Hi Ive recently carried out an experiment where different masses are hung from a string and then dropped from the same height. The other end of the string is wrapped around the axle of a flywheel and when the mass hits the ground, the time for ten revolutions of the flywheel is calculated to give angular velocity. The potential energy of each of the masses is calculated using mgh and a graph of Ep vs ω^{2} is then plotted with the gradient = 1/2I. Im a bit stuck as to how to explain the graph and explain why the graph doesnt go through 0,0. My thoughts are that as the potential energy of the masses is increased, the kinetic energy of the flywheel also increases, as the angular velocity increases. I think the graph doesnt go through 0,0 to show that the flywheel still has some potential energy in the system when the kinetic energy is 0. Am i correct? Sorry for writing loads :)
Welcome to PF. Ep is the potential energy of the mass and it is on the Y-axis, right? And the graph is crossing above 0 on the Y-axis? Then you are getting an output energy that is below your input energy. This would be because the weight hits the ground with kinetic energy: you aren't converting all of the potential energy to rotational energy in the flywheel.
Thats correct. So does that mean that because the mass still has kinetic energy when it hits the floor, some is converted into sound etc and not all into rotational energy of the flywheel?
It's simpler than that. The change in potential energy of the falling mass increases both the kinetic energy of the flywheel and the falling mass. (They are connected by a string.) The energy used to increase the KE of the falling mass is energy not available to increase the KE of the flywheel. Doesn't matter what happens when the falling mass hits the ground. See if you can derive the equation connecting the Δh of the falling mass with the resultant ω^{2}.
Another thing to do would be to alter the experiment. Replace your current axle with a conically shaped axle, that will release the weights at ~zero velocity immediately before they touch the ground. This eliminates the dropping mass kinetic energy variable. I'm sure there's a mathematical model for this, but my math skills are pretty much gone.