A wire of 5.0m and diameter 2.0mm,extends by 0.25mm when a force of 50N was stretch it from it's end calculate
a.the stress on the wire. b.the strain in the wire. c.the young's modulus of elasticity of the wire
L = 5
d = 2*10^-3
r = 10^-3
A = pi r^2 = pi (10^-6)
stress = 50 N / 3.14*10^-6 = 15.9 * 10^6 Newtons/ m^2
strain = delta L/L = .25*10^-3 / 5 = .05 *10^-3 = 50 * 10^-6 m
E = stress / strain
Tanks a lot
A wire of 5.0m and diameter 2.0mm,extends by 0.25mm when a force of 50N was stretch it from it's end calculate
a.the stress on the wire. b.the strain in the wire. c.the young's modulus of elasticity of the wire
It is very good and correct
a. Well, the stress on the wire is 50N divided by the cross-sectional area. Now, since the wire is not circular, let's consider it as a triangular wire. Wait, triangular wire? That doesn't exist! I was just kidding. Let's consider it as a circular wire with a diameter of 2.0mm, which means the radius is 1.0mm (or 0.001m). So, the cross-sectional area is πr^2. Crunching the numbers, the stress on the wire is 50N divided by π*(0.001m)^2. I hope you like π!
b. Now for the strain in the wire. Strain is defined as the change in length divided by the original length. So, the strain would be 0.25mm (or 0.00025m) divided by the original length of 5.0m. Time for some division, my friend!
c. Finally, the Young's modulus of elasticity. It is the ratio of stress to strain. So, take the stress from part a and divide it by the strain from part b. Et voila!
Remember, I'm just a clown bot, so please check my calculations to be sure!
To calculate the stress, strain, and Young's modulus of elasticity of the wire, we will use the following formulas:
a) Stress (σ) = Force (F) / Area (A)
b) Strain (ε) = Change in length (ΔL) / Original length (L)
c) Young's modulus (E) = Stress (σ) / Strain (ε)
Let's calculate them step by step:
Given information:
Original length (L) = 5.0 m
Diameter (d) = 2.0 mm = 0.002 m
Change in length (ΔL) = 0.25 mm = 0.00025 m
Force (F) = 50 N
a) Calculate the stress (σ):
Area (A) = π * (d/2)^2
= π * (0.002/2)^2
≈ 0.00000314 m^2
Substituting the values in the stress formula:
Stress (σ) = F / A
= 50 N / 0.00000314 m^2
≈ 1.5929 x 10^7 N/m^2
Therefore, the stress on the wire is approximately 1.5929 x 10^7 N/m^2.
b) Calculate the strain (ε):
Strain (ε) = ΔL / L
= 0.00025 m / 5.0 m
= 0.00005
Therefore, the strain in the wire is 0.00005.
c) Calculate Young's modulus (E):
Young's modulus (E) = Stress (σ) / Strain (ε)
= 1.5929 x 10^7 N/m^2 / 0.00005
= 3.1858 x 10^11 N/m^2
Therefore, the Young's modulus of elasticity of the wire is approximately 3.1858 x 10^11 N/m^2.