Sometimes people say that water is remoulgjzd j60v67chk5 s5 ved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong l5vdg76u0 k 5hzj6cjswith this statement?

Will the acceleration of a car be the same when th/b8)c86/hrb *dnsskyc ak , mqe car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? E s a,n8 )sd*mychkkbq8 /6rbc/xplain.

Suppose a car moves at constant speecd6gvxsl)wb b;rg5 *0py2g3m.y j v0 fd along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch y6c3;gvjy fxg0sb5)r g*0 bvm ld.pw2 near the bottom of a hill?

Describe all the forces acting on a childb1 es.,m*ww ik o4j(qp riding a horse on a merry-go-round. Which of these forces provides the centripetal acc .ib4m,o s(p wjeqw1*keleration of the child?

A bucket of water can be whircs0/lga 5rvf 4led in a vertical circle without the water spilling out, even at the t4 v5s /ra0flcgop of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three *u 6)a2x/la6o5jshb qcuwjr;controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produc/*2ahsblq5o6) j;j6uau w rxce?

A child on a sled comes 9- hjk5y,oox + o,ccamflying over the crest of a small hill, as shown in Fig. 5–31. His sled ojhookc+y5c9,am ,-xdoes not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders l8o6lhb/ cxw 9 shpd.71wj +ihwean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you computemo3ir ++9gtmw the banking angle given its spigwmm9+or t+3eed and radius of the turn?

A girl is whirling a ball on a string around her head in a horii+2p:bl kji7mx.6(fv9 .mtsxsjre /lzontal plane. She wants to let go at precisely the right time so that the :/92+slmiplj6xrib t.x vm j .ef 7ks(ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how k.tz q5jr/ vqjoih z3h/0qm:,large a force? Consider an apkr qq/.ohj, hzj:i qv03z5/mtple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublg ( kr5hqebl c bzg)8r34 1w*s9kdpm7be what it is, in what ways would the Moon’s orbit be differe()1 m3gksdhpbr qr 95 z47bewgblck*8nt?

Which pulls harder gravitationally, the Earth(jj1 6eutmb7x on the Moon, or the Moon on the Earth? Which ac1j (jtu7be m6xcelerates more?

The Sun's gravitational pull on the Earth is much larger than thets odrm9 6n/wwwj)5u 8 Moon's. Yet the Moon's is5/os9m)nwtj d6 r w8wu mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator fm(g-jw4wkf;- t5 cn otfb4. xor at the poles? What two effects are at work? Do th j(w fn. m-f- otcfkwbg54tx;4ey oppose each other?

The gravitational force g 8;xm5+no dtgon the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from thetd58 n+xo m;gg Earth?

Is the centripetal acceleration of Mars in its orbit around the w h(9cey,pq;+vqe * kguk/q;i Sun larger or smaller than the centripetal acceleration of the Earhyqw e( ;qvke ; kc/+*9u,pqgith?

Would it require less speed to launch a satellite (a) toward the east or (b) toga:cymc8 mqxoa3pm z2iu4bz/d (4;s1 5g urz7ward the west? Consider the Eibc :gu72dgypzacu4 zmqo (s18raxm/;m5 3z4arth’s rotation direction.

When will your apparent weigwk -a:4kq7t7 * nvopsrht be the greatest, as measured by a scale in a moving elevator: when the elevator (vqk:77w*pt n-a4os kra) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affecte.cupv a / 0qu3,dt;tiyd by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindru u;.0qd p,/3 ityvcatical 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 “appare9cszg0z 5 m.cwja.w7 bmyq30xck5yz 4nt weightlessness” between steps.. q 7j0bzky0 ayswz x 5gc5mmcw43c9z.

The Earth moves faster in its orbit around the Sun in Je8 d9dq8t -xllb-m dv5anuary than in July. Is the Earth closer to the Sun i db lle dx5q88-dtvm-9n 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.]

The mass of Pluto was not known untiqrm)z 32)g+c g hhsf.nl it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s.3gm h hzg2c+f))sq nr mass.

