A wire length 2m and radius 1mm is stretched by 25mm on application of a force of 1000N.Calculate the young modulus
Yes I response
Well, this sounds like a job for Clown Bot!
Young modulus is a measure of the stiffness of a material. To calculate it, we'll use the formula:
Young modulus = (Force * Length) / (π * Radius^2 * Extension)
Let's plug in the values and see what we get:
Young modulus = (1000 N * 2 m) / (π * (1 mm)^2 * 25 mm)
Young modulus = (2000 N) / (π * 0.001 m^2 * 0.025 m)
Now, let me ask my friends in the circus who are really good at math to help me calculate this.
[Calculating intensifies]
After some expert calculations, we get:
Young modulus ≈ 10^11 N/m^2
Voila! The Young modulus of this wire is approximately 10^11 N/m^2, but keep in mind that my calculations may contain a few clownish errors.
To calculate the Young's modulus of the wire, we can use the formula:
Young's modulus = (Force × Length) / (π × Radius^2 × Extension)
Given:
Force (F) = 1000 N
Length (L) = 2 m
Radius (r) = 1 mm = 0.001 m
Extension (e) = 25 mm = 0.025 m
Using these values, we can calculate:
Young's modulus = (1000 N × 2 m) / (π × (0.001 m)^2 × 0.025 m)
First, let's calculate the value of the denominator:
Denominator = π × (0.001 m)^2 × 0.025 m
Now, substitute the value of the denominator:
Young's modulus = (1000 N × 2 m) / Denominator
Now, calculate the value of the Young's modulus.
To calculate the Young's modulus, we need the formula:
Young's modulus (E) = (Force * Length) / (π * radius^2 * change in length)
Given:
Length (L) = 2m
Radius (r) = 1mm = 0.001m
Change in Length (ΔL) = 25mm = 0.025m
Force (F) = 1000N
Using the formula, we can substitute the values:
E = (F * L) / (π * r^2 * ΔL)
= (1000N * 2m) / (π * (0.001m)^2 * 0.025m)
Calculating the expression inside the brackets:
(π * (0.001m)^2 * 0.025m) = π * 0.000001m^2 * 0.025m
= π * 0.000000025m^3
Substituting this value into the equation:
E = (1000N * 2m) / (π * 0.000000025m^3)
= (2000N) / (0.000000025m^3)
= 8 * 10^10 N/m^2
Therefore, the value of Young's modulus is approximately 8 * 10^10 N/m^2.
strain = change in L/L = 25 * 10^-3 / 2
stress = F/A = 10^3/(pi*10^-6) =10^9/pi
E = stress/strain
=[10^9/pi] /[25 * 10^-3 / 2]