# Tension - Conservative/Nonconservative?

## Main Question or Discussion Point

My lecturer defined that tension can be both conservative and non conservative. I'm not sure exactly when the non-conservative part comes in. Hope somebody can help.

From my understanding:

Conservative forces do not alter the Mechanical energy of the system
Work done around a closed loop by a conservative force is zero
Work done by a conservative force is independent of path taken (i.e. only the final and initial coordinates of the displacement are needed)

So, I can define tension as being conservative in the example of a hockey puck swinging in a constant velocity in a circular loop, tied to the centre by a string. There is a tension force acting at all times that is effectively the radial force, but the hockey puck's KE does not change, hence its EMech does not change. (I zeroed PE).

But when is a tension force non-conservative? I.E it fails to satisfy any of the listed conditions above.

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kk now even the tension on the hockey puck which you just mentioned did not do any work hence it cannot even be called a conservative force, because it did not even do any work at any moment during the reaction(i mean during the experiment). Now well, most times tensions are not conservative like most tensions are not. However, there is a good example of a tension which may be conservative. Tension arising from very elastic strings. Such tensions are conservative. One way to know if a force is conservative is its ability to store energy and give back that same amount of energy. Conservative forces store and give back the same energy non conservative store but only release some. How does a spring store energy. Slide a block of mass against a spring. After some time the block comes to rest isnt it?Where did its initial kinetic energy got to. It went into the field associated with the spring force which may be a tension force in some cases. Later after the block moves up back again with almost the same velocity it started with. Hence the spring released back the energy stored into it. Now notice i sed almost becos not spring is perfectly elastic and some energy is not retrieved.The irretrievable energy are used to raise the entropy of the system. This rise in entropy is necessary lest the reaction,(the storing or d compressing of the spring ) cannot even occur in the first place. A more understanding on the nature of conservative fields would require your knowledge of Calculus 3 and eventually some thermodynamics to make you a pro.

Dale
Mentor
In keeping with CHUKKY's explanation, it is not really tension which is conservative or nonconservative, it is the material providing the tension which is elastic or inelastic. If it is elastic then any energy that you put in you can get out, and if it is inelastic then energy you put in will be permanently lost due to inelastic deformation. So, the hockey puck on a rope made of rubber is "conservative" and the hockey puck on a rope made of silly putty is "non-conservative".

An easy way to check if a force is conservative or not is to check for a time term in the equations of motion. Generally speaking if there is no time dependent term, then the force or motion is conservative. If you do see a time term, then usually it is non-conservative.

This is just a rule of thumb, so don't use it exclusively.

robphy
Homework Helper
Gold Member
A conservative-force has an associated potential energy function [scalar field].
(Don't confuse a constraint-force with a conservative-force.)