Motion of Body with Constant Mass
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Theorem
Let $B$ be a body with constant mass $m$ undergoing a force $\mathbf F$.
Then the equation of motion of $B$ is given by:
- $\mathbf F = m \mathbf a$
where $\mathbf a$ is the acceleration of $B$.
Proof
| \(\ds \mathbf F\) | \(=\) | \(\ds \map {\dfrac \d {\d t} } {m \mathbf v}\) | Newton's Second Law of Motion | |||||||||||
| \(\ds \) | \(=\) | \(\ds m \dfrac {\d \mathbf v} {\d t} + \mathbf v \dfrac {\d m} {\d t}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds m \dfrac {\d \mathbf v} {\d t} + 0\) | Derivative of Constant | |||||||||||
| \(\ds \) | \(=\) | \(\ds m \mathbf a\) | Definition of Acceleration |
$\blacksquare$
Sources
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $3$. Definitions of terms