4. Elastic Potential Energy & F = ke Equations

Formula: F = ke
F (Force): Measured in Newtons (N). This is the force applied to the object.
k (Spring Constant): Measured in Newtons per meter (N/m). This value represents how stiff or elastic an object is.
- Low spring constant: The object is more elastic and easier to stretch.
- High spring constant: The object is stiffer and harder to stretch.
e (Extension): Measured in meters (m). This is the change in length, not the total length.

Formula: Ee = 1/2 k e^2
Definition: The energy transferred to an object as it is stretched.
Energy Transfer: If you use energy to stretch a spring, that energy is stored in the elastic potential energy store. When released, it typically transfers back into kinetic energy.
Calculation Note: Only the extension (e) is squared in this equation, not the entire expression.

Extension is calculated by subtracting the natural (original) length from the new stretched length.
Example: If a spring stretches from 0.6m to 0.8m, the extension (e) is 0.2m.

To find the spring constant (k) when you know the force and extension, rearrange the formula to: k = F / e.
Example Calculation: Using a force of 14N and an extension of 0.2m:
- 14 / 0.2 = 70 N/m.

Gradient: On a graph of force against extension, the gradient of the straight-line section represents the spring constant (k).
Area Under the Curve: The area beneath the line represents the energy transferred to the spring (the elastic potential energy).

Elastic Limit: This is the point on the graph where the line stops being straight and begins to curve.
Hooke's Law: Beyond this point, the object no longer obeys Hooke’s law and will not return to its original shape.