Question

How do you use original diameter and gage length to find modulus of esticity

Answer 1

The modulus of elasticity is found by performing a tensile test, determining stress and strain, and dividing the stress by the strain. The original diameter is used to calculate the cross-sectional area, and the gauge length is used to calculate strain during the tension test.

Step-by-step explanation:

The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness of a material. It is defined as the ratio of the stress applied to a material to the resulting strain within the elastic limits. When you have the original diameter and gauge length of a cylindrical specimen, you can find the modulus of elasticity by conducting a tension test.

Steps to find the modulus of elasticity:

1. Determine the cross-sectional area of the specimen using the original diameter.
2. Perform a tensile test to apply a force on the specimen and measure the resulting change in length (elongation).
3. Calculate stress using the applied force and the cross-sectional area.
4. Calculate strain by dividing the elongation by the original gauge length.
5. Calculate the modulus of elasticity as the ratio of stress to strain within the elastic range.

For example, if your specimen has an original diameter of 10mm and a gauge length of 50mm, and during the tensile test the specimen elongated 0.5mm under a certain force, you can use these values to calculate the modulus of elasticity through the above steps.