Fast quick Energy Conservation Question

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Energy conservation applies specifically to conservative forces, where mechanical energy (kinetic plus potential) is conserved. In contrast, when non-conservative forces, such as friction, are present, mechanical energy is not conserved as it transforms into other energy forms like heat and sound. Despite this, total energy remains conserved in all scenarios. Therefore, while mechanical energy can be lost due to non-conservative forces, the overall energy in a closed system is always preserved. Understanding these distinctions is crucial for analyzing energy transformations in physical systems.
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For energy conservation does it apply to both conservative and non conservative forces?
 
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godkills said:
For energy conservation does it apply to both conservative and non conservative forces?

Mechanical energy (kinetic + potential) is conserved only if conservative forces act. If non-conservative forces act, then the sum of potential + kinetic energy may not be conserved. However, total energy is always conserved. It's just that when non-conservative forces act, the energy is converted into forms other than kinetic or potential.
 
Take friction for example. The kinetic energy is lost in the form of sound and heat. Total energy remains conserved but mechanical energy is lost.
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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