题目内容
如下图所示为某种电子秤的原理示意图,AB为一均匀的滑线电阻,阻值为R,长度为L,两边分别有P1、P2两个滑动头,P1可在竖直绝缘光滑的固定杆MN上保持水平状态而上下自由滑动.弹簧处于原长时,P1刚好指着A端,P1与托盘固定相连.若P1、P2间出现电压时,该电压经过放大,通过信号转换后在显示屏上将显示物体重力的大小.已知弹簧的劲度系数为k,托盘自身质量为m0,电源电动势为ε,内阻不计,当地的重力加速度为g.求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241207059867298.jpg)
(1)托盘上未放物体时,在托盘自身重力作用下,P1离A的距离x1;
(2)托盘上放有质量为m的物体时,P1离A的距离x2;
(3)在托盘上未放物体时通常先校准零点,其方法是:调节P2,使P2离A的距离也为x1,从而使P1、P2间的电压为零.校准零点后,将物体m放在托盘上,试推导出物体质量m与P1、P2间的电压之间的函数关系式.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241207059867298.jpg)
(1)托盘上未放物体时,在托盘自身重力作用下,P1离A的距离x1;
(2)托盘上放有质量为m的物体时,P1离A的距离x2;
(3)在托盘上未放物体时通常先校准零点,其方法是:调节P2,使P2离A的距离也为x1,从而使P1、P2间的电压为零.校准零点后,将物体m放在托盘上,试推导出物体质量m与P1、P2间的电压之间的函数关系式.
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706033527.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706002415.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706017555.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706033527.gif)
(1)由力平衡的知识m0g=kx1得
. ①
(2)由受力关系有:kx2=m0g+mg得
②
(3)由电学公式E=IR ③U=IR2 ④
⑤
据题意,x=x2-x1 ⑥
由①②⑥得
⑦
由③④⑤⑦得:
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706048477.gif)
(2)由受力关系有:kx2=m0g+mg得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706064617.gif)
(3)由电学公式E=IR ③U=IR2 ④
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706080350.gif)
据题意,x=x2-x1 ⑥
由①②⑥得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706095449.gif)
由③④⑤⑦得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120706033527.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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