A force of 40n is applied m at the end of a wire of length 4m and a diameter of 2.0mm process an extension of 0.24mm calculate (a) stress on the wire (b) strain on the wire (c) young modulus for the material of the wire (take π=3.14)
To solve this problem, we need to use the formulas for stress, strain, and Young's modulus. Let's break down the problem step by step:
(a) Stress on the wire:
Stress is defined as the applied force divided by the cross-sectional area of the wire.
1. Calculate the cross-sectional area of the wire:
The wire has a diameter of 2.0 mm, so the radius (r) is half of that: 2.0 mm / 2 = 1.0 mm = 0.001 m.
The formula for the area of a circle is given by A = πr^2. So, the cross-sectional area can be calculated as follows:
A = π * (0.001 m)^2
2. Calculate the stress:
The stress (σ) is the force (F) divided by the cross-sectional area (A):
σ = F / A
In this case, the force is given as 40 N, so we can substitute the values into the formula to find the stress.
(b) Strain on the wire:
Strain is defined as the change in length divided by the original length.
1. Calculate the change in length:
The problem states that the wire undergoes an extension of 0.24 mm. Since we are given the original length as 4 m, we need to convert the extension to meters:
Extension = 0.24 mm = 0.24 x 10^-3 m
2. Calculate the strain:
The strain (ε) is the change in length (ΔL) divided by the original length (L):
ε = ΔL / L
(c) Young's modulus:
Young's modulus (E) is a measure of the stiffness of a material. It is defined as the ratio of stress to strain.
1. Calculate Young's modulus:
Young's modulus (E) is the stress (σ) divided by the strain (ε):
E = σ / ε
Now, let's substitute the given values and solve the equations.
(a) Stress on the wire:
A = π * (0.001 m)^2
σ = 40 N / A
(b) Strain on the wire:
ε = 0.24 x 10^-3 m / 4 m
(c) Young's modulus:
E = σ / ε
With these equations and the given values, you can now substitute the values and calculate the stress, strain, and Young's modulus for the wire.