Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error.
\begin{align} \Delta PE = m*g*h_1 - m*g*h_2\\ \end{align}
However, expression for calculating systematic error is
\begin{align} \sigma_{\Delta PE} = \sqrt{(m*g*\sigma_{h_1})^2 + (m*g*\sigma_{h_2})^2}\\ \end{align}
Does any error due to center of mass get canceled out because unlike scale, it's not a percentage, but a fixed amount? Or does it get incorporated somehow? If it gets incorporated, how?
I've come up with something like below, but I don't think it's right:
\begin{align} \sigma_{h_1} = \sqrt{(\sigma_{h_{scale}})^2+(\sigma_{h_{CofM}})^2} \end{align}