Question

8£®ÈçͼËùʾ£¬¹âµç¼ÆʱÆ÷ÓɹâµçÃźͼÆʱÆ÷Á½²¿·Ö×é³É£¬´Ë×°ÖÃÄܾ«È·µØ¼Ç¼ÎïÌåͨ¹ý¹âµçÃÅËùÓõÄʱ¼ä£®ÏÖÒªÓôË×°ÖÃÀ´ÑéÖ¤»úеÄÜÊغ㶨ÂÉ£¬ÓÐһСÇò´ÓÁ½¹âµçÃŵÄÕýÉÏ·½¾²Ö¹ÊÍ·Å£®£¨ÒÑÖªÖØÁ¦¼ÓËÙ¶ÈΪÈÝ£©
£¨1£©ÐèÒª²âÁ¿µÄÎïÀíÁ¿³ýСÇòͨ¹ýÁ½¹âµçÃÅ1¡¢2µÄʱ¼ä£¬¡÷t₁¡¢¡÷t₂Í⣬»¹Ðè²âÁ¿Ð¡ÇòÖ±¾¶D¡¢Á½¹âµçÃżäµÄÊúÖ±¸ß¶ÈH£¨Ëù²âÎïÀíÁ¿ÓÃ×Öĸ±íʾ²¢ÓÃÎÄ×Ö˵Ã÷£©£®
£¨2£©ÑéÖ¤»úеÄÜÊغ㶨ÂɵĹØϵʽΪ$\frac{{D}^{2}}{¡÷{{t}_{2}}^{2}}-\frac{{D}^{2}}{¡÷{{t}_{1}}^{2}}=2gH$£¨ÓÃÉÏÊöÒѲâÎïÀíÁ¿×Öĸ±íʾ£©£®

Answer 1

·ÖÎö ¸ù¾Ý¼«¶Ìʱ¼äÄÚµÄƽ¾ùËٶȵÈÓÚ˲ʱËٶȣ¬¸ù¾ÝϽµµÄ¸ß¶È£¬Çó³öÖØÁ¦ÊÆÄܵļõСÁ¿£¬¸ù¾Ýͨ¹ý¹âµçÃŵÄ˲ʱËٶȵóö¶¯ÄܵÄÔö¼ÓÁ¿£¬´Ó¶øÑéÖ¤»úеÄÜÊغ㶨ÂÉ£®

½â´ð ½â£ºÉèСÇòµÄÖ±¾¶ÎªD£¬Ð¡Çòͨ¹ý¹âµçÃÅ1ºÍ2µÄ˲ʱËٶȷֱðΪ${v}_{1}=\frac{D}{¡÷{t}_{1}}$¡¢${v}_{2}=\frac{D}{¡÷{t}_{2}}$£¬Ôò¶¯ÄܵÄÔö¼ÓÁ¿Îª£º$¡÷{E}_{k}=\frac{1}{2}m{{v}_{2}}^{2}-\frac{1}{2}m{{v}_{1}}^{2}$=$\frac{1}{2}m£¨\frac{{D}^{2}}{¡÷{{t}_{1}}^{2}}-\frac{{D}^{2}}{¡÷{{t}_{2}}^{2}}£©$£¬
ÖØÁ¦ÊÆÄܵļõСÁ¿Îª¡÷E_p=mgH£¬HΪÁ½¹âµçÃżäµÄÊúÖ±¸ß¶È£®
ÒªÑéÖ¤»úеÄÜÊغ㶨ÂÉ£¬¼´¡÷E_k=¡÷E_p£¬¼´£º$\frac{{D}^{2}}{¡÷{{t}_{2}}^{2}}-\frac{{D}^{2}}{¡÷{{t}_{1}}^{2}}=2gH$£®ËùÒÔÐèÒªµÄÎïÀíÁ¿ÎªÐ¡ÇòÖ±¾¶D¡¢Á½¹âµçÃżäµÄÊúÖ±¸ß¶ÈH£®
¹Ê´ð°¸Îª£º£¨1£©Ð¡ÇòÖ±¾¶D¡¢Á½¹âµçÃżäµÄÊúÖ±¸ß¶ÈH£¬£¨2£©$\frac{{D}^{2}}{¡÷{{t}_{2}}^{2}}-\frac{{D}^{2}}{¡÷{{t}_{1}}^{2}}=2gH$£®

µãÆÀ ½â¾ö±¾ÌâµÄ¹Ø¼üÖªµÀʵÑéµÄÔ­Àí£¬¼´ÑéÖ¤¶¯ÄܵÄÔö¼ÓÁ¿ÓëÖØÁ¦ÊÆÄܵļõСÁ¿ÊÇ·ñÏàµÈ£¬ÖªµÀ¼«¶Ìʱ¼äÄÚµÄƽ¾ùËٶȵÈÓÚ˲ʱËٶȣ®