When a force that is perpendicular acts on an object, what can be implied regarding the work done?

When a force that is perpendicular to the direction of motion acts on an object, it can be concluded that no work is done on the object. In physics, work is defined as the product of the force applied to an object and the displacement of that object in the direction of the force. This relationship can be expressed mathematically as ( W = F \cdot d \cdot \cos(\theta) ), where ( W ) is the work done, ( F ) is the force, ( d ) is the displacement, and ( \theta ) is the angle between the force and the displacement vector.

When the force is perpendicular to the displacement, the angle ( \theta ) is 90 degrees, and the cosine of 90 degrees is zero. Therefore, the work done, in this case, becomes ( W = F \cdot d \cdot \cos(90^\circ) = 0 ). This means that despite the force being applied, since it does not contribute to the displacement in its direction, no work is accomplished on the object.

This is why the implication of zero work is crucial when analyzing scenarios involving forces acting perpendicular to the direction of motion, illustrating a fundamental concept in