When all the forces acting on a system are conservative forces, E k+E p = constant, where E k is the kinetic energy and E p is the potential energy. This fact is known as the energy equation or the principle of conservation of energy.
From the equation of motion m a=F for a particle with mass m moving with acceleration a, it follows that m a. v=F. v and hence (d/dt)(½m v. v)=F. v. When F is a conservative force, the energy equation follows by integration with respect to t.
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date: 09 September 2024