Sometimes people say that water is removed from clothes i)p sefs2ha* 8dn a spin dryer by centrifugal s*2hapsed8 f) force throwing the water outward. What is wrong with this statement?

Will the acceleration of a cei b:1qdx7b d9e5kv, lar be the same when the car travels around a sharp curve atekd5,b e7q9b: 1 vidxl a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where dolpgy5a y 2cj4zy8 -xx6es the car exert the greatest and least4-52zgyaly x8 pcjy6 x forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a chda:+k32cmeqfqi3fa4 .v wlmu gt. ,:rild riding a horse on a merry-go-round. Which of these forces provides the centripeta3.wad :afmgt.m,+3f4 irv2qc qk:e ull acceleration of the child?

A bucket of water can be whirl ktx(20rveg/k j 4ne+-pk)ulped in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. E (4+l/)pkkerve-kj tnxug0p 2xplain.

How many “accelerators” do you have in your car? Ts le9we 2s.1m*prf6 /kod xl0lhere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerw*ods fr x.1ml e09lksep6/l2 ations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fi7;)(lx arzz.mpmc.3szywg 4rg. 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 decre.xcl37(;)4zazwp r szmy.rmg ase as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean ugvp )3gp/k1qinward when rounding a curve at high speed?

Why do airplanes banvlxgno( 37i.3sri3 np k when they turn? How would you compute the banking angle given its speed and radius of the turn?v n3l 3snr7igi (.x3po

A girl is whirling a ball on a string around her head in .44b8 stxeayaroft/ 5a horizontal plane. She wants to let go at precisely the right time so that the ball wilerfty tb4 a x/8o.5as4l hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitationa*,a qgh4-;f0lr1 wukowht) m1pc8liul force on the Earth? If so, how large a force? Consider miu-,ag wu 1;4kol1wt p*qh )08lrfch an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whnu* jyz9la5gh,1jq g8 at it is, in what ways would the Moon’s orbit be jnga5,q9yjl ug8*z1 hdifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moe(ehwc+ z+o-2/8tny tc6hqi x on on the Earth? Whichzet8( chce/n xwt2 yi-q +6+oh accelerates more?

The Sun's gravitation/l grhwao::tj09dgnxh, / z7j al pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible fo:lr:j97/hz g ,j0/tngxad wohr 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 e5+t+cdgo -3 cmbr ls)jquator or at the poles? What two effects are at work? Do they opposeomd 3c+br- gct )5+lsj each other?

The gravitational force+ +-0o x wm3yvjse8sai on the Moon due to the Earth is only about half the force+vx js0+ias-e8mowy3 on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in cg .jf9a o-;vcits orbit around the Sun larger or smaller than the centripetal acg f9o;c-a.jc vceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east :mub,qsl i:1o or (b) toward the west? Coso i1mbq l,:u:nsider the Earth’s rotation direction.

When will your apparentmv6g0l79gv48: uf smnc zlj/h weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acceleratef8/j4 z nvlu6 mmlcs7 :h0v9ggs 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 ou5kc1c*l 9 eo) y d-hof0bw0fu3 ovxig7ter 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 simfbyc u7 xh-goo9i)*v5w0 e1 3d flkoc0ulates 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 “frayo(jdvq96g6d8l;0hcp yn,a ee fall” or “apparent weightlessness” between stpyy9qv 8(60dh gd 6aj aln,oc;eps.

The Earth moves faster in its orbit around thlfrwcc*h; 9 e9j0f *she 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 factor is the tilt of the r;l s0 c*ceh9 *wfjhf9Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not kok7u*2o;u40mkupzk t nown until it was discovered to have a moon. Explain how this discovery enabl7tkkmk*ouo2 0;4 zpuued an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the oe)rp 6c2*w 9ub j1cvnMoon's. Yet the Moon's is mainly responsible for the tides. Explainbw eou1rjnv9cp26c *). [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelingbmo: r8-)lvsj 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 centripet8gob uut45b2xx1a*s du jcc ;9al acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume th2*ugb;sc 4otuc18jx a5dbu9xat 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 ;whp2eyo9 r9nq- ej4t4yl:qr discus as it rotates uniformly in a horizontal circle (at arm’s length)9reqyn -hq:t ly r9;44ep2wo j of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ear 4zc cky/;pjtw l-t4:hth's surface, and circles the Earth about once every 90 minutes. Find the centripp44l y;z tkj c/:h-tcwetal 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 acceleoe0g;ugs4us a-kp.f 4ration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameesk 4op 4 -.fugug0sa;ter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a uvy1ycbph+ 6e ,u 6+vsii5 5fovertical circle of radius 72.0 cm , as shown in Fig. 5-3h 55f i,yvuyuecp 1vo+i 66bs+3. 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 slvgbx- xj**gps3c+,ch 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 is *plxc g,3sxjg+ vb-*ndependent of the mass of the car?   