  The Sun's gravitational pull on the Eargdwu9lwnk* ;2n r9 *zrth 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 o;*lzn nk rw92*gd9wruf 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 1980 ,4;kcfible 9w $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arofli)/p yrxpidf+ (5n )und the Sun, and the net force exe+xp)f)/lf dnir( 5y pirted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exe h2t w(s;g61kfp-lsx b v*1yjerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lpw s *x;eysjkt 1l1bh62g -vf(ength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shq m4kr2h1,r*bc v5l65inkrpw uttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of tcqprl 6vr,*h i1 b5k2 5m4nrkwhe space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a p e 9y9cag ,wzrasb8/d*ottes8 yeza a9cg,/ db*wr9r’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revoljy10 r2 l6v-f qo t-:y km8vlsb-jeb/mved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 - qobyjtvv 6ey bl/2 8 0-msljm1r:kf-$\mathrm{~m} / \mathrm{s}$ 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 62.vhl ,yavpr1050-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 thev, .a6l rphv2y mass of the car?   

  How large must the coefficient of static friction be between th/ipw a,4d bby4e tires and the roadb ywabd4/,ip 4 if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilo ko))mxk)um 9jts is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her bukk)9j mom) x)ack 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.mv75ps-5r aza 0 cm from the axis of a rotating turntable of variable speed. When the speed of the turntab5-aaps mv 7z5rle is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster bexf2,(hzol (2 bfcje ,-m; ikhp traveling when upside down at the flxcpj( ,;mzi2 hobk(h,- fe2top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded v,gr2h 3 b6acqtop of,v rgbha2 q3c6 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 xbjrwp)q:9d,*xus* e d pelc za46e/4 a 15-m-diameter Ferris wheel need to make for zd ,a*lxqepr x 6p4e)4ws9d/*c eu jb:the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle o3rgvdx96gz b1n:o nh nvs, e26f radius 1.10 m. At the lowest point of its motion the tension in tn, r:v 696on1vgnegxsdzb2 h3he rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm fh2tihn.fm)* v p1v si:rom the axis of rotation is to experience tivmh. v2* nphs1)f:ian acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a cra7 f:3tsvlv 2sho7 rsc.+vd7 arnival, people are rotated in a cylindrically walled "room.ts 7rdofvvvc hl 7a+.:3sr7s2" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tabl-k;a*xv.,uw no h8x :ov mm(dgetop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central homo, vwm*kx;gx- 8u. :anho d(vle 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 nowy. yc- a.w :-gk5k brt*szlz+t ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the rl+zw -:wk.kb5gz ayc*s-t.ymagnitude 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) 6c:mdby yax7d rf04 y9vm-nu 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 masseswngdn3o6 ng-4 $ 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 divef.ez-t/u7 9pc(w/v4mcqpaz0jpf/p ing 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 compxg4s:xw 0jlcnn -1*vqonents of the net force exerted on the g*40 s 1 xjwvnlx-cq:ncar (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 accelerdal.o q7+oco*2sj qne74b+ n+oj4c jw ates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangentia*4b+jdcojo72q al sc+eqnnjwo4 +.7o l 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 horizo 8 er.x5nlk2wbl ymg*ld26*kzntal circle of radius 2.90 m . At a particular instant, its acceleration is 1. nllr8dz2ky*kgmxb w.5*le2605 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 -j-akier/ )b8jzz* uyt- jdb- rh ls9)spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 ak u-bty)9h/i- j-rdb )se*-zlrj8 jzkg.   

  At the surface of a *c hcw nz)iyy5ewp2 9t,m7k 4tcertain planet, the gravitational acceleration g has a magnitude of 12 t)hny2e iyw cz p4k*5w97mc,t 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 1vltr)-7r nnj Moon's radius is 1.77n )rn-1trj vl4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, bu(f 3gxn8lfm ly-8ra6mt has the same mass. What is the accely(mflxf g- 3lnm688ar eration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times row+vsnr28:pi4m 8ysthat of Earth, but the same radius. What is g near its surfacerw+ mrvpi88on4 sy2:s ?   

