Young's modulus Formula

Young's modulus Formula

Young's modulus is used to represents how easy it is to deform a material. A modulus is a numerical value, which represents a physical property of a material. It compares the tensile stress with the tensile strain. This is written as:

Young's modulus = (Force * no-stress length) / (Area of a section * change in the length)

The equation is

Y = (F L) / (A ΔL)

We have:

Y: Young's modulus

F: Force applied

L: length of the material without force

A: area of a section of the material

ΔL: Change in the length of the material after a force is applied

Young's modulus equation Questions:

1) A cylindrical bar of width 10 mm is stretched from its original length of 100 mm to 90 mm using a force of 100 N. What is the Young's modulus of the system?

Answer: The Young's modulus is found from the equation:

Y = (F L) / (A ΔL)

The area is calculated using A = π (d/2)2, where d is 10 mm, then A is

A = π (5 mm)2 = π (0.005 m)2 = 2.5*10(-5) m2

substituting the value of area, the force and calculating the difference between the initial and final length,

Y = (100 N 0.1 m) / (2.5*10(-5) m2 * (0.1 m - 0.09 m))

Y = 10 N*m/0.025*10(-5) m3 = 40000000 N/m2 = 40000 KN/m2

Y = 40000 KPa

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