Here's why:
* Work is defined as the product of the force applied and the displacement in the direction of the force.
* Mathematically: Work (W) = Force (F) * Displacement (d) * cos(θ) where θ is the angle between the force and displacement vectors.
* When the angle is 90 degrees (perpendicular), cos(90°) = 0.
* Therefore, the work done becomes zero.
Example:
Imagine pushing a box horizontally across a floor. The force you apply is horizontal, but the box moves vertically due to gravity. Since the force and displacement are perpendicular, no work is done by your horizontal push on the box's vertical movement.
Important Note: While no work is done by the force directly causing the perpendicular displacement, other forces might still be doing work. For example, in the box example, gravity is doing work on the box as it moves vertically.
