When you extended or compress a spring, it exerts an opposite force to place it back to normal equilibrium state. The measure of force is the characteristic of the spring that’s symbolized by k being the constant value. Furthermore, Hooke’s law states that the relationship between force F and Extension x is characterized by F=−kx.
The equation has a (−) sign that signifies the force applied by the spring is directly opposite to the extension’s direction.
Additionally, there is a linear relationship between extension and force. In other words, if you draw a graph, you end up getting a straight line that passes through (x = 0; F = 0) being the origin. The slope is k, and it’s the spring constant.
How to Find Spring Constant from a Graph
- Start by Converting to Force
The best trick to find a Hooke’s law graph values is through suspending the spring from the hook then add a range of weighs with known measurements. However, measure the weights in either kilograms or grams. These are mass units, and you can easily convert them to force units.
You only have to find the product between the mass and the acceleration as a result of gravity. Also, you can draw a graph having a straight line, then k can be extrapolated from the line.
- Plot Two Points
When plotting a line. You must have at least two points. It’s a nice idea to make more points like four to work properly, promising you accurate results. They are also an assurance that what you are doing is correct. When the other points fail to fall on the original two points, you must go back to our calculation. Something could have gone wrong with the weights you are using or the spring itself.
However, to plot the points on the graph, start by suspending the spring vertically, then use a ruler to measure its extension. Fix a known mass to the far end of the spring, then measure and take measurements of the new extension. The result between the two is x. once done with that, do the calculation of the force exerted by the mass on the spring, and from there, you get your first point as (x1, F1).
Make sure your calculation is correct, then plot the different points through changing the weight then record the new extension. Once done with plotting the points, take a ruler then draw a straight line.
- Measure the Slope of the Force Extension Graph
Start by choosing two points to get the slope of the line, then come up with a ratio of the line movement between these two points. In case the original point that you selected is (x1, F1), while the other one is (x2, F2), then the slope of the line will be:
This is the value of the spring constant k. Now that you know how to find the spring constant, it’s easier to predict how the spring can compress or distend when subjected to any force.
David Nilsen is the former editor of Fourth & Sycamore. He is a member of the National Book Critics Circle. You can find more of his writing on his website at davidnilsenwriter.com and follow him on Twitter as @NilsenDavid.