Question

9£®Èçͼ£¬Õæ¿ÕÖдæÔÚÊúÖ±ÏòÉϵÄÔÈÇ¿µç³¡ºÍˮƽ·½ÏòµÄÔÈÇ¿´Å³¡£¬ÖÊÁ¿Îªm¡¢µçºÉÁ¿ÎªqµÄÎïÌåÒÔËÙÂÊvÔÚ³¡ÄÚ×ö°ë¾¶ÎªRµÄÔÈËÙÔ²ÖÜÔ˶¯£¬Éèt=0ʱÎïÌåÔÚ¹ìµÀ×îµÍµãÇÒÖØÁ¦ÊÆÄܺ͵çÊÆÄܾùΪÁ㣬ÔòÏÂÁÐÅжÏÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® ÎïÌåÒ»¶¨´øÕýµçÇÒÄæʱÕëÔ˶¯
• B£® ÎïÌåÔ˶¯¹ý³ÌÖУ¬»úеÄÜÊغãÇÒºãΪ$\frac{1}{2}$mv²
• C£® ÎïÌåÔ˶¯¹ý³ÌÖУ¬ÖØÁ¦ÊÆÄÜËæʱ¼ä±ä»¯¹ØϵΪmgR£¨1-cos$\frac{v}{R}$t£©
• D£® ÎïÌåÔ˶¯¹ý³ÌÖУ¬µçÊÆÄÜËæʱ¼ä±ä»¯¹ØϵΪmgR£¨cos$\frac{v}{R}$t-1£©

Answer 1

·ÖÎö ÎïÌå×öÔÈËÙÔ²ÖÜÔ˶¯£¬ÊÜÖØÁ¦¡¢µç³¡Á¦ºÍÂåÂ××ÈÁ¦£¬ÆäÖÐÖØÁ¦ºÍµç³¡Á¦Æ½ºâ£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£®½áºÏÔ²µÄ¹«Ê½ÕýÈ·±í´ïСÇòµÄ¸ß¶ÈµÄ±í´ïʽ£®

½â´ð ½â£ºA¡¢ÖØÁ¦Óëµç³¡Á¦Æ½ºâ£¬¹Êµç³¡Á¦ÏòÉÏ£¬ÓÉÓڵ糡·½ÏòÏòÉÏ£¬¹ÊµçºÉ´øÕýµç£»ÓÉÓڴų¡·½Ïò´¹Ö±Ö½ÃæÏòÀ¹Êת¶¯·½ÏòÒ»¶¨ÊÇÄæʱÕë·½Ïò£¬¹ÊAÕýÈ·£»
B¡¢ÂåÂ××ÈÁ¦²»×ö¹¦£¬Ö»ÓÐÖØÁ¦ºÍµç³¡Á¦×ö¹¦£¬¹ÊÖ»ÓлúеÄܺ͵çÊÆÄÜÏ໥ת»¯£¬×ÜÁ¿Êغ㣬ÔÚ×îµÍµãʱ£¬ÓÐE=$\frac{1}{2}$mv²£¬¶øËæ¸ß¶ÈµÄÔö´ó£¬»úеÄÜÔö´ó£®¹ÊB´íÎó£»
C¡¢ÖØÁ¦ÊÆÄܵıí´ïʽΪ£º${E}_{P}=mgh=mg£¨R-Rcos¦È£©=mgR£¨1-cos¦Øt£©=mgR£¨1-cos\frac{vt}{R}£©$£¬¹ÊCÕýÈ·£»
D¡¢µçÊÆÄܺÍÖØÁ¦ÊÆÄÜ×ÜÁ¿Êغ㣬¹ÊµçÊÆÄÜΪ£ºE_p¡ä=-E_p=mgR£¨cos$\frac{v}{R}$t-1£©£¬¹ÊDÕýÈ·£»
¹ÊÑ¡£ºACD£®

µãÆÀ ¸ÃÌ⿼²é´øµçÁ£×ÓÔÚ¸´ºÏ³¡ÖеÄÔ˶¯£¬½âÌâµÄ¹Ø¼üÊÇÃ÷È·ÖØÁ¦ºÍµç³¡Á¦Æ½ºâ£¬ÂåÂ××ÈÁ¦ÌṩÏòÐÄÁ¦£¬È»ºóÁÐʽ·ÖÎöÇó½â£®