A force of 40n is applied at the end of a wire 4m long and it produces 1km extension of 0.24mm. if the diameter of the wire is 2.00mm, calculate the stress and strain of the wire
To calculate the stress and strain of the wire, we need to use the following formulas:
Stress (σ) = Force (F) / Area (A)
Strain (ε) = Extension (ΔL) / Original Length (L)
First, let's calculate the Stress (σ):
1. The force applied (F) is given as 40 N.
2. The diameter of the wire is given as 2.00 mm, which means the radius is half of the diameter, so it is 1.00 mm or 0.001 m.
3. The area of the wire (A) is calculated using the formula for the area of a circle: A = π * r^2, where π is a mathematical constant approximately equal to 3.14159 and r is the radius. Therefore, A = π * (0.001 m)^2.
Now we can calculate the Stress (σ) using the formula mentioned above:
σ = F / A
Substituting the values, we get:
σ = 40 N / (π * (0.001 m)^2)
Next, let's calculate the Strain (ε):
1. The extension of the wire (ΔL) is given as 0.24 mm or 0.00024 m.
2. The original length of the wire (L) is given as 4 m.
Now we can calculate the Strain (ε) using the formula mentioned above:
ε = ΔL / L
Substituting the values, we get:
ε = 0.00024 m / 4 m
To summarize:
Stress (σ) = Calculated using the formula σ = F / A
Strain (ε) = Calculated using the formula ε = ΔL / L
Please substitute the values into the formulas to get the numerical results.