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 (A)stress (B)strain in the wire
I will be happy to critique your thinking on this.
To calculate the stress and strain in the wire, we need to use the formulas:
(A) Stress (σ) = Force (F) / Area (A)
(B) Strain (ε) = Change in length (ΔL) / Original length (L)
Let's break down the steps to find the answers:
(A) Stress (σ):
1. Calculate the cross-sectional area of the wire.
The cross-sectional area of a wire can be found using the formula for the area of a circle: A = π * r^2, where r is the radius of the wire.
The given diameter of the wire is 2.00mm, so the radius (r) is half of that: 2.00mm / 2 = 1.00mm = 0.001m.
Convert the radius to meters: 0.001m.
Substitute the values into the formula: A = π * (0.001m)^2.
2. Calculate the stress using the formula: Stress (σ) = Force (F) / Area (A).
The given force is 40N.
Substitute the values into the formula: Stress (σ) = 40N / A.
(B) Strain (ε):
1. Calculate the change in length of the wire.
The given extension of the wire is 0.24mm, which we need to convert to meters.
Convert the extension to meters: 0.24mm = 0.24 * 10^(-3)m.
Substitute the value into the formula: Change in length (ΔL) = 0.24 * 10^(-3)m.
2. Calculate the strain using the formula: Strain (ε) = Change in length (ΔL) / Original length (L).
The original length (L) of the wire is 4m.
Substitute the values into the formula: Strain (ε) = (0.24 * 10^(-3)m) / 4m.
Now, you can calculate the stress and strain by plugging the values into the respective formulas.