A FORCE OF 40N IS Applied at the end of wire 4m long and produced an extention of 0.24mm if the diameter of wire is 2.00mm.calculate stress on wire and strain in the wire
force/area=40N/(PI*.001^2) in n/m^2
strain=24E-5/4=6E-5
To calculate stress on the wire, we need to use the formula:
Stress = Force / Area
To determine the area of the wire, we first need to calculate its cross-sectional area using the formula:
Area = π * (radius)^2
Given that the diameter of the wire is 2.00 mm, we can calculate the radius by dividing the diameter by 2:
Radius = 2.00 mm / 2 = 1.00 mm = 0.001 m
Now we can calculate the cross-sectional area:
Area = π * (0.001 m)^2 = π * 0.001^2 m^2
Using the value of π as 3.14159, we can calculate the area:
Area = 3.14159 * (0.001 m)^2 = 3.14159 * 0.000001 m^2 = 0.00000314159 m^2
Now we can calculate the stress:
Stress = 40 N / 0.00000314159 m^2
Stress = 12,734,082.49 N/m^2 or Pascal (Pa)
To calculate the strain in the wire, we use the formula:
Strain = (Change in length) / (Original length)
Given that the extension of the wire is 0.24 mm and the original length is 4 m, we need to convert the extension to meters:
Extension = 0.24 mm = 0.24 × 10^(-3) m = 0.00024 m
Now we can calculate the strain:
Strain = 0.00024 m / 4 m
Strain = 0.00006