A force of 40N is applied at the end of a wire 4m long and it produces an extension of 0.24mm if the diameter of the wire is 2.00mm calculate the stress in the wire and the strain in the wire.
To calculate the stress and strain in the wire, we need to use the following formulas:
Stress = Force / Area
Strain = Extension / Original Length
1. Calculate the area of the wire:
The diameter of the wire is given as 2.00mm. We need to find the radius first, which is half the diameter.
Radius = 2.00mm / 2 = 1.00mm = 0.001m (convert mm to meters)
Area of wire = π * (radius)^2
2. Calculate the stress:
Stress = Force / Area
3. Calculate the strain:
Strain = Extension / Original Length
Let's calculate each step:
1. Calculate the area of the wire:
Radius = 0.001m
Area of wire = π * (0.001)^2 = π * 0.001^2 = 0.001 π m^2 (using the value of π as 3.14159)
2. Calculate the stress:
Stress = 40N / (0.001 π m^2)
3. Calculate the strain:
Strain = 0.24mm / 4m
Now, let's substitute the values and calculate the stress and strain:
Stress = 40N / (0.001 π m^2) ≈ 40 / 0.00314159 ≈ 12732.66 Pa (rounding to the nearest hundredth)
Strain = 0.24mm / 4m ≈ 0.00024 / 4 ≈ 0.00006
Therefore, the stress in the wire is approximately 12732.66 Pa, and the strain is approximately 0.00006.