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2009 ¦~ 2 ¤ë 25 ¤é  ¬P´Á¤T   ´¸¤Ñ


¶ê©P¹B°Ê©M¦V¤ß¤O Circular Motion and Centripetal Force µL©` ¤ÀÃþ: ª«²z

¶ê©P¹B°Ê©M¦V¤ß¤O Circular Motion and Centripetal Force

°²³]¤@ª«Åé¥H¤£Åܪº³t²v (constant speed) V ªuµÛ¤@¥b®|¬° r ªº¶ê§Î²¾°Ê¡C¦b A ÂI¡A¥¦ªºÀþ¶¡³t«× (instantaneous velocity) V¬OªuµÛ¤Á½u AC ©M¦bµuªº®É¶¡«á Dt¡A¦bBÂI¡A¥¦ªº·s³t«×V¬OªuµÛ BD¡C¦]¬°¤è¦V§ïÅÜ (direction changes)¡A©Ò¥H³t«× (velocity) ¥ç§ïÅÜ¡C
 

    ¥Ñ A ¹BÂà¨ì B ®É¡A©Ò¥H³t«×ªº§ïÅܶq¬O   Dv

·í¨¤«×ªº§ïÅÜ Dq ¬O«Ü¤p®É¡A·|«ü¦V¶ê¤ß O ¡A©Ò¥H³t«×ªº§ïÅܶq(¨Ò¦p¥[³t«× acceleration a) ¥ç¦]¦¹«ü¦V¶ê¤ß¡C

ª`·N a ¬O««ª½ (perpendicular) ©óÀþ¶¡ªº­y¸ñ(path) s¡C¦pª«Å骺½è¶q¬O m¡A¨º»ò
      F = m a      ©Î      F = m v2/r

¬O ¦V¤ß¤O centripetal force (¨Ò¦p¡G÷ªº©Ô¤O©Î««ª½©ó¶ê§Î­y¹Dªº¤Ï§@¥Î¤O) ¡A¥¦¨Ïª«Åé«O«ù¶ê¶g¹B°Ê¡C

Åã¥Ü¦V¤ß¤O¦s¦bªº¹ê¨Ò¡G

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¥Ü½dµu¤ù¤G


 

±q¥H¤Wµu¤ùÅã¥Ü¡A·íÂà°Ê³t«×¶V¤j¡A«h©Ò»Ýªº¦V¤ß¤O¥ç¶V¤j


 
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 ¤@½è¶q¬° m ªºª«Åé³Q¤@±øªø«× r ªºÃ·¸iµÛ¥H¤£Åܪº³t²v v ¦b¤@««ª½¶ê¤ß¬° O ªº¶ê§Îùز¾°Ê¡C¦V¤ß¤O¬O¥Ñ÷ªº©Ô¤O (tension) ©M­«¶q mg ´£¨Ñ¡C
 



¬¡°Ê:
1) ½ÐÆ[¬Ý¥H¤U¥Ü½dµu¤ù.¯d·N¶À¦â½¦±í¸Ì­±¸Ë¦³¤ô.
2) ¬°¤°»ò½¦±í¦b³Ì°ªÂI(A)®É,¸Ì­±ªº¤ô¤£·|­Ë¬y¤U¨Ó?
µª: 

3) ³o¶ê©P¹B°Êªº¥b®|¬°1.0¦Ì,¥¦ªº³t²v v ³Ì¤p¬°¦ó­È? (³] g = 9.8 m/s2)
´£¥Ü: ¦b³Ì°ªÂI(A)®É, m v2/r = mg. ½Ð¥Î­pºâ¾÷
µª: 


 
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¤@¨®½ø¥¿ªuµÛ¤@¤ô¥­¥b®|¬° r ªº¶É±×¶ê§Î­y¹D¤W¹B¦æ¡C¦b¨®½ü¤W¥H¤ô¥­­±²Õ¦¨ªº¤Ï§@¥Î¤O±N·|´£¨Ñ«ü¦V­y¹D¤¤¤ß©Ò»Ýªº¦V¤ß¤O¡C


¬¡°Ê:
¸Õ¥Î¤£¦Pªº¨®³t¤Î¸ô­±ªº©·«×¥b®|¨Ó¬Ý¬Ý³Ì¨Îªº¸ô­±±×²v.
¨®³t = ¨C¤p®É  ¤½¨½, 
¸ô­±ªº©·«×¥b®| =  ¦Ì. 
³Ì¨Îªº¸ô­±±×²vªº¨¤«× «× 
­pºâ¾÷
¤ÀªR:
(1) ©Ò»Ýªº¦V¤ß¤O¥ÑR1 ¤Î R2 ªº¤ô¥­¤À¶q´£¨Ñ:
   (R1 + R2) sinq = mv2/r
(2)  ¨®½øªº­«¶q:
   mg = (R1 + R2) cos
¥H¤W¨â¦¡¬Û°£ (1)/(2) ±o tan q =  v2/(rg), ³o¬O¨S¦³·Æ軚ªº ±ø¥ó.
 






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