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Very interesting approach!

When Paul presses a spring then work done by Paul is positive and work performed by spring is negative.

As per scalar product we have to use cos@

If @ is acute then cos @ is +ve and if @ is obtuse then it becomes -ve

As force applied and displacement are in the same direction as in the case of Paul's attempt then work becomes positive

But in case of spring's opposing force the displacement is in opposite direction and so work is negative

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Q: How can you have both positive and negative work at the same time?
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