Question

Èçͼ¼×Ëùʾ£¬³¡Ç¿´óСΪE¡¢·½ÏòÊúÖ±ÏòÉϵÄÔÈÇ¿µç³¡ÄÚ´æÔÚ×ÅÒ»°ë¾¶ÎªRµÄÔ²ÐÎÇøÓò£¬OµãΪ¸ÃÔ²ÐÎÇøÓòµÄÔ²ÐÄ£¬AµãÊÇÔ²ÐÎÇøÓòµÄ×îµÍµã£¬BµãÊÇ×îÓÒ²àµÄµã£®ÔÚAµãÓзÅÉäÔ´Êͷųö³õËٶȴóС²»Í¬¡¢·½Ïò¾ù´¹Ö±ÓÚ³¡Ç¿ÏòÓÒµÄÕýµçºÉ£¬µçºÉµÄÖÊÁ¿Îªm£¬µçÁ¿Îªq£¬²»¼ÆÖØÁ¦£®ÊÔÇó£º
£¨1£©µçºÉÔڵ糡ÖÐÔ˶¯µÄ¼ÓËٶȶà´ó£¿
£¨2£©Ô˶¯¹ì¼£¾­¹ýBµãµÄµçºÉÔÚAµãʱµÄËٶȶà´ó£¿
£¨3£©Ä³µçºÉµÄÔ˶¯µÄ¹ì¼£ºÍÔ²ÐÎÇøÓòµÄ±ßÔµ½»ÓÚPµã£¬¡ÏPOA=¦È£¬Çëд³ö¸ÃµçºÉ¾­¹ýPµãʱ¶¯Äܵıí´ïʽ£®
£¨4£©ÈôÔÚÔ²ÐÎÇøÓòµÄ±ßÔµÓÐÒ»½ÓÊÕÆÁCBD£¬C¡¢D·Ö±ðΪ½ÓÊÕÆÁÉÏ×î±ßÔµµÄÁ½µã£¬ÈçͼÒÒ£¬¡ÏCOB=¡ÏBOD=30¡ã£®Çó¸ÃÆÁÉϽÓÊÕµ½µÄµçºÉµÄÄ©¶¯ÄÜ´óСµÄ·¶Î§£®

Answer 1

£¨1£©¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨Âɵã¬a=

qE

m

£®
£¨2£©ÓÉR=v₀t£¬R=

1

2

at²  ¼°a=

qE

m

µÃ£¬
ÁªÁ¢Èý¸öʽ×ӿɽâµÃ£ºv₀=

qER 2m

£®
£¨3£©Rsin¦È=v₀t£¬R-Rcos¦È=

1

2

at²¼°a=

qE

m

Èý¸öʽ×ӿɵÃv₀²=

Rsin2¦È

2m(1-cos¦È)

1

2

m v₀²=

Rsin2¦È

4(1-cos¦È)

=

R(1+cos¦È)

4

¾­¹ýPµãʱµÄ¶¯ÄÜ£ºE_k=Eq£¨R-Rcos¦È£©+

1

2

m v₀²=

1

4

EqR £¨5-3cos¦È£© 
£¨4£©Óɵڣ¨3£©Ð¡ÌâµÄ½áÂÛ¿ÉÒÔ¿´³ö£¬µ±¦È´Ó0¡ã±ä»¯µ½180¡ã£¬½ÓÊÕÆÁÉϵçºÉµÄ¶¯ÄÜÖð½¥Ôö´ó£¬Òò´ËDµã½ÓÊÕµ½µÄµçºÉµÄÄ©¶¯ÄÜ×îС£¬Cµã½ÓÊÕµ½µÄµçºÉµÄÄ©¶¯ÄÜ×î´ó£®£¨2·Ö£©
E_kD=Eq£¨R-Rcos¦È£©+

1

2

m v_0D²=

1

4

EqR £¨5-3cos60¡ã£©=

7

8

 EqR
E_kC=Eq£¨R-Rcos¦È£©+

1

2

m v_0C²=

1

4

EqR £¨5-3cos120¡ã£©=

13

8

 EqR
ËùÒÔ£¬ÆÁÉϽÓÊÕµ½µÄµçºÉµÄÄ©¶¯ÄÜ´óСµÄ·¶Î§Îª[

7

8

EqR£¬

13

8

EqR]
´ð£º£¨1£©µçºÉÔڵ糡ÖÐÔ˶¯µÄ¼ÓËÙ¶ÈΪ

qE

m

£®
£¨2£©Ô˶¯¹ì¼£¾­¹ýBµãµÄµçºÉÔÚAµãʱµÄËÙ¶ÈΪ

qER 2m

£®
£¨3£©¸ÃµçºÉ¾­¹ýPµãʱ¶¯Äܵıí´ïʽ

1

4

EqR £¨5-3cos¦È£©
£¨4£©¸ÃÆÁÉϽÓÊÕµ½µÄµçºÉµÄÄ©¶¯ÄÜ´óСµÄ·¶Î§Îª[

7

8

EqR£¬

13

8

EqR]£®