What is the formula for work done on an object?

• A. W = Fd sin(θ)
• B. W = Fd
• C. W = Fd cos(θ)
• D. W = mgh

Answer: (C)

The formula for work done on an object, when a force is applied at an angle, is indeed given by the expression that involves the cosine of the angle. This is because work is defined as the product of the force applied on an object and the distance over which that force is applied, adjusted for the direction of that force relative to the direction of motion.

The correct formula, W = Fd cos(θ), reflects how much of the applied force actually contributes to the movement of the object in the direction of the displacement. In this context, θ is the angle between the force vector and the direction of motion. When the angle is zero degrees (meaning the force is applied in the same direction as the displacement), the equation simplifies to W = Fd, indicating that all of the force contributes to the work done. Conversely, if the angle is 90 degrees, no work is done because the cos(90°) equals zero, meaning the force does not aid in moving the object in the direction of displacement.

Other formulas listed do not account for the angle of the applied force in relation to the movement, such as the simple multiplication of force and distance, or work done against gravity (mgh), which is a specific case of work