POTENTIAL ENERGY
Potential energy in a system is due to its position in a force field or could also be due to its configuration. Potential energy exists when a force acts upon an object that tends to restore it to a lower initial energy configuration. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back down. Since the action of lifting a mass or stretching a spring will always require energy to perform, the energy used to stretch the spring or lift up the mass is stored in the metal or in its position in the gravitational field correspondingly. One should always remember the law of conservation of energy which says “Energy cannot be created or destroyed". Thus, this energy cannot disappear. Instead, it is stored as potential energy.
GRAVITATIONAL POTENTIAL ENERGY
Gravitational potential energy is stored energy that results from vertical position or height from a reference coordinate system, as well as the gravitational attraction of the Earth for the object. Potential energy is a function of mass and height assuming a constant gravity pull as one can see from the formula below:
PE = mgΔh
It is important to understand that potential energy is completely independent of the path. What this means is that if there is a hiker that takes path 1 which is five times longer than path 2 but they both lead to the summit of the mountain, he will have the same potential energy at the summit no matter which path he takes.
ELASTIC POTENTIAL ENERGY
Elastic potential energy is the energy stored in elastic materials as the result of displacement from an unstretched position (stretch or compression). The amount of elastic potential energy stored in a spring is directly related to its elasticity. In simple words, the more one can stretch a spring, the more stored energy that the spring will have. The opposing force that a spring has when is subjected by any compressive or extensive force can be modeled using Hooke’s law:
Fspring = k⋅x
where x is the distance that the spring was displaced from its original position and k is the spring constant.
A spring is said to be in equilibrium if it is not stretched or compressed. Thus, there is no potential energy stored in a spring that is in equilibrium. If one integrates the previous equation with respect to x, one gets the formula for potential energy of a spring.
A spring is said to be in equilibrium if it is not stretched or compressed. Thus, there is no potential energy stored in a spring that is in equilibrium. If one integrates the previous equation with respect to x, one gets the formula for potential energy of a spring.
PEspring = ∫k⋅xdx = (1)/(2)kx2
SUMMARY POINTS
⋅ Potential energy is the energy that is stored in an object due to its position relative to some zero position.
⋅ An object possesses gravitational potential energy if it is positioned at a height above or below the zero height.
⋅ An object possesses elastic potential energy if it is at a position on an elastic medium other than the equilibrium position.
⋅ An object possesses gravitational potential energy if it is positioned at a height above or below the zero height.
⋅ An object possesses elastic potential energy if it is at a position on an elastic medium other than the equilibrium position.