If a constant force doubles while the distance remains the same, what happens to the work done?

• A. Remains the same
• B. Halves
• C. Doubles plus a constant
• D. Doubles

Answer: (D)

Work is the energy transferred when a force acts over a distance in the direction of the force. It’s given by W = F d cos(theta). If the distance stays the same and you double the force, as long as the force is still in the same direction as the displacement (theta = 0, so cos(theta) = 1), the work becomes W' = (2F) d = 2(F d) = 2W. In other words, doubling the force over the same distance doubles the amount of work done.

If the force were not aligned with the motion (for example, opposite direction), the angle would change cos(theta), affecting the result (the work could be reduced or become negative), but with the same direction as the displacement, doubling the force doubles the work.