Pls break down this for me
Compute the modulus of elasticity when a 50 mm long by 20 mm (0.020 m) diameter sample compresses 0.50 mm upon loading by a 20 N force
To compute the modulus of elasticity, you need to know the original length, change in length, original diameter, and the applied force.
Given information:
Original length (L): 50 mm = 0.050 m
Change in length (ΔL): 0.50 mm = 0.00050 m
Original diameter (d): 20 mm = 0.020 m
Applied force (F): 20 N
Modulus of elasticity (E): ?
The modulus of elasticity (E) can be calculated using the formula:
E = (F * L) / (A * ΔL)
Where:
F is the applied force,
L is the original length,
A is the cross-sectional area (π * (d/2)^2), and
ΔL is the change in length.
Let's calculate the modulus of elasticity:
1. Calculate the cross-sectional area:
A = π * (d/2)^2
A = π * (0.020/2)^2
A = π * (0.01)^2
A = π * 0.0001
A = 0.000314 m^2
2. Substitute the values into the formula:
E = (F * L) / (A * ΔL)
E = (20 * 0.050) / (0.000314 * 0.00050)
E = 1 / (0.000000157)
E ≈ 6.37 x 10^6 N/m^2
So, the modulus of elasticity is approximately 6.37 x 10^6 N/m^2.