A wire of length 5.0m and diameter 2.0mm extends by 0.25mm when a force of 50N was used to stretch it from its end. Calculate the
(a) Stress on the wire (b) Strain on the wire(π=3.142)
(6)
F = k x
50 = k * 0.25 *10^-3 meters
k = 2*10^5 Newtons/meter
(Surely they asked)
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anyway
stress = force /area = 50 /[ pi * (2*10^-3)^2/4 ]
strain = elongation/length = 0.25^10^-3 / 5
To calculate the stress on the wire, we can use the formula:
Stress = Force / Area
First, we need to calculate the area of the wire. The formula for the area of a circle is:
Area = π * (radius)^2
Given that the diameter is 2.0 mm, we can calculate the radius:
Radius = diameter / 2 = 2.0 mm / 2 = 1.0 mm = 0.001 m
Using this radius, we can calculate the area:
Area = 3.142 * (0.001 m)^2 = 3.142 * 0.000001 m^2 = 0.000003142 m^2
Now, we can calculate the stress:
Stress = 50 N / 0.000003142 m^2
Stress ≈ 15,929,020.6 N/m^2 (rounded to one decimal place)
Therefore, the stress on the wire is approximately 15,929,020.6 N/m^2.
To calculate the strain on the wire, we can use the formula:
Strain = Extension / Original Length
The extension is given as 0.25 mm, which is equal to 0.00025 m. The original length is given as 5.0 m.
Strain = 0.00025 m / 5.0 m
Strain = 0.00005
Therefore, the strain on the wire is 0.00005.
To calculate the stress and strain on the wire, we first need to understand the formulas involved.
(a) Stress can be calculated using the formula:
Stress = Force/Area
(b) Strain can be calculated using the formula:
Strain = Change in Length/Original Length
Now let's calculate them step by step:
(a) Stress on the wire:
Given:
Force (F) = 50 N
Diameter (d) = 2.0 mm = 2 x 10^(-3) m
We need to find the area of the wire (A) before calculating stress.
Area of a wire can be calculated using the formula:
Area = π × (diameter/2)^2
Substituting the values in the equation:
Area = 3.142 × (2 x 10^(-3)/2)^2
Area = 3.142 × (10^(-3))^2
Area = 3.142 × 10^(-6) m^2
Now we can calculate the stress using the formula:
Stress = Force/Area
Stress = 50 N / (3.142 × 10^(-6)) m^2
Stress ≈ 15.91 × 10^(6) N/m^2
So, the stress on the wire is approximately 15.91 × 10^(6) N/m^2.
(b) Strain on the wire:
Given:
Change in Length (∆L) = 0.25 mm = 0.25 x 10^(-3) m
Original Length (L) = 5.0 m
We can now calculate the strain using the formula:
Strain = Change in Length/Original Length
Strain = (0.25 x 10^(-3))/5.0
Strain = 0.05 x 10^(-3) = 5.0 x 10^(-5)
So, the strain on the wire is 5.0 x 10^(-5).
To recap:
(a) The stress on the wire is approximately 15.91 × 10^(6) N/m^2.
(b) The strain on the wire is 5.0 x 10^(-5).