  Two objects attract each other g:hz -erel1(fg bd3p:i;po;; pto)jytravitationally 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 effecti ,zp (b. c/tz1wexvd0oveot 9+ve value of g , the acceleration of gravity, at (a) 3200 m d0x1 e tozp+,(tbz9vwe/.ov c   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinc-f + ;9 wez8/ruqnf ) crpa;+udzkyh1t outside the Earth where thegravitational aczef) za+q;ycwu /un - p1cr 9f+hd8r;kceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spheq92c kc*q3hm 7 kjw,xcre about 10 km in radius. Estimate the surfacecc qwkmkjxc3 h7 ,*2q9 gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avpt ;icsrw,*u3erage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What i*spu i,;t crw3s the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in th0 niefq4,)rj8l ,emfoe space shuttle. Your friends respond that they thought gravi4ff men0oq 8l,ir),jety 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 are lpfw8 zea8 8xn8z i(h/qocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force ewz 8i8/88hf(zepaqx nxerted 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 of the Sww 4 l ;0uq7932abz.) hoghgdhrd*nyiun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses arh 4lg)w*9n2.y0uaib 37 dhzq ;dwogrh e $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0jr ft r. t,sz nnfh9oa8k)j z.m7c;+-b.38 of what it is on Earth, andrb+m-ts.z.jz o;h j8c fnf9 n ta7,k)r that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass o (8zny i9wgpi6f the Sun using the known value for the period of the Earth and its dg(npw y9i 8z6iistance 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 about the En (usw ,ak0c4narth at c(wa4suknn,0 a height of 3600 km.    $\times 10^3$

  The space shuttle releas3thb-c wn5 ,fj to8wr8es a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be mov hnt tw8wr,o- 5j8f3cbing (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occungmu skhyu. 6vd-0u 6)pants are to experience simulated gravity of 0.60 g? Assume the sp0 ud6gsmu6.hv- unk)yaceship’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 folm4j b/ofnvf-9 itv8 .r a satellite to orbit the Earth in a circular “near-Earth” orbit. 8 nil-9vov t4/fbfm j.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?    s ~    min

  At what horizontal velo;l:.q3 ku ucbn7iz8ev city would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orb zun: b;.lc7ueq v8ki3it around the Earth?   

  During an Apollo lunar landing mission, the command module continued7yvhw80 i4 oln to orbit the Moon at an altitude of about 100 km. How long did it 4y08 li ohw7vntake to go around the Moon once?    s

  The rings of Saturn are composed of chunks of icp lby z,ucsc2/+( ylq b9tc4vc,p)8u fe that orbit the planet. The inner radius of c cz,2(yqupl,yf+ 9c)/vbl8 ucp t 4bsthe 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 p/1rotqq6p , ;hi/gd/g+zditrotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s appareqzqg 1toi/;p g/h6+,/dpdtri nt 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 astronaut 4200 km from the center j-aep a;kx-hzap3jsc:b 6;gq -c8(ubof the Earth's Moon in a space vehs6ha:-kp a( b -zexjac -pucjq3;8 ;gbicle (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. They an ljq 4lu+h/4are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. Whan4j ulah/4 lq+t is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator tc enpea4h z2-(hat move hnpezac(- e24s
(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 cd4:l;k9imy ux4 xo7 gqord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accellq: xd74o9y4xu ki;m gerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbi, 6vavztq6t6 vts very near the surface of a planet with period T , va66 v6q,vttzthe density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the perio;. k)gy kzgxz+k-4j kcbif feko/- :q:d of an artificial satellite orbiting very near the Earth’s surface.y;/b z+gkkj- )o:4.:qef zckxgk ki-f    s

  The asteroid Icarus, though only a few hundred meters across, oms xc5ay( 5q1orbits the Sun like the planets. Its period 5sm1yq a5x (ocis 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ym 2cll1h(l+ /,dnelhof 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 onc01 sjv7pyy7a xe 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 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 1vp07 jay7y xsthe Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy:.0dqgs0wpb k2 hz3vm $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 largest kn,; ohiv,8xumoons of Jupiter (thos ;,nouhk8xvi,e 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 p.unwm i,2nrabvgs ;0 *g31 j.:,z pjbvfv1g ekeriod and distance of the Moon. v2, ;ga.f1,ukwn3*i :01 pj. vsmbz ebgjvrgn   $\times 10^{24}$

