# Homework Help: Stat Mech Problem

1. Feb 21, 2005

### pt176900

A weight of mass m is fixed to the middle point of a string of length l and rotates about an axis joining the ends of the string. The system is in contact with its environment at temperature T. Calculate the tension R between the ends of the string in terms of its dependence upon distance x between the ends and the temperature.

My thoughts:

clearly, the x-components of the tension will cancel and we are left with the y-components of the tension which provides the centripital force.

The energy of the rotating mass is given by 1/2 I w^2 (where w is the angular frequency). Since the string is in thermal equilibrium with the envrionment we can equate it with the average thermal energy for 1 degree of freedom: 1/2 kT

What I don't understand, is how to go from the energy to the tension on the string.

2. Feb 21, 2005

### Davorak

Well you know the energy of the string plus the mass. Since the string is assumed to be massless(right?) then you know the velocity as mass rotates.

The distance between the two ends of the string X will decide the radius at which the mass rotates.

Does this help?

3. Feb 22, 2005

### dextercioby

I'm very sure u can't equate anything macroscopic with $\frac{1}{2} kT$

Daniel.

4. Feb 22, 2005

### Davorak

Is there a way to solve the problem if it is macroscopic?

5. Feb 23, 2005

### kanato

even if you did, if a macroscopic energy system had kT worth of energy, ie. 0.026 eV at room temperature, it'd be basically zero relative to the moment of inertia of the mass.

is there a coefficient of thermal expansion for the string or something like that, which would affect the length of the string as a function of temperature?