Question

A 2.2-m-long steel rod must not stretch more than 1.2 mm when it is subjected to a 10.0-KN tension force. It is given that E = 200 GPa. Determine the smallest diameter rod that should be used. The smallest diameter rod that should be used is 9.96 mm.

Answer 1

To identify the smallest diameter rod for these conditions, one must calculate the tensile stress and strain, then use Young's Modulus to find the required cross-sectional area and solve for the rod's diameter.

Step-by-step explanation:

The size of the smallest diameter rod that should be used to ensure that a 2.2-m-long steel rod does not stretch more than 1.2 mm under a 10.0-KN tension force can be calculated using the relationship between stress, strain, and Young's Modulus (E), which is 200 GPa for steel.

Strategy

First, we calculate the tensile stress (σ) using the formula σ = F/A, where F is the force applied and A is the cross-sectional area of the rod. Then, we apply Hooke's Law to find the stretch (ε), where ε = σ/E, and E is Young's Modulus for steel. Rearranging for A, we get A = F/(E×ε). Since the area of a circle is A = πd^2/4, where d is the diameter, we can solve for d after calculating A.