Question

# 1. Physical units in mechanics are usually some combination of the dimensions time T, mass M,...

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  #### Earn Coins

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