Scientific Skills & Tools (id: a2de21b43)

本题目来源于试卷: Scientific Skills & Tools，类别为 IB物理学

[单选题]
A spring with spring constant $k$ is extended by a distance $x$.

The uncertainty of $k$ is 2% and that of $x$ is 3%.

What is the uncertainty of the potential energy stored in the spring?

A. 8%
B. 11%
C. 12%
D. 18%


参考答案:  A


本题详细解析:

The formula for potential energy stored is ${�}_{�}=\frac{1}{2}�{�}^2$

Since ${�}_{�}$ is calculated from multiplying $�$ and ${�}^2$ (ignoring the constant $\frac{1}{2}$ as there is no uncertainty for it), then the uncertainty of ${�}_{�}$ is calculated by adding the fractional uncertainties of ${�}^2$ and $�$.

The fractional uncertainty of ${�}^2$ is double the fractional uncertainty on x, which gives $2\times 3\mathrm{\%}=6\mathrm{\%}$

The uncertainty of ${�}_{�}$ therefore = 2% + 6% = 8%

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