A wire of length L and cross-sectional area A is stretched by a force F. What is
Practice Questions
Q1
A wire of length L and cross-sectional area A is stretched by a force F. What is the expression for the elongation of the wire?
ΔL = (F * L) / (A * Y)
ΔL = (Y * F) / (A * L)
ΔL = (A * Y) / (F * L)
ΔL = (F * A) / (Y * L)
Questions & Step-by-Step Solutions
A wire of length L and cross-sectional area A is stretched by a force F. What is the expression for the elongation of the wire?
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 Y is Young's modulus (a measure of the material's stiffness).
Step 3: Recognize that Young's modulus (Y) relates stress (force per unit area) to strain (relative change in length).
Step 4: Stress is calculated as F/A (force divided by area), and strain is ΔL/L (change in length divided by original length).
Step 5: The relationship between stress and strain is given by the formula: Stress = Y * Strain.
Step 6: Substitute the expressions for stress and strain into the formula: F/A = Y * (ΔL/L).
Step 7: Rearrange the equation to solve for ΔL: ΔL = (F * L) / (A * Y).
Step 8: This final expression gives you the elongation of the wire when a force is applied.
Hooke's Law – The relationship between the force applied to a material and its elongation, which is linear up to the elastic limit.
Young's Modulus – A measure of the stiffness of a material, defined as the ratio of stress (force per unit area) to strain (relative change in length).
Stress and Strain – Stress is the force applied per unit area, while strain is the deformation experienced by the material relative to its original length.
