who discovered the law of conservation of matter
Conservation of mass The principle of conservation of mass was first outlined by Mikhail Lomonosov (1711–1765) in 1748. He proved it by experiments—though this is sometimes challenged.[9] Antoine Lavoisier (1743–1794) had expressed these ideas in 1774. Others whose ideas pre-dated the work of Lavoisier include Joseph Black (1728–1799), Henry Cavendish (1731–1810), and Jean Rey (1583–1645).[10]
Conservation of energy Émilie du Châtelet (1706 – 1749) proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem 's Gravesande in 1722 in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy - as indicated by the quantity of material displaced - was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height the balls were dropped from, equal to the initial potential energy. Earlier workers, including Newton and Voltaire, had all believed that "energy" (so far as they understood the concept at all) was not distinct from momentum and therefore proportional to velocity. According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped from. In classical physics the correct formula is   E k  =  1 2  m v 2   {\displaystyle E_{k}={\frac {1}{2}}mv^{2}} , where   E k   {\displaystyle E_{k}}  is the kinetic energy of an object,   m  {\displaystyle m}  its mass and   v  {\displaystyle v}  its speed. On this basis, Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to relate it in different forms (kinetic, potential, heat…).[9][10]