A student wishes to determine the density of an irregularly shaped mineral sample

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A student wishes to determine the density of an irregularly shaped mineral sample. The sample is first weighed in air using a spring scale and found to have an apparent weight of

9.4\,\text{N}

. The sample is then completely immersed and suspended at rest in a liquid of density

1.20\times10^{3}\,\text{kg\,m}^{-3}

. In the liquid, the spring scale reads

7.2\,\text{N}

. Assume the density of air is negligible and that temperature effects are insignificant. (a) Derive an expression for the density

\rho_s

of the sample in terms of the two scale readings

W_\text{air}

and

W_\text{liq}

, the fluid density

\rho_f

, and

g

. (b) Use the measured values to calculate the numerical value of

\rho_s

\text{kg\,m}^{-3}

. (c) Suppose the spring scale has an uncertainty of

\pm0.05\,\text{N}

in each reading. Estimate the absolute uncertainty in the calculated density. Outline your procedure clearly. (d) Comment on whether the percent uncertainty in the density measurement could be reduced more effectively by improving the precision of the scale or by choosing a different immersion liquid. Support your answer with reasoning based on your expression from part (a).

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