A group of students wish to determine the density of a cylinder to be used in a design project. They plan to determine the density from measurements of the cylinder's mass, length, and diameter, which have instrument resolutions of 0.1 lbm, 0.05 in., and 0.0005 in., respectively. The balance used to measure the weight has an instrument uncertainty (accuracy) of 1 %. The rulers used to measure the length and diameter present negligible instrument uncertainties. Nominal values of the mass, length, and diameter are 4.5 lbm, 6.00 in., and 4.0000 in., respectively. (a) Estimate the zero-order uncertainty in the determination of the density. (b) Which measurement contributes the most to this uncertainty? (c) Estimate the design-stage uncertainty in the determination of the density.
A group of students wish to determine the density of a cylinder to be
used in a design project. They plan to determine the density from measurements
of the cylinder's mass, length, and diameter, which have instrument
resolutions of 0.1 lbm, 0.05 in., and 0.0005 in., respectively.
The balance used to measure the weight has an instrument uncertainty
(accuracy) of 1 %. The rulers used to measure the length and diameter
present negligible instrument uncertainties. Nominal values of the mass,
length, and diameter are 4.5 lbm, 6.00 in., and 4.0000 in., respectively.
(a) Estimate the zero-order uncertainty in the determination of the density.
(b) Which measurement contributes the most to this uncertainty?
(c) Estimate the design-stage uncertainty in the determination of the
density.
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