Sometimes people say that water is removed from clothes in a spin dryer by ce.te pt-muq:9 mac43 zentrifugal force th4pc 9-t.3tqemumaez: rowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around af./(notfow 0o peh6*5p hlnv) sharp curve at a constant 60 km/h as w.hof*hfn( )tl 60vp5w/e o onphen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed y2h5e5oy .acr/p hi9oalong 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) oe r9c h./yoihy5 5pa2on a level stretch near the bottom of a hill?

Describe all the forc-kd9d 1 vc0aates acting on a child riding a horse on a merry-go-round. Which of these forv1d-90ak da ctces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cp )ookih.zw73r7vji4 ircle without the water spilling out, even at the top of the circle when the or.i k v p7)w4jizh3o7bucket is upside down. Explain.

How many “accelerators” do you have in your oa6ko xe)e: (tcar? There are at least three controls in the car which can be used to cause the car to accelkt(aoee6 xo ):erate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest omgf -- hf6r6mzj4 dq3zmc .s,af a small hill, as shown in Fig. 5–31. His sljd6a6f rsz- m.3qfm 4 hc,mgz-ed does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundingqpx61hc*ps+ ,j ms (od3vbrwm25y*yr a curve at high speed?

Why do airplanes bank when they turn? How would you compute tpo26*sjbaxt-nr b0 /v vgjcg-z+ g+ -mhe banking angle given its speed and radius of axp2+6-g-* +s-ovgm0 c/nv bzjgjbrtthe turn?

A girl is whirling a ball on a string(yr*rs. p( e2 lzfnhq8 around her head in a horizontal plane. She wantsq2(frs8p* he( nryl. z to let 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 forc):n e byea0od+ 3qqh 9abq)gj4e on the Earth? If so, how large a force? Consideo)bg3ye j : e0h)+aaqqqn4b d9r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass w0xizu 4j 2d(ejere double what it is, in what ways would the Moon’s orbit be differede0xu2jj 4z i(nt?

Which pulls harder gravitationally, the Earjik500 cqz5bw th on the Moon, or the Moon on the Earth? Which accelezbqiwc05j 5 k0rates more?

The Sun's gravitational pull on the Earth is much larger than the Moon',3 dw0i8vr agas. Yet the Moon's is mai8d0,ra ga3vwinly 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 olnu 37 l:amz l7;reb3kr at the poles? What two effects are at worrkz e7: lnll u73;am3bk? Do they oppose each other?

The gravitational force on the Moon due to the Ear-mp t wgscw;/mj1 t+,sth is only about half the force on the Moon due ,t/sj-+t p gw1; mwcsmto the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal accelerad/3 d/tyjwbrg, a7f+l tion of Mars in its orbit around the Sun larger or smaller than the cenb7fdr/ ayg/+jlwdt 3, tripetal acceleration of the Earth?

Would it require less speed to lautfo9u dxy 8r+c2ym/ )x9.qxrknch a satellite (a) toward the east or (b) toward the qxc.kx/dy2rf9y8)m+tx9 o ur west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale iny 4aj)6zkdb 7y a moving elevator: when the elevator (a) accelerates downward, (b) accelk6)7jdyb a4y zerates 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 oute5z k pq.d4tpbf-0a7azr 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) the force we q5dfz7zp.0a a btpk -4feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experien.vfqmr6;mz6o4oju h n+;a*i xces “free fall” or “apparent weightlessness” between +6.ozmi hnfva;xmq o4 r*j;6usteps.

The Earth moves faster in itj3)s-fn vn 0ah ;ahra8s orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main ahra3 fv -s ;h8)nn0jafactor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known un mj9b10v +snpmj0k sm7til it was discovered to have a moon. Explain how this discovery enabled an m7 9pk+ ssbmj0vn10mj estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth lbh.9w9 .vxr phxgg.1 is much larger 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 othx.w9h1.9.xglphr b vg er.]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 1 wjh7 *hd *7bfgc,n l9k-mdx/r980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit aroundz0 lb:d qeqyb+ o8e50m the Sun, and the net force exerted on d+e :be8 yblq o0zq0m5the 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 dqv(t+ j .kb-wzp4+f6y zgku n5 (zt)wa 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the divtnfb wz( y(z gzpkk.)j +54dqu-+w t6scus.   

