Does anyone know the spring force constant of Vex rubber bands (size 32)?
Rubber bands are far from ideal springs.
You should characterize them yourself:
Get an inexpensive spring scale and track the force applied by the rubber band at various different stretch distances. Repeat many times to get a good sample size. Then compute a regression on the data.
That would be a good learning experience and shouldn’t take more than an hour or two once you get the hang of the process.
You can also try using a plastic milk jug or other lightweight container and pour X amount of water into it and observe Y amount of stretch. 1 cc of water weighs 1 gram. Or you can measure in ounces and make the conversion. You should try not only a fair number of different rubber bands, you should also test one rubber band multiple times to observe how the rubber bands change their effective spring constants after a certain number of stretches. Some rubber bands will change by 20% or more after a single stretch.
These are definitely worthwhile considerations too.
I calculated the spring constant of a size 64 band to be right around 60 by hanging some steel C channels from it, but like everyone’s been saying, it’s non linear. Anyhow, a size 32 band should have about half of that, so it should be ballpark of 30 for large displacements. I would assume it’d be smaller for smaller displacements but I have no idea what the function would look like. Good luck!
Thanks for all the advice, everyone! I’ve done some measurements where I took a spring scale and stretched a rubber band a certain distance (20 cm) and recorded the force that was measured on the spring scale. However, when I use Hooke’s law (k=-F/x), I end up with negative numbers for k. Is this normal or am I doing something wrong?
That’s because you’re mixing up your directions. The negative is there for the vector to indicate direction. If you draw a free-body diagram, you’ll have the elastic force aimed up and gravity aimed down. Let’s call upward positive y, with y=0 where the elastic’s bottom end is before stretching. (The starting period on each line is there because the auto-formatting was messing up my negative signs. Ignore those periods.)
. Fnet,y = Fe - Fg = 0
. Fe = Fg
. - k y = m g
. - k (-0.2 m) = (mass used in kg) (9.8 m/s^2)
. k= 49 * (mass in kg), with final units in N/m
Note the lack of a negative in k at the end.