In the context of gravitational potential energy, the potential energy of an object depends not only on its mass but also on its height or position in a gravitational field. The potential energy associated with an object's mass arises from its ability to do work due to its position relative to other objects.
When comparing two objects with the same kinetic energy but different masses, it's important to consider their heights or positions. If both objects are at the same height, then their potential energy would be the same since their positions are identical.
However, if the objects are at different heights, the object with more mass would generally have greater potential energy than the object with less mass, given the same amount of kinetic energy. This is because the potential energy depends on both the mass and the height of the object.
The formula for gravitational potential energy is:
Potential Energy = mass * gravitational acceleration * height
As the mass increases, assuming the heights are the same, the potential energy increases proportionally. This is because the gravitational potential energy is directly proportional to the mass of the object.
To summarize, if two objects have the same amount of kinetic energy but different masses, the object with more mass will have greater potential energy if their heights or positions are different.