Work

Definition

Work is said to be done when a force causes a displacement.

Mathematically:

$$ W = \vec{F} \cdot \vec{d} $$

Expanded Form

$$ W = Fd \cos\theta $$

Where:

• $F$ = magnitude of force
• $d$ = displacement
• $\theta$ = angle between force and displacement

Physical Interpretation

• If force is in direction of motion $\rightarrow$ positive work
• If opposite $\rightarrow$ negative work
• If perpendicular $\rightarrow$ zero work