Weight of Body at Earth's Surface
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Theorem
Let $B$ be a body of mass $m$ situated at (or near) the surface of Earth.
Then the weight of $B$ is given by:
- $W = m g$
where $g$ is the value of the acceleration due to gravity at the surface of Earth.
Proof
The weight of $B$ is the magnitude of the force exerted on it by the influence of the gravitational field it is in.
By Newton's Second Law of Motion, that force is given by:
- $\mathbf W = -m g \mathbf k$
where:
- $g$ is the value of the acceleration due to gravity at the surface of Earth
- $\mathbf k$ is a unit vector directed vertically upwards.
Hence the magnitude of $\mathbf W$ is given by:
- $W = \size {-m g \mathbf k} = m g$
$\blacksquare$
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): weight
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): weight