Sometimes people say that water is rbsp/h6mg9d8, jz t xq0emoved from clothes in a spin dryer by centrifugal force throwing the water outward. Whatz, b0xs8 9qg6pmt/jdh is wrong with this statement?

Will the acceleration of a car be the same o2sb2r tzw44d)kf-a gwhen the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expla-s4bwfgadk)z t 4 2o2rin.

Suppose a car moves at constant speed along a hilly roadrmbrlux. y6* +. 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* ryu6l.bx+m r, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on asj/93/ ccerav child riding a horse on a merry-go-round. Which of these forj39 vcc/ars/e ces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without t.:hld4w uuik-he water spilling out, even at the top of the circle when the d.-wlki uuh:4bucket is upside down. Explain.

How many “accelerators” do yohsf:iaby i:/ l1u+*t mu have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations doilit a 1u*:/m+fhb ys: they produce?

A child on a sled comes flyir1*;wxw o rgi/ng over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he fee*gri xw/ro 1;wls 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 rounding a curve at h4) w 4kqdwjav2igh speed?

Why do airplanes bank when they turn? How would yoh3s 1ug9c7g5ri2p en xu compute the banking angle given its speed and radius of the turngushi5 9n7rg x13e2 pc?

A girl is whirling a ball on a string around her head in a horizontal plane.n2f s+wk; xx94 pze0z7 gjjlp( 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 s zz lfgpe27k; (4w90njjxp+s xhould she let go of the string?

Does an apple exert a gravip0nclw1p3 /o w +rvn6ytational force on the Earth? If so, how large a force? lov 3yp1/+wrp6 wc0nnConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wayq9 r 4ykguo(y fmgu1)j3x7( cws would the Moon’s orbit u3my gwyx 1 ((f9kgrj4quc7o)be different?

Which pulls harder gravitat 8z z16hsjmeb.83xa ltionally, the Earth on the Moon, or the Moon on the Earth? Which bma. 3lxsh1jez 886ztaccelerates more?

The Sun's gravitationz(o xwnz5tyk9 85ets9x.m gkp mo: * ir2c.4wnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conse c5o85t(nr.mmx. xzo9 pg*: izn kyswk4w2t9 ider 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 twt)wo. z3ceo2s o effects are at work? Do they oppot.s c)3oo2ezwse each other?

The gravitational force on the Moon due to the Earth i imw;:rh n0bx*s only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from theh:*0wm b xn;ir Earth?

Is the centripetal acceleration of vjip ts* gnz22ym5t frm7pidon37h r*m -x15 4Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth7 *j4xrps p2v37*thmz-ndg5n1mo fr5 t iy2mi?

Would it require less speed to launch a sate :g0o( bnya+m lzr2ov6q azxa8.6(ylr llite (a) toward the east or (b) toward the west? Consider the Earth’s rotation d zn(ol0 a6yq z8r vla2r(:bx6y+.gaomirection.

When will your apparent weight be thvrxl-,u5r) b;eym:)jh ek z(se greatest, as 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 cas lkzs5x m eeru-h; r)j(v:y,b)e 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:pe7:c w dtcwhu3:-jk periods in outer space could be adversely affected by c3-k:h ew::jt wdu7p cweightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “app3kgzdwp/ ) v hai +e-mh 7z4xu5;ay(tvarent weightlessness” betweenx auhvv)aeh z(p/+g3457dz- im wykt; steps.

The Earth moves faster in its orbit around the Sun in Jan lf*, ;vl 75ffdj,r5xvah:fzouary than in July. Is the Earth closer to the Sun in January, or injfof7 vl5 faz: hr;5 lf,*vdx, July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discot 38lrl-svi,i y3 onalu-cs36vered to have a moon. Explain how this discovery enabled allcivya3 s3l -6,no3ius t8r- n estimate of Pluto’s mass.

