A force of 40N applied at the end of a wire of length 4m and diameter 2.00m process and extension of 0.24mm. Calculate the stress of the wire and the strain in the wire
To calculate the stress of the wire, we need to find the cross-sectional area of the wire. The cross-sectional area of a wire with diameter d can be calculated using the formula:
A = π * (d/2)^2
Given that the diameter of the wire is 2.00 mm, the radius would be 1.00 mm or 0.001 m. Plugging this value into the formula, we get:
A = π * (0.001)^2 ≈ 0.00000314 m^2
Now, we can calculate the stress using the formula:
stress = force / area
Given force = 40 N and area ≈ 0.00000314 m^2, we can calculate the stress:
stress = 40 N / 0.00000314 m^2 ≈ 1.27 × 10^7 N/m^2
The stress of the wire is approximately 1.27 × 10^7 N/m^2.
Next, to calculate the strain in the wire, we use the formula:
strain = extension / original length
Given extension = 0.24 mm and original length = 4 m, we can calculate the strain:
strain = 0.24 mm / 4 m ≈ 0.00006
The strain in the wire is approximately 0.00006.
A force of 40n applied at the end of a wire of length 4m and diameter 2.00m process and extension of 0.24m. Calculate the stress of the wire and the strain in the wire. Show your workings
To calculate the stress of the wire, we need to find the cross-sectional area of the wire. The cross-sectional area of a wire with diameter d can be calculated using the formula:
A = π * (d/2)^2
Given that the diameter of the wire is 2.00 mm, the radius would be 1.00 mm or 0.001 m. Plugging this value into the formula, we get:
A = π * (0.001)^2 ≈ 0.00000314 m^2
Now, we can calculate the stress using the formula:
stress = force / area
Given force = 40 N and area ≈ 0.00000314 m^2, we can calculate the stress:
stress = 40 N / 0.00000314 m^2 ≈ 1.27 × 10^7 N/m^2
The stress of the wire is approximately 1.27 × 10^7 N/m^2.
Next, to calculate the strain in the wire, we use the formula:
strain = extension / original length
Given extension = 0.24 m and original length = 4 m, we can calculate the strain:
strain = 0.24 m / 4 m ≈ 0.06
The strain in the wire is approximately 0.06.
To calculate the stress of the wire, we can use the formula:
Stress (σ) = Force (F) / Area (A)
The area of a wire can be calculated using the formula:
Area (A) = π * (d/2)^2
where, d is the diameter of the wire.
Given:
Force (F) = 40N
Length of the wire (L) = 4m
Diameter of the wire (d) = 2.00mm = 0.002m
Extension of the wire (ΔL) = 0.24mm = 0.00024m
First, let's calculate the area of the wire:
A = π * (d/2)^2
A = π * (0.002m/2)^2
A = π * (0.001m)^2
A = π * 0.001^2 m^2
A = 0.000001π m^2
Now, let's calculate the stress of the wire:
σ = F / A
σ = 40N / 0.000001π m^2
σ ≈ 127,323.95 N/m^2
The stress of the wire is approximately 127,323.95 N/m^2.
To calculate the strain in the wire, we can use the formula:
Strain (ε) = ΔL / L
where, ΔL is the extension of the wire and L is the original length of the wire.
ε = 0.00024m / 4m
ε = 0.00006
The strain in the wire is 0.00006.