Investigating the Physics of a Candle Seesaw

[Robben]

Homework Statement

This isn't homework but I don't know where to post this type of questions so I will post it here.

But, I am wondering what are the physics equations that describes the system of a candle that is lit and behaves like a seesaw?

I have attached an image.

Explanation:

A candle, which is balanced between a pair of glasses (can be anything really), seesaws up and down on its own. The motion continues as long as the candle continues to burn.

Homework Equations

Newton's Laws

The Attempt at a Solution

Lets neglect the air currents in the room and since we can't easily calculate the mass distribution as a function of time, let's make assumptions for the mass and length of the candles. Can we estimate an equation for how mass is loss and thus, how the center of mass moves and taking into account that there is chaos in the system?

 

[Bystander]

Can we estimate an equation for how mass is loss

Anything can be estimated. Can there always be a good estimate? Who knows. In this case, you've got two approximately matched wick lengths, a higher melting rate and drip rate on the "low" end of the candle, leading to higher rate of mass loss, on the "heavy" end, and oscillation. Hunt up enthalpy of fusion of paraffin, beeswax, whatever, surface tension of molten wax (gives you drop size), actual burning rate for given wick length, enthalpy of combustion, and have a party.

 

[Robben]

I was more concerned with the classical mechanics equations (like torque) behind it rather than the thermodynamics.

 

[Bystander]

Torque is going to be a function of rate of mass loss, drip rate, a function of the burning rate. If you want just to count the drip rates at high and low ends, and look at oscillation rates as a function of how far the pivot axis is above the center of mass that also works.

 

[Robben]

But what will the equation of motion for the candle seesaw be? For example, the equation of motion for a pendulum would be $\theta''=-g/R\sin\theta.$

 

[bigfooted]

It's like a horizontal pendulum with two weights, except that the weights decrease in time and the rate of weight loss depends on the angle.

 

[Robben]

It's like a horizontal pendulum with two weights, except that the weights decrease in time and the rate of weight loss depends on the angle.

I see, thank you!