Exploring Energy of a Vertical Spring System

AI Thread Summary
In a vertical spring system with a mass, energy dynamics change based on the reference point chosen for zero potential energy. When the zero point is set at the unstretched spring, the energy equation reflects negative gravitational potential and positive elastic potential as the mass passes through the equilibrium point. Conversely, if the zero point is moved to the new equilibrium, both gravitational and spring potential energy are present at the top, leading to a different energy equation. This discrepancy arises because the reference point affects the calculation of elastic restoring force. Understanding these variations is crucial for accurately analyzing the energy of the system.
nothing123
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Hi,

If we have a vertical spring with a mass attached to it, how does the energy of the system work. Let's say we set the zero point as the point where the spring is unstretched (basically with no mass attached). Then at the top we have zero kinetic, zero spring potential as well as zero gravitational potential. As it passes through its new equilibrium point, it will have negative gravitational and positive elastic potential and kinetic energy so 1/2kx^2 + 1/2mv^2 - mgh which rearranged is mgh - 1/2kx^2 = 1/2mv^2. Now let's say we take the zero point to be where the new equilibrium point is. At the top, we have gravitational potential as well as spring potential. As it passes through the equilibrium point, it would only have kinetic. By conservation of energy, mgh + 1/2kx^2 = 1/2mv^2. Why are the two equations different if we change the reference point?

Thanks.
 
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Hi nothing123! :smile:
nothing123 said:
… Now let's say we take the zero point to be where the new equilibrium point is …

Your equations are completely confusing me (especially since h is related to x). :confused:

But if by "zero point", you mean for calculating the elastic restoring force, it has to be the "old" equilibrium point … that's how springs work! :smile:

(unless, I suppose, you take g out of the equation completely :rolleyes:)
 
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