Energy produced by a swing? Please can someone help me with a equation for how much energy a person generates when swinging on a swing?
 A: To calculate the maximum energy of the swinger one could use either the gravitational potential energy at the swinger's highest position, $GPE=mg(h_{max}-h_{min})$, or the kinetic energy, $KE=mv^{2}/2$, at the lowest of the swinger's positions; where the speed (and therefore KE) would be greatest. Experimentally, this would involve measuring either the change in verticle height or the speed attained at the low-point, respectively.
The energy in the system is converted from one form to the other for every quarter-wavelength, e.g. high behind swing position to bottom of swing position. Equating the kinetic energy at the minimum height with the change in gravitational potential energy from the maximum height one obtains: 
$mv^{2}/2=mg(h_{max}-h_{min})$.
This shows that the the maximum speed one can obtain is in fact indepenent of the mass of the person (it appears on both sides of the equation so it cancels out.)
Solving for $v$ we get: $v=\sqrt{2g(h_{max}-h_{min})}$.
For a normal garden-variety swing, the change in vertical height would be about $1m$. This would give a maximum speed of $v=\sqrt{2g(1)}=4.4ms^{-1}$. Where I used $g=9.81ms^{-2}$.
Bare in mind that this approach does not account for wind resistance which, IMO, would be pretty much negligable at these speeds anyway.
