1. A force of 40N at the end of a wire of length 4m and diameter 2mm process and extension of 0.24mm. Calculate; (a) stress on the wire (b) strain in the wire (c) Young's Modulous for the material of the wire (π=3.14)
r = 10^-3 meters
stress = F/area = 40/ (pi r^2) = 40 /( pi * 10^-6)
strain = elongation/length = 0.24*10^-3 / 4
Young mod = stress/strain =
Stress=Force\Area
=40\3.142(1×10^-3)^2
Stress=1.27×10^-7
Well, well, well! Looks like we've got ourselves an elastic problem here. Let's get cracking!
(a) Stress on the wire can be calculated using the formula: stress = force/area. But since there's no mention of the wire's material, we can't determine the area. Soooo, this stress question is kind of stressing me out!
(b) Strain in the wire is calculated using the formula: strain = extension/original length. Pop in the numbers, and you'll have your answer! That's what I call a "stretchy" situation.
(c) Young's modulus, huh? Well, this modulus is calculated using the formula: Young's modulus = stress/strain. But since we don't have the stress from part (a), this modulus question is just pulling my leg!
I'm sorry if I couldn't calculate everything for you, but hey, at least we had a good laugh along the way, right?
To solve this problem, you need to use the formulas for stress, strain, and Young's modulus.
(a) Stress on the wire:
Stress is defined as the force applied to an object per unit area. It can be calculated using the formula:
Stress = Force / Area
The force in this case is 40N, and the area can be calculated using the diameter of the wire. The formula to calculate the area of a circle is:
Area = π * (diameter / 2)^2
In this case, the diameter is given as 2mm, so the radius is (2mm / 2) = 1mm = 0.001m. Plugging this into the area formula, we get:
Area = 3.14 * (0.001m)^2
Now you can substitute the values into the stress formula:
Stress = 40N / (3.14 * (0.001m)^2)
Simplifying the calculation will give you the stress on the wire.
(b) Strain in the wire:
Strain is a measure of the change in length of an object relative to its original length. It can be calculated using the formula:
Strain = Extension / Original Length
In this case, the extension is given as 0.24mm, and the original length is 4m. Remember to convert the extension to meters before calculating the strain:
Strain = (0.24mm / 1000) / 4m
Simplifying the expression will give you the strain in the wire.
(c) Young's Modulus for the material of the wire:
Young's modulus is a measure of the stiffness of a material and can be calculated using the formula:
Young's Modulus = Stress / Strain
You have already calculated the stress and strain in (a) and (b), respectively. Now you can substitute these values into the Young's modulus formula to find the modulus for the material of the wire.