Question

20£®ÈçͼËùʾ£¬Íæ¾ßС³µÖÃÓڹ⻬ˮƽµØÃæÉÏ£¬³µÉϹ̶¨×ÅÒ»¸ö°ë¾¶ÎªRµÄÄڱڹ⻬µÄÓ²ÖÊСԲͰ£¬Í°ÄÚÓÐÒ»ÖÊÁ¿Îªm£¬¿ÉÊÓΪÖʵãµÄ¹â»¬Ð¡Ç¦Çò¾²Ö¹ÔÚԲͰµÄ×îµÍµã£®ÏÖÈÃС³µºÍǦÇò¾ùÒÔËÙ¶ÈvÏòÓÒ×öÔÈËÙÔ˶¯£¬µ±Ð¡³µÓöµ½¹Ì¶¨ÔÚµØÃæµÄÕÏ°­Îïºó£¬ÓëÖ®Åöײ£¬ÅöºóС³µËÙ¶ÈΪÁ㣬¹ØÓÚÅöºóµÄÔ˶¯£¨Ð¡³µÊ¼ÖÕûÓÐÀ뿪µØÃ棩£¬ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® ÈôǦÇòÉÏÉýµÄ×î´ó¸ß¶È´óÓÚR£¬ÔòǦÇòÔÚ¾­¹ý×î¸ßµãʱÆäÖØÁ¦ÊÆÄܵÄÔö¼ÓÁ¿Ð¡ÓÚСÇò³õʼ¶¯ÄÜ
• B£® ÈôǦÇòÄܵ½´ïԲͰ×î¸ßµã£¬ÔòǦÇòÔÚ×î¸ßµãµÄËٶȴóСΪ$\sqrt{gR}$
• C£® ÈôǦÇòÉÏÉýµÄ×î´ó¸ß¶ÈСÓÚR£¬ÔòǦÇòÉÏÉýµÄ×î´ó¸ß¶ÈµÈÓÚ$\frac{{v}^{2}}{g}$
• D£® ÈôǦÇòÄܵ½´ïÓëÔ²ÐĵȸߵÄAµã£¬ÔòÔÚAµãʱ¶ÔԲͲµÄѹÁ¦Îª$\frac{m{v}^{2}}{R}$-2mg

Answer 1

·ÖÎö ¸ù¾Ý¶¯Äܶ¨ÀíÇó³öµ½´ïAµãµÄËٶȣ¬Í¨¹ýÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö¶ÔԲͲµÄѹÁ¦£®Ð¡Çòͨ¹ý×î¸ßµãµÄÁÙ½çËÙ¶ÈΪ$\sqrt{gR}$£¬ÈôÉÏÉýµÄ×î´ó¸ß¶ÈСÓÚR£¬ÔòÄ©ËٶȿÉÒÔΪÁ㣬¸ù¾Ý¶¯Äܶ¨ÀíÇó³öÉÏÉýµÄ×î´ó¸ß¶È£®

½â´ð ½â£ºA¡¢Ç¦ÇòÉÏÉýµÄ¹ý³ÌÖУ¬Ö»ÓÐÖØÁ¦×ö¹¦£¬»úеÄÜÊغ㣬¼´ÖØÁ¦ÊÆÄܵÄÔö¼ÓÁ¿Ó붯ÄܵļõСÁ¿ÏàµÈ£¬ÓÉÓÚ×î¸ßµãµÄ¶¯Äܲ»ÎªÁ㣬ËùÒÔÖØÁ¦ÊÆÄܵÄÔö¼ÓÁ¿Ð¡ÓÚСÇòµÄ³õ¶¯ÄÜ£¬¹ÊAÕýÈ·£®
B¡¢Ç¦Çòͨ¹ý×î¸ßµãµÄ×îСËÙ¶ÈΪ$\sqrt{gR}$£¬µ«ÊÇ¿ÉÄܱÈ$\sqrt{gR}$´ó£¬¹ÊB´íÎó£®
C¡¢ÈôǦÇòÉÏÉýµÄ×î´ó¸ß¶ÈСÓÚR£¬¸ù¾Ý$-mgh=0-\frac{1}{2}m{v}^{2}$µÃ£¬h=$\frac{{v}^{2}}{2g}$£®¹ÊC´íÎó£®
D¡¢ÈôǦÇòÄܵ½´ïÓëÔ²ÐĵȸߵÄAµã£¬¸ù¾Ý¶¯Äܶ¨ÀíµÃ£¬-mgR=$\frac{1}{2}m{v¡ä}^{2}-\frac{1}{2}m{v}^{2}$£¬½âµÃv¡ä²=v²-2gR£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵã¬N=$m\frac{v{¡ä}^{2}}{R}=m\frac{{v}^{2}}{R}-2mg$£¬¹ÊDÕýÈ·£®
¹ÊÑ¡£ºAD

µãÆÀ ±¾Ìâ×ۺϿ¼²éÁ˶¯Äܶ¨ÀíºÍÅ£¶ÙµÚ¶þ¶¨ÂɵÄÔËÓã¬ÖªµÀǦÇòÔÚAµãÏòÐÄÁ¦µÄÀ´Ô´£¬ÒÔ¼°ÔÚ×î¸ßµãµÄÁÙ½çÇé¿ö£¬½áºÏÅ£¶ÙµÚ¶þ¶¨ÂɽøÐÐÇó½â£®