题目内容
在相互垂直的匀强磁场和匀强电场中,有一倾角为θ的足够长的光滑绝缘斜面,磁感应强度为B,方向水平向外,电场强度为E,方向竖直向上,有一质量为
带电荷量为
的小滑块静止在斜面顶端时对斜面的正压力恰好为零,如图所示。
(1)如果迅速把电场方向转为竖直向下,求小滑块能在斜面上连续滑行的最远距离L和所用时间
;
(2)如果在距A端L/4远处的C点放入一个相同质量但不带电的小物体,当滑块从A点由静止下滑到C点时两物体相碰并黏在一起.求此黏合体在斜面上还能再滑行多长时间和距离.![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154453444510.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445297204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445312212.gif)
(1)如果迅速把电场方向转为竖直向下,求小滑块能在斜面上连续滑行的最远距离L和所用时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445328185.gif)
(2)如果在距A端L/4远处的C点放入一个相同质量但不带电的小物体,当滑块从A点由静止下滑到C点时两物体相碰并黏在一起.求此黏合体在斜面上还能再滑行多长时间和距离.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154453444510.jpg)
(1)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154454061027.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445375836.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445390834.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154454061027.gif)
(1)由题意知
场强转为竖直向下时,由动能定理,有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445453806.gif)
即2
① 当滑块刚离开斜面时有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445484674.gif)
即
② 由①②解,得L=![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445515711.gif)
根据动量定理,有![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445375836.gif)
(2)两不物体先后运动,设在C点处碰撞前滑块的速度为
,则
③
碰撞过程有
④
当黏合体将要离开斜面时有 ⑤
由动能定理,碰后两物体共同下滑的过程中,有
⑥
联立③④⑤⑥解,得
⑦ 将L结果代入⑦式得
.
碰后两物体在斜面上还能滑行的时间可由动量定理求得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154454061027.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445437427.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445453806.gif)
即2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445468658.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445484674.gif)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445500638.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445515711.gif)
根据动量定理,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445375836.gif)
(2)两不物体先后运动,设在C点处碰撞前滑块的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445578193.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445593717.gif)
碰撞过程有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445593436.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154456091204.gif)
由动能定理,碰后两物体共同下滑的过程中,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445640891.gif)
联立③④⑤⑥解,得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445656865.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115445390834.gif)
碰后两物体在斜面上还能滑行的时间可由动量定理求得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241154454061027.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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