  The Sun's gravitational pullmhp8a4c,, nvd yz, 6kb on the Earth 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 other.]A child sitting 1.10 m from the center of a merry-go-round moves witn8,kc yhpmad 4v,b,6zh 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 1lhygexj;tohpz i-d1ma4 *d 8s ;*m,k-980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 n; )kcr 48+jt2 waq zj,itrm;lits orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume th;wq 4i m l2n jc+;)ttjkz8,arrat the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifo ce1pfvjd-tl 1nt /r voiz6v.m.;rr25rmly in a horizontal circle (acp vfr-d zim . vjrtrneto.651lv/21;t arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle to5jl:-:s w2kkuzrr/bh 0rs1is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal ac:j rr0:kzo-5swsb2k1 r ul/ thceleration 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 n(sasnmc qoiy -*.; )jo;;1lrp mt) ntacceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rq* otm; ;tsr pn(-lm;s)oi jan1 ync).pm (revolutions 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 awhe6djs k x 6t4m9nrx.rtt)y, 0+7xj .hih+sp vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its +nkw.xp+e 9 6mhjh).y ,s dj47tsixrx r ht60tspeed 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 v2fe(3wz iv bws) gx 5,3-j m8 mug6esmh/x5ph1050-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 the mass of the car?mezmiwxs5,3 ju5mfw2gxsbp36/ vg8 hh v e-) (   

  How large must the c; lbiii/5 s5u.esuy9br;) ltk ht3ay4oefficient of static friction be between the tires and the road if a car is to round a level curve of)yl ;it3ks 5t/ usblu;4 hie5ab.iy r9 radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to pa6+t6 x-nqylbrr 0 le -h*h6urotate a trainee in a horizontal circle of radius 12.0 m . If tht-66lehn+ 6 h- ulr *yapq0brxe 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 f6i hm 7,l)90efefc4k jc3ouhzrom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin andlehe6,43 jimc u)7o 9f0f zkhc the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at thbwibe * 40r(5j dceia(e top of a cir*ii ce4wd0 be5rb(aj(cle
(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 ro2 + 9mgc1sbplzslab5cog5+ y ;unded top of aoll sm1+g9bsccz2y ;5a pb+g5 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 fffjp34yg8 e5p,gtu ,wheel need to make for the passengeep48 f y5gg,ff ju3tp,rs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radxsug+c9 i.o f5 yrs/j.ius 1.10 m. At the lowest point of its mot j/+5 uxsr .c9.ysigfoion 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 if ad7 s 6usxbcb95 particle 9.00 cm from the axis of rx sub5d69 scb7otation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivad k7gvtd-li m,: y9ckf;i +m 5/3zldctl, people are rotated in a cylindrically walled "room." (See Fig. 5-3m/ dkly livtf3-d,gk7td9c ;z +i cm5:5.)
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 04 ulcfk +wiy kfj15e/ ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a k jywekf5u+lf/i 04 c1light 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 time, by not ignoring the c6b3+px-j9 fk jehmc2weight of the ball which revolves on a string 0.600 m long. In particular, finc23hp -kcjjbxf+e9 m6d 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 perfectly6kfz 0dhr(uo ; yq1tur1es uu -bu.k5qskc+63 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 /jiq gi*21wsgpm5 )hcs $ 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 maneus7oi ph2. lsx*-ea0javer 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 cent2bd+ 7iz83h4l sug bioripetal components of the net force exerted on the car (by the ground)i8 b+g47uozl3b s h2di 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 accelernoki -g;d yiwv:1k,3xates 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 the road to 1ing :k3 yv,;wxd ok-iprovide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circq f4ht 0zu-,uele of radius 2.90 m . At a particular insta4u- , eqfz0hutnt, 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’(r,kr8 4e c8i ou4cjtivg)h.is gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mach , (8 v8g44ktjc.oriieu r)iss is 1350 kg.   

  At the surface of a certain planet, the gravitational aipr zn zip uj1wz(mq,/+z)nhy3)x)h)cceleration g has a magnitude of x hh(n)r,p)zipymzz j3nq /+1))uwiz 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1.7qci )dgjx(zgj4ed if5.+ .y8 l4eg j 8f.zldjixq.(i)d4y5 c g+ $\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 : jvstdow(ggm2k: ;y(Earth, but has the same mass. What is the accelerati2tsydo kj(gg w;v::m(on due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. mt: j 6axmqy97What ay:7qmxtm 96j is g near its surface?   

