Final answer:
The elastic strain energy in a material from a FORCE EXTENSION graph can be calculated by finding the area under the graph. This can be done by calculating the areas of individual shapes formed by the graph and summing them up. The elastic strain energy represents the work done in deforming the material and storing potential energy.
Step-by-step explanation:
The elastic strain energy in a material can be found from a FORCE EXTENSION graph by calculating the area under the graph. The area under the graph represents the work done in deforming the material and storing the elastic potential energy. This can be done by finding the area of each individual shape formed by the graph and then summing them up.
For example, if the graph consists of a straight linear portion, you can calculate the area of the triangle formed by the base (force) and height (extension). If the graph has a curved portion, you can approximate the area by splitting it into multiple small rectangles and triangles.
In mathematical terms, the elastic strain energy, U, can be calculated as U = ∫Fd(x), where F is the force and d(x) is the differential displacement. By finding the definite integral of Fd(x) over the range of interest, you can determine the elastic strain energy in the material.