Calculate Young's Modulus of L₁ = 287 mm, L₂ = 286.5 mm, A = 551.1600000000001 mm² and F = 257 N

Young's Modulus states that a measure of elasticity is equal to the ration of the stress acting on a substance to the strain produced. Young's Modulus is also known as modulus of elasticity.

The formula to calculate Young's Modulus is:

Where,

Step by Step Solution to find Young's Modulus :

Given that,

Stress (σ) = ?

Strain (ε) = ?

Initial Length (L₁) = 287 mm

Final Length (L₂) = 286.5 mm

Change in Length (ΔL) = ?

Area (A) = 551.1600000000001 mm²

Force (F) = 257 N

Calculating Stress

=> Convert the Area (A) 551.1600000000001 mm² to "square meter (m²)"

F = 551.1600000000001 ÷ 1000000

F = 0.000551 m²

Substitute the value into the formula

Stress (σ) = 466289.28079 Pa

Calculating Strain :

=> convert the L₁ value to "meters (m)" unit

r = 287 ÷ 1000

r = 0.287 m

=> convert the L₁ value to "meters (m)" unit

r = 286.5 ÷ 1000

r = 0.2865 m

ΔL = 0.2865 - 0.287

ΔL = -0.0005 m

Substitute the value into the formula

Strain (S) = -0.001742

As we got all the values we can calculate Young's Modulus

E = -267650047.173234 Pa

∴ Youngs's Modulus (E) = -267650047.173234 Pa