) gt;h pta 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 travelinjt(5n6r -gczow.( xip g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal accelerati83, s, xzoxtiqon of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? A,,io xqzx8s3 tssume 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 dyp0ed98,be d siscus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed 9sb ed ,edp80yof the discus.   

  Suppose the space shuttle is ing 5mo m(rtz+3 :zgqc(q orbit 400 km from the Earth's surface, and circles the Earth about once every 9(z(t+cr g3qo:mz5m gq 0 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 of the acceleration of a speck of clay on the edge mukou(2*f7 ackvn -7) 94rh ojx8bqla of a potter’s wheel turning at 45 rpm (revolutions per mcamfx l qk2n*ov774k ro ( 98uahbj)-uinute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved a4 p cxj*3 1zs)cwjpnc2t a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3wjzc)cj *3s412xp npc3. 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 car can round()lsm ny 3 m7wi+qf7quqg p20k a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this 3m7nlqk q)si pfm+7gyu0(q 2wresult independent of the mass of the car?   

  How large must the coefficient of static friction be betw0p 4dtziyn3iti -ic8grow(::een the tires and the road if a car is to round a level curve of radius 85 m at a speed of 9:80 pr(ygzi:wt4c3 tnodii- i5km/h ?   

  A device for training astronauts and jet fighter pilots is designk+3xhc29r0 r9nyk kq eed 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 c2qeknr90 k9h3+kxry, 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 oc:th;; a ct4jff a 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 of static friction between the coin and the turn;:tca 4;tfhj ctable?   

  At what minimum speed muxb o wzn braxtf,-./84st a roller coaster be traveling when upside down at the top ofnb-aw8x.fx t4,zr b/ o 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 roubh lc)/ma-6t)wpjp( pd/cl/7 wg el,xnded top o/6)m p) - /pab(gpjl7/c cx ,wwhdleltf a hill (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 15-m-diameth39t 15k hm y.zz/rkpler Ferris wheel need to make for the passengers to fee/h zkr9 k3phmty15l. zl “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg ,63hrk1 r iaub*lazp+ is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the ua+r hl3ia* zrk16,b ptension 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 particivtt8)rq vkn0qu9 3h1,fzd,ry ;n*f ple 9.00 cm from the axis of ro1 fu tnd,;*zh irqykvvft0p98r3q,n)tation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are ro9 )bj- 8kf v6jg,nq(8slhdxlttated in a cylindrically walled "roo q6nk )d-,lbxsg(jt9hlj 8f v8m." (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 circle on a frictionless air-hockey tae 0+b mbocr.l7bletop, and is held in this orbit by a light cord connected to 0b+ oc7rmb.l ea 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, byazve* f7q6qri8d .b/l not ignoring the weight of the ball which revolves on a string 0.600 m long. In partiqz7e.8r6 i /vald*bqf cular, 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 fot,s m wkeo0d6l(k.gd wo ,8u0or a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses vcmzjb o ;00yhqin ez ;lw)pj8: h6:m8$ 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 verticanl*ff3 rrr/g rjr9i( 6vva)c)lly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the nn4z8 v68pcuw get force exerted on the car (by the ground) in Example 5-8 when its speed is 1548uwg68pnzc v$ \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 areaazz;n9(4w d7u w8 g-ix zhlum., going from ahxz zg4.u78 wu9w -d;in(zlmrest 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 with no slipping or skidding? $\approx$   

  A particle revolves in a horizonta8)km,(l ;okwbpv-lbhw , uvv ;l circle of radius 2.90 m . At a particular instant, its accelerationblp(kl)bw ; k-8vvvhu,, ;omw 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 rh+ 17,likhhd km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. li1dh,7 rk+hh  

  At the surface of a certain planet, the grav/ycrd1g0s+ f p(t+mt0 qai0um3db-vyitational acceleration g has a magnitudryft0a(umm t0bpc+01dg3vd s /+ y-qie of 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's radius is 1.e no2 gh0l5+ ty*zp*frie9d3tm jne 9474 tt+z5n *2e0ho3e4n l 9grd*ejfyim9 p$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius6. bn(gev*wld07cfb g s bvdz;5-o4fy 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity7d szb0 yv5w.b;bl dfn*evc o4g -(fg6 near its surface?   

  A hypothetical planet has a mass 1.66 times that ofqvdw8r xjv ge13-y,+,xgjd,y Earth, but the same radius. What is g near it,wqg8 yd ej+dr-yg3,1jx ,vx vs surface?   

