How do you calculate work done by non-conservative forces?

Work done by non-conservative forces is calculated by the formula W = Fd cos θ, where F is force, d is displacement, and θ is the angle.

In more detail, non-conservative forces are those forces that do not have the property of path independence. This means that the work done by these forces depends on the path taken, not just the initial and final positions. Examples of non-conservative forces include friction, air resistance, and tension.

The formula W = Fd cos θ is used to calculate the work done by these forces. Here, W represents the work done, F is the magnitude of the force, d is the displacement (or the distance over which the force is applied), and θ is the angle between the force and the displacement. The cos θ term accounts for the direction of the force relative to the displacement. If the force is applied in the same direction as the displacement (θ = 0), then cos θ = 1 and the work done is simply Fd. If the force is applied perpendicular to the displacement (θ = 90°), then cos θ = 0 and no work is done.

It's important to note that the force and displacement in this formula should be in the same unit system (for example, both in Newtons and meters, or both in pounds and feet) and the angle should be in degrees. Also, the force should be the net force acting on the object, taking into account all the forces acting on it.

In the case of variable forces, the work done can be calculated by integrating the force over the displacement. This involves a bit more complex mathematics, but the principle is the same: the work done is the area under the force-displacement graph.

Remember, the work done by non-conservative forces can be positive, negative, or zero, depending on the direction of the force and displacement. Positive work is done when the force and displacement are in the same direction, negative work is done when they are in opposite directions, and zero work is done when the force is perpendicular to the displacement.