Sometimes people say that water is removed from c me0 es zy+*gc ugt7zb;+lvf2/lothes in a spin dryer by centrifugal force throw + +72/tc smue lgfg*;zebvyz0ing the water outward. What is wrong with this statement?

Will the acceleration of a car be *uxo ac*z 6,h) 8uj n8b xhzem)nh;/lbthe same when the car travels around a sharp curve at a constant 60 km/h as when it travels around o8e /u, nb; aj*)bn6x8zml*hc)hxh zua gentle curve at the same speed? Explain.

Suppose a car moves at constant speed 7 zi/nk.8 pe 7elfl/(nx3r hmhbouw4-along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top pexw n /ke- 78( .7mflholn3rzu h/b4iof 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 a hb-spoewpynm6: u a(2 5orse on a merry-go-round. Which of these forces provides the centripetal acceleration of the china y2o w- mpeu6b5:s(pld?

A bucket of water can be whirled ;wmscqe7g )66 8dhrfu in a vertical circle without the water spilling ouefwu;6g rshmq86)7 cd t, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least t jw 7ore3n93 nin5ol- h9ui)eghree controls in the car which can be used to cause the car to accelerate. What are theoo )lg9w95e-7n n i3ujrh3en iy? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, t/0a0nz3jbz a)eld l-as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he ean -) z0j 30bdzat/llfeels 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 ,h oixrlj8( 1ra/7 i(ey)phfn rounding a curve at high speed?

Why do airplanes bank when th/dweojd n- ms;ioc*5y/xg p, /ey turn? How would you compute the banking angle given its speed and radius of the t/ic;dwoxynp/ *m sje5 ,d -og/urn?

A girl is whirling a ball on a string around her head in a horizontal plapng6 znsvm:2y(crj7w1*k)hgf ah n1 6 ne. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the strin k1)zsg w62:7njcnmhpryav *(6h1 gf ng?

Does an apple exert a gravitational force on the Earth? If so, how large a fvn. gl+ug// ukorce? Consiluk/vg ng+u. /der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were d+:exip-kt 7s/; pra agouble what it is, in what ways would the Moon’s orbit be di-pa sit g/;pex +ak:7rfferent?

Which pulls harder gravitationally, the Earth on the Moonee/,.w hsevs ( 4,ehwl, or the Moon on the Earth? Which acceleev we/wh he(4 s.e,sl,rates more?

The Sun's gravitational pull on the Ea4 wc a9vkej rd/zt-8x8:g nx x-f9nj)arth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides.4jzgtj)d8-ac8wn /k x xer9:n fa9v x- Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two8+ k9jhnpi*4j9up 6o8ymn6t pictz +k effects are at work? Do they oppose eacytnic+om t zp98h*p9+ 4pjkni k68ju6h other?

The gravitational force on the Moon due to the Earth is only about hal/ a:hav(pkr t)f the force on the Moon due to va( )par:/tkhthe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largefx3 *n jhamx2 y862cier or smallye6a hf*xi38mn2 2 jxcer than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the ea2wb j8 3 ydxju+)4mi8vf-kf epst or (b) toward the weskyb+ 8di-x u)w83 pevmjf4fj2t? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, ae ;x pa:l8n0vzs measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight bel; n0e8:zap xv 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 affected z.ngdrcd rhl z1/f;qfc7 t 13:by weightlessness. One way to simulate gravirczd 7/hfd1 tqr3g: 1.nfz;c lty is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weighte-t(pnpx+08yazzp y, lessness” between stxny(pz ya+0 8t,-zpp eeps.

The Earth moves faster in its orbit arounwlag(k f2/zilg+9 yp 9d 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 factor is the tilt of the Earth’s axis relative to the plane of its orbit w gpfzy9+/i gl(2l9ak.]

