Did you know?
Did you know that stress and strain are important concepts in the field of materials science and engineering? Stress refers to the internal resistance of a material to deformation, while strain is the measure of the amount of deformation experienced by a material.
In the given scenario, a force of 40N is applied to a wire that is 4m long. This force causes an extension of 0.24mm in the wire. By calculating the stress and strain, we can better understand the wire's behavior under this applied force.
(i) To calculate the stress on the wire, we divide the force applied (40N) by the cross-sectional area of the wire. The diameter of the wire is given as 2.0mm, which means the radius is 1.0mm or 0.001m. With the radius, we can determine the cross-sectional area using the formula for the area of a circle (πr^2). By substituting the values, we find that the cross-sectional area is approximately 0.003142 square meters. Dividing the applied force by the cross-sectional area, we discover that the stress on the wire is 12,730 Pascals (Pa).
(ii) Strain can be calculated by dividing the extension length (0.24mm or 0.00024m) by the original length of the wire (4m). Dividing these values, we discover that the strain in the wire is 0.00006.
Understanding stress and strain is crucial in various industries and fields, such as structural engineering, material testing, and product design. These calculations help engineers and researchers determine the mechanical properties of materials, assess their reliability, and analyze their performance under different conditions.
