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well the sum of potential and kinetic energy must equal zero because if a body is at rest initially it possess potential energy but when it gets into motion all those potential energy will be converted to kinetic energy, Basically kinetic energy is a result of potential energy.

Answer2:

The sum of potential energy and Kinetic energy is quaternion energy. kinetic energy is vector energy and potential energy is scalar energy. The sum of a scalar and a vector is a quaternion. William Rowan Hamilton discovered this in 1843. Currently Physics does not recognize kinetic energy as a vector.

The sum of gravitational potential and kinetic energy is E = -mMG/r + mcV where mcV is the kinetic/vector energy. This vector energy is the source of "dark energy". It is also the reason the Cosmos is in equilibrium (not contracting), in that it balances the gravitational force of attraction with mcDel.V, the centrifugal force of expansion. The centrifugal force is the divergence force from a vector, the kinetic energy mcV, a vector energy.

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