Question

Physics question!



When are the initial and final total energies the same?
When are they different? Explain.

Answer 1

@shamim hi my friend. Can you help me with this question after you are done.

Answer 2

?

Answer 3

If by total energy you mean mechanical energy (the sum of kinetic and potential energy), then the initial and final totals will be the same if you have an isolated system (a system where neither matter nor energy can enter or leave) that experiences only conservative forces (forces which, if they were to move something from one position to another, the work done by the force would always be the same regardless of the path taken). Gravity is an example of a conservative force.

The mechanical energy will change if you're dealing with non-conservative forces (such as friction). With a non-conservative force present, some energy will be lost in the form of heat. This means the final mechanical energy will be less than the initial mechanical energy.

However, if we're considering ALL energy in the system (not just mechanical energy), and the system is isolated, the total energy will always be the same (by the law of conservation of energy), even if it's converted into different forms.

If you need me to clarify something, please let me know!

Answer 4

matt101, in my text book it mentioned the information which you included above, but I do not understand something.

Answer 5

If friction is present, the sum of kinetic and potential energies will not be constant. But, (the sum of the kinetic energy, potential energy, and the work done against friction will be constant.)

Answer 6

can you explain me what is the main message. I do not understand the information in the bracket. Can you draw me the formulas or anything which can help me? Thank you :)

Answer 7

Sure! Let's call potential energy P, kinetic energy K, and work done against friction W. I'll call the total energy E, and the subscripts i and f refer to initial and final conditions respectively. Under your initial conditions:

\[E_{i}=P_{i}+K_{i}\]
All the energy is in the form of P or K. Nothing has happened so there has not yet been an opportunity for friction to act on the system.

However, once something changes, some of the energy will be lost as it works to counteract friction. Due to the law of conservation of energy, this means that you will lose some energy from P, K, or both, so that the total energy stays the same. The final total energy will be:

\[E_{f}=P_{f}+K_{f}+W\]
Now we know E(i) and E(f) have to be the same, so we can set these equations equal to each other:

\[P_{i}+K_{i}=P_{f}+K_{f}+W\]
Now to make things easier to see, I'll just replace each P+K with ME (for mechanical energy):

\[ME_{i}=ME_{f}+W\]
So looking at the equations above, you should be able to see that the TOTAL energy of the system (including P, K, and W) will always be the same. The value of ME on it's own is changing, however - in fact, if you look at the last equation, you need to add W to ME(f) in order to get ME(i). In other words, ME(f) MUST be less than ME(i).

Hope that makes things a bit clearer!

Answer 8

That was awsome! You explained things much better than my teacher and way more faster. I wish I could give you more medals. Thank you so much. :)

Answer 9

Glad I could help :)