题目内容
如图甲所示, A、B、C、D为固定于竖直平面内的闭合绝缘轨道,AB段、CD段均为半径R=1.6 m的半圆,BC、AD段水平,AD=BC=8 m.B、C之间的区域存在水平向右的有界匀强电场,场强E=5×105 V/m.质量为m=4×10-3kg、带电量q=+1×10-8C的小环套在轨道上.小环与轨道AD段的动摩擦因数为μ=
,与轨道其余部分的摩擦忽略不计.现使小环在D点获得沿轨道向左的初速度v0=4 m/s,且在沿轨道AD段运动过程中始终受到方向竖直向上、大小随速度变化的力F(变化关系如图乙)作用,小环第一次到A点时对半圆轨道刚好无压力.不计小环大小,g取10 m/s2.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014465475157.jpg)
(1)小环运动第一次到A时的速度多大?
(2)小环第一次回到D点时速度多大?
(3)小环经过若干次循环运动达到稳定运动状态,此时到达D点时速度应不小于多少?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001446532352.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014465475157.jpg)
(1)小环运动第一次到A时的速度多大?
(2)小环第一次回到D点时速度多大?
(3)小环经过若干次循环运动达到稳定运动状态,此时到达D点时速度应不小于多少?
(1)4m/s (2)6m/s (3)2
m/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001446563382.png)
试题分析:(1)由题意及向心力公式得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001446578786.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014465941097.png)
(2)小物块从D出发,第一次回到D的过程,由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014466101038.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014466251246.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001446641718.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001446672637.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014466881310.png)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014467031039.png)
则可知环与杆的摩擦力
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014467191074.png)
稳定循环时,每一个周期中损耗的能量应等于补充的能量
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014467502300.png)
而
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014467661535.png)
所以稳定循环运动时小环在AD段运动时速度一定要大于等于8 m/s,即到达A点的速度不小于8 m/s
稳定循环运动时小环从A到D的过程,
由动能定理得
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014467811023.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250014467971344.png)
达到稳定运动状态时,小环到达D点时速度应不小于2
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825001446563382.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目