In which of the following does work done depend on the angle between the force direction and the displacement direction?

The relationship between work done and the angle between the force direction and the displacement direction is essential in understanding how work is calculated in physics. Work is defined mathematically as the product of the force applied and the displacement in the direction of that force, multiplied by the cosine of the angle between the force and the displacement vectors. This is expressed in the formula:

[ W = Fd \cos(\theta) ]

where ( W ) is the work done, ( F ) is the magnitude of the force, ( d ) is the displacement, and ( \theta ) is the angle between the force and the displacement.

In the case of a constant force, the work done will be directly influenced by that angle, as the formula applies universally when a force is constant and acts over a displacement. If the angle is 0 degrees (forces in the same direction), all the work done is positive. If the angle is 90 degrees (force perpendicular to the displacement), no work is done. Similarly, for angles greater than 90 degrees, the work can be negative, indicating that the force opposes the displacement.

When considering gravitational force, centripetal force, and frictional force, while they can involve displacement, their