The mass of Pluto was64kdlpm b .9/iav:los not known until it was discovered to have a moon. Explain how this discovery enabled an estimatesbvi/4a:.om9 pll 6 dk of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much u.igyd js7 ;-5evbm- alarger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cond.- -jes g uambi5;y7vsider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 198 w c2m7ms.yhqg;tb ;/d s0qwu90 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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:gu k jy+8-mci its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a cigi:u+ -k8 cymjrcle 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 oag8 yv +y9pq gf tkb tc9,9b80mk0p(guf 210 N is exerted on a 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 discus. 8ukb9f9 ttpg 0 yg(9g+v0ka8 qc,p bmy  

  Suppose the space shuttle is in orbit 400 km from. ttp 0.n0.npcg vyiy) the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g t) v.gcn..tipny 0py0, the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on theck;5)v:pabpj w vfe3+ edge of a potter’s wheel turning at 45 rpm (revolutio:ke3p5 baj pw+vvfc ;)ns per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ver 3 bg*5xb0krejtical circle of radius 72.0 cm , as shown in Fig. 5-33.0bbr e5x3gk*j 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 a turn of radius 6io 5;szbo8 ra0y5rm /xlxky7 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result irk8z57lxobr 5o y/;6si0xam yndependent of the mass of the car?   

  How large must the coefficienty lu6,2qhf +kqld2,p ns:.8uvj how/ q of static friction be between the tires and the road if aq.2slk2,n,pf+j/wu qhd86oyu h lv: q car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronaut2t d,ak6*:yvrngb 3uos and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If tb2 *6vrnyd,:utakog3 he 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 spe4 b oemim1ti)lws(t95 ed. When the speed of the turntable is slowly incrl1 ( 4i5mtbweitom s)9eased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down(vjpm i tw,u e4x0ya3pk0)j(z at the top of a cie 0j0(kw3 ,i)tjvzx(4pmypua rcle
(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 (includin 8:cq0my hq5y3(axu owg the driver) crosses the rounded top of : 3qwa x(y0uyoc hq58ma 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 minutlhjb 9m(c6.ys e would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the(cl.m 9ybh j6s topmost point?    rpm

  A bucket of mass 2.00 rqt2x 76 kg p,:lvaw-2 r:vneh2qsq/l kg is whirled in a vertical circle of radius 1.10 m. At the lowest poi hlpq,k 7 x6tg/v:w rsqr v-2a:eql2n2nt 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 rotate i(;40. inga e7e6 bbaish6sd cjf a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000i.g64s haes;icbadbj 60 (e7n $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in ecj,*xd s o2pb6f rz5 (6pyc7ha cylindrically walled "room." (5y6 be( f27xrs*c och6 zj,pdpSee 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 cj09k xv eq18,; qvf,0qo hlzhlircle on a frictionless air-hockey tabletop, and is held in this orbitxhq0o jfllv1ekh 08qvq ; z,,9 by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this tit8jjq,d 3)lmrme, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the ) mrt38jlq,jdmagnitude 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 i *0l8sdh- bqa88 m 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 masses6utf,k *zax lz u-bya3ho *u6: $ 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 evs+ot-p)h - gh0g 6a a.imh5nxlasive maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal comp gstjdp;+m: 3gonents of the net force exerted on the catmpgd s 3+g;j:r (by the ground) in 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 a k7wz+ f/tes0yccelerates 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 yestz7w fk0+/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 t. uzvt :2z5m gp :xhx2y2uam*2.90 m . At a particular insty2h *tmu2a5:2 m:xg z xpz.vtuant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth rminsb* a nlsx)jfub0 rc, 2;ruf87n 0(adii) above the Earth’s surfac lf,bfrnn2u*i nj0;s c0mau r8sx) b(7e if its mass is 1350 kg.   

  At the surface of a certain planlbp t1,9z6 jqel- h9whet, the gravitational acceleration g has a magnitude of 11zqh jellt,99p b-6 hw2 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 Moo kcs023h gnjs.n. The Moon's radius is 1.74 2c s.ng0k3jsh $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planetwv y.aom,adw .7x5ac 62i945 caxwvwn has a radius 1.5 times that of Earth, but has the same mass. Wha7.5 aw659wmavxvwc4i ,xo2cwy nd.aa t is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same a(; t t93)gu ;xhaqeymradius. What is g near its surfa;h(yetg aqt;9ax)m u3ce?   

