Question

4£®ÖÊÁ¿Îªm=1kgµÄСÇòÖÃÓÚ¸ßh=0.8mµÄˮƽ×ÀÃæµÄÓÒ±ßÔµAµã£¬ÏÖ¸øÆäһˮƽÏòÓҵijõËٶȣ¬Ð¡ÇòÇ¡ºÃÎÞÅöײµØÑØÔ²»¡ÇÐÏß´ÓB µã½øÈëÊúÖ±¹â»¬Ô²¹Â¹ìµÀ£®B¡¢C ÎªÔ²»¡µÄÁ½¶Ëµã£¬ÆäÁ¬Ïßˮƽ£¬ÒÑÖªÔ²»¡°ë¾¶R=1.0m£¬Ô²»¡¶ÔÓ¦Ô²ÐĽǦÈ=106¡ã£¬¹ìµÀ×îµÍµãΪO£¬¹Ì¶¨Ð±Ãæ¸ÕºÃÓëÔ²»¡µÄCµãÏàÇУ®Ð¡ÇòÀ뿪Բ»¡¹ìµÀºóÑØбÃæ¼ÌÐøÏòÉÏÔ˶¯£¬ÆäÄܵ½´ïµÄ×î¸ßµãΪD µã£®Ð¡ÇòÓëбÃæ¼äµÄ¶¯Ä¦²ÁÒòËØΪ0.5£®£¨g=10m/s²£¬sin37¡ã=0.6£¬cos37¡ã=0.8£©ÊÔÇó£º

£¨1£©Ð¡Îï¿éÀ뿪AµãµÄˮƽ³õËÙ¶Èv_A£»
£¨2£©Ð¡Îï¿é¾­¹ýOµãʱ¶Ô¹ìµÀµÄѹÁ¦£»
£¨3£©Ð±ÃæÉÏCD¼äµÄ¾àÀ룮

Answer 1

·ÖÎö £¨1£©Ð¡Îï¿é´ÓAµ½BµÄ¹ý³Ì×öƽÅ×Ô˶¯£¬¸ù¾Ý¸ß¶ÈÇó³ö¾­¹ýBµãʱÊúÖ±·½ÏòÉϵķÖËٶȣ¬¸ù¾ÝƽÐÐËıßÐζ¨ÔòÇó³öÎïÌåÔ˶¯µ½AµãµÄËٶȣ®
£¨2£©ÓÉËٶȵĺϳÉÇó³öBµãµÄËٶȣ®Ð¡Îï¿é´ÓBµ½0£¬ÔËÓö¯Äܶ¨Àí¿ÉÒÔÇó³öСÎï¿é¾­¹ýOµãʱµÄËٶȣ®ÔÚOµã£¬ÓɺÏÁ¦ÌṩÏòÐÄÁ¦£¬ÓÉÅ£¶Ù¶¨ÂÉÇóѹÁ¦£®
£¨3£©Ð¡Îï¿éÑØбÃæÉÏ»¬Ê±×öÔȼõËÙÔ˶¯£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÇó³ö¼ÓËٶȵĴóС£¬ÔÙÓÉÔ˶¯Ñ§¹«Ê½ÇóCD¼äµÄ¾àÀ룮

½â´ð ½â£º£¨1£©¶ÔСÎï¿é£¬ÓÉAµ½B×öƽÅ×Ô˶¯£¬ÔòÓÐ
  ${v}_{y}^{2}$=2gh
µÃ¾­¹ýBµãʱÊúÖ±·½ÏòÉϵķÖËÙ¶È v_y=4m/s
ÔÚBµã£¬ÓÐ tan$\frac{¦È}{2}$=$\frac{{v}_{y}}{{v}_{A}}$    ËùÒÔ v_A=3m/s
£¨2£©¶ÔСÎï¿é£¬¾­¹ýBµãµÄËÙ¶È v_B=$\sqrt{{v}_{A}^{2}+{v}_{y}^{2}}$=5m/s
ÓÉBµ½O£¬Óɶ¯Äܶ¨ÀíÓÐ
   mgR£¨1-cos53¡ã£©=$\frac{1}{2}m{v}_{O}^{2}$-$\frac{1}{2}m{v}_{B}^{2}$
ÔÚOµã£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÓÐ N-mg=m$\frac{{v}_{O}^{2}}{R}$   
 ËùÒÔ  N=43N
ÓÉÅ£¶ÙµÚÈý¶¨ÂÉÖª¶Ô¹ìµÀµÄѹÁ¦Îª N¡ä=N=43N
£¨3£©Îï¿éÑØбÃæÉÏ»¬Ê±£¬ÓÉÅ£¶ÙµÚ¶þ¶¨ÂÉÓУº
   mgsin53¡ã+¦Ìmgcos53¡ã=ma
½âµÃ¼ÓËٶȴóС a=11 m/s²£»
ÓÉ»úеÄÜÊغãÖª v_C=v_B=5m/s
СÎï¿éÓÉCÉÏÉýµ½×î¸ßµãDµãµÄλÒÆΪ x=$\frac{{v}_{C}^{2}}{2a}$=$\frac{25}{22}$m
´ð£º
£¨1£©Ð¡Îï¿éÀ뿪AµãµÄˮƽ³õËÙ¶Èv_AÊÇ3m/s£®
£¨2£©Ð¡Îï¿é¾­¹ýOµãʱ¶Ô¹ìµÀµÄѹÁ¦ÊÇ43N£»
£¨3£©Ð±ÃæÉÏCD¼äµÄ¾àÀëΪ$\frac{25}{22}$m£®

µãÆÀ ¶ÔÓÚƽÅ×Ô˶¯£¬ÒªÖªµÀƽÅ×Ô˶¯ÔÚˮƽ·½ÏòÉÏ×öÔÈËÙÖ±ÏßÔ˶¯£¬ÔÚÊúÖ±·½ÏòÉÏ×ö×ÔÓÉÂäÌåÔ˶¯£¬ÕÆÎÕ·ÖÔ˶¯µÄ¹æÂÉ£¬ÒÔ¼°Ã÷È·Ô²ÖÜÔ˶¯ÏòÐÄÁ¦µÄÀ´Ô´Êǽâ¾ö±¾ÌâµÄ¹Ø¼ü£®