Sometimes people say that water is removed from clothes in u7rq3 ,9k r,wvklskm-a spin dryer by centrrs79,- rw luv3mk,kqk ifugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the saqluwklf:m of6xv y+k( a 1:5bk:g1 ob6me when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the sa(: 6fmkuo5:lw6yklvf+k: bq1 a xgb1ome speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whv9e7) jyg;l nsere does the car exert the gv)9e7y ;jnglsreatest 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 near the bottom of a hill?

Describe all the for(3cedhgy+ox6 23qqqkt*vg i s d2l08rces acting on a child riding a horse on a merry-go-round. Which of these forces provqqlqsi0yd8 rhte*v 36+cgx2 gdk3(o 2ides the centripetal acceleration of the child?

A bucket of water can be whirled ihm. nbu4ck-/ r8nxs2hqij2 ( fn a vertical circle without the water spilling out, ek q (- /ch4mxhnj82ruf2bns .iven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you hpcvb +m0gzr 61djs /h/ave 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 6/mj b0rgzdh 1+v/scp do they produce?

A child on a sled comes flying over the crest of a small hill, ass- 6 mezs ghlrr(,+ys l;t1wa4 shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes o azt6ywgmes( r; ,r41slshl-+ver the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speej/o mc(c/ao 6p )g/h5 ,utdbfid?

Why do airplanes bank when they turn? How would you compute the banking angjn 3ycp7j wx*17 ;gwhyle given its speed and radius ofxg1j* ;w7y7cnj3hypw the turn?

A girl is whirling a ball on a string around rz*ye *4 aboc:her head in a horizontal plane. She wants to let go at precisely th 4or:*azc*eybe right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitc(i6kqq7b3y 95iz6 i-ad8 dyx1 mmt uqational force on the Earth? If so, how large a force? Consider an apple dk3i 56(dic u87qqqy yi9z6tmx1b ma-
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what iee/d 4 iwffe;k7bk )5at is, in what ways would the Moon’s orbit be diekiw74a ; f kefb5)d/efferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on tv*- d:3jwg z(ewow73 lrkx/ cahe Earth? Which accelerates mxl3wrowd/kza* e-v (wc g73: jore?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet59l) tzw h q lum)jgu9,2xx2sf 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 2jfl2x q9m s tzwghxul),5)u 9other.]

Will an object weigh4rxp lnwc:bqvpv /2 (1 more at the equator or at the poles? What two effects are at wor4 l 21ppv:wcv/qbr( nxk? Do they oppose each other?

The gravitational force on the -0zsf+a c :79kkaq vfu*7kp uaMoon due to the Earth is only about half the force on the Moon due to tha+kq- kf*fuk z 7:7cv9saapu0 e Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around tyxi et b)/z-8hhe Sun larger or smaller than the centripetal accelera8eh-z) bxt /yition of the Earth?

Would it require less speed to launch a satellite (a) toward the east or 7 e53+49exnykpji yxo kggxq;:+ut8io4cyf9(b) toward the west? Consider the Eax7+9cgkuo:tiye g pe5kxi j+8f o 394ynqx y4;rth’s rotation direction.

When will your apparent weight duz *62xwhxwc07rsfek )ddm:* s 1)oabe the 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 whif) e)ua w codhrd s*s16 70m*2zk:dwxxch 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 affected y4:ascdg -g4n3p2rjq(xike9 by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shx( 4ni p:3 cg9qk24y-jga rsdeell 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 “)b2*s8 wrg z a83oz xefqj9c9afree fall” or “apparent weightlessness” between steps.)9soaz2 3 rexagwf j8q9b*z8c

The Earth moves faster 1 jo;s-spaq 5-sm7b plin its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not muc-sbj m1 l7p;sp-sqoa5h 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 discovered to have a moon. Explabcg kxke(p4qls)4m ;: in how this discovery engs4:kp;)b( lqc k 4xemabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth ig *.t*j*; 3 w- hrobzuvudh(cbs 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 *dvh.3b-u; wuojt*r z*chb g( 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 19u /l,oac:c gq+80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelzt2:rw 3twogh,)(v)onhr 9 gleration of the Earth in its orbit around the Sun, and the net force exerted ow3 n()w zvth:o),otr hg9lg2r n 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 exerted on a 2.0-kg discus as it rotates uxstoiv59u; c5niformly in a horizontal circl9s5 uxc;tvoi5e (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface,uf dvy7; h b1fth;gv62.erzf1 and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your 7f.hut1ev6fyv2r1fd bzh;g; answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration t5 3htcqncuwxfn-tb) e- 2lbdv82*4j of a speck of clay on the edge of a potter’s whe-v bj4htfq)uc5dbe-tx*23w l8c n n2tel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stri-ttslf30sz 8 vng is revolved at a uniform rate in a vertical circle of radiustslzs 0fvt-38 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turdn/cro5unfx4 qb81h. n 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 onho1/d 8u5xq.4crf nbf the car?   

