What is the formula for the increase in potential energy (U) of a mass m after moving distance d?

The correct answer for the increase in potential energy (U) when a mass (m) moves a distance (d) against the force of gravity is expressed through the relationship U = mgh. Here, h represents the height the mass has been raised, which is directly connected to the distance d when lifting vertically.

In this formula, potential energy is derived from the gravitational force acting on the mass. The force of gravity (F) acting on a mass is given by the product of its mass (m) and the acceleration due to gravity (g). Therefore, when you move the mass vertically over a distance corresponding to height (h), the increase in potential energy can be formulated as U = mgh.

Choosing the formula U = mgd does not directly represent the change in potential energy in a gravitational field because it implies a relationship that is not dimensionally consistent as potential energy—it lacks the correct reference to height. The formula U = Fd, while related to work done (where F is the force and d is distance), is not specific to gravitational potential energy and can be applicable for other forms of work. Lastly, U = 0.5mv^2 pertains to kinetic energy, indicating the energy of an object in motion, and