Ejercicio Lab 1 · Física II URV 2024

Explain how the volume resolution error would change if all length dimensions were determined solely by using a caliper instead of other instruments. Compute the quantitative magnitude of this change using your experimental laboratory data. Would the random error be affected as well? Justify your answer.

Solución: A caliper typically provides a resolution of $\Delta l = 0.05\text{ mm}$ or $0.02\text{ mm}$, which is significantly finer than that of a standard ruler ($1\text{ mm}$). Since the volume resolution error propagates from the length uncertainties (for instance, for a cylinder $V = \pi r^2 h$, $\Delta V = |2\pi r h|\Delta r + |\pi r^2|\Delta h$), measuring all dimensions with a caliper decreases the resolution uncertainty $\Delta V_{\text{res}}$ by approximately an order of magnitude (from around $\sim 1\text{ mm}$ precision down to $\sim 0.05\text{ mm}$ or $0.01\text{ cm}$). Regarding the random error: the random (statistical) error arises from repeated independent trials and reflects accidental fluctuations and user reproducibility. While improving instrument precision narrows the uncertainty interval of each reading, the statistical standard deviation of the mean depends primarily on the dispersion of the repeated measurements and the sample size $N$, though it sets a lower bound equal to the instrument resolution.