Mass Weight

Overview

Engineering reference data for Mass Weight in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Mass of Fundamental Particles

Unit Systems for Mass and Weight

English Engineering System Proportionality Constant

In the English Engineering (EE) system, a proportionality constant $g_c$ is introduced to reconcile force and mass units. Newton's Second Law is modified as:

$F = \frac{m a}{g_c}$

For weight (force), this becomes:

$F_g = \frac{m a_g}{g_c}$

The constant $g_c$ is defined by the standard acceleration of gravity:

$g_c = \frac{1 \, \text{lbm} \times 32.17405 \, \text{ft/s}^2}{1 \, \text{lbf}} = 32.17405 \, \frac{\text{lbm} \cdot \text{ft}}{\text{lbf} \cdot \text{s}^2}$

This relationship also defines that 1 slug = 32.17405 lbm.

Example: Weight on Earth vs. the Moon

The acceleration of gravity on the moon is approximately $\frac{1}{6}$ of that on Earth ($g_{earth} \approx 9.81 \, \text{m/s}^2$).

Weight on Earth: $F_{g, \text{earth}} = m \times g_{\text{earth}} = (1 \, \text{kg}) \times (9.81 \, \text{m/s}^2) = 9.81 \, \text{N}$

Weight on the Moon: $F_{g, \text{moon}} = m \times g_{\text{moon}} = (1 \, \text{kg}) \times \left( \frac{9.81 \, \text{m/s}^2}{6} \right) = 1.64 \, \text{N}$

Interactive Charts

References

• Original Source