Question: Why is the GPC (Gravitational Potential Energy) equal to the KE (Kinetic Energy)?

Piers Barnes answered on 13 Jan 2017:

The gravitational potential energy of an object is not generally considered to equal the objects kinetic energy.

However there are often cases where a given amount of gravitational energy is converted to the same quantity of kinetic energy or the opposite case where kinetic energy is converted to gravitational energy. A simple example would be dropping an object from a the top of a tower (in a vacuum!). At the top, the object has gravitational potential energy. Just before it hits the ground all of its gravitational potential energy will have been converted to kinetic energy because the force of gravity accelerates the object, increasing its velocity from zero. As the object falls there is progressively less far for it to go so there is less gravitational potential the further it drops, it simultaneously speeds up as it drops because gravity has been acting on it for longer the further it goes. Eventually all the gravitation potential is converted to kinetic by the moment it hits the ground. Once it hits the ground the much of the kinetic energy is then converted into other forms of energy. In this example the amount of gravitational potential was defined by how far the object could drop before hitting the ground, the amount of kinetic energy it gains can’t be more than that unless you threw it.