Answer:
Here is the example how to do it
Explanation:
We can use the formula for the modulus of elasticity to solve for the diameter of the steel rod:
modulus of elasticity = (stress / strain) = (force / area) / (change in length / original length)
Solving for the area of the steel rod, we get:
area = (force * original length) / (modulus of elasticity * change in length)
Substituting the given values, we get:
area = (8,000 lb * 420 in) / (30,000,000 psi * 0.266 in) = 0.105 in^2
The area of a circle is given by the formula:
area = pi * (diameter/2)^2
Substituting the value we just calculated, we get:
0.105 in^2 = pi * (diameter/2)^2
Solving for the diameter, we get:
diameter/2 = sqrt(0.105 in^2 / pi) = 0.182 in
diameter = 2 * 0.182 in = 0.364 in
Therefore, the diameter of the steel rod is 0.36 in (to two decimal places).