Good day. A teacher of mine has stated that the sum of initial kinetic energy, i

Question

Good day.

A teacher of mine has stated that the sum of initial kinetic energy, initial gravitational potential energy and the work done to the system equal the sum of final kinetic energy and final gravitational potential energy, denoted by the following formula:

Where T denotes te Kinetic Energy, V denotes the Potential Energy and U the work done to the system.

What I wonder is if this is... true. It seems to me like it violates the law of conservation of energy.

Greetings and thanks for your answers.

Explanation / Answer

yes this equation is correct. In simple terms conservation says that energy in must equal energy out. In this equation you have initial kinetic and potential energies and you are adding energy in the form of work. In order to be conserved the energy provided for the work must be accounted for in the end result. This equation could be used for a cart moving at a specific velocity up a hill and it is being pushed by a motor keeping it at the same velocity. In this case your potential energy has increased but your kinetic has not. the only way for the equation to be in balance is by adding work to the left side. Hope that helps.

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