Mechanical energy swing because of the work done by the pendulum to oppose these non-conservative forces. That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that comprise matter. This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision,
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