A weight of 40N was attached to the end of a wire during modulus experiment, if the length of the wire is 4m and the diameter is 0.44mm and the extension recorded is 0.30mm. calculate the stress and strain of the wire?.
stress= 40n /area
so it depends the units. If you want Pascal (N/m^2), then
strss= 40N/(.44e-3)^2=206MegaN/m^2
strain: deltaL/L= .30e-3/4= ....
To calculate the stress and strain of the wire, we can use the following formulas:
Stress = Force / Cross-sectional area
Strain = Extension / Original length
1. Calculate the cross-sectional area of the wire:
Given diameter = 0.44 mm
Radius = diameter / 2 = 0.44 mm / 2 = 0.22 mm = 0.22 × 10^-3 m
Area = π * (radius)^2 = π * (0.22 × 10^-3 m)^2
2. Convert the weight from Newtons to Force:
Given weight = 40 N
3. Calculate stress:
Stress = Force / Cross-sectional area
4. Calculate strain:
Given extension = 0.30 mm
Given original length = 4 m
Strain = Extension / Original length
Let's substitute the values into the formulas now:
1. Cross-sectional area:
Radius = 0.22 × 10^-3 m
Area = π * (0.22 × 10^-3 m)^2
2. Convert the weight from Newtons to Force:
Force = 40 N
3. Stress:
Stress = Force / Cross-sectional area
4. Strain:
Extension = 0.30 mm = 0.30 × 10^-3 m
Original length = 4 m
Strain = Extension / Original length
Let's calculate the stress and strain:
1. Cross-sectional area:
Area = π * (0.22 × 10^-3 m)^2
Area ≈ 1.517 × 10^-7 m^2
2. Stress:
Stress = Force / Cross-sectional area
Stress = 40 N / 1.517 × 10^-7 m^2
3. Strain:
Strain = Extension / Original length
Strain = (0.30 × 10^-3 m) / 4 m
Now we can calculate the actual values:
1. Cross-sectional area:
Area ≈ 1.517 × 10^-7 m^2
2. Stress:
Stress = 40 N / 1.517 × 10^-7 m^2
3. Strain:
Strain = (0.30 × 10^-3 m) / 4 m
To calculate the stress and strain of the wire, you'll need to use the formulas for stress and strain.
Stress (σ) is defined as the force applied (F) divided by the cross-sectional area of the wire (A). It is given by the equation:
σ = F / A
To find the cross-sectional area, we need to first calculate the radius (r) of the wire using the diameter (d). The radius is equal to half the diameter:
r = d / 2
In this case, the diameter (d) is 0.44mm. Therefore, the radius (r) can be found as:
r = 0.44mm / 2 = 0.22mm = 0.22 × 10^(-3)m
The area (A) of the wire can be calculated using the formula for the area of a circle:
A = πr^2
where π is a constant approximately equal to 3.14.
A = 3.14 × (0.22 × 10^(-3)m)^2
Strain (ε) is defined as the change in length (ΔL) divided by the original length (L). It is given by the equation:
ε = ΔL / L
In this case, the extension recorded is 0.30mm and the original length is 4m. We need to convert the extension to meters:
ΔL = 0.30mm = 0.30 × 10^(-3)m
Now we can calculate the stress and strain of the wire:
Stress (σ) = Force (F) / Area (A)
Strain (ε) = Change in length (ΔL) / Original length (L)
To calculate the stress, we need the force which is given as 40N:
σ = 40N / A
And to calculate the strain:
ε = 0.30 × 10^(-3)m / 4m