calculate the force required to produce an elongation of 0.1 cm in a steel wire of radius 1mm and length 2m.( Youngs modulus of the wire = 20×10^10 N/m^2).
Answers
The force required to produce an elongation of 0.1 cm in a steel wire is 31.4 N
Explanation:
The initial length of the wire, l = 2 m
The radius of the wire, r = 1 mm = 1 * 10⁻³ m
The extension or the elongation of the steel wire, I = 0.1 cm = 1 * 10⁻⁴ m
The Young’s modulus of the wire, Y = 20×10¹⁰ N/m²
Let the force required to produce an elongation in the steel wire be denoted as “F”.
Now, we know that the formula of Young’s modulus is given by,
Y = [F*L] / [A*I]
⇒ F = [AYI] / [L]
⇒ F = [πr²YI] / [L] …… (i)
Substituting the given values in eq. (i), we get
F = [3.14 * (1 * 10⁻³)² * (20×10¹⁰) * (1 * 10⁻⁴)] / [2]
⇒ F = 3.14 * 10 * [10⁽⁻⁶⁻⁴⁺¹⁰⁾]
⇒ F = 3.14 * 10
⇒ F = 31.4 N
Thus, the force required to produce an elongation of 0.1 cm in the steel wire is 31.4 N.
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