Question

12£®ÈçͼËùʾ£¬Ò»×ã¹»¸ßµÄÔ²ÖùÐξøÈÈÆø¸×ÊúÖ±·ÅÖã¬Í¨¹ý¾øÈÈ»îÈû·â±Õ×ÅÒ»¶¨ÖÊÁ¿µÄÀíÏëÆøÌ壮»îÈûµÄÖÊÁ¿Îªm£¬ºá½ØÃæ»ýΪS£¬ÓëÈÝÆ÷µ×²¿Ïà¾àh£¬ÆøÌåµÄζÈΪT₁£®ÏÖÔÚ»îÈûÉÏ·ÅÖÃÒ»¸öÖÊÁ¿Îª2mµÄÎï¿é£¨Í¼ÖÐδ»­³ö£©£¬»îÈûϽµÁËO.2h´ïµ½Îȶ¨£¬ÆøÌåζÈΪT₂£¬ÔÙͨ¹ýÆø¸×ÄڵĵçÈÈË¿»ºÂý¼ÓÈÈÆøÌ壬µ±ÆøÌåÎüÊÕÈÈÁ¿Qʱ»îÈû»ºÂýÏòÉÏÒƶ¯1.2h´ïµ½Îȶ¨£¬´ËʱÆøÌåµÄζÈΪT₃ÒÑÖª´óÆøѹǿΪP₀£®ÖØÁ¦¼ÓËÙ¶ÈΪg£¬²»¼Æ»îÈûÓëÆø¸×¼äĦ²ÁºÍÀíÏëÆøÌåµÄÖØÁ¦ÊÆÄÜ£®Çó£º
£¨i£©Î¶ÈÖµTÓëT₁µÄ±ÈÖµ£»
£¨ii£©¼ÓÈȹý³ÌÖÐÆøÌåµÄÄÚÄÜÔö¼ÓÁ¿£®

Answer 1

·ÖÎö £¨1£©ÓÉÓÚÊǾøÈÈÆø¸×Óë¾øÈȵĻîÈû£¬ÆøÌåÔڴ˹ý³ÌÖÐζȡ¢Ñ¹Ç¿¡¢Ìå»ý¶¼·¢Éú±ä»¯£¬ÓÉÀíÏëÆøÌåµÄ״̬·½³Ì¼´¿ÉÇó³öÆøÌåµÄζÈÖ®¼äµÄ¹Øϵ£»
£¨2£©ÏȼÆËã¼ÓÈȹý³ÌÖÐÆøÌå¶ÔÍâ×öµÄ¹¦£¬ÔÙÓÉÈÈÁ¦Ñ§µÚÒ»¶¨ÂÉÇó³öÆøÌåµÄÄÚÄÜÔö¼ÓÁ¿£®

½â´ð ½â£º£¨1£©É迪ʼʱÆøÌåµÄѹǿΪP₁£¬¶Ô»îÈûÓÉƽºâÌõ¼þµÃ£º
P₁S=mg+P₀S
Ôò£º${P}_{1}={P}_{0}+\frac{mg}{S}$¡­¢Ù
ÔÚ»îÈûÉÏ·ÅÖÃ2mµÄÎï¿éÎȶ¨ºó£¬ÉèÆøÌåµÄѹǿΪP₂£¬Ôò£º
P₂S=£¨m+2m£©g+P₀
ËùÒÔ£º${P}_{2}={P}_{0}+\frac{3mg}{S}$¡­¢Ú
ÓÉÀíÏëÆøÌåµÄ״̬·½³Ì£º$\frac{{P}_{1}hS}{{T}_{1}}=\frac{{P}_{2}£¨h-0.2h£©}{{T}_{2}}$
ÁªÁ¢µÃ£º$\frac{{T}_{1}}{{T}_{2}}=\frac{4£¨3mg+{P}_{0}S£©}{5£¨mg+{P}_{0}S£©}$
£¨2£©¼ÓÈȹý³ÌÖÐÆøÌå¶ÔÍâ×ö¹¦Îª£º
W=£¨p₀S+3mg£©¡÷h=£¨p₀S+3mg£©•1.2h
ÓÉÈÈÁ¦Ñ§µÚÒ»¶¨ÂÉÖªÄÚÄܵÄÔö¼ÓÁ¿Îª£º
¡÷U=Q-W=Q-1.2h£¨p₀S+3mg£©
´ð£º£¨i£©Î¶ÈÖµTÓëT₁µÄ±ÈÖµÊÇ$\frac{4£¨3mg+{P}_{0}S£©}{5£¨mg+{P}_{0}S£©}$£»
£¨ii£©¼ÓÈȹý³ÌÖÐÆøÌåµÄÄÚÄÜÔö¼ÓÁ¿ÊÇQ-1.2h£¨p₀S+3mg£©£®

µãÆÀ ±¾Ì⿼²éÀíÏëÆøÌåµÄ״̬·½³ÌºÍÈÈÁ¦Ñ§µÚÒ»¶¨ÂÉ£¬½âÌâ¹Ø¼üÊÇ·ÖÇåÀíÏëÆøÌåÊÇ·¢ÉúµÈÈÝ¡¢µÈѹ»¹ÊǵÈα仯£¬ÔÙºÏÀíÑ¡Ôñ¹«Ê½Çó½â£®