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The headache ball conundrum Professor Sir Alan Harris asked us in November to look at a paradox and examine our use of strain energy methods in structural analysis. His question concerned where the increase in potential energy comes from when a system consisting of a weight suspended by chain from an immovable support undergoes a reduction in temperature which raises the weight and reduces the thermal energy stored in the system. The response of our readers has been generous and varied. The first letter was from Mr L. Wadsworth of Worcester: I think that the answer is to be found by examining more closely the specification that the support for the suspension chain must be ‘immovable’. Nothing is immovable. If a practical, buildable system is considered it is immediately obvious that the change in temperature will affect the supports as well as the chain and ball. The legs of the supports will be longer than the chain (they must be to keep the ball off the ground!) and so they will shorten more than the chain. Thus, although the ball moves up relative to the suspension point, it will have a net downward movement relative to the ground, thereby preserving the theory of the conservation of energy. Verulam