  How large must the coefficient of static frhfbk; blr;b48y t *1obiction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed ;ylh kborb ; 8b4t*b1fof 95km/h ?   

  A device for training astronauts and jet fighter pilots is d g(b+s2n-i0mjkf1g1c xi* q rqesigned to rotate a trainee in a hoxjii0-s2 ng(cq11g q*m+bfrkrizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable .xr1f jgjfb12 w ng:pl7s(u8zspeed. 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 thn g l(8r1buz1:p2x7jgs jwff.e coin and the turntable?   

  At what minimum speed must a se(:c 2i ;yo9uz4on4 qbfr al7roller coaster be traveling when upside down at the top of a cuc s ;l( en2oa94:f4broz 7yqiircle
(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 thet cd 6dkt-avbb 6s+t66 rounded top of a hill (radius =9dtsv6 t66 + 6d-abktcb5$ \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-mkq lh kc2,z:99r r6ucf-diameter Ferris wheel need to make for the passengers to feel “weightlesu,9rqckzc krh6 2: f9ls” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vun6 (bztn-,jsertical circle of radius 1.10 m. At the lowest poin j,sbun- ztn6(t 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 rotatep6.jo8u -rt cn if a particle 9.00 cm from the axis of rotation is to experienuot.p c8r6-n jce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatedj02lxrnc 7qtv1i s 6 wt2o,k9q in a cylindrically walled "room." (S l q1nvktc,xo0i q w2rs2976jtee 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 rqj 90 g27sxey.y.ugrrotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord conny.u rqg2sjr97gx 0y.eected 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 ignorin+9 k ,ml;soi .ee/zspqg the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude 9./;kop lqezm,se is+of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fovo0tfs( 89ub3 wv9ovlr 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 massesfx/tq ru-rt kmt )jvn.*0g)(o $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving verti+(1x s(mgp3 ke qeyx7ocally at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exel t ,87.fnrx8b kiy*wnrted on the car (by the ground) in Example 5-8 when its sp8 8*,wn7yxitf .knblr eed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500a0(i ;tpzrm*bf8lq*m accelerates 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 provi8mlai mtz; fr(qb 0*p*de this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius rae.*xc)e tt) 2.90 m . At a particular inset*c)e trx.)atant, 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 120d -s yzxz.,zy,800 km (2 Earth radii) above the Earth’s zsz,xyzyd .-0surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitn 5y8ez7w 4 0(mrzu wbpz d)ir/fnt-r*ational acceleration g has a magnitude of 12 m-b5r rryn07*nud)m w4wpf ezt (iz z/8/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 Mo2r27wjpj j)72ehq ou+ muv5tjon's radius is 1.7m rjuv+2hj 2ojq75)u7 tje2wp4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same s9mx09 ngglz+uh,0ibmass. What is the acceleration due to gravity near itsmbs,x0h n g9+zgl 9ui0 surface?   

  A hypothetical planet has a mass 16 c0: kwgpqzr(.66 times that of Earth, but the same radius. Whatgpz (c :0kwq6r is g near its surface?   

