Finding Lagrangian for Overhanging String on Frictionless Table

[Boltzman Oscillation]

Homework Statement

B is 10kg
C is 20kg
can I find a lagrangian for this system? If so how?

Diagram: http://imgur.com/j811rzw

Homework Equations

L=T-V
Kinetic = .5mv^2
Potential = mgh

The Attempt at a Solution

I know the kinetic energy must be 0 right? How could I find the potential?

 

[kuruman]

Hi Boltzmann Oscillation and welcome to PF.

Yes, the kinetic energy is zero. If you take the zero of potential energy to be at the same height as the lights, the potential energy will also be zero, so the Lagrangaian is zero. May I ask why you are looking for the Lagrangian in relation to a statics problem?

 

[Boltzman Oscillation]

Hi Boltzmann Oscillation and welcome to PF.

Yes, the kinetic energy is zero. If you take the zero of potential energy to be at the same height as the lights, the potential energy will also be zero, so the Lagrangaian is zero. May I ask why you are looking for the Lagrangian in relation to a statics problem?

I have statics class and this was assigned but I am quite bored with statics. I want to apply what I've learned in calculus and physics courses. Lagrangian are only used for moving objects? Thank you so much for the help.

 

[kuruman]

Lagrangian are only used for moving objects? Thank you so much for the help.

Lagrangians are used to find equations of motion and if something is not moving, well ...

If you want a diversion from statics and SOH-CAH-TOA, try this simple problem using a Lagrangian:
A uniform supple string of length $L$ and mass $m$ is held on a frictionless table with one of its ends overhanging the edge of the table. The overhanging length is $\alpha L$ ($\alpha<1$). The mass is released at time t = 0. Find the time it takes for the rope to fall off the table. Check your answer in the limiting cases $\alpha=0$ and $\alpha=1$.