  Two objects attract each other gravitationally withrmtia8du ao -r69m 3/r a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a)4 jxhb px 0vmu-qlt i-uj91)k+ 3200 m+up-xtk v0lmj4buqi9-h x)1 j    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from ul8u 0uk-ub/ wu/x6 3jmll e6cthe Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earthbu3uju um 8l6xe/w-l /0k6 luc is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ourht8ox w;uq , )d lj2.dr;cgj8n Sun packed into a sphere about 10 km u j;;cqotd,xd l2wg)hrn8j8.in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun taq in/juv8vj anr7ebtk/a-d.-2-,co b d)z3but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Wb 82/o7 ak ,etvi -bt )vqj-du3darznj. n/-cahat is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronaut/yx(zab.x 8wqpdn g74 5*a gzvs feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a vg4qp5xzaw7g /.8 anzd( *byxlot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the c vu: 0f6 thy6x7y(jpsjorners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the ojh t6 0y: s6jvpxfyu(7ther three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most co p 18)dppf/wof the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four p pc8d/fppo )1wlanets 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 of Marsks4 6g. , nx soef.(pyuio9og bd-on9- is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determ n,9ofs-ey u-.po6 4osg 9nibx kgd(.oine the mass of Mars.    $\times 10^{23}$

  Determine the mass of ta .,ri/xe w6 8;l7 .yjhucvbnwhe Sun using the known value for the period of the Earth and , vwne a/xhibc.w8.76lyu; rjits 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 ab z)vv 9h0gs6x/oxdz+tout the Earth at a height of 369o)6 t+dsxg zvz/hv 0x00 km.    $\times 10^3$

  The space shuttle releases a sateln;ah.4btlr;q).d4k l cc ki/glite into a circular orbit 650 km above the Earth. How fast must the g.qk lk .n);bcirdh c44a l;/tshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaklx0w7-t2 59 a5vcs kow0ktuk5zhw ky:b+ 4 kyceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameterox k5ly5+ :k kz uyht20kskv4t9cab w5-70wkw 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 m9 d1ws -by,jythe 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 of the Earth. Does your result depend on the mass of the satellite? ws9m, db 1y-jy   s ~    min

  At what horizontal velocity wur9lxn6f21 +haxa* sgould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbitxlf69 2 g+na1shar*xu around the Earth?   

  During an Apollo lunar landing mission, the command module continu d 2-6awwgt oui21rcropjtg f:z*/3i-ed to orbit the Moon at an altitude of aboutt ww2agotcjfg idir1* zr - -pu:o632/ 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunksuvin,*:(k jmbwyl +;j of ice that orbit the planet. The inner radius of the rings is mni*jlu+k v yw,( :j;b 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 inh(qoe9zxhqpq- ub.thcv.7 9+w * 2ua d diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weighthae9+7z.uq(ctv9pud *hhq2- qbwo .x to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 3 ss7(m.uf g rcqv.)xz75-kg astronaut 4200 km from the center of the Earth's Moon inq .(). fru3sgzcmv x7s a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. qj )9t/lgggp)79si3 ukj hta+ They are observed to be separated by 360 million km and take 5.7 Earth ye7ul sg/ijg+t9)jk3g qtha)p9 ars to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scud x3bd:5tb(+vm m0bgale read for the weight of a 55-kg woman in an elevator that moves3bbb :5tdmdguv0x+m (
(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 az3(kr0k2ie4 . zg s309xl0sprk jqsunn elevator. The cord can withstand a tension of 220 N and breaks as the elevator acce r zgqn24 (330k0kjr9u0lpess izsxk .lerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a plan a rn.kmea.ygxk-, -u8et with period T , the density (mag.,m au--xra. nkke8y ss/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) tvb26gbf5kg r954ylbi o determine the period of an artificial satellite orbiting very near the Earth’s r 9ib4g 52b6yflkgbv5surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Suts ;chqs(1c 0gj; i5ran like the planets. Its period is 41(c qti1cs; ;r5ah0gjs0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o-pwo3uy77j oi f 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 oncey *u4f fih/s cmwz+/.w every 76 years. It comes very 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 stilf.u mc fi+s* h/y/wz4wl “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 Gscr im65: v3boalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 larzvhwm(x jc4b t h- 0ke98xt4(ggest moons of Jupiter (those discebh9(-z0wc4(xj4mx g t 8 tvkhovered 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 an9m/ii, zgbt qe5 q:.rkd distance of the Moon. tek:m r,i 5z/ q.q9ibg   $\times 10^{24}$

