Please how do i get an answer to this answer that goes like this
a wire of length 5.0m and diameter 2.0cm extends by 0.25mm when a force of 50n was used on its end. Calculate
(i) stress
(ii) strain in the wire (pi=3.142)
stress=force/area=50/(PI*.02^2) N/m^2
strain=extension/length=2.5E-4/5
= .5E-4
To calculate the stress and strain in the wire, you will need to apply some basic formulas and understanding of the concepts. Here's how you can obtain the answers step by step:
Step 1: Calculate the original cross-sectional area of the wire.
The diameter of the wire is given as 2.0 cm. We can use this to calculate the radius (r) of the wire.
Radius (r) = diameter / 2 = 2.0 cm / 2 = 1.0 cm = 0.01 m (converting cm to m).
The cross-sectional area of the wire (A) can be calculated using the formula:
A = πr^2 where π is approximately 3.142.
A = 3.142 x (0.01)^2 = 3.142 x 0.0001 = 0.0003142 m^2.
Step 2: Calculate the stress.
The stress (σ) is defined as the force applied (F) divided by the cross-sectional area (A).
σ = F / A.
Given: F = 50 N, A = 0.0003142 m^2.
σ = 50 N / 0.0003142 m^2 = 159238.651 N/m^2 (rounded to 4 decimal places).
The stress in the wire is approximately 159238.651 N/m^2.
Step 3: Calculate the strain.
The strain (ε) is defined as the change in length (ΔL) divided by the original length (L) of the wire.
ε = ΔL / L.
Given: ΔL = 0.25 mm = 0.25 x 10^(-3) m (converting mm to m), L = 5.0 m.
ε = (0.25 x 10^(-3) m) / 5.0 m = 0.00005 (rounded to 5 decimal places).
The strain in the wire is approximately 0.00005.
So, the answers are:
(i) stress ≈ 159238.651 N/m^2.
(ii) strain ≈ 0.00005.