A weight of 40N was attached to the end of a wire during modulus experiment, if the length of the wire is 4m and the diameter is 0.44mm and the extension recorded is 0.30mm. calculate the stress and strain of the wire?. take[Pi=3.142
The strain is:
epsilon = (extension)/(length)
= 0.30 mm/4000 mm = 7.50*10^-5
The stress is
sigma = (tension force)/wire area)
= 40N/[(3.142)(0.22*10^-3)^2] N/m^2
Finish the calculation.
The value of Young's modulus is
E = (stress)/(strain)= sigma/epsilon
To calculate the stress and strain of the wire, we need to use the following formulas:
Stress = Force / Area
Strain = Extension / Original Length
1. Calculate the area of the wire:
The wire is given with its diameter, so we first need to calculate the radius:
Radius = Diameter / 2 = 0.44mm / 2 = 0.22mm = 0.22 × 10^(-3) m
Now, we can calculate the area using the formula for the area of a circle:
Area = π × radius^2
Area = 3.142 × (0.22 × 10^(-3))^2
2. Calculate the stress:
Stress = Force / Area
Stress = 40N / Area
3. Calculate the strain:
Strain = Extension / Original Length
Strain = 0.30mm / 4m
Now, let's substitute the values into the formulas to find the stress and strain:
Area = 3.142 × (0.22 × 10^(-3))^2
Stress = 40N / Area
Strain = 0.30mm / 4m
Calculating the values:
Area = 3.142 × (0.22 × 10^(-3))^2 = 0.00015209 m^2 (rounded to 8 decimal places)
Stress = 40N / 0.00015209 m^2 ≈ 263061.57 Pa (rounded to 2 decimal places)
Strain = 0.30mm / 4m ≈ 0.000075 (rounded to 6 decimal places)
Therefore, the stress of the wire is approximately 263,061.57 Pa, and the strain is approximately 0.000075.