  Determine the mean distance from Jupitej 3; k:9ce2l( rziqplxr for each of Jupiter’s moons, using Kepler’s third law. Use3jrqll:2 k i;cxpz (e9 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 consir. tc fcykh44;sts of many fragments (which some space scientists think came fr4y tch.r4cf;k om 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 descr,4clih7f3x zx ibes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g asiz3x,4 f cx7hl on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a 3wyhb/au2fje o; 51r2slsw: z/pqn .bgorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass i e1usyj/./b:fh3wl sn2;rz5qp aob2ws 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of graf1.gued r+ ;by9lodg+vity be half what it is on the surf.;uly r g9ddob+g 1+eface?    $\times 10^6$

  On an ice rink, two skaters o0g7:kbc6ocx af equal mass 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 60gco60 b:7kacx.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the t7 : xu7rdq8t fiwxm:yl*m5.h apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is thistt ir:lyx5f: h7xu.q8wdm7* m ?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraf8ctdqy+0uy+ q t traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opp8qcy++yt 0qud osite forces?    $\times 10^8$

  You know your mass is 65 f,iid)q l gc; 4skd(m-kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kf4q(kd;ilic-g )d,m sg. 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 abo mno *i;8hfbo9jn--jpk9e (b put 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 (1.0(n;b-oj99ehkf m n o8bjpp*-i g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircracdz;0 +jofbzd; 16tkfft 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 accelerq5a(qs i4g1ik ation due to gravity at i51qk4qgi sia( ts surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from thedqn( j z 8bz(-tvn64vy vertical by an (yz(j 6d8 zqtb-vn4vn 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 coefficient ork9-da/fk1l: xhlt j3 f static friction is 0.30 (wet pavement), at wh -x:jl a1rf9ktl/k3dhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast thatvpi( uk84c*k3.oa s)cb +ssra objects at the equator were apparently weightlescu4*aks+o rs. )a3pc8v( bksi s?    $\times 10^3$s

  Two equal-mass stars maintain a consgsbuh09 d7 uk5tant 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 curvec5g6kc a 4:7ohcp r5aupbf,o, 5 (vcpm of radius 235 m. A lamp suspended from the ceiling swiu kro5,cgp:aav6p,h 75(cb oc5f4 mpc ngs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as ma7ggaxv ;(x q9lssive as the Earth. Thus, it has been claimed that a person would be crushedvx(x9g; lq7ag 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 prejd1/k s8ydk3jsence of an extremely massive core in8sj1d 3k /ydjk 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 speed p0n6fjwt*r5 hrqw9w;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 0n p r6rfhwtq9 ;*wj5wcompare? (Which is largest? Smallest?) Explain. (b) Where 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 Posifii5h)n**4/l bbv la o la6cm8tioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a rhv ll bmi*l4f/ ai*5a)nb8co6 eceiver 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 Rendezvous (NEAR), afteric plkz-on(t,y:)hw qq;8t2v traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 1lz8 c,qitvnkwt:-)2 qo;(y ph5 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in)g58qg t1mu5w/(ta vmou5by g need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earvumy8 5ggtaqbm)/w(u ot515g th), 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* nyn.f 8llgj9(pwu8xz (b s0a a period of 3000 years. (a) What is its mean distance from 8jfl z*a( gxnl9uy0spw.(8n bthe 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 woujzdh 9+9 dle+s+kgp:hld need to be if you could actually "feel" yourself gr+p 9jes hghddk9+l: z+avitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wa+i j:g9cwlpt* y Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the : wi9+cptlg j*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 square 0.50 m on ea22phef 6od 9e97qmqcg ho1 u* cd:zusb*f/sg2ch side. Find the magnitude and direction of the gravitational fo6 desfue9:g*7gum p 2of s/chcoqh2z2 9bd1q*rce 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 orbo78q4 xw3bgu5 ynfo e9ixvk;ngcq 535its 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-cievc 5*6yfgv s p7+h;xm-long sweep second hand on your wrist yeh*ig5fs+ ;p7cv6vx watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arouno h )-*iij(q*y v*eh btp.-lbsnw0fp 1d 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 fishiso bi *bhpl*v0*p1- -e.yji(htn fqw )ng line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway isu /w*oy,:tval4 v* en+8qc pl*qobei+ designed so that a car traveling at*lv ueol+ qo,ivw+*/nc*ya t8e4bpq: speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the car marcz:* ;r8jqx7v3bk s 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 norm8z qrcx;m3rab 7:k* jval 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 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.$\approx$    $\times 10^2$