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