15. 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
Explanation:
The formula for potential energy stored is Ep=1/2kx^2
Since EP is calculated from multiplying kk and x^2 (ignoring the constant 1/2 as there is no uncertainty for it), then the uncertainty of EP is calculated by adding the fractional uncertainties of x^2 and k.
The fractional uncertainty of x^2 is double the fractional uncertainty on x, which gives 2×3%=6%
The uncertainty of EP therefore = 2% + 6% = 8%