Question

20£®ÀûÓÃÆøµæµ¼¹ìÑéÖ¤»úеÄÜÊغ㶨ÂÉ£®ÊµÑé×°ÖÃʾÒâͼÈçͼËùʾ£¬ÊµÑé²½Ö裺

A£®½«Æøµæµ¼¹ì·ÅÔÚˮƽ×ÀÃæÉÏ£¬×ÀÃæ¸ß¶È²»µÍÓÚ1m£¬½«µ¼¹ìµ÷ÖÁˮƽ£®
B£®ÓÃÓα꿨³ß²âÁ¿µ²¹âÌõµÄ¿í¶Èd
C£®Óɵ¼¹ì±ê³ß¶Á³öÁ½¹âµçÃÅÖÐÐÄÖ®¼äµÄ¾àÀës£»
D£®½«»¬¿éÒÆÖÁ¹âµçÃÅ1×ó²àij´¦£¬´ýíÀÂë¾²Ö¹²»¶¯Ê±£¬ÊÍ·Å»¬¿é£¬ÒªÇóíÀÂëÂäµØÇ°µ²¹âÌõÒÑͨ¹ý¹âµçÃÅ2£»
E£®´ÓÊý×Ö¼ÆʱÆ÷£¨Í¼ÖÐδ»­³ö£©ÉÏ·Ö±ð¶Á³öµ²¹âÌõͨ¹ý¹âµçÃÅ1ºÍ¹âµçÃÅ2ËùÓõÄʱ¼ä¡÷t₁ºÍ¡÷t₂£»
F£®ÓÃÌìƽ³Æ³ö»¬¿éºÍµ²¹âÌõµÄ×ÜÖÊÁ¿M£¬ÔٳƳöÍÐÅ̺ÍíÀÂëµÄ×ÜÖÊÁ¿m£®
Óñíʾֱ½Ó²âÁ¿Á¿µÄ×Öĸд³öÏÂÁÐËùʾÎïÀíÁ¿µÄ±í´ïʽ£º
£¨1£©»¬¿éͨ¹ý¹âµçÃÅ1ºÍ¹âµçÃÅ2ʱ˲ʱËٶȷֱðΪv₁=$\frac{d}{{¡÷t}_{1}}$ºÍv₂=$\frac{d}{{¡÷t}_{2}}$£®
£¨2£©ÔÚ»¬¿é´Ó¹âµçÃÅ1Ô˶¯µ½¹âµçÃÅ2µÄ¹ý³ÌÖУ¬ÏµÍ³ÊÆÄܵļõÉÙ¡÷E_p=mgs£¨ÖØÁ¦¼ÓËÙ¶ÈΪg£©£®ÏµÍ³£¨°üÀ¨»¬¿é¡¢µ²¹âÌõ¡¢ÍÐÅ̺ÍíÀÂ룩¶¯ÄܵÄÔö¼ÓÁ¿¡÷E_k=$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{2}}$£©² -$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{1}}$£©²
£¨3£©Èç¹û¡÷E_P=¡÷E_K£¬Ôò¿ÉÈÏΪÑéÖ¤ÁË»úеÄÜÊغ㶨ÂÉ£®

Answer 1

·ÖÎö ¹âµçÃŲâÁ¿Ë²Ê±ËÙ¶ÈÊÇʵÑéÖг£Óõķ½·¨£®ÓÉÓÚ¹âµçÃŵĿí¶ÈlºÜС£¬ËùÒÔÎÒÃÇÓúܶÌʱ¼äÄÚµÄƽ¾ùËٶȴúÌæ˲ʱËٶȣ®
Ö½´ø·¨ÊµÑéÖУ¬ÈôÖ½´øÔȱäËÙÖ±ÏßÔ˶¯£¬²âµÃÖ½´øÉϵĵã¼ä¾à£¬ÀûÓÃÔȱäËÙÖ±ÏßÔ˶¯µÄÍÆÂÛ£¬¿É¼ÆËã³ö´ò³öijµãʱֽ´øÔ˶¯µÄ˲ʱËٶȺͼÓËٶȣ¬´Ó¶øÇó³ö¶¯ÄÜ£®¸ù¾Ý¹¦ÄܹØϵµÃÖØÁ¦ÊÆÄܼõСÁ¿µÈÓÚÖØÁ¦×ö¹¦µÄÊýÖµ£®

½â´ð ½â£º£¨1£©ÓÉÓÚµ²¹âÌõ¿í¶ÈºÜС£¬Òò´Ë½«µ²¹âÌõͨ¹ý¹âµçÃÅʱµÄƽ¾ùËٶȵ±×÷˲ʱËٶȣ®
v₁=$\frac{d}{{¡÷t}_{1}}$£¬
v₂=$\frac{d}{{¡÷t}_{2}}$
£¨2£©¸ù¾Ý¶¯ÄܵĶ¨ÒåʽµÃ£º
ͨ¹ý¹âµçÃÅ1£¬ÏµÍ³£¨°üÀ¨»¬¿é¡¢µ²¹âÌõ¡¢ÍÐÅ̺ÍíÀÂ룩µÄ×ܶ¯ÄÜΪE _k1=$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{1}}$£©²£»
ͨ¹ý¹âµçÃÅ2£¬ÏµÍ³£¨°üÀ¨»¬¿é¡¢µ²¹âÌõ¡¢ÍÐÅ̺ÍíÀÂ룩µÄ×ܶ¯ÄÜΪE _k2=$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{2}}$£©²£»
ϵͳÊÆÄܵļõÉÙ¡÷E_P=mgh=mgs£¬
¶¯ÄܵÄÔö¼ÓÁ¿¡÷E_k=$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{2}}$£©² -$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{1}}$£©²
¹Ê´ð°¸Îª£º£¨1£©$\frac{d}{{¡÷t}_{1}}$£¬$\frac{d}{{¡÷t}_{2}}$
£¨2£©mgs£»$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{2}}$£©² -$\frac{1}{2}$£¨M+m£©£¨$\frac{d}{{¡÷t}_{1}}$£©²

µãÆÀ ¹âµçÃŲâÁ¿Ë²Ê±ËÙ¶ÈÊÇʵÑéÖг£Óõķ½·¨£®ÓÉÓÚ¹âµçÃŵĿí¶ÈdºÜС£¬ËùÒÔÎÒÃÇÓúܶÌʱ¼äÄÚµÄƽ¾ùËٶȴúÌæ˲ʱËٶȣ®