Elastic and gravitational energy "mismatch"

[Paul King]

The elastic potential energy stored in a stretched spring ( or a bent bar )
at equilibrium is always half of the gravitational potential energy lost by
the mass whose moving down has caused the spring to stretch. The "missing"
energy goes into heating the spring, or (as Francis has said ) into heating
something else if the falling mass has been lowered with the help of a force
other than gravity.

This apparent mismatch between the lost GPE and the EPE gained by the spring
should be made obvious to the students, probably by way of calculations
followed by the question " How do we explain this?" An  answer of " The
spring gains heat  energy as well as elastic energy " will probably be
enough at this stage - everyone should be familiar enough with repeatedly
bending a paperclip till it snaps and knowing how warm it gets, to feel
cheerful about a stretched spring warming up.

Paul King