  How large must the coefficient of static frictisyhem.- q.3un on be between the tires and the road if a car is to round a level curve of radius 85 m at a spees-quh3m.n y. ed of 95km/h ?   

  A device for training astronauts and ).-aguxt/l,o n lr1 rkjet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fastart1.k lr ,l)-nx go/u 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 variab5 9efmmg0w t*zb)49z.yhdo :hggah 4nle 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 :. 4wdbo 5f0he*z at g n9mgyg9zm)hh4turntable?   

  At what minimum speed must a roller coaster be traveling whev05t/qnry -p.xhf jg 3n upside down at the top of a ci-f0qy/3n tghxv r.5 pjrcle
(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 r,e.qqmcn75 fbdw,+1 nxt ry8the rounded top dn .r 7t e,,m5ycqnr fbqw1+x8of 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-diameter Ferris wheel need to w y .v2)uyp98a a7f9nglql*td make for the passengers to feel “weightless” at the topmost poi2 ltnaw qyfvyal 97)*dpg9 8u.nt?    rpm

  A bucket of mass 2.00 kg is w,3h5carjj +/otpf1bchirled in a vertical circle of radius 1.10 m. At the lowes5 afc+h3/o1ctj r,bpjt point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge r8r* )dj hv/ ckw4f4uymotate if a particle 9.00 cm from the axis of r j4yu8 f*md /rc)wvhk4otation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated. psdd+c8n y/ 5kqrc1d in a cylindrically walled "room." (See Fin.+dpc q8 rc/y15ksdd g. 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 ivm1d1it2+hwg6b app;y p/kn 3n a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglwh/+p6 2 1ypn kg mp3itadv1;bing 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 , precis/6wf us azku. g73fy3jely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mag/kw6sz uugaj f3 f7y.3nitude 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 m52iku:f a8n4lu n o+wf is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masse ) uyqy8.macqp2 be/j,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 diving vertically at 3h/0butsnsof/db l (v y9f11qr 3 (*vsl10 $\mathrm{~m} / \mathrm{s}$ . 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 a))l-oyyui d9en/ ;:m zq1bsk jnd centripetal components of the net force exerted on the car (by the ground) inq /kmb 9z)y-:ydnei)uo j 1l;s Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit arex4+lkav lvr072:w v ,gzalz x*a, 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 7a v: *a vlxgwzv0 xr,l4kl2z+it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pa 2i g m1jv*i-luylj)o60sxhw 4rticular instant, its acceleration is iylj64u)-ilw o vmsx0jh2g1 * 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 E520lz es):rww4 0l-ykbtiz tmarth radii) abov r4lzes:002l bmwwz-)i t5kyte the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational 0xy h/ ,p*8ic mjjkx(vacceleration g has a magnitude0h*cxjmvypi(k / x8, j 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 4y3b;dph 5nhiagfp9i oy07o 3;yo 6gbgravity on the Moon. The Moon's radius is 1.740 bi53gnyp9dhf; io4 ;ayog oy h3b76p $\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 ofeao77l.iz,s - g4 w9 wsptgg(mn7y e0a Earth, but has the same mass. What is the acceleration due to7 (e0gsi7l7-notapm , ez 4a9g .wwsyg gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the2nj)nz w;v5h8v8.dq7kzh9 1 m pasxpl same radius. What is g near its surfacms28jlh. 7h );w19 q 8akpxnzdvvz5pne?   

