Pls clarify my doubt.

Question

Why cos θ is used in work done formula? I saw on internet that they form a triangle and then apply trigonometry. But my question is that Force is not a length rather it is a physical quantity. Then how can we can we consider it a length and apply trigonometry there?

Answer 1

Force is a vector quantity. While deriving the formula W=F.S Cos(theta) we do not consider force as a length we take force as a component and the arrow denotes the direction of applied force. Using the dot product of vectors we derive the formula for workdone which is W=F.S Cos(theta)