So a little background before stating the problem:
During a lecture a couple weeks prior to lab, the instructor did an example where we were told to find the max height of a ball launched upwards by compressing a spring. In order to calculate that, he showed that E1 is the position of ball before the launch off a spring, E2 is at Xo or at equilibrium and E3 is at max height. Then he stated that all these energies are equal to one another--so E1=E2, E2=E3, thus E1=E3.
A couple weeks later for a lab, we had to show that the mechanical energy of a ball (.0096kg) shot straight up is conserved.
From relative graphs and for trial 1, I found the height of the ball and the velocity at the same time--.978m and -1.169m/s respectively--and I calculated the total mechanical energy to be 9.86 x 10^-2 J (KE=6.56 x 10^-3 J and Ugrav=9.20 x 10^-2 J).
Based on my notes just before this lab, our instructor told us that the total mechanical energy (KE + Ugrav) should be equal to the energy in the spring before the ball was launched.
But I'm confused, why shouldn't the Uspring just equal the potential energy or just the kinetic energy as he showed in lecture?
Total Energy=KE + Ugrav
Uspring = Total energy = KE + Ugrav
The Attempt at a Solution
I think while typing out the problem I may have come to an answer and just need confirmation.
The reason why Upsring = KE + Ugrav from the lab versus the lecture is because in the lab we did not use the KE at equilibrium (Ugrav = 0) and the Ugrav at the max. height (KE = 0). If that was the case then the scenario from the lecture would apply for the lab. Is this correct?