A force of 40N is applied at the end of a wire 4m long and produces an extension of 0.24mm. If the diameter of the wire is 2.00mm calculate the stress on the wire and strain in the wire.
With full workings please
F=40n
L=4m
D=2m/100
E=0.24mm/100
A=PIE D2/4=3.14multiplied by 0.02/4
If a force of 40newton is applied to the end of a wire 4m long and produces an extension of 0.24mm. If the diameter of the wire is 2mm, calculate the strain energy
I need the full working problem please
To calculate the stress on the wire, we will use the formula:
Stress = Force / Area
First, we need to find the area of the wire. The wire is cylindrical in shape, so we can calculate the cross-sectional area using the formula:
Area = π * (diameter/2)^2
Given that the diameter of the wire is 2.00mm, we can convert it to meters by dividing by 1000:
Diameter = 2.00mm / 1000 = 0.002m
Substituting the values into the formula, we get:
Area = π * (0.002/2)^2 = 3.14 * (0.001)^2 = 3.14 * 0.001^2 = 3.14 * 0.000001 = 0.00000314 m^2
Now, we can calculate the stress by dividing the force by the area:
Stress = 40N / 0.00000314 m^2 = 40 / 0.00000314 = 12,739,808.92 Pa
Therefore, the stress on the wire is 12,739,808.92 Pa.
To calculate the strain in the wire, we will use the formula:
Strain = Extension / Original length
Given that the extension is 0.24mm, we can convert it to meters by dividing by 1000:
Extension = 0.24mm / 1000 = 0.00024m
The original length of the wire is given as 4m.
Substituting the values into the formula, we get:
Strain = 0.00024m / 4m = 0.00006
Therefore, the strain in the wire is 0.00006.
stress=force/area (n/m^2)
strain=deformation/length (m/m)