  Suppose the space shulan;sszs00 0 uttle 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 space0za s ln;s0us0 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 2xdyli5 erf fdgdrn- ),k+f)4 the edge of a potter’s wheel turning at 45 rpm (revolutions pe2+ 4gfir )f-ldkdf )yxdnr,5 er minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unif6jbdmf 7 rb)0uorm rate in a vertical circle of radius 72bumb )760 rfdj.0 cm , as shown in Fig. 5-33. 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 whi 98 b/-dx33rj -asd)nykzkt eoch a 1050-kg car can round 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 result independent of thjd89saoktx- y zkr- /bd3)3ene mass of the car?   

  How large must the coefficient of static friction be between the tires and th6t 9nkf 6cn+sfrise) 6e road if a car is to round a in6set+ 9)sfcfk6nr6 level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet goxoer +)ztvla(f0v58 bs4k+fighter pilots is designed to rotate a trai4o e k8rlb5(+vgo) f0zvt ax+snee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable speedj j/*qog,9q2eq-otb c/ eam a-. When the speed of the turntaaeqoj */ea m9 -/gj2,q-obqtc ble 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 traveliwcdqs2ubafc3f.b8 *0s ,l3m vng when upside down at the top2ssdmq3*fw b,l 8uc . v0bac3f of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundebqq 9 b /5pl*n mha2az4xwugl;,ff)p-d top of a hill (radius =bbm gxp hp*9,u4f2nz/af-ll)qqw 5;a 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 Ferrd 2gw9 0jyigr ,a3jq 9n4z7cqris wheel need to make for the passengers to feel “weightless” at the topmost pcjr7 4gjzn d9qaq0, g9iwy r32oint?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.48dr79 ga6 qyzbynqq8wk+if; 10 m. At the lowest point of its motion the tension in thqqk86wq4y; di8+bf gzanry79e 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 ax0en3oyc9tq.vkp yu ,ak1 u)1 kx85uyvis of rotat0 vq na u9)pyy u51.k,euvx1k8koc ty3ion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carni+) pn+oa :+an.pze pub9 q5ggfval, people are rotated in a cylindrically walled "room." (See Fig. 5-35.+u:q.+ag9ozpef p5nap)g+nb)
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 ) ip nd jf02scai1+pmham 13 *ce3s rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglingac mcpems13i0pf2jn+d h 1*3a block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the wew q/qym -kcxqf:yzf; q ;1kc9+ight of the ball which revolves on a string 0.600 m long. Icq/y:f k; qw1qmx+;y9q cfk z-n 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 fo(g,+ y.:c)hl hqya(c,ff vsyupbx a ;eg+ *u4or 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 massedb(o* f3,l.i9tgvuxmy2z z *v 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 evasive maneuver by div32whq0l lw.,uer 7zd6z upl* ping 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 the net forb8r)h :l rykidhjye *ux;e81:ce exerted on the car (by the ground) in Example 5-8 when its e *rrjxby ;l8k18ei::d) huhyspeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerc qpzq6,g7v e8ap ifd 9csreok72p62(ates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway 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 theaesp q 9 co872p, ipc( 2dr6evkg7qfz6 road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At2yfe)s.ouqry 1.gw r 9 a particular instant, its acceleration is 19y1 rfwy. )eursq 2go..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 12,8l.fog 25)9 vln6roc oq4shuy ,00 km (2 Earth radii) above the Earth’n9 ov.q yo ) cuh45rsl6og,fl2s surface if its mass is 1350 kg.   

  At the surface of a certainddl6fqtfdm1 m3v2e 8 8 planet, the gravitational acceleration g has a magnitude of f8dmem3162v dqftl d8 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 to0 od6 6/qzzamwzeb/ 6-*peaiy gravity on the Moon. The Moon's radius is 1.74*d emz6o/6eby iq6/p-aza wz0 $\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 .v8m6sxzimw(yj*:qk * *bjslhas the same mass. What is the acceleration due to gravity near itssx( *j vjbymmi.6klz :*qw8*s surface?   

  A hypothetical planet has a mass 1 ba+5d(-x gserbrgb-2.66 times that of Earth, but the same radius. What is ar s5-+xg2b erbgb -d(g near its surface?   