  Two objects attract each(j7am1 c 8fkmy 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 ) wpx1zoe3hw:k6pv:+ e( ujjw 0a) gxcacceleration of gravity, at (a) 3200 m wj1oj6e0ega( 3+wpxuxh:):cp z w ) vk   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E6vtojzwrlf28/iy4 c .arth’s center to a point outside the Earth where thegravitational accelerati8j/.2vwiyro 6fz4 cl ton 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 s ,w,ahz ptvd fj e0wl4r-5w5s0phere about 10 km in radius. Ej0ew50 vrwwpas-,h,df 54 lz tstimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf skvf 9;h7a-5e ug )3 jkm2ucxwttar, which once was an average star like our Sun but is now in the last stage of its evolution, iw -)tk7jfau ;u3v5 2hg9m kcexs the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whilei jd*, 5cvm6k fqv,pq4 orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yoursel,v qkc5 dfp* mjq64i,vf 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 gyk+ ) 27yh2lw4l2 0yxqkiht1 crgspya -i3 ,lcorners of a square of side 0.60 m. Calculate the magni7t0 gc12ls ah2 y-yl+qkwrii)k2xgy3 py,l4htude 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 ssj0y 2boq xihc;ga (7:2.j ajup on the same side of the Sun. Calculate the total force on the Earth:s.0abqjh(; jic 72s2xgyja o due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfazkv8 * rmjhxrqpal:9t 3c6f: 1xh;+fk ce of Mars is 0.38 of what it is on Earth, and that Mars’ rhpxc*at 8+q1h kf6jrx:lmk:fz;9r 3vadius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period (,lsn g z:zn2q1/.jho(k)qmh or3ijb of the Earth and its distance from the Sun. [Note: Compare your answer to that obtaine(1 2ozq/zji)ml bnqh n:o g,s (j3hr.kd using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a sjm s9k.hoie3+ x 9zolp4e04h otable circular orbit about the Earth atp90j94 x4ks o3 h. lozhoei+em a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular fezq q27hgi0dv+-7y9pltwu ,orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) - l 97e70hwydi,zf+2q pg uvqtwhen the release occurs?    $\times 10^3$

  At what rate must a cylc8vot:,nfb:r* 9+y7yn zpt bjindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m,f ojb7cztb8n: t9rp*,+ yynv: and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time ir y,me1la;vq/.a i:uo2y(ufyt takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the sur /yqmlv o:e a(uir,; 12ya.yfuface 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 velocity would a satellite have to be launched fro7 -xlg )cschr9m the top of Mt. Everest to be pla-h )ls7gxrc c9ced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to om6f :+p4 gnjy 4*0uasbrl5fau) ua (cvrbit the Moon at an altitude of ab4ygf 56jlpsna)r+baucu0 : *(m4fuv aout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed (w)w 7f7iiizd of chunks of ice that orbit the planet. The inner radius of the rings is 7iwfzdi)(iw7 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates od4:nyg /t*hm2 0m hsn ce2zo.lnce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom? g 0tny2*lnzo sme4 dc:h2./hm
(a)    (b)   

  What is the apparent weight of a 75-knu7(wu p8ptnhf gd (x84rq-o*g astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant 8hndnftxqp g47urp (wu8 -*(ovelocity,     ----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 arem.+elh sap 8+mbb .8 pac 9:-f.bblwmk observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of 9c f:ml.+l.bb.akhpwm8 e+smba8pb- each?    $\times 10^{29}$

  What will a spring scale re 6x5,id(uvx rjad for the weight of a 55-kg woman in an elevator that mo6( vd jr,i5uxxves
(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 f5;o(s/x 4jafyc - lfr;+j fdoudbft2, rom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magntffa(b-ruo;2sjf+;of y/ d xl4 d,5cjitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period ,la qsyu8/,as T , the density8/s a,sl, uayq (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 rkfe l96 ic:n6period of an artificial satellite orbiting very near the Earth’s surcke:fr n6l96 iface.    s

  The asteroid Icarus, though only a few hundred meters acrosl5*.w jfv:gnq n0b8cl s, orbits the Sun like the planets. Its period is 410 d. What is its mean distance.50fl8lnbq cwg*jvn: from the Sun?    $\times 10^{11}$

  Neptune is an average distani8c ai14ru+4gj6w0eiq se8q j ce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years.u bpohyk3c( rx cx*5/, It comes very close to the surface of roykch5c(bx *,xup/3 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 the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the 1cj8pr m4ud9 bGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 bz *yr+mea8eb:e2y*n :/tsqrqac39 1cv; nim moons of Jupiter (those discover nzq vqm* ee+yscn b;t1/yracarm:8:39 b2e*ied 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 knowns(v.e pn4c t p*qvnv73 period and distance of the Moon. s.q*vpne43t (vp cvn 7   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using 1,;v og (rrbc7xyi/zh6xkv2fh6 iw+ fKepler’s third law. Uo vgz,xhr2wc ;x(6+v6i71b/ rfyifhkse 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 consists of man+lrfg6.ff*z* b z5qnzy fragments (which some space scientistsfnbg.fzlr * 6zq z+f5* 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 th-ton4ab8 auvxt.ei6b0 g ;/al e 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 as on Earth. What will be the period of revolution, this pl.a4 xo8ig; ba -a/lb t6evntu0anet's year, in Earth days?   

