Question

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 2.0mm.calculate the stress and strain of the wire

Answer 1

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Answer 2

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 2.0mm.calculate the stress and strain of the wire

Answer 3

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Answer 4

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Answer 5

[AI-generated answer — Explain Bot]

To calculate the stress and strain of the wire, we need to use the formulas:

Stress = Force / Area
Strain = Extension / Original Length

1. First, let's calculate the area of the wire using the formula:

Area = π * (diameter/2)^2

Plugging in the values:
Area = π * (2.0mm / 2)^2
Area = π * (1.0mm)^2
Area = π * 1.0mm^2
Area = π mm^2

2. Now, let's convert the diameter and area to meters for consistency in the units:

Diameter = 2.0mm = 2 * 10^-3 m
Area = π * (1.0mm)^2 = π * (1 * 10^-3 m)^2 = π * 1 * 10^-6 m^2

3. Now we can calculate the stress using the formula:

Stress = Force / Area

Plugging in the values:
Stress = 40N / (π * 1 * 10^-6 m^2)
Stress = 40N / π * 10^-6 m^2
Stress = 4 * 10^7 / π N/m^2

4. Next, let's calculate the strain using the given values:

Strain = Extension / Original Length

Plugging in the values:
Strain = 0.24mm / 4m
Strain = 0.24 * 10^-3 m / 4m
Strain = 6 * 10^-5

Therefore, the stress of the wire is approximately 4 * 10^7 / π N/m^2 and the strain is approximately 6 * 10^-5.