10£®Ä³ÐËȤС×éÔÚ×ö¡°Ì½¾¿×ö¹¦ºÍÎïÌåËٶȱ仯¹Øϵ¡±µÄʵÑéÇ°£¬Ìá³öÁËÒÔϼ¸ÖÖ²ÂÏ룺¢ÙW¡Ø$\sqrt{v}$£¬¢ÚW¡Øv£¬¢ÛW¡Øv2£®ÎªÈ·¶¨ÄÄÒ»ÖÖ²ÂÏëÕýÈ·£¬ËûÃÇÉè¼ÆµÄʵÑé×°ÖÃÈçͼËùʾ£¬PQΪһ¿éÇãб·ÅÖõÄľ°å£¬ÔÚQ´¦¹Ì¶¨Ò»¸öλÒÆ´«¸ÐÆ÷£¬Ã¿´ÎÎïÌå´Ó³õʼλÖô¦Óɾ²Ö¹ÊÍ·Å£®Í¨¹ý´«¸ÐÆ÷¿ÉÒÔ²â³öÎïÌå³õʼλÖõ½´«¸ÐÆ÷µÄ¾àÀëLºÍÎïÌåµÄ˲ʱËÙ¶Èv£®
£¨1£©ÄãÈÏΪËûÃǵÄÄÄÒ»ÖÖ²ÂÏëÕýÈ·£¿ÎªÊ²Ã´£¿W¡Øv2ÕýÈ·£¬²ÉÓñí¸ñ·½·¨¼Ç¼Êý¾Ý£¬ºÏÀí»æÖÆL-v2ͼÏó£¬Äܹ»ÊÇÒ»Ìõ¹ýÔ­µãµÄÖ±Ïߣ¬¹ÊLÓëv2³ÉÕý±È£®
£¨2£©ÔÚ´ËʵÑéÖУ¬Ä¾°åÓëÎïÌå¼äĦ²ÁÁ¦µÄ´óС»á²»»áÓ°Ïì̽¾¿³öµÄ½á¹û£¿ÎªÊ²Ã´£¿²»»á£¬ÒòΪÖØÁ¦ºÍĦ²ÁÁ¦µÄºÏÁ¦¶ÔÎïÌå×öµÄ×ܹ¦W=mgL£¨sin¦È-¦Ìcos¦È£©Ò²Óë¾àÀëL³ÉÕý±È£®£®

·ÖÎö ¸ù¾ÝʵÑéÊý¾ÝÁгöÊý¾Ý±í²¢Ãèµã×÷³öL-v2ͼÏ󣬴ӶøÕÒµ½Î»ÒÆÓëËٶȱ仯µÄ¹Øϵ£»
ÔÚÔ˶¯¹ý³ÌÖУ¬ÓÉÓÚÎïÌåÊÜÁ¦ÊǺ㶨µÄ£¬ËùÒԵóöºÏÍâÁ¦×ö¹¦ÓëÎïÌåËٶȱ仯µÄ¹Øϵ£®Òò´ËÔÚʵÑéÖÐÎïÌåÓëľ°å¼äµÄĦ²ÁÁ¦²»»áÓ°Ïì̽¾¿µÄ½á¹û£®

½â´ð ½â£º£¨1£©²ÉÓñí¸ñ·½·¨¼Ç¼Êý¾Ý£¬ºÏÀí»æÖÆL-v2ͼÏó£¬Äܹ»ÊÇÒ»Ìõ¹ýÔ­µãµÄÖ±Ïߣ¬¹ÊLÓëv2³ÉÕý±È£®
£¨2£©²»»á£¬ÒòΪÖØÁ¦ºÍĦ²ÁÁ¦µÄºÏÁ¦¶ÔÎïÌå×öµÄ×ܹ¦W=mgL£¨sin¦È-¦Ìcos¦È£©Ò²Óë¾àÀëL³ÉÕý±È£®
¹Ê´ð°¸Îª£º£¨1£©W¡Øv2ÕýÈ·£¬²ÉÓñí¸ñ·½·¨¼Ç¼Êý¾Ý£¬ºÏÀí»æÖÆL-v2ͼÏó£¬Äܹ»ÊÇÒ»Ìõ¹ýÔ­µãµÄÖ±Ïߣ¬¹ÊLÓëv2³ÉÕý±È£®
£¨2£©²»»á£¬ÒòΪÖØÁ¦ºÍĦ²ÁÁ¦µÄºÏÁ¦¶ÔÎïÌå×öµÄ×ܹ¦W=mgL£¨sin¦È-¦Ìcos¦È£©Ò²Óë¾àÀëL³ÉÕý±È£®

