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Research on Young’s Modulus Measurement Error and Improvement of Experimental Instruments
DOI: 10.12677/APP.2019.911055, PDF, HTML, XML, 下载: 548  浏览: 3,509

Abstract: Through the analysis of the principle and data error of the Young’s modulus of wire, several key factors affecting the experimental error are studied, and a design scheme to reduce the experi-mental error is proposed. The experimental equipment is improved by increasing the number of optical levers to enlarge the magnification; fixing the relative position between the experimental instruments and reducing the unstable factors of the measurement. The experimental measure-ment using the improved experimental device can significantly reduce the uncertainty and improve the reliability of the measured value.

1. 引言

2. 实验原理

Figure 1. Experimental principle of Young’s modulus measurement

$\theta \approx \mathrm{tan}\theta =\frac{\Delta l}{K}$ (1)

$\mathrm{tan}2\theta \approx 2\theta =\frac{b}{D}$ (2)

$\Delta l=\frac{Kb}{2D}$ (3)

$Y=\frac{Fl}{S\Delta l}$ (4)

3. 实验存在的误差分析

3.1. 仪器误差分析

3.2. 实验操作的误差

4. 设计方案

4.1. 实验装置的改进方案

Figure 2. Experimental schematic diagram of the improved device

$\theta \approx \mathrm{tan}\theta =\frac{\Delta l}{K}$ (5)

$\mathrm{tan}6\theta \approx 6\theta =\frac{b}{{D}^{\prime }}$ (6)

$\Delta l=\frac{{K}^{\prime }b}{12{D}^{\prime }}$ (7)

$Y=\frac{Fl}{S\Delta l}=\frac{12Fl{D}^{\prime }}{\pi {d}^{2}{K}^{\prime }b}$ (8)

4.2. 实验操作方法的改进

4.3. 实验操作方法的改进

Table 1. Measurement data of wire diameter

Table 2. Measurement data of scale reading before device improvement

Table 3. Measurement data of scale reading after improvement of the device

5. 结论

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