The potential energy can be exactly defined as the work required to place an object into a certain position - which is the integral of the dot product of force and displacement. In the case of gravitational potential energy, and for small differences in altitude (so that gravity doesn't change too much), that simplifies to mgh (mass x gravity x height).
The potential energy voltage equation used to calculate the electrical potential energy stored in a system is given by the formula: Potential Energy Charge x Voltage.
To calculate the elastic potential energy of an object, you can use the formula: Elastic Potential Energy 0.5 k x2, where k is the spring constant and x is the displacement of the object from its equilibrium position.
The mechanical energy of an object is the sum of its kinetic energy (energy due to its motion) and potential energy (energy due to its position or condition). The formula to calculate mechanical energy is ME = KE + PE, where ME is the mechanical energy, KE is the kinetic energy, and PE is the potential energy. You can calculate the kinetic energy using the formula KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity. The potential energy can depend on various factors, such as gravitational potential energy or elastic potential energy.
The rotational potential energy formula is E 1/2 I 2, where E is the rotational potential energy, I is the moment of inertia of the object, and is the angular velocity of the object. This formula is used to calculate the energy stored in a rotating object by taking into account the object's moment of inertia and how fast it is rotating.
The formula to calculate gravitational potential energy is: GPE = mgh, where GPE is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the height above the reference point.