题目内容
一宇宙人在太空(万有引力可以忽略不计)玩垒球。如图所示,辽阔的太空球场半侧为匀强电场,另半
侧为匀强磁场,电场和磁场的分界面为垂直纸面的平面,电场
方向与界面垂直,磁场方向垂直纸面向里,电场强度大小
。宇宙人位于电场一侧距界面为
的
点,
为
点至界面垂线的垂
足,
点位于纸面上
点的右侧,
与磁场的方向垂直。垒球的质量
,电量
。宇宙人从
点以初速度
平行于界面投出垒球,要使垒球第一次通过界面时就击中
点,求:(计算结果保留三位有效数字)
(1)
、
两点之间的距离。
(2)垒球从抛出到第一次回到
点的时间。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241230271344491.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412302666665.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412302668172.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026697439.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026728361.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026744197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026759196.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026744197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412302668172.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026790200.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026759196.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026946225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026978416.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026993438.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026744197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027024419.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026790200.gif)
(1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026759196.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026790200.gif)
(2)垒球从抛出到第一次回到
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026744197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241230271344491.jpg)
(1)3.46m (2)1.53s
(1)设垒球在电场中运动的加速度大小为a,时间为
,
,则:
(3分,每式1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241230274615132.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027492863.gif)
即O、D两点之间的距离为
。(2分,没有保留三位有效数字的扣1分)
(2)垒球的运动轨迹如图所示。
由图可知,
,速度大小为:
。(1分)
设垒球作匀速圆周运动半径为R,磁感应强度大小为B,则
(1分)
根据牛顿第二定律,有:
(1分)
垒球在磁场中运动的时间为:
(2分
)
垒球从抛出到第一次回到
点的时间为:
(2分,没有保留三位有效数字的扣1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027180189.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027196260.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027258675.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241230274615132.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027492863.gif)
即O、D两点之间的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027508365.gif)
(2)垒球的运动轨迹如图所示。
由图可知,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027539654.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027555564.gif)
设垒球作匀速圆周运动半径为R,磁感应强度大小为B,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027570528.gif)
根据牛顿第二定律,有:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027586721.gif)
垒球在磁场中运动的时间为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027602864.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/2014082412302668172.gif)
垒球从抛出到第一次回到
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123026744197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824123027648698.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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