µãÆÀ ͨ¹ýʵÑéÊý¾ÝÁÐ±í¡¢Ãèµã¡¢×÷ͼ´Ó¶ø̽¾¿³öÎÊÌâµÄ½áÂÛ£®ÖµµÃ×¢ÒâµÄÊÇ£ºÓÉÓÚºÏÍâÁ¦ºã¶¨£¬Òò´ËºÏÍâÁ¦×öµÄ¹¦Óë·¢ÉúµÄλÒÆÊdzÉÕý±È£®¹Ê¿ÉÏÈ̽¾¿Î»ÒÆÓëËٶȱ仯ÓкιØϵ£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®ÈçͼËùʾ£¬ÎïÌåÑØÁ½¸ö°ë¾¶ÎªRµÄ°ëÔ²»¡ÓÉAÔ˶¯µ½C£¬ÔòËüµÄλÒƺÍ·³Ì·Ö±ðÊÇ£¨¡¡¡¡£©
A£®0£¬0B£®4R ÏòÎ÷£¬2¦ÐRC£®4¦ÐR Ïò¶«£¬4RD£®4R Ïò¶«£¬2¦ÐR

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£º½â´ðÌâ

1£®¡¾ÊµÑé²½Öè¡¿
£¨1£©½«¹â¾ß×ù·ÅÔÚˮƽ×ÀÃæÉÏ£¬½«¹âÔ´¡¢ÕÚ¹âͲˮƽ°²·ÅÔÚ¹â¾ß×ùÉÏ£¬ÕÚ¹âͲµÄ³¤¶ÈÔ¼
1m£¬µ÷ÕûͲµÄ¸ß¶È£¬Ê¹¹âÔ´·¢³öµÄ¹âÄÜÑØÕÚ¹âͲµÄÖáÏßÕÕÉäµ½¹âÆÁÉÏ£®
£¨2£©½«µ¥·ì¡¢Ë«·ìÒÀ´Î°²×°ÔÚ¹â¾ß×ùÉÏ£¬µ÷ÕûÆä¸ß¶È£¬Ê¹ÏñÆÁÖÐÑë³öÏÖ²ÊÉ«É«µÄ¸ÉÉæͼÑù£»µ¥¡¢Ë«·ìÆÁÖ®¼äµÄ¾àÀëÔ¼5-10cm±È½ÏÊÊÒË£»ÎªÁ˲âÁ¿µÄ·½±ã£¬Ë«·ìÆÁ×îºÃ´¦ÔÚ¹â¾ß×ùÉϿ̶ȳߵÄÕû¿Ì¶È´¦£®
£¨3£©½«Â˹âƬ°²×°ÔÚ¹âÔ´ºÍµ¥·ìÆÁÖ®¼ä£¬Ê¹ÏñÆÁÉÏÄܹ۲쵽Ã÷°µÏà¼äµÄµ¥É«¸ÉÉæͼÑù£®
£¨4£©ÀûÓòâÁ¿Í·²â¡÷x£¬¾ßÌå²Ù×÷£ºÊ¹²âÁ¿Í·µÄ·Ö»®°åµÄÖÐÐĿ̶ÈÏ߶ÔÆëÌõÎÆÖÐÐÄ£¬¼ÇÏ´ËʱÊÖÂֵĶÁÊý£¬×ª¶¯²âÁ¿Í·µÄÂÝÐýÊÖÂÖ£¬Ê¹·Ö»®°åµÄÖÐÐĿ̶ÈÏßÒƶ¯ÖÁ¶ÔÆëÁíÒ»ÌõÎÆÖÐÐÄ£¬¼ÇÏ´ËʱÊÖÂֵĶÁÊý£¬Á½¶ÁÊýÖ®²î¼´ÎªÕâÁ½Ìõ¸ÉÉæÌõÎÆÖ®¼äµÄ¾àÀ룮
