Question

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) K=1/2mv^2
[K] =

(b) p=mv
[p]=

(c) k=-ma/r
[k]=

2.

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).

?=??/?
?^2/2?=?
??=?
?=??
?=(2??)^2

Answer 1