After going over some homework problems and lecturing on work (Ch 13), the students did a lab on Hooke’s Law, which states that the force exerted by a spring is related to the distance it stretches :
F = -k x.
The negative sign is there because if you stretch a spring (positive x), it will pull back, wanting to return to its relaxed position, so the vector F is in the negative direction. The spring exerts a force on the mass hanging off it, but the mass exerts an equal and opposite force on the spring and we can measure that force, its just the weight of the masses and hangar. Luckily for us, those are labeled so we just have to read numbers off the masses as we pile them on. Each group picked a spring and measured how far it stretched (x) as they exerted a known force on it by hanging known masses on the end. By clipping a large bulldog clip on to the end of a meter stick, you can hang it off a ring stand as shown in the photo. I bought a cheap set of springs for this lab that have nice red indicators that the students used to measure the distance. Students made a table in their lab books to record the mass, m, in grams since thats what they are marked as, then a column for mass in kg, the Force exerted by the mass on the spring is just the F of gravity, F = mg, where g is 9.8 m/s2, exerted on the spring by the hanging mass, m, and the distance the spring stretched, x (meters).
When they were done taking the data, they made a graph of Force, F, versus distance, x. Most of them used their iPads to make the graph and do a linear fit of the slope, which gives them the spring constant, k. This graph is of the force exerted on the spring, hence the positive slope. To show the force exerted by the spring on the masses, it would be basically the same graph but the F values would be negative and the slope would be negative. We just wanted the slope of the graph so either graph would suffice.
They also preformed the experiment with a rubber band to see if it obeys Hooke’s law. The graph of F vs x for the rubber band was not nearly as linear as the spring data and some found that a quadratic fit the data better than a line.
We ran out of time in class but I sent the students an email link to a video by Destin from SmarterEveryDay on youtube, where he talks about rubber bands in relation to sling shots.
I came across this video from an article on wired.com, Do Rubber Bands Act like Springs? Rhett Allain, the author, basically does the same experiments we did, but he also had a force sensor that let him take data while the rubber band was moving. Go check it out!