  Two objects attract each other gravitationally with a force of 2.g5vasu;k m:erm o r vtvxh57r1d278j/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 graq do)4ys2vm,us uxg(+vity, at (a) 3200 m( 2usoguvxsm +y,d q)4    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E c:j3gq1 scga/arth’s center to a point outside the Earth where thegravitational acceleratio asj:g /qg1c3cn due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into ayl/ qj -ywm ms(rg*4/n sphere about 10 km in radius. Estimate the surface( jy w/y-ql4rnmg* ms/ gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an af,qt07cna/bchi7s7sp 6c- kv verage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravitynpf6c-0cs hqb ki77 vts7ca ,/ on this star?    $\times 10^7$

  You are explaining why astre;raw4 13nhzj 0ojw5 vkn33 yr:ncx4qonauts feel weightless while 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 acceleration of gravity 250 km above the Earth’s surface 4 :njr 4qe vyw0crjn3 kh3o13x;wn z5ain terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcu- 2fzvz)oxu5s+ifv+xt6+anr late the magnitude and direction of the total gravitational force exerted on one sphere by5an)ivsv+z ft6f-+2x + z uorx the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Su li27/yezqc :ti7tb l;n. Calculate the tot:cti qbzll7/; y7eit2al force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface jwye 4li1x(8jof Mars is 0.38 of what it is on Earth, and that Mars’ rlyej4ij8wx (1adius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for thecn/:n hrbd7t)+kam* q period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Ke +q/7adrmk*h n ct)b:npler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a x*y8b b5c 7(brp:onp isatellite moving in a stable circular orbit about the Earp5*i bcyorb7nx: pb8 (th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satmfgje-6h(z.nv )* j/hu5s j xtellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when them.)t sv/hjjzn- j 5x(g6hf *eu release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arrjb 2w ofes zcp c3/vmku3.568e to experience simulated gravity of 0.60 g? As k 35 fw2mj/o3bsez.p6vr8ucc sume 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 orx)w76lzrcaczj w 9 w/50axf5g bit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth wgcl 9rw6 )w05xz/faxc5wj 7zahich 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 satellitelp2z f* -cfj;m have to be launched from the top of Mt. Everef *p;jlfmzc -2st to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module c9c7q wxmug6om;cy3c 6ontinued to orbit the Moon at an altitude of about 100 km. H7 oc6c9mw3ux qc6m;ygow long did it take to go around the Moon once?    s

  The rings of Saturn are vz9q3 1h6p mgfcomposed of chunks of ice that orbit the planet. The inner radius of the rings is 73,0 f69zpgmv1 hq300 $\mathrm{~km}$ , 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 r0ive-.n-bas+avz 0)ysmh p0b ;vh b*z otates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight tbs-;y)0*ip-z eh0bh a .vv sa nzbmv0+o her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of awvf m k3s9,pk* 75-kg astronaut 4200 km from the center of the Earth's Moon in pswv9*mk,kf3a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal massyq4 z-cb6fpv( . They are observed t(v 4zy 6pbc-fqo be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg womaojm+ ; 3cbbl*u pa x1yy9o.-iyn in an elevator that moves c; m 3uioyyby.9*px-j1 bao+l
(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 elevator. Tw1;4 pslx*igf7 )3tgw .bwas yhe co7g )g wp;by*s3.wt wi4xal1 sfrd can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pla jb e; +6qe vut)vrf1 ,pcj+mjwu:(-ubnet with period T ,- vc(ewjuqv+6e f+ ujjbru t:,;p )m1b the 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 perkrp f8ga p;2r5iod of an artificial satellite orbiting very near the pg8rpfa;2 kr5 Earth’s surface.    s

