Finding conservation of energy through Newton's Law.

[D3xus]

Homework Statement

I'm devising a lab to find/prove the conservation of energy through one of Newton's laws. I can substitute variables when do the lab, but I need to design it first before I assign variables or data.

Homework Equations

K.E.(initial) + P.E(initial) = K.E.(final) + P.E.(final)
X = x(initial) – v(initial)t + ½*a*t^2
v = a/t

The Attempt at a Solution

I assumed that you could find the velocity (to be used in the conservation of energy formula) from the acceleration formula, and plug it into the Newton's law formula, but that didn't work out. I'm at a stalemate and need some help forward.
Thank you.

 

[haruspex]

To verify the conservation law as you've written it, you will need expressions to define the KE and PE (these are not defined by Newton's laws). I think you're also going to have to assume that g is constant (within the lab).
What went wrong with your attempt?

 

[D3xus]

For K.E and P.E I used 1/2 m*v^2 and mgh respectively.
With my attempt, I realized that because, in the system I was trying to work with (free fall), the initial velocity was zero, so I couldn't prove that the net forces in a system before and after were the same.
Is there a way to use some variable or aspect of the conservation of energy formula in a Newton's Law formula?

 

[haruspex]

Not sure what to advise on this. If you measure mass, height and time, and assume constant acceleration, you can use Newton's equations of motion to calculate the acceleration (a) and final velocity. You can then calculate the final KE, but it will inevitably equal mah. I.e., it doesn't matter what height and time you measure, you cannot get a result that contradicts conservation of energy. So it would not constitute a lab experiment which verifies conservation.
You could conduct tests with different heights, but that will only serve to confirm the acceleration is constant.