True or False: The change in the potential energy of a particle when it moves from an initial position to a final position is equal to the work done by the force during the motion.
In order to answer this question, we will recall two key definitions. Firstly, the gravitational potential energy 𝐸 sub 𝐺 of an object with a mass 𝑚 that is a height ℎ above the ground is given by 𝐸 of 𝐺 is equal to 𝑚𝑔ℎ, where 𝑔 is the local acceleration due to gravity with a value of approximately 9.8 meters per second squared.
Secondly, for a conservative force, the change in the potential energy of an object Δ𝐸 sub 𝑃 is equal to the negative of the work done 𝑊 by the force on the object. Δ𝐸 sub 𝑃 is equal to negative 𝑊. Since the statement said that the change in potential energy was equal to the work done and not the negative of this, we can conclude that the statement is false.