  The asteroid Icarus, tof abde1zp2 lf1, rw30hough only a few hundred meters across, orbits the Sun like the planets. Its period is 41frwef aoz1lbp02 ,13d0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofaukx cdaa)87x tb5y2: 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 comes verm xr ofafz:q-jn 7c2ec rmt 6jr-63/u.y close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the near/ozma2t6qfm 6rj. rcx3-jn uf 7r: c-eest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about uos-pp 6p)3dj 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, pedn u /0)aunv:-; i a9nxwon9hlriod, and mean distance for the four largest moons of 0nv;9ua/ xd -o nl)nhan:u9iwJupiter (those discovered 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 period and distance of n)3j/q 5snw pythe Moon. j nn3wq)/y5s p   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kev p)how0a5fr* n7s a8mcbkl- *pler’m7 rsvobw*5)pah cnl k*f0-8 as third law. 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 Jupiter consistsucjg0ph*(c6lt3xu .q of many fragments (which some space scie3jcl .6pqug0*h ct(ux ntists 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 5m.h f;nx7 cp7kkysf3an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-43sk.m7;5 hkfn y7 cxfp0). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vid2x5ja17igbu c(v 9cq ne (Fig. 5–41). If his arms are( q cabg5d2v 1ujc9i7x 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 Eart5 yop96)inhrzbe c9f)pp,j9ph’s surface will the acceleration of gravity be half what it is on the surfhzpe)jopi5 ,c9r9f9 n6p) ybpace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a wzz-p7giawz5m-ke shi;:9tm;o8a5 p 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 hat-z 7m mip;5kgz 8i zwh:aes; -ap5o9wrd are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of/-nuev b.8w wowv4.h e gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effnw8 uh -we.vw /vb4oe.ect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a s-bg;vii s9qs.pacecraft traveling directly from the Earvi-g ;ibs s9q.th to the Moon experience 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 st2eh*t:wg,kzak rs04y and on a bathroom scale in an elevator, 2 wzrsh:,kgeyk a*0t4 it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about-ftu n9h33uq q 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 (rev u3ft39qqnu- holutions 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 h1yke( kblkpj, +f10g aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the(uq nl*+kjm+fixada8za .2 )n acceleration due to gr k(adafajluix)+q2m*nn + 8.zavity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on azb1m xcy7zorcth8(+ :s a+.+wg aohg1 string) is deflected from the vertical by an +zo:w.s1 gy rc bcm+tgaaxoz(1h87 h+angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffm5+u ,mqm n-q b4(y*b5 m3atzxz he4czicient of staticyu4zb5, 4*m 3bq nc x hmea-mt+qm(5zz friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at xv/ jhz88f nj ekiu23;the equator were appae2vu 8f3j8x/j zkh;inrently weightless?    $\times 10^3$s

  Two equal-mass stars - v7alb6n9aiz maintain 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 car b36ep .orjh:bce+(urve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17:eor6bc3 +jr eph b(a..5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth.phpuw17ob (2oma5j5 f 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 equator of such a planet. U5 a5(ohjmpwoup f12 b7se 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 kbwic:x7 p+q5 Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light eqb 7w5 xk:+picscapes). 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 asa1 ky4 e) i/n7v crdbgtc8tx(2 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) Whe dtnit8yr4 gce b7)c a21v/kx(re would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group (sfqc-w1f a-(fea)a (ok ;g: 5,+qddscnqekx of 24 satellites orbi;kqfgqxa)-qc+: f ekass d oa ewf(,1cn5d-((ting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid R( 2ebn 67x gr8sycef51jx f9zgendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roune7s (6jxfc yrx9f e1zg5 28gbghly 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 repaicjc)l5nm6 d6, k7eodbr. You are in a circular orbit of the same radius as the satellite (400 km above the Ebd jl k)7d6ncmcoe,56 arth), 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 yu dl0uc;9 cgdi y eb9y;.7aj5vears. (a) What is its mean distance from th buc5jl7a;0y 9v;ed. yi ugc9de 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 wb; j66l4gelvfould need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiofbg e6v 6llj;4ns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Finf,k6ug q2p u0;qe.wkoa 7:1cx 9vut3,j xygng. 5-46) at a distance of about 30,000 light-years from the centcy qx.29n ,wouvjg , e:1tpnuqa6xkug3fk 0;7er $ \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 squarec urlzz8i;ic7k:, 8zf 0.50 m on each side. Find the magnitude and direction of the gravi8f k7;lc:z8u, r czziitational 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 5500 kg orbits the Eartyt61;;jmsgkmd.dae 0 h $ \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 second ux+tuf8dt1i4 qzt y87;8sjlfhand on your wrist w8i lsfu4q+f;8 z7 dt x8t1jyutatch?    $\times 10^{-4}$

  While fishing, you get bored and start,g9 3fgf ;b9l zd 6zwynyip4x7 to swing a sinker weight around in a circle below you on a 0.25-m piec76b;9fg3 iy,l9wfp4z gdy x zne 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 ace0i04v :/lxkt;obl je, 9hj .qs q8x-zzyw6o new highway is designed so that a car traveli ;je zwo,ov bez8l 4x0hqcq i xk.l0-j/9s:y6tng 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 Acen 3yik8o-10iwjt myos + 80q x3:5lgzgqmgey.la, utilizes 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 experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds aly0oq+nmkgi. em5y- jt8i1s0 ygxq3g w: 83oz 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.$\approx$    $\times 10^2$