The work of weight

A special force: weight

The weight P of an object of mass m is given by P = m * g (g ~= 9.8 N/kg, often rounded to 10 N/kg in high school). Weight is always vertical, directed downward.

Formula for the work of weight

For an object moving between a starting point and an ending point, the work of weight depends only on the height difference h between these two points, and not on the path taken:

W(P) = m * g * h (if the object descends) W(P) = - m * g * h (if the object rises)

where h is the absolute value of the altitude difference.

Concrete example

A ball of mass m = 0.2 kg falls from a height h = 5 m. We take g = 10 N/kg.

W(P) = m * g * h = 0.2 * 10 * 5 = 10 J

If the ball rose 5 m instead (thrown upward), the work of weight would be W(P) = -10 J.

Essential property

The work of weight is independent of the trajectory: whether the object falls vertically or slides down an inclined plane, only the height difference h matters. Weight is said to be a conservative force.

Classic pitfall

Do not confuse "rising" and "descending": the work of weight is positive when altitude decreases, negative when it increases, regardless of the direction of horizontal motion.