Question

What hanging mass will stretch a 2.3-m-long, 0.30 mm - diameter steel wire by 1.1 mm ? The Young's modulus of steel is 20×1010N/m2.

Answer 1

Be careful with your units!

strain = stretch / original length = (0.0011 m / 2.8 m) = 3.93 × 10^-4 {Strain doesn't have units.}

Young's modulus = stress / strain
re-arranges to:

stress = Young's modulus * strain = (20×10^10 N/m² * 3.93 × 10^-4) = 7.86 × 10^7 N/m²

stress = force / cross-sectional area

re-arranges to:

force = stress * cross-sectional area

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We need to calculate the cross-sectional area of the wire in m²
Area (A) of a circle of radius (r) is given by:
A = πr²

Here r = (0.44/2) = 0.22 mm = 2.2 × 10^-4 m

A = π * (2.2× 10^-4)² = 1.52 × 10^-7 m²
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Force = (7.86 × 10^7 N/m² * 1.52 × 10^-7 m²) = 11.95 newtons

That is the weight of the required mass (m).

weight = mg

where g is the acceleration due to gravity { = 9.81 m/s² }

mass = (11.95 N/ 9.81 m/s²) = 1.22 kg
I hope this will help you
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