If the diameter of a wire is halved while keeping the length constant, what happ

If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)

If the diameter of a wire is halved while keeping the length constant, what happens to its tensile strength? (2019)

Step 1: Understand what tensile strength is. It is the ability of a material to withstand tension (being pulled apart).
Step 2: Know that tensile strength is related to the cross-sectional area of the wire.
Step 3: Remember that the cross-sectional area of a wire is calculated using the formula A = π(d/2)², where d is the diameter.
Step 4: If the diameter is halved, the new diameter is d/2.
Step 5: Calculate the new cross-sectional area using the new diameter: A' = π((d/2)/2)² = π(d/4)² = π(d²/16).
Step 6: Compare the new area A' to the original area A: A' = A/4 (since A = π(d/2)² = π(d²/4)).
Step 7: Since tensile strength is inversely proportional to the cross-sectional area, if the area is reduced to a quarter, the tensile strength increases by a factor of 4.
Step 8: Conclude that halving the diameter of the wire while keeping the length constant results in the tensile strength quadrupling.

Tensile Strength – Tensile strength is the maximum amount of tensile (stretching) stress that a material can withstand before failure.
Cross-Sectional Area – The area of a cut made perpendicular to the length of the wire, which affects the tensile strength.
Proportional Relationships – Understanding how changes in dimensions (like diameter) affect properties (like tensile strength) through mathematical relationships.