What does the variable ‘e’ stand for in the equation for energy in an elastic potential energy store?
In the equation for energy in an elastic potential energy store, the variable 'e' represents the amount of elastic potential energy stored in the system. To explain how to find the equation, I can take you through the process step by step.
1. Start with the basic concept of elastic potential energy. Elastic potential energy is the energy stored in an object when it is compressed or stretched. This energy is proportional to the amount of deformation and can be calculated using Hooke's Law.
2. Hooke's Law states that the force required to compress or stretch an object is directly proportional to the displacement caused by this deformation. The equation for Hooke's Law is F = -kx, where F is the force, k is the spring constant, and x is the displacement.
3. Now, let's consider how energy is related to this force-displacement relationship. Energy is defined as the capacity to do work. In the case of elastic potential energy, work is done to compress or stretch the object against the force.
4. The work done (W) can be calculated as the force (F) multiplied by the displacement (x). So, W = F * x.
5. Substituting the Hooke's Law equation (F = -kx) into the work equation, we get W = -kx * x, which simplifies to W = -kx^2.
6. Finally, since the energy (E) in an elastic potential energy store is equal to the work done, we can express it as E = -kx^2. And that's the equation for energy in an elastic potential energy store.
In summary, the variable 'e' in the equation you mentioned is more commonly represented as 'E', which stands for energy. It is the amount of elastic potential energy stored in a system and is calculated using the equation E = -kx^2.