02-Oct-2014 Conservation of Energy Mass/Spring Lab

The purpose of this lab was to prove that energy of a system is conserved by demonstrating that the total energy is constant over time.

To do so we used the motion detectors hoked up to LoggerPro. We hung a mass on a long spring, mounted to a tall metal stand, and released it in order to record the motion of the oscillating system, from unstretched to fully stretched. The motion detector gave us position and velocity values which we then used to find our different values for energy.

M = hanging mass

m = mass of spring

v = velocity of hanging mass
h = height from floor to top of spring
y = distance from floor to bottom of hanging mass
k = spring constant

Gravitational Potential Energy = Kinetic Energy + Elastic Potential Energy

GPE = KE + EPE
GPE(hanging mass) = Mgy

GPE(spring) = mg[h-(h-y)/2] = .5mgh + .5mgy = constant + .5mgy
GPE(total) = GPE(hanging mass plus spring mass) = (M + .5m)gy

Similarly we derived an expression for kinetic energy

KE(total) = .5(M + m/3)v^2

EPE(spring) = .5k*stretch^2 = .5k*[(initial height of hanging mass)-(y)]^2

Once measuring the necessary values for mass and lengths then collecting enough data points on LoggerPro we could create new data tables using the equations from above. Below you can see we plotted the tables of KEtotal, GPEtotal, EPE, and the sum of the energies vs. time.

At the very top of the graph there is a light green line that is as close to horizontal as we could get it to be and what that proves for us is that energy of a system is conserved.