½×¨ì BB ¼uªºªk©w¼Ð·Ç¡A¼u¤Y±¿n°Ê¯à 20J/cm^2¡A¦³»~®t¤£±o¤j©ó 24J/cm^2¡C¨£©ó¥qªk°|¯µ®Ñªø¤K¤Q¤@¦~¤»¤ë¤Q¤@¤é²Ä06985¸¹¨ç¥Ü¡C
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1. °Ê¯à¤½¦¡¬° m * V^2 / 2, ¨ä¤¤ m ¬°½è¶q, V ¬°³t«×¡C¨Ò¦p 0.2g ¶ì½¦ BB ¼u¡Aªì³t 150m/s¡A¦bºj¤fªº°Ê¯à´N¬O .0002 * 150^2 /2 = 2.25 J
2. ¶ê²yªÅ®ðªý¤O¬° £l * C * A * V^2 /2, ¨ä¤¤ £l ¬°ªÅ®ð±K«×(¬ù¬°1.205 kg/m^3)¡A C ¬°ªÅ®ðªý¤O«Y¼Æ(¥ú·Æ¶ê²y¦b¯¿¬y®É¬ùµ¥©ó0.5)¡A A ¬°¯S¼xºI±¿n (¶ì½¦ BB ¼u¬° 3.14/4*0.006^2 = 28.26e-6 m^2)¡C
3. ¼u¤Y±¿n°Ê¯à¬°°Ê¯à°£¥H¯S¼xºI±¿n¡C¦b¦¹ 2.25/(28.26e-6 * 1e4) = 7.962 J/cm^2
4. ¶¶¹D¤@´£¡A¦P¼Ëªº³t«×¡A4.5mm 0.34g ¿û¯]¼uªº±¿n°Ê¯à¬O 6mm 0.2g ¶ì½¦¼uªº
3.02¿¡I
(0.34/0.2) * (6/4.5)^2 = 3.02
4. ¤û¹y²Ä¤G¹B°Ê©w«ß¬° f = m * a, ¨ä¤¤ f ¬°¤O¶q¡A a ¬°¥[³t«×¡C
5. ·í BB ¼u®g¥X«á¡AªÅ®ðªý¤O³y¦¨t¦V¥[³t«×¡A®Ú¾Ú¤Wz°²³]¡AªÅ®ðªý¤O¶È¬°³t«×ªº¨ç¼Æ(·íµM¤£§¹¥þ¥¿½T°Õ)¡A¤]´N¬O
1.205 * 0.5 * 28.26e-6 /2 * V^2 = 8.513e-6 * V^2 (Newton)
©Ò¥Ht¦V¥[³t«×¬° a = f / m
-8.513e-6 * V^2 / 0.2e-3 = -0.0426 * V^2 (m/s^2)
6. ³t«×¤½¦¡ V = Vo + a*t, ¨ä¤¤ Vo ¬°ªì³t¡At ¬°®É¶¡
7. ±µ¤U¨Ó´N¥Î¦³®t¤Àªk(finite difference method)ªº·§©À¡A¥H¤@©T©wªº¤p¬q®É¶¡pºâ³t«×¡A¨Ò¦p1²@¬í (0.001s)¬°³æ¦ì¡A¨Ã§Q¥Î Excel¸Õºâªí¡C
¥Hªì³t150 m/s ¨Ó»¡¡Aªì©l°Ê¯à¶W¹L2µJ¦Õ¡A³o¬O°ªÀɳf³á¡I
®Ú¾Ú¥H¤W¤½¦¡¡A²Ä 0.001s ³t«×°¬°
V(0.001s) = 150 + (-0.0426 * 150^2) *0.001 = 149.04 m/s
¥H¥§¡³t«×pºâ®g¥X¶ZÂ÷ (150+149.04)/2 * 0.001 = 0.1495 m
²Ä 0.002s³t«×¤S°¬°
V(0.002s) = 149.04 + (-0.0426 * 149.04^2) *0.001 = 148.09 m/s
¶ZÂ÷¦A¼W¥[ (149.04+148.09)/2 *.001 = 0.1486 m
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²Ä 2.66s ®É¡A³t«×¶È 8.32m/s¡AÁ`¶ZÂ÷ 67.736m.
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9. ®Ú¾Ú»ZºÖ·¯Åªí¡A¥|¯Å©M·¤Þ°_¹Ð¨F¸´¡A¯È¤ù¸»R¡A¤p¾ð·F·n°Ê¡F¤pªiº¥°ª¡Aªi®p¥Õªjº¥¦h¡A¥i¹F 7.9m/s¡C ©Ò¥H¦b¤á¥~·³t»P°¸ªºpºâ³t«× 8.32 m/s ¤£¬Û¤W¤U¡C¥i¥H»{©w¦³®Ä®gµ{¤j·§´N¬O 67.73m¡I
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