£¨5£©»»ÓÃË«·ìS1¡¢S2Ö®¼äµÄ¾àÀëd²»Í¬µÄË«·ìÆÁÖظ´µÚËIJ½µÄʵÑé²âÁ¿£¬²¢½«Ïà¹Ø²âÁ¿Êý¾ÝÌîÈë¼Ç¼±í¸ñÖУ¬²¢ÀûÓÃÿ´Î²âÁ¿µÄ½á¹û´úÈ˹«Ê½£º¦Ë=$\frac{¡÷xd}{L}$£¬Ëã³öÓëÂ˹âƬÑÕÉ«Ïà¶ÔÓ¦µÄ¹â²¨µÄ²¨³¤£¬²¢Çó³ö¹âµÄ²¨³¤µÄƽ¾ùÖµ£®
£¨6£©»»Óò»Í¬ÑÕÉ«µÄÂ˹âƬ£¬Öظ´µÚËÄ¡¢Îå²½µÄʵÑ飬¿É²â³ö²»Í¬ÑÕÉ«µÄ¹âµÄ²¨³¤£®
¡¾ÊµÑéÊý¾Ý¼Ç¼¡¿
¹âµÄÑÕÉ«Ë«·ìµÄ¿í¶ÈË«·ìÓëÏñÆÁµÄ¾àÀëLÏàÁÚÃ÷ÎƼäµÄ¾àÀë¡÷x²¨³¤¦Ë²¨³¤µÄƽ¾ùÖµ
¡¾ÊµÑé½áÂÛ¡¿ÔÚʵÑéÎó²îÔÊÐíµÄ·¶Î§ÄÚ£¬¶ÔÓÚͬһ¸ÉÉæÒÇ£¬ÔÚ²âͬÖÖ¹âµÄ²¨³¤Ê±£¬¸Ä±äË«·ìµÄ¿í¶Èd£¬²âµÃ¹âµÄ²¨³¤£¨¾ßÌåÊýÖµÓÉʵÑéÊý¾ÝµÃ³ö£©£®
¡¾»ù´¡ÖªÊ¶¡¿
£¨1£©¹ØÓÚ±¾ÊµÑéµÄÏÖÏó£¬ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇAB
A£®Èç¹ûûÓвåÂ˹âƬ£¬¿ÉÒԹ۲쵽ÖмäÊÇ°×É«£¬Á½±ßÊDzÊÉ«µÄÌõÎÆ
B£®²åÉÏÂ˹âƬºó£¬¹Û²ìµ½µÄÊÇÃ÷°µÏà¼äµÄÌõÎÆ
C£®»»Óò»Í¬µÄÂ˹âƬʱ£¬ÌõÎƼä¾àûÓб仯
D£®Ë«·ì¼ä¸ôÔ½´ó£¬ÌõÎƼä¾àÔ½´ó
£¨2£©ÔÚ±¾ÊµÑéÖУ¬ÔÚ¹âÔ´Õý³£·¢¹âµÄÇé¿öÏ£¬¹âÆÁÉϸù±¾¿´²»µ½¹âÁÁµÄºÛ¼££¬ÆäÔ­ÒòÊÇBC
A£®Ã»ÓвåÂ˹âƬ
B£®¹âÔ´¸ß¶ÈÆ«µÍ
C£®ÕÚ¹âͲÓë¹âÔ´µÈÔª¼þ²»¹²Öá
