Confused...calculating energy in a spring before launch of a ball

[Fatima Iqbal]

Homework Statement

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?

Homework Equations

KE=1/2mv^2
Ugrav=mgh
Uspring=1/2kx^2
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?

 

[haruspex]

I'm not sure what you are saying in that last paragraph. In the three states discussed in the lecture:
Before release of the spring, all the energy was as PE of the spring. (This assumes we are taking the altitude of the ball at this point as our zero height reference.)
At equilibrium, the spring has no PE left, but the ball has gained both GPE and KE. Ignoring losses, the sum of these would equal the original energy.
At max height, all the energy is in GPE of the ball.

 

[Fatima Iqbal]

Ohhhh ok. I think I was combining two examples from my notes so I got confused at what types of energy would be at equilibrium. This whole time I have been incorrectly thinking that at equilibrium, when the obj is moving at max speed (regardless if it is launched horizontally or vertically), there's only kinetic energy and that was probably due to me misinterpreting what my instructor said in class. I see what you mean when you say that the total energy of the spring before the launch should equal to the GPE and KE. Thanks!