Question

A rubber band at absolute temperature T is fastened at one end to a peg, and support from its other end a weight W. Assume as a simple microscopic model of the rubber band that it consists of a link polymer chain of N segments joined end to end segment has a length a and can be orientated either parallel or antiparall to the vertical direction. Find an expression for the resultant mean length l of the rubber band as a function of W.

Hint: neglect the kinetic energies of the weights of the segments themselves, or any interaction between the segments

Answer 1

The expression for the resultant mean length l of the rubber band as a function of W is l = W / k.

Step-by-step explanation:

To find an expression for the resultant mean length l of the rubber band as a function of W, we can consider the equilibrium condition of the system.

The tension force in the rubber band, T, balances the weight force, W.

Using Hooke's law, we can write T = k * l, where k is the proportionality constant and l is the elongation of the rubber band.

By solving these equations, we get l = W / k.