Mechanical energy nonconservative forces, like frictional forces, will be present, but often they are of negligible values and the mechanical energy's being constant can therefore be a useful approximation. In elastic collisions, the mechanical energy is conserved but in inelastic collisions, some mechanical energy is converted into heat. The equivalence between lost mechanical energy (dissipation) and an increase in temperature was discovered by James Prescott Joule. Many devices are used to convert mechanical energy to or from other forms of energy, e.g. an electric motor converts electrical energy to mechanical energy, an electric generator converts mechanical energy into electrical energy and a
Biproduct If the product formula_9 and coproduct formula_10 both exist for some pair of objects "A", then there is a unique morphism formula_11 such that It follows that the biproduct formula_15 exists if and only if "f" is an isomorphism. If C is a preadditive category, then every finite product is a biproduct, and every finite coproduct is a biproduct. For example, if formula_9 exists, then there are unique morphisms formula_17 such that To see that formula_9 is now also a coproduct, and hence a biproduct, suppose we have morphisms formula_22 for some object formula_23. Define formula_24 Then formula_25 is a