Energy of a Pendulum: Friction vs. No Friction

[jumbogala]

Homework Statement

Let's say I wanted to find the total energy of a pendulum.

First, I ignore friction. Then, I take friction into account. Will the total energy change?

I just made this question up so hopefully there are no issues with it.

Homework Equations

The Attempt at a Solution

So for a pendulum with no friction, my textbook gives me a formula for the position of the mass.

Then it says the total energy E = (1/2)mv² + (1/2)(mg/l)x², where m is mass, v is velocity, l is length and x is position.

Now I want to do this but with friction! So I can figure out what the equation of motion is. (Except that friction changes direction opposite to velocity, and that's confusing me)

But once I have the equation of motion, can I use it in the equation for E? And differentiate it to get v? Or does that equation for E not hold anymore?

 

[PhanthomJay]

Homework Statement

Let's say I wanted to find the total energy of a pendulum.

First, I ignore friction. Then, I take friction into account. Will the total energy change?

I just made this question up so hopefully there are no issues with it.

Homework Equations

The Attempt at a Solution

So for a pendulum with no friction, my textbook gives me a formula for the position of the mass.

Then it says the total energy E = (1/2)mv² + (1/2)(mg/l)x², where m is mass, v is velocity, l is length and x is position.

This is the total mechanical energy (kinetic energy plus potential energy) with only the gravity force acting or other forces acting that do no work. When other forces act, like friction, total energy (mechanical plus other forms of energy ) must always be a constant. Energy can neither be created or destroyed, it just takes on different forms.

Now I want to do this but with friction! So I can figure out what the equation of motion is. (Except that friction changes direction opposite to velocity, and that's confusing me)

But once I have the equation of motion, can I use it in the equation for E? And differentiate it to get v? Or does that equation for E not hold anymore?

You picked a rather complex problem when friction, due to air resistance or torsional frictional at the pivot point, for example, is involved. You might want to look at a simpler problem, like the energy of an object sliding along a rough level surface with friction opposing the motion until it comes to rest. The work done by friction or other non-coservative forces results in other forms of energy like heat, sound, chemical energy, etc. You should be familiar with the total conservation of energy equation when such other forces that do work are involved.