Your "Elastic Potential Energy Calculator" is a tool designed to calculate the elastic potential energy stored in a spring when it is either stretched or compressed. The formula for calculating elastic potential energy(E_elastic) is derived from Hooke’s Law and is given by:
E_elastic = 12kx^2
Where:
- E_elastic is the elastic potential energy in joules (J),
- k is the spring constant (also called spring force constant) in newtons per meter (N/m),
- x is the displacement of the spring from its equilibrium position (stretch or compression) in meters (m).
Inputs:
1. Spring Force Constant(k): This value, also called the spring constant, represents the stiffness of the spring. The larger the value of k, the stiffer the spring is, meaning it will resist deformation more strongly when stretched or compressed.
- Unit: Newtons per meter (N/m)
2. Spring Stretch Length(x): This is the displacement of the spring from its rest position, whether the spring is stretched or compressed. If a spring is compressed, x will be negative, and if stretched, x will be positive.
- Unit: Meters (m)
How it Works:
When the spring is either stretched or compressed, energy is stored in the spring in the form of elastic potential energy. The amount of energy stored depends on how much the spring is deformed (i.e., how far it is stretched or compressed) and the spring's stiffness.
- If you provide a larger spring constant k, it will require more force to stretch or compress the spring by the same amount, and as a result, the elastic potential energy will be higher.
- If you increase the displacement x, the stored energy increases exponentially because the formula involves x^2, meaning that even small increases in the displacement result in a large increase in potential energy.
Example Calculation:
For example, if you have a spring with a spring constant k = 150 N/m and it is stretched by x = 0.2 m, the elastic potential energy stored in the spring would be:
E_elastic = (1/2) x 150 x (0.2)^2
E_elastic = (1/2) x 150 x 0.04 = 3 J
So, the elastic potential energy in the spring would be 3 joules.
Your Elastic Potential Energy Calculator takes the spring constant and displacement as inputs and applies the formula E_elastic = 12 k x^2 to determine the energy stored in the spring. This tool can be used to understand how much potential energy is stored based on the spring's stiffness and how far it is stretched or compressed.
