What is the equation for work done by a constant force?

The equation for work done by a constant force is expressed as the product of the force exerted, the displacement of the object, and the cosine of the angle between the force and the direction of displacement. This relationship is encapsulated in the equation (W = F \Delta d \cos \theta), where:

• (W) represents the work done,
• (F) is the magnitude of the constant force,
• (\Delta d) is the magnitude of the displacement, and
• (\theta) is the angle between the force vector and the displacement vector.

The cosine function is important here because it accounts for only the component of the force that acts in the direction of the displacement. If the force is applied at an angle to the direction of motion, not all of the force contributes to the work done in achieving that displacement.

In situations where the force is applied in the same direction as the displacement, (\theta) is 0 degrees, and (\cos(0) = 1), simplifying the equation to (W = F \Delta d). Conversely, if the force is perpendicular to the displacement ((\theta = 90^\circ)), ( \cos(90