Question

link phenomena at these measurements, if we have a reliable model and appropriate mathematical skills to two length scales. You will be able to predict the behavior of rubber under a variety of practical Preliminary calculations Consider a piece of rubber with initial dimensions and orientation shown in the diagram below: to bo where lo, bo, and to are the unstretched length, width, and thickness, respectively Then L./ lo A force F is applied parallel to the x-axis, stretching the rubber to a new length l. defines a quantity known as the extension ratio, commonly denoted by the symbol a: 2, The work done (W) when a force F acts in this way to achieve an extension ratio i, is described by the following equation: elice) Equation 1) where: . N is the number of chain segments per unit volume. A chain segment is a piece of molecule that connects adjacent cross-links; therefore, the number of chain segments per unit volume increases as the number of cross-links increases k is Boltzmann's constant 1.38 x 103 J.K-1. Some of you may recognize this from high school physics or chemistry as the number you get when you divide the molar gas constant by Avogadro's number. . T is absolute temperature. This is temperature on the Kelvin scale, where zero Kelvin is the lowest temperature that has any physical meaning. Temperatures on the Celsius scale can be converted to temperatures on the Kelvin scale by adding 273 (at a level of accuracy appropriate to the present exercise): T(in Kelvin)- T(in Celsius)+ 273. Equation 1 can also be interpreted as showing how much energy is stored in the rubber when it is stretched to the extension ratio ho. The equation is fairly easy to derive if you have learned some college- level thermodynamics. In the present semester, you learn that when a force F performs work by causing a series of incremental displacements ds, the work done (W) is given by wJFds This relationship between work, force and displacement can also be written as: dW ds In the present context, this becomes: dW dl, (Equation 2) 1. (Complete before coming to lab) Starting with Equation 1, and applying Equation 2, show that the stretching of rubber to a new length, I requires a force given by: Show your work here:

Answer 1

Γ.dw dl, 0