Question

7£®±Ä´²ÀàËÆÓÚÊúÖ±·ÅÖõÄÇᵯ»É£¨¹²µ¯Á¦Âú×ãF=kx£¬µ¯ÐÔÊÆÄÜÂú×ãE_P=$\frac{1}{2}$kx²£¬xΪ´²ÃæϳÁµÄ¾àÀ룬kΪ³£Á¿£©£®ÖÊÁ¿ÎªmµÄÔ˶¯Ô±¾²Ö¹Õ¾ÔڱĴ²ÉÏʱ£¬´²ÃæϳÁ£»±Ä´²±ÈÈüÖУ¬Ô˶¯Ô±¾­¹ý¶à´Î±ÄÌø£¬Öð½¥Ôö¼ÓÉÏÉý¸ß¶È£¬²âµÃij´ÎÔ˶¯Ô±À뿪´²ÃæÔÚ¿ÕÖеÄ×ʱ¼äΪ¡÷t£®Ô˶¯Ô±¿ÉÊÓΪÖʵ㣬¿ÕÆø×èÁ¦ºöÂÔ²»¼Æ£¬ÖØÁ¦¼ÓËÙ¶ÈΪg£®Ôò¿ÉÇ󣨡¡¡¡£©

• A£® ³£Á¿k=$\frac{mg}{{x}_{0}}$
• B£® Ô˶¯Ô±ÉÏÉýµÄ×î´ó¸ß¶Èh=$\frac{1}{2}$g£¨¡÷t£©²
• C£® ´²ÃæѹËõµÄ×î´óÉî¶Èx=x₀+$\sqrt{\frac{1}{4}{x}_{0}g£¨¡÷t£©^{2}+{{x}_{0}}^{2}}$
• D£® Õû¸ö±ÈÈü¹ý³ÌÖÐÔ˶¯Ô±Ôö¼ÓµÄ»úеÄÜ¡÷E=$\frac{1}{8}$mg²£¨¡÷t£©²

Answer 1

·ÖÎö Óɺú¿Ë¶¨ÂÉ¿ÉÇóµÃ³£Á¿k£»
¸ù¾ÝÔȱäËÙÖ±ÏßÔ˶¯µÄ¹æÂÉ¿ÉÇóµÃÉÏÉýµÄ¸ß¶È£¬Ôò¿ÉÅжÏÊÇ·ñ·ûºÏÒªÇó£»
¸ù¾Ý¹¦ÄܹØϵ¿ÉÇóµÃ´²ÃæѹËõµÄ×î´óÉî¶ÈºÍÕû¸ö±ÈÈü¹ý³ÌÖÐÔ˶¯Ô±Ôö¼ÓµÄ»úеÄÜ£®

½â´ð ½â£ºA¡¢¸ù¾ÝÔ˶¯Ô±¾²Ö¹Õ¾ÔڱĴ²ÉÏʱ£¬´²ÃæϳÁx₀£»Ôò£ºmg=kx₀
½âµÃk=$\frac{mg}{{x}_{0}}$£»¹ÊAÕýÈ·£»                                      
B¡¢¸ù¾ÝÔȱäËÙÖ±ÏßÔ˶¯¹«Ê½£¬ÉÏÉýÏÂÂäʱ¼äÏàµÈ£¬¼´ÉÏÉýʱ¼äΪ$\frac{¡÷t}{2}$£¬ÉÏÉýµÄ×î´ó¸ß¶È£ºh=$\frac{1}{2}•g£¨\frac{¡÷t}{2}£©^{2}=\frac{g¡÷{t}^{2}}{8}$£®¹ÊB´íÎó£»
C¡¢Ô˶¯Ô±´Ó×î¸ßµãµ½×îµÍµãµÄ¹ý³ÌÖÐÖØÁ¦ÊÆÄÜת»¯Îª±Ä´²µÄµ¯ÐÔÊÆÄÜ£¬¼´£º$\frac{1}{2}k{x}^{2}=mg£¨x+\frac{g¡÷{t}^{2}}{8}£©$
ËùÒÔ£ºx=${x}_{0}+\sqrt{\frac{1}{4}{x}_{0}g£¨¡÷t£©^{2}+{x}_{0}^{2}}$£®¹ÊCÕýÈ·£»
D¡¢Õû¸ö±ÈÈü¹ý³ÌÖÐÔ˶¯Ô±Ôö¼ÓµÄ»úеÄܵÈÓÚÔ˶¯Ô±´Óx₀´¦µ½×î¸ßµãµÄÖØÁ¦ÊÆÄÜÓë¼õСµÄµ¯ÐÔÊÆÄܵIJ¼´£º¡÷E=mg£¨x₀+h£©-$\frac{1}{2}k{x}_{0}^{2}$=mgx₀+$\frac{1}{8}$mg²£¨¡÷t£©²-$\frac{1}{2}$•$\frac{mg}{{x}_{0}}$•${x}_{0}^{2}$=$\frac{1}{2}$mgx₀+$\frac{1}{8}$mg²£¨¡÷t£©²£®¹ÊD´íÎó£®
¹ÊÑ¡£ºAC

µãÆÀ ±¾Ì⿼²éÎïÀí¹æÂÉÔÚÉú»îÖеÄÓ¦Óã¬Òª×¢ÒâÕýÈ··ÖÎöÎïÀí¹ý³Ì¼°×öºÃÊÜÁ¦·ÖÎö£¬È»ºó²ÅÄܸù¾ÝÌâÒâÑ¡ÔñºÏÊʵÄÎïÀí¹æÂÉ£®