How do you derive this formula?

[Trickster_00]

How do we come to the formula for Conservation of Mechanical Energy?
[Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy]

It's not a part of our syllabus, but I'm just curious how to derive that formula.

Also, could you please clarify to me what's the formula for work-energy principle?

My book says it's [Work done = Change in Kinetic Energy]... but what if it involves external forces (e.g., friction) and change in potential energy? I'd appreciate it too if you break down the formula for me. Much appreciated. Thanks.

 

[Feldoh]

You can't really derive conservation of energy it's sort of like what a mathematician would call an axiom.

There are many ways however in which you can see conservation of energy come into play but they all require that it is taken to be true.

 

[wheelatharm]

Feldoh is absolutely right.

When you have work done by an external force, it will either take away or add to the total energy of the system. The energy is not destroyed, just moved from one system to another.

For Friction ---> Initial PE + Initial KE = Final PE + Final KE + Work done by Friction.

M

 

[wheelatharm]

Just to clarify, the work energy principal should state that work done on a system is equal to the total energy change of the system. This means work can increase PE, KE, spring PE, internal energy, etc, of the system.
For example, raising an object slowly and coming to rest has no change on KE, but requires work to increase the PE. Compressing a spring has no effect on KE, but still requires work to increase the spring energy. Even the work done by friction is never lost, it raises the internal energy of the objects in contact.

M