The uncertainty budget for a spring constant has two rows: the scale's reading resolution

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Monte Carlo and the bootstrap: uncertainty by sampling

Problem

The uncertainty budget for a spring constant has two rows: the scale's reading resolution, rectangular with half-width a=0.35 N m−1a = 0.35\,\mathrm{N\,m^{-1}}, and the scatter of repeated extensions, Gaussian with standard uncertainty 0.030 N m−10.030\,\mathrm{N\,m^{-1}}. A partner combines them in quadrature and quotes a 9595 per cent interval as ±2uc\pm 2u_{\rm c}. A simulation of four million draws of the sum of the two rows finds its 9595 per cent half-width to be 1.67uc1.67u_{\rm c}. ((a)) Find ucu_{\rm c}. ((b)) Say which row dominates, and decide from the simulated half-width whether the sum's 9595 per cent interval is close to the Gaussian one. ((c)) Give the 9595 per cent half-width the simulation supports, and compare it with the partner's 2uc2u_{\rm c}.

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