D£®·ì±¾ÉíµÄ¿í¶È¹ý´ó
£¨3£©Òª²âµ¥É«¹âµÄ²¨³¤ÐèÒª²âµÃµÄÎïÀíÁ¿ÊÇË«·ì¼ä¾à£¬Ë«·ìµ½¹âÆÁµÄ¼ä¾à£¬ÏàÁÚÌõÎƵļä¾à£®ÆäÖÐÌõÎƼä¾àÓɲâÁ¿Í·²âÁ¿£®
£¨4£©²âÁ¿Í·ÓÉ·Ö»®°å¡¢Ä¿¾µ£®ÊÖÂֵȹ¹³É£¬²âÁ¿Ê±Ó¦Ê¹ÆäÖÐÐÄ¿ÌÏ߶ÔÆëÌõÎÆÖÐÐIJ¢¼ÆÏ´ËʱÊÖÂÖÉϵĶÁÊý£¬×ª¶¯²âÁ¿Í¼£¬Ê¹·Ö»®°åÖÐÐÄ¿ÌÏ߶ÔÆëÁíÒ»ÌõÎÆÖÐÐÄ£¬¼ÇÏ´ËʱÊÖÂÖÉϵĶÁÊý£®
£¨5£©ÊµÑéÖÐΪÁ˼õÉÙʵÑéÎó²î£¬¿É²ÉÈ¡µÄ°ì·¨ÊÇD
A£®¼õÉÙÆÁµ½Ë«·ìµÄ¾àÀë
B£®»»Óò»Í¬µÄÂ˹âƬ½øÐжà´Î²âÁ¿È¡Æ½¾ùÖµ
C£®Ôö´ó·ìµÄ¿í¶È
D£®²â³ö¶àÌõÁÁÎÆÖ®¼äµÄ¾àÀ룬ÔÙËã³öÏàÁÚÌõÎƼä¾à
£¨6£©ÔÚË«·ì¸ÉÉæʵÑéÖУ¬´ÓÖÐÐÄÃ÷ÌõÎÆÏòÒ»±ßÊý£¬µÚÈýÌõÃ÷ÌõÎÆÔÚÆÁÉϵÄp´¦£¬Èô´ÓË«·ìµ½pµÄ·³Ì²îΪ8.1?m£¬ÔòËùÓùâµÄ²¨³¤Îª2.7?m
£¨7£©Óúì¹â×öÀÖµÄË«·ì¸ÉÉæʵÑéʱ£¬ÒÑ֪˫·ì¼ä¾àΪ0.20¡Á10-3m£¬²âµÃË«·ìµ½ÆÁ¼äµÄ¾àÀëΪ0£¬700m£¬·Ö»®°åÖÐÐÄ¿ÌÏ߶ÔÆëµÚÒ»ÌõÁÁÌõÎÆÖÐÑëʱÊÖÂÖ¶ÁÊýΪ0.52¡Á10-3m£¬µÚ4ÌõÁÁÌõÎÆËùÔÚλÖÃΪ7.47¡Á10-3m£¬Çó´Ëºì¹âµÄ²¨³¤£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®ÏÂÁÐÇé¿öÖеÄÎïÌ壬»úеÄÜÒ»¶¨ÊغãµÄÊÇ£¨¡¡¡¡£©
A£®ÔÈËÙÉÏÉýµÄµçÌÝB£®Ñع⻬бÃæ×ÔÓÉÏ»¬µÄÎï¿é
C£®ÔڲݵØÉϹö¶¯µÄ×ãÇòD£®ÔÚ¿ÕÖмÓËÙϽµµÄÌøÉ¡Ô˶¯Ô±

