A circular metal column is to support a load of 500 Tonne and it must not compress more than 0.1 mm. The modulus of elasticity is 210 GPa. the column is 2 m long.
Calculate the cross sectional area and the diameter. (0.467 m^2 and 0.771 m)
Note 1 Tonne is 1000 kg.
0.467m²
0.771m
solve please
Please solve
Activity
To calculate the cross-sectional area and diameter of the circular metal column, we can use the formula:
A = F / (E * δ)
Where:
A = Cross-sectional area of the column,
F = Load the column supports,
E = Modulus of elasticity of the material, and
δ = Compression or deflection of the column.
Let's plug in the given values:
F = 500 Tonnes = 500 * 1000 kg = 500,000 kg
E = 210 GPa = 210 * 10^9 Pa
δ = 0.1 mm = 0.1 * 10^-3 m
Substituting these values into the formula, we get:
A = 500,000 kg / (210 * 10^9 Pa * 0.1 * 10^-3 m)
First, let's simplify the units:
A = 500,000 kg / (210 * 10^9 N / m^2 * 0.1 * 10^-3 m)
Next, let's cancel out units:
A = (500,000 kg * m) / (210 * 0.1 * 10*6 kg * m / m^2)
Now, let's calculate:
A = (500,000 * 10^-6) / (210 * 0.1 * 10^-3) (divide both numerator and denominator by 10^6)
A = 2.38 * 10^-3 / 21 * 10^-3
A = 2.38 / 21
A = 0.1133 m^2
So, the cross-sectional area of the column is approximately 0.1133 square meters.
To calculate the diameter, we can use the formula:
A = π * r^2
where A is the cross-sectional area and r is the radius of the column.
Now, let's calculate the radius:
A = π * r^2
0.1133 = π * r^2
r^2 = 0.1133 / π
r^2 ≈ 0.0361
r ≈ sqrt(0.0361) ≈ 0.19 m
Finally, to find the diameter, we multiply the radius by 2:
d = 2 * r ≈ 2 * 0.19 ≈ 0.38 m
So, the diameter of the column is approximately 0.38 meters.