  Two objects attract each other gravitationally with a force o9 b j,5uh1xjvs ) ggyj5jq2s-df 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 or2 9y9y27y+isebb yrvalue of g , the acceleration of gravity, at (a) 3200 my 2r7+9ebyb9ior yy 2s    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point owj*tg,tlv sz6 )8uo7xutside the Earth where thegravitational acceleration due to the Earthtt,jzwos8x*)gl7u6 v is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star l/ 1cqm8 q yaivi*rr:7has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster. qql 1 m:8*r7a c/viyri   $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but ih5ph3d3zap) is now in the last sth) 3p5hapdzi3 age 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 whilem c+t5)x ox+vbpc r d:4pa0et6 orbiting in the 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 accele4+a0cc rdm6v xo xeb5)t :t+ppration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of q ua56r*w f5y*qb4jwu a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted q*5jf 5u6 *bwuyr4qwaon one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the ssjq e /vz*bq8y 4zhb15ame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The mb1*8qsyve zj/b4 qzh5asses 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 what ujg( bch.99p rit 99jbghp (.urc is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Ea,vjk mq-y)q3--2g h mayc y+rarth and its distance from qm -ryhc y-,g-)kvqa mayj 32+the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular ot/depk vz 5z /x-ycqb*)ib;j2i,i t1frbit about the Ead)j;, 5x1ieqfb /btck/* zzviipt -y2rth at a height of 3600 km.    $\times 10^3$

  The space shuttle releasep7hhv o5 nwz 5f4iqj+0s a satellite into a circular orbit 650 km above the Earth. How fast must the pvzoq5ni05f 4w+h7hjshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rot2p)0c) cayshmxx 6.yl ate if occupants are to experience simulated gravity of 0.60 g? 2xxp.6ycamh0)y c s)lAssume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in al6y5vb id1 m)pb*mx8d circular “near-Earth” orbit. A “near-Earth” orbit is o)bmy8bi1lmpvdx *d56ne 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 would a satellite have to be launche-xe;5wbudg)e d from the top of Mt. Everest to be placed in a circulau5xb gwee-)d; r orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conu bp mr/dtj8j h8ot(o 4d))*tntinued to orbit the Moon at an altitude of4 rh 8bjuod*8jtt )tdmo (pn/) about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbia2d87+b5mk d6kf xv8wkms ku-yuiq 7 8t the planet. The inner radius of the rings is 732uu-sv b imw 8m87kk+8yqx6k5kfad7d,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 pubg7i m)08hv0,rncemykam91 qnd 63 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the3n u 0m9c07,nri mm1g8qey6bdkp)a vh top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-ky )q9t7 e/k6;ii jpbjrg astronaut 4200 km from the center of the Earth's Moon in a space vehic /k7)jt6 i;jr 9iqbpyele (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 sys +nbv /0ieik5 lab(hj.tem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is thekl(ib.n +j0e5hb a/iv mass of each?    $\times 10^{29}$

  What will a spring scal)j;uupu8 u6h he read for the weight of a 55-kg woman in an elevator that moveh6uuu) p; hj8us
(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 ceiling of an elejwn 2b bn 8k9j87wx.buvator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s min ub829b8w n7 bxwjnkj.imum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the sup+or yo f)v rm94,io5trface of a planet with period T , thep9 tyo ir+oofv),m4r5 density (mass/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 determine the ppxxyv03 k0b,fln icn6 -n e/v8eriod of an artificial satellite orbkcx bfx y6en ,0n3pi-0/vv 8lniting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few huq jkj(eum5 0 7m7dzdq+ndred meters across, orbits the Sun like the planets. Its period is 410 d. What is its meq+zqm m0(57dkudj7je an distance from the Sun?    $\times 10^{11}$

  Neptune is an average disv(w u.zk+ij:rq0 9bgx tance 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 roughly once every 76 years. It((sd ; 43lzanhz owcp* comes very close to the surface of the Su(zohpwcz*a n4( d sl;3n 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 about tmq4; .f j u79r u.mssf+z;acuphe center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largesw0jj4(ztkt:4o x.f4l 4pj hidt moons of Jupiter (those discovered by Galileo in 1609)fklt0(dojt zh i4 .4:xjw4 4jp.
(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 k o2r4gil23f shnown period and distance of the Moon. ior2hf2sl 34g   $\times 10^{24}$

