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## 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?

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