# Conservation of mechanical energy

1. Aug 9, 2009

### Amith2006

1. The problem statement, all variables and given/known data

I have a doubt on total mechanical energy conservation in a non conservative system. I think, in such a system there are dissipative forces as a result of which the total mechanical energy is not conserved because there may be loss of energy in the form of heat or other forms. In the case of rocket propulsion, if the air resistance is neglected it becomes a conservative system and hence the mechanical energy is conserved while dealing non relativistically. Is it right?

2. Relevant equations

total mechanical energy = K.E + P.E

3. The attempt at a solution

2. Aug 9, 2009

### diazona

Yep, sounds right. But is there a specific problem you're thinking of?

3. Aug 9, 2009

### PhanthomJay

Total mechanical energy is not conserved when non conservative forces that do work act.
How about a gain in total mechanical energy?
Suppose for simplicity that the rocket is propelled horizontally, starting from rest and and accelerating to some high speed. Is mechanical energy (in this case kinetic energy) conserved (delta KE = 0) or increasd (delta KE>0)?

2. Relevant equations

total mechanical energy = K.E + P.E

3. The attempt at a solution[/QUOTE]

Last edited: Aug 10, 2009
4. Aug 10, 2009

### Amith2006

Ya! In that case K.E will increase. But if gravity is taken into account it will follow a parabolic path and then P.E comes into picture isn't it?

5. Aug 10, 2009

### PhanthomJay

I assume the parabolic path you are talking about is the path of the object taken when it is subject to gravity forces only, as would occur if the rocket, assumed not in orbit, ran out of fuel. This is a conventional parabolic motion problem, in which case, since only a conservative force acts (gravity), total mechanical energy is conserved (KE + PE is constant, that is , the change in KE plus the change in PE sums to zero). But in the more general case when the rocket is subject to other forces besides gravity, like the propelling force from the rockets escaping gasses, its motion could be in any shaped curve. The point I am trying to make is that when an object is subject to non conservative forces that do work, total mechanical energy is not conserved (delta KE plus delta PE is not equal to zero). Incidentally, if you look up the definition of a non conservative force in Wiki, it is likely to confuse the living daylights out of you. Basically, in Mechanics, gravity and ideal springs/ideally elastic bodies, exert conservative forces. Most every other force is non conservative. The literature usually talks about friction being a non conservative force. Correct. But tension, normal forces, pushing forces, applied forces, and all other so called 'contact' forces, are also non conservative in nature.

6. Aug 13, 2009

Thanx guys.