Rubber Band Launch
By Austin Lohr
I will be using the above rubber band and tennis ball to find the energy transfer when the rubber band launches the tennis ball, including the energy lost to heat within the rubber band. I will also be solving for the forces on the tennis ball, including drag. But to do this, I first need to calculate the spring constant of the rubber band.
To calculate the spring coefficient I hung the rubber band from a hook on the ceiling and used a force sensor to measure it at 1.5 meters. It looked something like this:
So now I plugged those numbers into the Hooke's Law equation which states that F=-kx and find that the spring constant of this rubber band is 142.6875N/m. For those of you who like math you can check out all my calculations for the capstone here. With this, I can now move on to launching a tennis ball from the rubber band.
What I expect to happen is shown in the LoL diagram above. The energy will start as elastic potential in the rubber band and transfer to the tennis ball in kinetic and gravitational energy. Some energy will be lost to heat since the rubber band heats up when stretched, and that is what I am trying to figure out: the energy lost to heat in this process.
There was it being filmed and here is the Logger Pro analysis (I colored in the dots to make it more visible):
With this data I calculated the kinetic energy and gravitational energy of the tennis ball right after launch. The kinetic energy is Ek=1/2(m)(v)^2 which came out to be 1.399J. The gravitational was Eg=mgh which ended up being 0.927J. Finally, I used the spring constant to calculate the force the rubber band would exert on the tennis ball and to do that I did El=1/2(k)(x)^2 and that was 7.443J. To find the energy lost, simply do -Q=Eg+Ek-El and you get 5.117J. This is a huge amount and way more than I expected. Obviously something went wrong and energy was lost somewhere else, I think it was that the rubber band couldn't adequately transfer all of the energy into the tennis ball due to the tennis ball not being held in place when it launched, so it fell as the rubber band contracted and thus didn't leave the rubber band with the full force behind it.
The next thing I did was calculate the forces on the tennis ball as it left the rubber band.
First was the force of the rubber band on the ball Frb=kx which was 46.088N. Then the force of gravity was Fg=ma which was -.49N. Finally I calculated the drag on the tennis ball and I used the drag equation Fd=1/2φ(v^2)Cd(A) which equaled .06128N which makes sense because it is a small sphere.
If I were to do this again, I would find a better launching technique so 100% of the rubber band's force is transferred to the tennis ball. I would also like to look at the elastic extreme of the rubber band, as in how far you could stretch it before it no longer adds elastic force.