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

5£®ÖÊÁ¿Îª1ǧ¿ËµÄÎïÌå´ÓÇã½ÇΪ37¡ãµÄ¹â»¬Ð±Ã棨бÃæ×ã¹»³¤£©ÉÏÓɾ²Ö¹¿ªÊ¼Ï»¬£¬ÔòÖØÁ¦ÔÚÇ°2ÃëÄÚ×ö¹¦36½¹£¬Ç°3ÃëÄÚÖØÁ¦µÄƽ¾ù¹¦ÂÊΪ27Íߣ®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£º¶àÑ¡Ìâ

15£®½«Ò»¸öÁ¦F·Ö½âΪÁ½¸ö·ÖÁ¦F1ºÍF2£¬ÔòÏÂÁÐ˵·¨ÖÐÕýÈ·µÄÊÇ£¨¡¡¡¡£©
A£®FµÄ·Ö½â·½Ê½ÊÇΨһµÄ
B£®F1ºÍF2Á½¸ö·ÖÁ¦ÔÚЧ¹ûÉÏ¿ÉÒÔÈ¡´úÁ¦F
C£®ÎïÌåÊܵ½F1¡¢F2ºÍFÈý¸öÁ¦µÄ×÷ÓÃ
D£®FÊÇF1ºÍF2µÄºÏÁ¦

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

2£®ÏÂÁÐÆ÷¼þÖУ¬ÀûÓõçÁ÷µÄÈÈЧӦ¹¤×÷µÄÊÇ£¨¡¡¡¡£©
A£®ÑéµçÆ÷B£®µçÈÝÆ÷C£®µç¸ÐÆ÷D£®µçÈÈË®Æ÷

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÓÐÒ»ÈËÔÚƽֱÂí·±ßÂþ²½£¨ËٶȲ»±ä£©£¬Ëû·¢ÏÖÿ¸ôt1ʱ¼äÓÐһ·¹«¹²Æû³µÓ­Ã濪¹ý£¬Ëû»¹·¢ÏÖÿ¸ôt2ʱ¼äÓÐÒ»Á¾Õâ·¹«¹²Æû³µ´ÓÉíºó¿ª¹ý£¨¹«¹²Æû³µÔÈËÙÐÐÊ»£©£¬ÓÚÊÇËû¼ÆËã³öÕâ·³µ´ÓÆû³µÕ¾·¢³µµÄʱ¼ä¼ä¸ôÊÇ£¨¡¡¡¡£©
A£®$\frac{\sqrt{2}{t}_{1}{t}_{2}}{{t}_{1}+{t}_{2}}$B£®$\frac{\sqrt{2}{t}_{1}{t}_{2}}{2£¨{t}_{1}+{t}_{2}£©}$C£®$\frac{{t}_{1}{t}_{2}}{2£¨{t}_{1}+{t}_{2}£©}$D£®$\frac{2{t}_{1}{t}_{2}}{{t}_{1}+{t}_{2}}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÎïÀí À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®Ò»Áлð³µÓÐ3½ÚÏàͬµÄ³µÏᣬһ¹Û²ìÕßÕ¾ÔÚµÚÒ»½Ú³µÏáµÄÇ°¶Ë£¬µ±»ð³µÓɾ²Ö¹¿ªÊ¼×öÔȼÓËÙÖ±ÏßÔ˶¯Ê±£¨¡¡¡¡£©
A£®Ã¿½Ú³µÏáÄ©¶Ë¾­¹ý¹Û²ìÕßʱµÄËÙ¶ÈÖ®±ÈÊÇ1£º2£º3
B£®Ã¿½Ú³µÏá¾­¹ý¹Û²ìÕßËùÓõÄʱ¼äÖ®±ÈÊÇ1£º£¨$\sqrt{2}-1$£©£º£¨$\sqrt{3}-\sqrt{2}$£©
C£®Ã¿½Ú³µÏá¾­¹ý¹Û²ìÕßµÄƽ¾ùËÙ¶ÈΪ$\overline{V_1}$£¬$\overline{V_2}$£¬$\overline{V_3}$£¬Ôò$\overline{V_1}$£º$\overline{V_2}$£º$\overline{V_3}$=1£º$\sqrt{2}$£º$\sqrt{3}$
D£®Èç¹ûµÚ3½Ú³µÏáÄ©¶Ë¾­¹ý¹Û²ìÕßʱµÄËÙ¶ÈΪv£¬ÄÇôÔÚÕû¸öÁгµ¾­¹ý¹Û²ìÕߵĹý³ÌÖУ¬Æ½¾ùËÙ¶ÈΪv/3

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