Abstract: A relativistic four-vector fundamental equation formalism is used to analyse processes that are carried out on a conveyor belt, in reference frames S (with the conveyor belt at rest, ground) and S ¯ (moving conveyor belt frame); these processes involve thermal effects. Examples solved are: a block thrown with initial speed on an inclined plane conveyor belt, and a ring launched with initial linear velocity on a moving belt. For each process, a four-vector fundamental equation is obtained, first in frame S, and then it is transformed by the Lorentz transformation to the process- four-vector fundamental equation in S ¯ . It is shown that Newton's second law and the first law of thermodynamics are no-independent equations. In this description, Newton's second law in frame S ¯ , in which forces are non simultaneously applied, includes terms related to linear momentum for heat (relativistic Doppler effect). The first law of thermodynamics in S ¯ includes the motor's performed work to keep the belt moving at a constant speed (conveyor belt effect). Classical descriptions of processes are obtained by taking the relativistic equations' low-speed limit, keeping the conveyor belt effect.

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