A wire length 2m and radius 1mm is stretched by 25mm on application of a force of 1000N.Calculate the young modulus
To calculate the Young modulus, we need to use Hooke's Law, which states that the stress applied to an object is directly proportional to the strain experienced by the object.
Given:
- Initial length of the wire, L₀ = 2m
- Change in length of the wire, ΔL = 25mm = 0.025m
- Radius of the wire, r = 1mm = 0.001m
- Force applied to the wire, F = 1000N
To calculate the Young modulus (Y), we need to calculate the stress (σ) and strain (ε) first.
1. Calculate the stress (σ):
Stress is defined as the force applied divided by the cross-sectional area of the wire.
The cross-sectional area (A) of a wire is given by the formula:
A = π * r^2
Substituting the given values, we have:
A = π * (0.001m)^2
Next, we can calculate the stress (σ) using the formula:
σ = F / A
Substituting the given values, we have:
σ = 1000N / (π * (0.001m)^2)
2. Calculate the strain (ε):
Strain is defined as the change in length divided by the original length of the wire.
The strain (ε) can be calculated using the formula:
ε = ΔL / L₀
Substituting the given values, we have:
ε = 0.025m / 2m
3. Calculate the Young modulus (Y):
The Young modulus (Y) can be calculated using the formula:
Y = σ / ε
Substituting the calculated values of stress (σ) and strain (ε), we have:
Y = (1000N / (π * (0.001m)^2)) / (0.025m / 2m)
Now, you can simplify the equation and calculate the value of Young modulus (Y).
To calculate the Young's modulus, we need to gather the necessary information:
Force applied (F) = 1000 N
Original length (L0) = 2 m
Extension (ΔL) = 25 mm = 0.025 m
Radius (r) = 1 mm = 0.001 m
Young's modulus (Y) is given by the formula:
Y = (F * L0) / (A * ΔL)
Where A is the cross-sectional area of the wire.
To find A, we can use the formula:
A = π * r^2
Plugging in the values:
A = π * (0.001)^2
A = π * 0.000001
A ≈ 0.0000031416 m^2
Now we can calculate the Young's modulus:
Y = (1000 * 2) / (0.0000031416 * 0.025)
Y ≈ 637593984 mm^-1 or N/m^2
Therefore, the Young's modulus is approximately 6.38 x 10^8 N/m^2 or Pa.