Calculate mechanical work based on force, distance and the angle between the force and the direction of motion.
Work (W) is the force (F) multiplied by the distance (s) the object moves, multiplied by the cosine of the angle (θ) between the force and the direction of motion. Work is measured in joules (J), the same unit as energy.
When the force acts in the same direction as the motion (θ = 0°), cos(θ) = 1, and the work is at its maximum. If the force is perpendicular to the direction of motion (θ = 90°), cos(θ) = 0, and the force does no work at all — even though it's still acting on the object.
Only the part of the force pointing in the direction of motion contributes to the work. The cosine term in the formula adjusts for how much of the force actually "pulls" the object forward along the direction of motion.
Then the work becomes zero, even if the force is large. A classic example is carrying a suitcase horizontally while walking: gravity acts downward, but the motion is horizontal, so gravity does no work on you.
Work is the process by which energy is transferred to or from an object via a force. When work is done on an object, its energy changes by exactly that amount — the two quantities are therefore measured in the same unit, joules.