  Two objects attract each other gravitationally withimf5fm/zb6;p i xm*bja 6n b po7,+ct1 a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravygee/ -b( (ef jys;g ;pnl+nxb9s .,pxity, at (a) 3200 mbn./n s9g(x b j+gpe,;py(e-y;xl s ef    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where ,fcn;17 0tq:guc cw .buf)um fthegravitati n 7b)w:cuu .qg,f1t0u c;ffmconal acceleration 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 packed2n)f5 wpz :x kwwz3q9y into a sphere about 10 km in radius. Estimate the surface gravity 3 )qzwn 9xyfw5kwp:z2on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is rb.:t7 kks qwk:g42einow in the last stage of its evolut4e.k 7ik: w2rqt b:skgion, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbtenyqoz ;e ),/iting in the space shuttle. Your friends respond that they thoughnz y),;eqeot/t 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 arg0,wky4 v 4 ox9:ghscze located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphswxkzc0gg 9h4:v,o4 yere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up kdxw;nw-3df t*rqa0 pq 1qe /1on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sap0f/ wdeq3qqrwn x 1ta;1- d*kturn, 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 gczml(;1k o iq:y*ak+ 3fhwy- gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of kg m: -w;fzyqykhoc1i(a l3 *+Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knowndtaxmkk.q-n;j ;ym 0; value for the period of the Earth and its x; -jtadk0qmkn y;.m; 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 a satellite moving in a stable circular orbit abop9by3wlpgan/(rh(- q ut the Earth at a height of 3600 km. q3(r /ghwa-b9nl(pyp    $\times 10^3$

  The space shuttle releases a satellite into a circularv9;qlv p3x jeweqhsm7q*- 7v9 orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whlvq;9-j7q3* xe9 p vemh7wqvsen the release occurs?    $\times 10^3$

  At what rate must a cylc6w;eyu f;.eh73yy j.rws* oaindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m,sjeo* r73;h e.wyy. c;6fwauy 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 tpvzr,q 5f 3.vwhe Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius oqr.w fvp, 3vz5f the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launches g5u*7s6 5;tallwqgp d from the top of Mt. Everest to be5gp6*s;7 tqluglsa5 w placed in a circular orbit around the Earth?   

  During an Apollo lun 9pjoq(himr*, msk 99car landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onceri*99 mj9(,m hsq okpc?    s

  The rings of Saturn are composed of chunks of iph/lq ybjd8yh 7u+k/(ce that orbit the planet. The inner radi dh+ y/j ky(7plbu/hq8us 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 hd.5if tb 0 v*9ak5(2zxx o2pm( tigdc15.5 s (see Fig. 5–9). What is the rat5(fpdx 2d9am.to 0 *g5zv(ihkc2 bxitio 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 75-kg astsmaqos)k0np 51. byo/ronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) m5y o s/qabsnm0ok1.)poving 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 mass. They affp 27*imej fac0o5)icp,;po0ls p/f:3muw yre observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between thfj fp, fi;cp2 pcas* o:mym00w)f7epoil /u 53em. What is the mass of each?    $\times 10^{29}$

  What will a spring scale reaa y5*l.9x; ig *mbnocsd for the weight of a 55-kg woman in an elevator thao *l;snc.xa*ybg5im9t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from t/d1xgw *ph -cvp7aps ,he ceiling of an elevator. The cord can withstand a tc-saw7/gxpp,1v pdh* ension 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-muur,i-jc 2zz(vkp 7 near the surface of a planet with period T , thep( jc zki-z7v2,uur m- 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) too;rg0o 9b:6ipm7x oju determine the period of an artificial satellite orbiting ve6o xgri :up om7;0j9obry near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred6:h +xgh6g iny meters across, orbits the Sun like the planetsgg iy6+ hh:nx6. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dfs m( de(s;5esistance 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 comel1p y1wkr2y6w s very close to the surface of the Sun on its closest approk rl6w12p1wyy ach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galn -buwx: k),r+e0xmm(;sx k ee, sjb5haxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 l 4 spptmwd7ugt em0m /+5ih5,hargest moons of Jupiter (m u4/ h 5,pttwedg7h0 5p+mmsithose 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 tx 52bz1pz+ag. hcbi0zhe Moon. gi+czb2bz05. hxa pz 1   $\times 10^{24}$

  Determine the mean distance from Jupiterzug5aua 3 48du 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 Tabl5dza8 34ugauue.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (w8sf gaq1 yl/b2x.e*,;g7- voikytfhqhich some space scientists think came from a planet that once orbited the Sun but was destroyed).tqeh.xkf;s* 7f -2vqy goayl8i/ b1g,
(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" ig/fjnk95t 8 4sjbh ln3n 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 than4 fb 3gn9jl8ktj /sh5t 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 ro u+6c1k/w p*fh5mfzvine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speeof/k fwm*5u r61hp+z cd 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 wiej/wamfpt, 6aw(zvu8)j *4rd ll the acceleration of gravity be half what it is on the surface,v*dj 4/afetaju) z( 8 wrmw6p?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cirq :/vb1ua4u 83dsuqg*4vur gzcle once every 2.5 s. If we assume their arms are each 0.80 m lu udvr/4us g gu1*qqa 8:4vb3zong and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravi :0+q,hwnkj+,(vv2eyf( z cmevkct j7 ty at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect,h wvjky 7qejk,+vnf(ct mze cv+ 0(:2. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dire-mqvc)izzpvwh3i(6.k ,2u xtctly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite force2. mix q3 -wzv izpc(6)u,kthvs?    $\times 10^8$

