A rectangular metal plate has length and width

PHYSICS · Multi-part · 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 metal plate has length

L = (15.00 \pm 0.05)\,\mathrm{cm}

and width

W = (8.00 \pm 0.04)\,\mathrm{cm}

, each uncertainty a standard deviation from repeated readings with a steel rule, and the two lengths measured independently. The area is

A = LW

. ((a)) Find the contribution of

L

A

by moving

L

up to

L+u(L)

with

W

fixed, and the contribution of

W

by moving

W

up to

W+u(W)

with

L

fixed. ((b)) Combine these to give

u(A)

and quote

A = \bar A \pm u(A)

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