1. Physical units in mechanics are usually some combination of the dimensions time T, mass M, and length L. Consider the physical quantities ?, ?, ?, ?, and ? with dimensions [?]=M, [?]=L, [?]=LT^−1, [?]=LT^−2, and [?]=T. Enter the dimensional expression of the quantity on the right-hand side of each equation. Your answers may contain only M, L, T, and exponents. Assume that each of the following equations is dimensionally consistent.
A typical human cell is approximately 12.0012.00 μm in diameter and enclosed by a membrane that is 8.0008.000 nm thick. What is the volume of the cell including the membrane?
To simplify the calculations, model the cell as a sphere.
total volume: _____μm3
What is the volume of the cell membrane?
membrane volume: ____μm3
What percent of the total volume does its membrane occupy?
membrane percentage: _____%
3. Consider the physical quantities ?, ?, ?, ?, and ? with dimensions [?]=L, [?]=LT^−1, [?]=LT^−2, [?]=M, and [?]=T.
Select the dimensionally consistent equation(s).
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