Spring coefficient

This section is a lot more theory than construction, which is good because if there was no theory in this basement we couldn’t call this science.

For our force measurement we are going to use springs as discussed earlier. I explained in “Lift and Drag Measurement Gauge” a little about linear springs. But here is a little refresher. Your common daily use springs are pretty closely defined as linear springs. This means that the force exerted by the spring varies linearly with the length stretched by the springs. This idea is captured by the equation F=-k*x. Force equals the negative of the spring coefficient, k, times the length stretched, x. There is a negative because if you pull it to the right, it pushes to the left. Not all springs are linear and even your common springs are not exactly linear, but it is close enough. As you dig into science, you will find that many of the things you learn are not exact but pretty close. Maybe that is more true for engineering than science.

Anyways, the spring coefficient is a constant of each spring. For our measurements we can measure “x”, so if we know “k”, we can really easily calculate the force “F”. This is our goal. But with our new springs the “k” is currently unknown. To find “k”, we need a known “x”, and “F”. This is easy, apply a known force and measure the distance.

Alright, what do we have available. For me, I don’t own any weights. I need to make a weight. What I, and hopefully anyone reading this, have readily available is water. The density of water is pretty much a constant at about 998kg/m^3. So we need a known volume to get a known mass. I filled up a 16oz bottle of water and poured the water into a zip lock bag, which we will assume has no mass. Eliciting the help of http://www.onlineconversion.com/volume.htm 16oz is 0.000 473 176 m^3. Great! Therefore, with density times volume we get the mass to be 0.472 kg. The force of gravity is mass times acceleration due to gravity, F=m*a. Therefore, the force on the spring due to our little bag of water is 9.8*0.472=4.62 Newtons, which is the right units to get the spring coefficient.

As a note, I use metric units whenever I can because it is much less confusing. But those of us in America (and perhaps elsewhere, I am not sure) often have to contend with both systems.

To the experimental table! Grab you springs, your bag of water, and your measuring stick. Its easy from here on out. Hold up the measuring stick, hold the top of the spring along side it, record the location of the bottom of the spring, hang the bag from the spring, record the new location of the bottom of the spring. Voilà! With that change in distance you can not easily calculate your spring coefficient.

Easy, fun, and a little bit of theory.

Sorry, no pictures with time, but now we have our springs and completely finished our measurement system for the lift and drag gauges.

On to the next…
Ben Washington.

1 thought on “Spring coefficient”

Comments are closed.