What is the formula for calculating work done by a force?

• A. W = F × d × cos(θ)
• B. W = F × d
• C. W = F ÷ d
• D. W = F + d

Answer: (A)

The formula for calculating work done by a force is expressed as W = F × d × cos(θ), where W represents the work done, F is the magnitude of the force applied, d is the distance over which the force is applied, and θ is the angle between the direction of the force and the direction of motion.

This formula effectively accounts for the directional component of the force. If the force is applied in the same direction as the displacement (θ = 0 degrees), the formula simplifies to W = F × d, indicating that all of the force contributes to the work done. Conversely, if the angle θ is larger, such as 90 degrees, the work done becomes zero since cos(90°) = 0, meaning no effective work is being performed in the direction of the displacement.

Correctly incorporating the angle ensures that the calculation of work reflects only the portion of the force that acts in the direction of motion. This understanding is crucial for accurately determining the work done in various physical situations.