A wire of length L and cross-sectional area A is stretched by a force F. What is

A wire of length L and cross-sectional area A is stretched by a force F. What is the expression for the elongation ΔL?

A wire of length L and cross-sectional area A is stretched by a force F. What is the expression for the elongation ΔL?

Step 1: Understand that when a force is applied to a wire, it stretches or elongates.
Step 2: Identify the variables involved: L is the original length of the wire, A is the cross-sectional area, F is the force applied, and E is Young's modulus (a measure of the material's stiffness).
Step 3: Recognize that Young's modulus (E) relates stress and strain in the material. Stress is the force per unit area (F/A) and strain is the change in length per original length (ΔL/L).
Step 4: Write the formula for stress: Stress = F / A.
Step 5: Write the formula for strain: Strain = ΔL / L.
Step 6: Set up the relationship using Young's modulus: E = Stress / Strain = (F / A) / (ΔL / L).
Step 7: Rearrange the equation to solve for ΔL: ΔL = FL / (AE).
Step 8: Conclude that the elongation ΔL of the wire can be calculated using the formula ΔL = FL / (AE).

Hooke's Law – The relationship between force, elongation, and material properties in elastic materials.
Young's Modulus – A measure of the stiffness of a material, defined as the ratio of stress to strain.
Stress and Strain – Stress is the force applied per unit area, and strain is the deformation per unit length.