Calculate Young's Modulus of L₁ = 208 mm, L₂ = 207.5 mm, A = 472.16 mm² and F = 178 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) = 208 mm

Final Length (L₂) = 207.5 mm

Change in Length (ΔL) = ?

Area (A) = 472.16 mm²

Force (F) = 178 N

Calculating Stress

=> Convert the Area (A) 472.16 mm² to "square meter (m²)"

F = 472.16 ÷ 1000000

F = 0.000472 m²

Substitute the value into the formula

Stress (σ) = 376990.850559 Pa

Calculating Strain :

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

r = 208 ÷ 1000

r = 0.208 m

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

r = 207.5 ÷ 1000

r = 0.2075 m

ΔL = 0.2075 - 0.208

ΔL = -0.0005 m

Substitute the value into the formula

Strain (S) = -0.002404

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

E = -156828193.832599 Pa

∴ Youngs's Modulus (E) = -156828193.832599 Pa