What is the cross-sectional area of an aluminum wire, the relative elongation of which became equal to 0.004 after a 7 kg load was suspended from its free wire? Young’s modulus of aluminum is 7 * 10 ^ 10 Pa.
To determine the value of the cross-sectional area of the specified aluminum wire, we use the formula: F = E * S * Δl / l = E * S * ε = m * g, from where we express: S = m * g / (E * ε).
Variables and constants: m is the mass of the suspended load (m = 7 kg); g – acceleration of gravity (g = 9.81 m / s2); E – Young’s modulus for aluminum (according to the condition E = 7 * 10 ^ 10 Pa); ε – relative elongation (ε = 0.004).
Calculation: S = m * g / (E * ε) = 7 * 9.81 / (7 * 10 ^ 10 * 0.004) = 0.24525 * 10 ^ -6 m2 = 0.24525 mm2.
Answer: The cross-sectional area of the specified aluminum wire is 0.24525 mm2.
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