Weight of Body at Earth's Surface

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:
 * $W = \size {-m g \mathbf k} = m g$