A wire of length L and diameter d is stretched by a force F. What is the express
Practice Questions
Q1
A wire of length L and diameter d is stretched by a force F. What is the expression for the elongation of the wire? (2020)
(F * L) / (A * Y)
(F * Y) / (A * L)
(Y * A) / (F * L)
(L * d) / (F * Y)
Questions & Step-by-Step Solutions
A wire of length L and diameter d is stretched by a force F. What is the expression for the elongation of the wire? (2020)
Step 1: Understand that when a force (F) is applied to a wire, it stretches or elongates.
Step 2: Identify the original length of the wire, which is denoted as L.
Step 3: Recognize that the diameter of the wire is given as d, which will help us calculate the cross-sectional area.
Step 4: Calculate the cross-sectional area (A) of the wire using the formula A = π * (d/2)², where π is a constant approximately equal to 3.14.
Step 5: Understand that Young's modulus (Y) is a property of the material that measures its stiffness.
Step 6: Use the formula for elongation (ΔL) of the wire, which is ΔL = (F * L) / (A * Y).
Step 7: Substitute the values of F, L, A, and Y into the formula to find the elongation of the wire.
Hooke's Law and Young's Modulus – The relationship between stress and strain in materials, where elongation is proportional to the applied force and inversely proportional to the material's cross-sectional area and Young's modulus.
Cross-Sectional Area Calculation – Understanding how to calculate the cross-sectional area (A) of the wire based on its diameter (d), which is crucial for applying the formula correctly.
