When a wire of length 5m and radius 0.5mm is stretched by a load of 49N,the elongation produced in wire is 0.1cm.
Find the energh stored per unit volume of the wire.
To find the energy stored per unit volume of the wire, we need to calculate the strain energy.
The strain energy stored in a wire is given by the formula:
Strain Energy = (1/2) * (Stress) * (Strain) * (Volume)
In this case, the stress (σ) can be calculated using the applied load (F) and the cross-sectional area (A) of the wire:
Stress (σ) = F / A
The strain (ε) can be calculated by dividing the elongation (ΔL) by the original length (L) of the wire:
Strain (ε) = ΔL / L
First, let's calculate the cross-sectional area (A) of the wire:
A = π * (radius)^2
Given that the radius is 0.5 mm, we can convert it to meters by dividing it by 1000.
radius = 0.5 mm = 0.5 / 1000 m = 0.0005 m
Now, let's calculate the cross-sectional area:
A = π * (0.0005)^2 = π * 0.00000025 = 0.0000007854 m^2
Next, let's calculate the stress (σ) using the formula above:
Stress (σ) = F / A = 49 N / 0.0000007854 m^2 = 623094.777 N/m^2
Now, let's convert the elongation (0.1 cm) to meters:
Elongation = 0.1 cm = 0.1 / 100 m = 0.001 m
Finally, let's calculate the strain energy per unit volume using the formula:
Energy per unit volume = (1/2) * (Stress) * (Strain)
Energy per unit volume = (1/2) * (623094.777 N/m^2) * (0.001) = 311.55 J/m^3
Therefore, the energy stored per unit volume of the wire is approximately 311.55 J/m^3.