Question

5£®¸ßѹ¹øÊÇÉú»îÖÐÒ»ÖÖÃܱյļÓÈÈÈÝÆ÷£®¹ø¸ÇÖÐÑëÓÐÒ»³öÆø¿×£¬¿×ÉϸÇÓÐÏÞѹ·§£¬µ±¹øÄÚÆøѹ´ïµ½ÏÞ¶¨ÖµÊ±£¬ÏÞѹ·§±»¹øÄÚ¶¥Æð·Å³ö²¿·ÖÆøÌ壬ʵÏÖÁ˶ԹøÄÚÆøÌåѹǿµÄ¿ØÖÆ£®ÈçͼËùʾ£¬Ä³¸ßѹ¹ø¹øÌåµÄÄÚµ×Ãæ»ýΪS£¬²à±ÚÊúÖ±£¬³öÆø¿×ºá½ØÃæ»ýΪS₀£¬ÏÞѹ·§ÖÊ×îΪm₀£¬¸ßѹ¹ø¶¥²¿Ãæ»ýΪS_t£¬¸ßѹ¹ø¹ø¸ÇÖÊÁ¿Îªm₁£¨ÒÑÖª´óÆøѹǿΪp₀£©
£¨1£©ÒºÌå·ÐµãÓëÆøѹµÄ¹Øϵ£®
£¨2£©ÇóʹÓøßѹ¹øʱ¹øÄÚÆøÌåµÄ×î´óѹǿ£¿
£¨3£©Çó¹øÌåÓë¹ø¸ÇÒ§ºÏ´¦¹øÌå¶Ô¹ø¸ÇµÄ×î´ó×÷ÓÃÁ¦£¿
£¨4£©Îª±£Ö¤Ê¹Óð²È«£¬²»¿ÉËæÒâÔö¼ÓÏÞѹ·§ÖÊÁ¿£®Èç¹ûÏÞѹ·§µÄÖÊÁ¿Ôö¼ÓÁËm£¬Çë¼ÆËã¹øÌåÓë¹ø¸ÇÒ§ºÏ´¦¹øÌå¶Ô¹ø¸ÇµÄ×î´ó×÷ÓÃÁ¦Ôö´ó¶àÉÙ£¿

Answer 1

·ÖÎö £¨1£©ÒºÌåµÄ·ÐµãËæÆøѹµÄÔö´ó¶øÉý¸ß£¬ËæÆøѹµÄ½µµÍ¶ø½µµÍ£»
£¨2£©¸ù¾ÝÏÞѹ·§µÄÖÊÁ¿Çó³öÆäÖØÁ¦£¬¸ÃÖØÁ¦µÈÓÚѹÁ¦£¬ÀûÓÃÏÞѹ·§µÄ³öÆø¿×µÄºá½ØÃæ»ýÒÔ¼°ÏÞѹ·§µÄÊÜÁ¦Æ½ºâ¼´¿ÉÇó³ö´ËʱµÄѹǿ£»
£¨3£©½áºÏ×÷ÓÃÃæ»ýµÄ´óС£¬¼´¿ÉÇó³ö×î´ó×÷ÓÃÁ¦£»
£¨4£©ÏÞѹ·§µÄÖÊÁ¿Ôö¼Ó£¬Ôò¸ù¾ÝÏÞѹ·§µÄÊÜÁ¦Æ½ºâºÍ³öÆø¿×µÄºá½ØÃæ»ý¼´¿ÉÇó³ö¹øÌåÓë¹ø¸ÇÒ§ºÏ´¦¹øÌå¶Ô¹ø¸ÇµÄ×î´ó×÷ÓÃÁ¦Ôö´óÖµ£®