  Tarzan plans to cross a g8r78j ( qr +exsv4o +qnft;a,xxqtqj5orge 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 80r;xa4 nq8ejt,7q xxvq8j +ot5(r s+qf kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravi//k e2xf2pl nxty be half what it is on the sur22l ex/nxp /fkface?    $\times 10^6$

  On an ice rink, two skaters of equal ma(blkzvd;oxa cy245z7 o)n /nzss 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 60.0 5z l )/o;by nknco( 74zda2xvzkg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appare0id i)8ym3rv ,vj: djcnt acceleration of gravity at the equator is slightly less than it would be if the Earthr idvmyj,jc0i :dv 8)3 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 spacecraft trr)4q9-lv5iyi 66wakkor xkr8 i)1y pgaveling directly from the Earth to the Moon experience zero net forcix5 qpyriv9kl)8yr1 a 64 iro-gkwk6)e because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 6 nvoe tq bftu4/+cij+z;,grm1i 2re 465 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of ttin2i +gv ,/r1qz jm e;f4c6t4+ebo urhe elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statio2c8z/zq08 +ti1lvg j0yel:pggpcc/p n consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation spelt g v jz 0p/z/ep+ccqp:188g2i 0lcyged (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertica vruoc+ woxya(*7q2mujx9j 6 1l 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,x4*d +q v/+bg edw+fcc the acceleration due to gravity at its surface and the gc*c+ d/d4+evqfg b+wxravitational constant G.

A plumb bob (a mass m hangi4wqk z-a /q8ggng on a string) is deflected from the vertical by an angle gqq w-a8kg 4/z $\theta$ 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 banke.y35ni, ohfr bd for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range oribf. ,5yo h3nf speeds can a car safely handle the curve?

  How long would a day be if the Eart n f-p e )dn,bdk-r;yw)c*6dgmh were rotating so fast that objects at the equator were ,6n* yd kbn-)er cwddg -fp)m;apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constau(-p jscpi-j2 nt 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 ricc +kbun /g1.adius 235 m. A lamp suspended from the ceiling swings out to an ak/cn+ cbi.u 1gngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as tj a+p+a(uyl0v he 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 data for Jupitp ly+u(av0+j aer: 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 Sa9 x z8+n*6 piab .ridkry,yp4pace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whnyz d p*p8ry+abkaii.x 6r4,9 ich 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 as it traverses the hill and valwtu hh66,t: kp 5k0y6g8:z pd8cx. hhg;yi rwjley 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 witwkcz.:p8wxthu6:66r g 8,j0hh5; yith kp dyghout losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 +zwrpk g 6(n0v-d2y+f3 u)h4akhygeosatellites 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 11goh upyn (-w)frdze+hy4vk6 0 k a3+2g,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 u/bge xcn9n.-,kz 46 ;kyk5lv, p szixRendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40s b,nku cx5;/pvn 9gzkx4ek.zl- 6,iy $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 shuttleb xew .g5s8l4q7txfn/t 9no+h pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 kmws9/. 7nq+hext8 x ongt4b lf5 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 ir)8( qd- 3la zezzxa.qs its mean distance fr(q ezrdlaq3) ax .8z-zom 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 t x5 ,p+rfuoep*ga u/:ho be if you could actually "feel" yourself gravitationally attracted to someone nep: /*h p5f+xgou a,eurar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center o1 ofxqjtjs38a l zlp.:3/;qfyx4 g5zaf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light53; zzl8jx pg4qjy1.3alt fsaoxq:/ f-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.e 3g,8 gi8khmx50 m on each side. Find the magnitude and direction of the gravitational force on gxm ,8gh ki3e8a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth jvt41:lrfk3 he ol96f$ \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 th8/)ga f h,bm sp:d0gtxe tip of the 1.5-cm-long sweep second hand on your wdg :gp s0x/t)afb ,8mhrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker.q- -rnir i*3vcxwbi7 weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete rvq3 w7i rn- *-icxbi.circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hp wmjf +rdy5ec4+).wqighway is designed so that a car traveling at sp +5 cp4jf +)w.mydwerqeed $ 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 th q,sro1 ih1t, r0bh5bxe 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 m at a speed of (approximately ). r,h5oih1 rbxt,0b s1q(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.$\approx$    $\times 10^2$