A solid aluminum cylinder of radius and height is completely coated with a uniform…

PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

A solid aluminum cylinder of radius

1.50\,\text{cm}

and height

10.0\,\text{cm}

is completely coated with a uniform layer of nickel. The combined mass of the coated cylinder is

620\,\text{g}

. The densities of aluminum and nickel are

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

and

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

, respectively. (a) Calculate the mass the cylinder would have if it were made entirely of aluminum with the stated dimensions. Provide your answer in grams. (b) Using your result from part (a) and the measured total mass, determine the mass of nickel present on the cylinder. (c) Derive an expression for the thickness

t

of the nickel layer in terms of the known cylinder dimensions, the densities of the two metals, and the mass of nickel found in part (b). Then calculate the numerical value of

t

in millimeters. (d) Discuss one practical manufacturing consideration that could cause the actual thickness to differ slightly from the theoretical value you calculated.

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