How do you calculate the work done by a force?

To find the work done by a force, the formula involves the component of the force acting in the direction of the displacement. Specifically, work is calculated as the product of the force, the distance moved in the direction of that force, and the cosine of the angle between the force and the direction of motion.

Option C states that work (W) equals force (F) multiplied by distance (d) multiplied by the cosine of the angle (θ) between the force and the direction of motion. This is the correct approach because it effectively takes into account that not all the applied force contributes to the work if it is not acting directly along the direction of motion. The cosine factor adjusts the magnitude of the force to find just the effective component working in the direction of the movement.

In contrast, other options do not reflect the correct relationship essential for calculating work. For instance, the first option erroneously adds force and distance instead of multiplying them and considering the direction. The second option involves the sine function, which would apply if you were calculating the work done in a direction perpendicular to the force, but that is not the case here. The last choice mentions mass and gravity, which pertains to gravitational potential energy rather than the work done by a force over