  You know your mass is 65 kg, but whnp;vh4m ;tg wphy.i*b( u/5l den you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and/4.;p;im uy gl 5b(hpw*dn vth in which direction?     ----待选择----upwartddown 

  A projected space station consists mn2ds qmf / l,cf2t16rof a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.fqnfl/dmc2r sm,16t 20 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.n*lg d 4g:1pkp 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, tezyhh3 e)xd5 25gnw gq43d1v che acceleration due to gravity at its surfac )wg cynehvxe51zd3 5dqhg432e and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is def x th8m5bfyx ywl 0+:4dhg3jp4lected from the vertical by an angle hwxjg:y f4y mtd08 b+4lx3hp5 $\theta$ 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 desitt030opu zhm8c w:0 oxgn speed of If the coefficient of static friction is 0.30 (wet p:uo8hpxc000mow3 zt tavement), 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 tvlbl(o -j 8d(phat objects at the equator were apparently weightll( dpj(bv-o8 less?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartfl(u 7/l) 6hnbhltu/u 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 speedbkgkao7dxg, dn)h *, 0ji*owsq3,l y7 rounds a curve of radius 235 m. A lamp suspended from the ceiling sw i0 go,dk o)h7xg*qs*bal3 n y7,wdjk,ings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tim)/sz uatg1 db7l +nr8+wf5 ymweb7qt3 es as massive as the Earth. Thus, it has been claimed that a glwn8wue 3/ db7qz m y5tat)rb1s++f7 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. 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 an extremel2pok 2y*4lw:e h2f axmy 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 measuring the speed of g * he2f xkp4ymal2o:w2as clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley sh 8 j1n0uc9crjkown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feen cjjru9c1 80kl 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 of 24 satellites o7 d1y/oyn;(xwtold9q rbiting 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 satelli; o7nyl1(d9 todq yxw/tes 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 tra/mf;j7yvq ydft0 hkjqw u,,.1l;nq2vveling 2.1 billion km, is meant to orbit the asteyvv2 0wj, h qf;/7d;ytjnklq1fuq.m,roid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle 1:;s8uk*owv p lxq ,4 tqdw3a a6x;wdfpursuing a satellite in need of repair. You are in a circular orbit tl4x;qwfqu8k w*6 p,:dvoax3 s; wad 1of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp hafnxt160d(u jb ce 7fy7*m7auf s a period of 3000 years. (a) What is its mean distance from the tfue67bfn71 7d y(*xjcam0fuSun?   
(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 cohxzrm5+v7tq j(d d1o;uld actually "feel" yourself gravitationally attracted to someone n7vd(q+ dz5;jxr 1o mthear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galhxn kf9z )l+p(axy (Fig. 5-46) at a distance of about)nf9lkxpz(+ h 30,000 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 ovwj.g )2h5gxphms i3cn.::(z3cc g8 q e9kurhf a square 0.50 m on each side. Find the magnitud2cgnq:(.p)e.5h3 :9jxu8gm sich w3 vch r zgke 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 5500 kg orbits the Eari2d uf(z6hy y(o 7ua7eth $ \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 ofp ydkro:82eo:6 n zb.q the 1.5-cm-long sweep second hand on youk2.qon:r6pe: 8b z dyor wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroun ) +m7/k6ixuminej zzf oqyn,u b46g7: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 vertical? [Hint: See Fig. 5–f qi:ixynjm+6zuz g6 ku74oe/bn7m ),10.]    $^{\circ}$

A circular curve of radius R in a new highway is designedxv.ouy-:lxo bf 61 w4n so that a car traveling at sx6v boy -l14onf :xwu.peed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the carsn8se:o r,o0 nca -q8dq 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 ,8 s -0qacqerdo:non 8of 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.$\approx$    $\times 10^2$