  Two objects attract ova8 3u3x cy+zlu. fywli)5q 9each other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200r+ o1/h) gpgyj m ) jhg+/go pry1   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Euuuhee2rnwl+domdw 0e33 a:h) 7iu *:arth where thegr: ul u)u:*w0di7hedem2h+enar u3 3o wavitational 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 packed in;hd3h 5uccl )wto a sphere about 10 kw3 lc 5c)hduh;m in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf sp8vuc)0 rs78gwei :ap-zcs5w tar, which once was an average 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 ocsw 7s p5z r8g)cape0w:8vi u-ur Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlel 1 1rbj*ck4geave vtf(ivi6(fv6/t)ss 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 gravit4tiv bj 1e ev*(ig 6(v/)6v1 afrlcfkty 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corn ,-p)eotwd8x rers of a square of side 0.60 m. Calculate the txopd-,e8 )wr magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side qftfpf 2 ;p25xof the Sun. Calculate the total force onp25 ;xpfff t2q 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 a imxwjlpp6/ 36t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determin6pxi 6mlj/3wpe the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eaqup6 frpku )ft6j)* /q,je-fn rth and its distance from the Sun. [Note: Compare your answer to that obtaf j*qepu n / ,p-jutr6f)fk6q)ined using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about tj.0gjate 67rshe Earth at a height of e.jj g67ras t03600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circu;eu6;aoi4 o*z b 4kylwpih,-flar orbit 650 km above the Earth. How fast mus le b6wzo4iyh;u-po4fa; k*, it the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatydk9 fi1/-y5r*2rd:vy u igvavd.n) ke if occupants are to experience simulated gravity of 0.60 g 2vyd y1air ivk9vddn*/:.u5- r fgyk)? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earthm)h ;/c9:ztn7gy eyfc+*sqyz 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 th7 /zct c zys *gyy9q:;e+n)fmhe satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the*ash t/y05nq t top of Mt. Everest to be placed in a circular oht/qy*at05 n srbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to or-yoy/yv 0aercm m3facn h) je +08yf y0t1h7d;bit the Mooe1-r d/7yv3 ;8aty+0 mhc0ya oj)ch yfyfmn0e n at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice thac9 b;*8 (;qpub*ny0 *wbii5snb vcz xyt orbit the planet. The innerc(n 8uqsn* ;bbw ;0*yy9bp iivz x*5bc radius 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 rotate /w r35 ds3t5nqkvvzf.i1dtb 7s once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to he5 /5w1bs v d337 dn.rkfzqvtitr real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cente 3yiwf6gyc,k+ud+ oj4r of the Earth's Moon in a space vehicwcjk3o6+g4 y+ ufd iy,le (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 (bk 629yikswp,t j qs,stars of equal mass. They are observed to be separated by 360 mili( ,2pkb swqk,ty 6j9slion 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 woman in an elect(dv6lbtt a(pa44r ,vator that mc4datpbl(t a64 vr, t(oves
(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 hanh 8ul hk(e, .jg2sdz.ags from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elej8.d,ae zsk2u.(hgh l vator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellpeor70io7 5odzcu8r, jl kpt.8z7yx ;ite orbits very near the surface of a planet with period T , the density (mass/volumecjoo07trx8. ye5zz ,rdp7 p7u8ok;l i) 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 de) 1u6d2dekb i8en) jnutermine the period of an artificial satellite orbiti)ni 2bd6kjue 1u e)d8nng very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundre82lpo7n ,rkpym wqnmw q;-1 )ld meters across, orbits the Sun like the planets.m8q7-, ony plp)mwrn2;w1lkq Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of kbl3ygx; y k vc:;zg4(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.wx8zqdvr:c fz8(um, 5 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 still “in” the Solar Syst ur(z:88,dm5wfvcqx z em? 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 Galaxy ;m o y toockxs40s.tcy6q51u;w0)tzo $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 qfy, j i.-(edymass, period, and mean distance for the four largest moons of Jupiter ( qdy-j(. ,fieythose 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 k+zwk)dz.kz0k nown period and distance of the Moon. dk)kzzw0.+zk   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, lriy-7 *aki7jsb 4ak8 using Kepler’s third law. Use the distanceys akbi7 74r-a* lki8j 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 consis;ux qy(om 3)p6-c 2y1 3ql/p6 exqfewf dnjtv(ts of many fragments (which some space3n - ql u6wmo2py;qd(x6p)e t1qfy(v3xjef c/ scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band chb5 12idemx) zompletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this mxhidezb2)51 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 13oj0ez -( crgz 6en*-moijsugorge 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 is 80 kg, and the vinej6*smz i-- 13jeuz(corn ego0 is 5.5 m long.   

