A force of 400N is applied to a brass of length 1.9m and cross-sectional area 1.2*10^11, find the extension of the brass?
To find the extension of the brass, we need to use Hooke's Law, which states that the extension of a material is directly proportional to the force applied, given that the material is within its elastic limit.
Hooke’s Law is given by the equation:
F = k * ΔL
Where:
F is the force applied to the material,
k is the spring constant (also known as the modulus of elasticity) of the material,
ΔL is the change in length (extension) of the material.
In this case, we have:
F = 400N (force applied)
ΔL = ? (extension we want to find)
We are not given the spring constant (k) for brass. However, we can use another equation to find it:
k = stress / strain
Where:
stress = force / area
strain = ΔL / original length
In this case, we have:
area = 1.2 * 10^11 (cross-sectional area of the brass)
original length = 1.9m (length of the brass)
First, let's calculate the stress:
stress = F / area = 400N / (1.2 * 10^11) m²
Next, let's calculate the strain:
strain = ΔL / original length
Now, we can rearrange the Hooke's Law equation to solve for ΔL:
ΔL = F / k
By substituting the value of k as stress / strain, we can calculate ΔL.