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 the category, and the empty coproduct is always an initial object in the category. Thus an empty, or nullary, biproduct is always a zero object. In the category of abelian groups, biproducts always exist and are given by the direct sum. Note that the zero object is the trivial group. Similarly, biproducts exist in the category of vector spaces over a field. The biproduct is again the direct sum, and the zero object is the trivial vector space. More generally, biproducts exist in the category of modules over a ring. On the other hand, biproducts do not exist in the