  How far above the Earth’s surface will the acch zipz 8ec ci-gd6),.veleration of gravity be half what it p)h6cc.,-vdi zz e8gi is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands andku+ rs0hsc 1+b spin in a mutual circle once every 2.5 s. If we assume their arms ar+hu 1 r0kss+bce each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparend6;qg /ximj l;xqx r;+t acceleration of gravity at the mx;+;i rg/dj; qx6qlxequator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a /gkr pz 4-p+/xpxs+sf ( .rddkspacecraft traveling directly from the Earth to the Moon experienc/xr(.rgd+p+sd/pz-s k4x pf ke 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 stand on a bathroom s;psde )hmuxe(kq h: 94cale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,p()x:hqus k4 dhmee 9; and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circultd:4fmpzw obeta+7c+ ) r q+ p7xz(lk12ag(crar 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 ofakr oec pft:+7(z+q)7 bm2 arzg cd+ wlx(pt41 the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig.: 1md4 c;otjdt) pczc9 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 rahl/l*h92 ji8fzhq5s v dius r, the acceleration due to gravity at i/fi8lzq2 h5ljs*9hhv ts surface and the gravitational constant G.

A plumb bob (a mass m ha mp8ve1gt 1tn0nging on a string) is deflected from the vertical by an angle vtg1n t1 08emp $\theta$ 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 -gku .h4cmr2xm is banked for a design speed of If the coefficient of static frict g24xukrc-.m hion 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 rwvv: z/4/8j gt: ejvvrotating so fast that objects at the equator were apparentle:/ zv 4w:/8vvjvt rgjy weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartgdzad0/cfx,x1( 1b d y;; ruif of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A wf n+n( ang)wz0 f.7wilamp suspended ng+ fn7(.iwf0z )naww from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, i:f 9g*r(x cwigdoeo2) t 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 experxg2 eo):9 *ocidfg w(rience 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 p4*xwxjmulbgfl/p 7b )3/ueb 8;bh s5 extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no*53 4l;mwh87 x gpb//)lusfpjbuebx b 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 as it traverses the hill and 6 vm0r ygh us t)a/+u 38vz1g(6nduisivalley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal force)0i6atsgi1 3dh ( ruvz8u gs/mvnu+y6s acting on the car at A, B, and C compare? (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 Positionin0ur)q2c8mu ax 6 ei,zkg System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an 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 11,02k),a6zr q0um8uxi e c00 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 Rendezvoullpoyr17q/ 8hs (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height /7q rl8plh1yoof 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 shut0w4fz 9emgc9mtle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth),wgz9c f9em0m4 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 yeq ikb t1( tg:0a/cdy5 xf*ag4vars. (a) What is its mean distance from the Sun? :/05ax1ta(gt y4 qgcfiv bd*k   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actu*dvk fjx +805 x3mxn27afwyica akm20ally "feel" yourself gravitationally attractedm5axm kijnck8x3dv 0 yf2*a+fx72a0w to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gglsisp:arvz+e *,-/k 6im yp: alaxy (Fig. 5-46) at a distance of about 30,000 lighvgksi-e,zyr*p +pa mi6l:s/:t-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 l 4lbql; v.j6ujr/el f3ocated at the corners of a square 0.50 m on each side. Find the magnitude and6u b4v;ljf/l j.rqle3 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 o1/k-rl r1w ercrbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep second +)e3e *l d9s gy+jtxpmhand on your wrist l+xe+9p) mgt e d3sy*jwatch?    $\times 10^{-4}$

  While fishing, you get bored andg v qqcpsqxm(,+ow7*9k7ur5o start to swing a sinker weight around 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 witu5 wqxoq9pmo*7rq+g(, vck 7sh the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car traf5lvq1 k0 ddxbxw ) eczno6t81:0na f4veling at sponql1z41 bx0vexf6acn 5 )dwtf08: kdeed $ 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 h0j5;nlg *u31g msmcg, 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 a curve with a radius of 620 0g c 3*smg1;u5 lghmjnm 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.$\approx$    $\times 10^2$