The Spring Lab

diagam of Hooks Law Lab

From the spring lab, the experiment graphically and mathematically models the relationship of displacement and force.
The longer the spring is pulled, the more force is needed.

From the graph, the best fit line has a constant slope which indicates the equation of the graph is y= mx+b.
The slope is Force per displacement (N/m), also known as the spring constant (how stiff the spring is).
The intercept of the graph should be zero since when the spring is not stretched, it should not need any force.

We can rewrite the equation as Force (y variable) = k (slope/ spring constant) x Δx (displacement)
F=kx which is one of the Hooke's Law.
From Hooke's Law, we can derive the elastic potential energy equation.
Work equals force times displacement. The area covered by the line is 1/2 FΔx.
Eel= 1/2FΔx we can substitute F by kx since F=kx.
We can rewrite the equation as Eel= 1/2 k Δx^2