  Determine the mean dista0ccptol( h/ v3nce from Jupiter for each of Jupiter’s moons, using Kepler’s third law. p t0l/3coc( vhUse 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 Ma9nxre-qi 8l7prs and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was 7x 8q il9en-prdestroyed).
(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 tg7 *;+ jmr; bky(p:1hizosabg he 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 q*m(zjb :;s;ypgh1b +ogr 7aik uickly 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-h(m0h zs kj/uer-bi6 swinging in an arc from a hanging vine (Fig. 5–41). If his arms arejzhhe-iu0sk - b6r(/ m capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accele5r+3ttq) yx:rfhc 3jjcs0 fq +ration of gravity be half what it3 0q+r :rscjx+3h 5fqtjfy )tc is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass g)pne,b nh5c q 4 v7/n9f(pcgrrrab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?/)rvb5n ,7cqnnrpcg pe (f9 4h    $\times 10^2$

  Because the Earth rotates ; wxtj32f8 (:l-i e n9e6twrbdfule.monce per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rota-tlew xw3fedrfu.n;j 86m i9b t:l2(ete. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecra j;h.o0be 0;uxn-6,suzv4si 6/cjwk baj xpw 0ft traveling directly from the Earth to the Moon experience zero net force because th;p04ak wx6o , uvj ju0j;bw ss-/i0.nb6zec hxe Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, l/sa r2g:h fdqhzaa9 jb10m4. but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and ina. fba:s 2zq ar1l0djhh/g 94m which direction?     ----待选择----upwartddown 

  A projected space station consists of a circuldr t) j5ds+0itar 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 d+jr50s itt)d to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a ve 9mmohvcw((+avi iw+9 rtical 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 it zki071h tw3cxs radius r, the acceleratkc3x z1iw07htion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical byl 1y pc)tef5:u an ancpl15eu:y)tf gle $\theta$ 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 coeffici2 bnzrz-whkt3) bqub 3,c;b2 fent of static friction is 0.30 (wet pavement), at what range of speeds can a car safely habt hz -2b2un3kc;r 3z,qwfbb)ndle the curve?

  How long would a day be isst o h-4o33r;6me.:dqjg wk87i yuwif the Earth were rotating so fast that objects at the equator werh46sko: us33oyr;iiw7 mtgjwq. 8d-e e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cons8t7( hovdk6k)r9i jxq tant 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 curve of radius 235 m. A lam2kefc ia(x 3aj/u; 9fkp sus;kfa xjicaek 29/3(fupended 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 rm0ryb+ vyi u:1c7sey:z j2s1the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following:iyr2ebu:yc0 1svj 7+y s 1zmr 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 o eihqm oc/kf5 e -k;u-/v/xa.Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a blaoe ekic kvo;q-5 /-hf/.a/umx ck 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 conjm i)ff ;5v5pastant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the ro; a fp55)fjmviad at A?

  The Navstar Global Positiontf)v1dire1 1/e+ ru t(n8jsloing 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 fe1ejtud)+ tf1 ero sr1lin/v(8w 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), after traveling 2.1 billion km, is meragdy t1.;3k,v s/wup ant to orbit the asteroid Eros at ua w dk3ps.yr1/,gv t;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 t4 mb0isrt71 :i (als tq+wm6t xfx/7igq.-ixqhe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of r0 t7 mt.lsi-+:g bfxx7qsamxw6 q1qtii4(i/ 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 has a period of 3000 years. (a) What is its rzoyn3i:tkw 2y5+b3 jbvf :6xmean distance fryzowf ::32 rb+y tkb65njixv3 om the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you brqdl-xb*:a:uzw 3a6could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable as:rw *-3dalb z6ux :qabsumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a di( 1syhalx*um 7tj0hm4stance of about 30,000 light-years fromt7hxh y0sj1 4u* (mlma the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m o4wl5 u+fv-a2o/xde zj n each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the+24wv z -u aej5/fxdol square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kx(d 6w( fcc-f vfgni/) t1n9vug orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by tho uc::n)-krio e tip of the 1.5-cm-long sweep second hand on your wriso:k :rnu- )ioct watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight / z :b6c xj.u9jmxhhag-7hk9iaround 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 linx bzi9hgc- .6hxh/:uka9j 7jm e makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed sb 1,l4oqhal:ao that a car traveling a,aaqloh: b41l t 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, toq6md* uled (oblt(/ (he Acela, 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 mbd((t l6o(/*ou lmq edore 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.$\approx$    $\times 10^2$