Answer Total Work Question: Understand Why Total Work is Zero with ΔPE

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The discussion centers on the equation for total work, specifically questioning why the total work equals zero when considering changes in potential energy (ΔPE). The key point is that the sum of work done by the spring (Wspring) and gravity (Wgravity) cancels out, resulting in zero total work. This occurs because gravitational potential energy (GPE) is effectively counted twice in the calculations. The confusion arises from misunderstanding how energy contributions from different forces interact within the system. Ultimately, the total work is zero due to the conservation of energy principles at play.
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Below is the question:

upload_2014-11-16_17-4-49.png


My equation for Work Total is:

Delta PE = Wspring + Wgravity

However, the solution key says that the Wspring + Wgravity = 0

I fail to understand this, why is the total work zero when there is a change in potential energy?
 

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[edit: better way to say it]
If you come up with both gravitational PE and another total PE, you end up with more energy than the spring put into the system. You're counting the GPE twice.
 

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