Is There an Equation for the Law of Conservation of Energy?

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The law of conservation of energy can be expressed mathematically, with various equations applicable depending on the context. A common formulation is E_1 + E_2 + ... + E_n = C, where E represents different energy types in a system and C is a constant. This illustrates that energy can transform between forms but remains constant in an isolated system. The principle is frequently applied in physics, particularly in problems involving kinetic and potential energy. Overall, energy conservation is a fundamental concept that is essential for solving numerous physical problems.
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Is there an equation for the law of conservation of energy?
 
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50936 said:
Is there an equation for the law of conservation of energy?
There are numerous mathematical statements of the concept of conservation of energy, depending on which field the concept is applied to.
 
How about
E_1+ E_2+ \cdot\cdot\cdot+ E_n= C
where E_1, E_2, E_n are all the different kinds of energy in a system and C is a constant? In other words, energy can change from one form to another or from one object to another but in a given isolated system the total remains constant.

I started that a little facetiously but we use "kinetic energy+ potential energy= constant" in simple problems all the time.
 
Only a little facetiously - there are lots and lots of problems that are solved by writing an energy conservation statement and solving it (or the similar sum of forces = 0).
 

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
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