Question

What is total mechanical energy? Show
that total mechanical energy is conserved in a
conservative force field.
​

Answer 1

Answer:

The principle of the conservation of mechanical energy states that the total mechanical energy in a system (i.e., the sum of the potential plus kinetic energies) remains constant as long as the only forces acting are conservative forces.

Answer 2

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The total mechanical energy (E) of a particle, or a system, is the sum of the kinetic and potential energies of the particle or the system at any moment.

E = KE + PE

By the work-energy theorem, the work done by a conservative force W=ΔKE.

Also, the change in potential energy associated with a conservative force is the negative of the work done by that force.

W=-ΔPE = ΔKE

..ΔKE + ΔPE = 0

.. (KE2, - KE1,) + (PE2, -PE1,) = 0

where the subscripts denote some initial time 1 and any later time 2.

..KE2 + PE2 = KE1 + PE1

..E2= E1 = constant

That is, the total mechanical energy of a particle system is conserved in the absence of dissipative forces

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