A research lab prepares a composite block used as a calibration standard. The block is formed by casting molten zinc (density 7.05×103kgm−3) into the pores of a rigid open-cell foam made from a lightweight polymer of density 120kgm−3. In the final product, the polymer occupies 65% of the block’s total volume, with the remaining void space completely filled by zinc.
(a) Derive an algebraic expression for the overall density of the composite block in terms of the given volume fraction of polymer and the densities of the two constituent materials.
(b) Calculate the overall density of the block in kgm−3. Show all steps clearly.
(c) The lab needs blocks of mass 2.50kg. Determine the volume of composite material that must be produced for each block. Express your answer in cubic centimeters.
(d) If a manufacturing error changes the polymer volume fraction from 65% to 60%, compute the percentage change in the overall density and discuss qualitatively how this would affect the calibration accuracy of mass-measuring instruments that use the block.