A rectangular plate has width with uncertainty (one standard deviation) and height…

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Propagating uncertainty into the quantity you actually want

Problem

A rectangular plate has width

w = 25.40\,\mathrm{mm}

with uncertainty

u(w) = 0.10\,\mathrm{mm}

(one standard deviation) and height

h = 10.00\,\mathrm{mm}

with uncertainty

u(h) = 0.05\,\mathrm{mm}

(one standard deviation), measured independently with two different gauges. The area is

A = wh

. (a) By substitution, or using

(1+\delta)^n\approx1+n\delta

, show that moving

w

up by a fractional amount

\delta_w

moves

A

up by the same fraction

\delta_w

, with

h

held fixed, and likewise for a fractional move of

h

. (b) State the general relative-uncertainty rule for a product of two independent quantities, and use it to find

u(A)/A

and

u(A)

for the plate. (c) Explain briefly why this quadrature combination, rather than the linear sum of the two relative uncertainties, is the one to trust.

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