A 15 kg long tendon was found to stretch 3.7 mm by 13 N .The tendon was approximately round with average diameter of 8.5 mm.Calculate the youngs modulus of this tendon
A kilogram is a unit of mass.
If your question means:
A 15 cm long tendon was found to stretch 3.7 mm by 13 N
then
E = σ / ε = ( F / A ) / ( dℓ / ℓ )
where
E = Young’s modulus
σ = tensile stress
ε = tensile strain
F = Force
A = Area of tendon
dℓ = amount of deformation
ℓ = length
In this case:
F = 13 N
A = d² π / 4 = 8.5² π / 4 = 56.745 mm²
1 m = 1000 mm
1 mm = 1 m / 1000
1 mm² = ( 1 /1000² ) m²
A = 56.745 mm² = ( 56.745 / 1000² ) = 0.000056745 = 5.6745 ∙ 10 ⁻⁵ m²
1 cm = 10 mm²
1 mm = 1 / 10 cm
dℓ = 3.7 mm = 3.7 / 10 cm = 0.37 cm
ℓ = 15 cm
dℓ / ℓ = 0.37 cm / 15 cm = 0.0246 = 2.467 ∙ 10 ⁻²
E = ( F / A ) / ( dℓ / ℓ ) = ( 13 / 5.6745 ∙ 10 ⁻⁵ ) / 2.467 ∙ 10 ⁻²
E = 2.2909 5∙ 10⁵ / 2.467 ∙ 10 ⁻²
E = 0.928638 ∙ 10 ⁵ ⁺ ² = 0.928638 ∙ 10⁷ N / m²
E = 9.28638 ∙ 10⁶ N / m²
1 N / m² = 1 Pa
E = 9.28638 ∙ 10⁶ Pa
where
Pa = Pascal