½â´ð ½â£º£¨1£©ÒºÌåµÄ·ÐµãÓë´óÆøѹµÄ¹ØϵΪ£ºÒºÌåµÄ·ÐµãËæÒºÌå±íÃæÆøѹµÄÔö´ó¶øÉý¸ß£¬ËæÆøѹµÄ¼õС¶ø½µµÍ£»
£¨2£©ÒÑÖª´óÆøѹǿΪp₀£¬³öÆø¿×ºá½ØÃæ»ýΪS₀£¬ÏÞѹ·§ÖÊ×îΪm₀£¬µ±ÏÞѹ·§¸ÕÒª±»¶¥Æðʱ£¬ÏÞѹ·§ÊÜÁ¦Æ½ºâ£¬¹øÄÚÆøÌåµÄ×î´óѹǿ£º
$P={P}_{0}+\frac{{m}_{0}g}{{S}_{0}}$    ¢Ù
£¨3£©ÉèÒ§ºÏ´¦¹øÌå¶Ô¹ø¸ÇµÄ×î´ó×÷ÓÃÁ¦ÎªF£¬Ôò£º
$F=PS=£¨{P}_{0}+\frac{{m}_{0}g}{{S}_{0}}£©•S$   ¢Ú
£¨4£©Èç¹ûÏÞѹ·§µÄÖÊÁ¿Ôö¼ÓÁËm£¬ÔòѹǿµÄÔö¼ÓÁ¿£º$¡÷P=\frac{mg}{{S}_{0}}$
Óɹ«Ê½F=PS¿ÉÖª£¬Ñ¹Á¦µÄ±ä»¯¾ÍµÈÓÚѹǿµÄ±ä»¯ÓëÊÜÁ¦Ãæ»ýµÄ³Ë»ý£¬Êµ¼Ê¹ø¸ÇµÄÊÜÁ¦Ãæ»ýΪ£ºS-S0
ËùÒÔ¹øÄÚµÄÆøÌå¶Ô¹ø¸ÇµÄ×÷ÓÃÁ¦µÄÔö¼ÓÁ¿£º
¡÷F=¡÷P£¨S-S₀£©=$\frac{mg}{{S}_{0}}•£¨S-{S}_{0}£©=mg£¨\frac{S}{{S}_{0}}-1£©$
´ð£º£¨1£©ÒºÌå·ÐµãÓëÆøѹµÄ¹ØϵÊÇÒºÌåµÄ·ÐµãËæÒºÌå±íÃæÆøѹµÄÔö´ó¶øÉý¸ß£¬ËæÆøѹµÄ¼õС¶ø½µµÍ£®
£¨2£©Ê¹Óøßѹ¹øʱ¹øÄÚÆøÌåµÄ×î´óѹǿÊÇ${P}_{0}+\frac{{m}_{0}g}{{S}_{0}}$£»
£¨3£©¹øÌåÓë¹ø¸ÇÒ§ºÏ´¦¹øÌå¶Ô¹ø¸ÇµÄ×î´ó×÷ÓÃÁ¦ÊÇ$£¨{P}_{0}+\frac{{m}_{0}g}{{S}_{0}}£©•S$£»
£¨4£©¹øÌåÓë¹ø¸ÇÒ§ºÏ´¦¹øÌå¶Ô¹ø¸ÇµÄ×î´ó×÷ÓÃÁ¦Ôö´ó$mg£¨\frac{S}{{S}_{0}}-1£©$£®

µãÆÀ ´ËÌâÉæ¼°µ½´óÆøѹµÄ×ÛºÏÓ¦Óá¢Ñ¹Ç¿µÄ¼ÆËãµÈÏà¹ØµÄ֪ʶµãµÄÄÚÈÝ£¬ÊÇÒ»µÀÊýѧÓëÎïÀíµÄ×ÛºÏÐÔµÄÌâÄ¿£¬ÒªÇóѧÉú¾ß±¸Ò»¶¨µÄѧ¿Æ×ÛºÏÄÜÁ¦£¬»áÓÃ×Öĸ±í´ïʽÀ´±í´ïÎïÀíÁ¿£®