  Determine the mean distance from Jupiter ghj9to6*pz5 a for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the T6*j5 toaghpz 9able.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jc 0* ciqvctsvvlc8 52k+8j 7u0nnv/o vxl5r/aupiter consists of many fragments (which some space scientists think came from a 8vvcaoil/s2c0nv0c 8 q5+ k vjcl7v*u/ n5trxplanet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a bekb:)aa/wk d) and 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 w )b)/k:eadakour own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc fr *yoss6g0z 4zrxid4uy :9dn7 wom a hanging vine (Fig. 5–41). If his arms ag 4: s ydz4ys7wiu9n0*x6zodrre capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be halqd* ggok0c5n v +4,fvv3;ymtp8/dghi p;vm,hf what it is on the surface? ;pvo3g08,d,p *5qv4g+k /;nhtgmvd vi mhc yf    $\times 10^6$

  On an ice rink, two skaters of equal masscdkxw4s8782x )q /go3hhur ij 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 are 60.0 kg, how hard are they pulling on one anothqcd38x hh/x7 ij)kw82sr4 uoger?    $\times 10^2$

  Because the Earth rotates once per day, the apparenuclgm p ual)b72(d/,vyh0x(k t acceleration of gravity at the equator is slightly less than it would be i(lxhcklua7 m/0py,() d2ug vbf 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 kqgf o g;dm*3js5.lb:q(okt3will a spacecraft traveling directly from the Earth to the Moon experience zero net force because thsq klo(fbj:3tk*m .g5qd3g o;e Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a b5xoaj af0z. 5cathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, aofa z5a0x j.5cnd in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wi-y)xti1ffe) g ll 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 th-gity ))ex1ffe 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 )nyb mb1(/ os llyl k-g;wn+isnnl8)-(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 xx2 qn5fz(d:d in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constan5 fzq(nx2xd:dt G.

A plumb bob (a mass m hanging on a string) is dem4br. /p8;sdrkn : ft9fr9 qneflected from the vertical by an angefsmp 9 n4/9:8b;rnkdqt. f rrle $\theta$ 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 deisymt 2om khvzd(a p27g8ha6w 73g1u1sign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds chwu(m 31i d yso2hg61t kma8a2v pzg77an a car safely handle the curve?

  How long would a day be if thxwl+;hra +wqodm ;a8:y vxlz,u+6mje10 qx3i e Earth were rotating so fast that objects at the equator were apparently weigxy1vqa+dj8wz rx + l l;qum wa;3o:ihe6x0,+m htless?    $\times 10^3$s

  Two equal-mass stars maintai6) mmeje k(m4en 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 constafh++ qd8 cjw124a ,fj7ujsazent speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings waf h2fze c7 14,8as++jjqjud 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 op-q1a z 86 bn.jgi1hvas 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 the equat1jn io bz. 6-v8qgh1paor 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 an0m tws+0fyj+ j7sq3fwyy*da9 extremely massivef fysdyq ya9w 0+mj7s*3+w 0tj core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds 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 spi:h10g7 ob r)s9qyyaz )ehq.leed 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 the driv)yq)s zi. b7g1yo:qhle9 0arher feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizl1eu)r26zd-+s fgv t9sv, zqzes 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 cenq- 2er6zvu,l)dz ts g9f+svz1timeters. 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 Ren w.d2 fz59nds hclq;x9dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about9;n.2wcz9 sddf5ql h x 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 pub cpo c-z8k1/zrsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400b1cozkc / pz-8 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distanc5k3 f0 6on) scdldv -8vuk*jdae fro-dj 0 c*kf 3dn8ou5v6sdkvl)am the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" b aaxi4q)h3 ve62 ru0lyourself gravitationally attracted to someone near you. Make reasonable assumptions, likei abl r23u6)4a0xvq he F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fusdogvp ;(7k+ig. 5-46) at a distance of about 30,00 uskdpg(7;ov+ 0 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 located at the corners of a sqn lqh1.slcy,,uare 0.50 m on each side. Find the ma ,1 hn.qlslyc,gnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 554kxw :z.n(my e00 kg orbits 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-long7npy1jb-8cax tom*h 0 sweep second hand o m*7-xnhyo1pb t80ajcn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroun,84 6ppir33 qfg0;bqnaxa1jz lwjhq8 d in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical3 4pbw38q qr ph1 za6qx ;,gaj8j0ifln? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travelhmss :wce,-np*jh0lf-y6 hz( ing ats-yh h 6-0 wesjlhpm*,zcfn:( 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 tili4;ek1nujc *vt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that 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 notn*1cui4v kje ; 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.$\approx$    $\times 10^2$