Hello and welcome to the physics community! It's great to have you here. As for your question, let's break it down step by step.
First, it's important to understand what Young's modulus represents. It is a measure of the stiffness or elasticity of a material, specifically how much it will stretch or compress under a given amount of stress. In other words, it tells us how much force is needed to cause a certain amount of deformation in the material.
Now, in order to calculate stress, we need to know the formula for stress. It is defined as the force applied divided by the cross-sectional area of the material. In mathematical terms, it is expressed as:
Stress = Force / Area
In your case, the force is the stress needed to produce a strain of 1.44*10^-3, and the area is the cross-sectional area of the metal. So, we can rewrite the formula as:
Stress = (1.44*10^-3) / Area
Next, we need to find the cross-sectional area of the metal. This can vary depending on the shape and size of the metal, but for the sake of simplicity, let's assume it is a rectangular bar with a length of 1 meter and a width of 1 meter. In this case, the area would be 1 square meter or 1 m^2.
Now, we can plug in the values into the formula:
Stress = (1.44*10^-3) / (1 m^2)
Stress = 1.44*10^-3 N/m^2
Finally, we can use the value of Young's modulus to convert this into the stress needed for the metal. Young's modulus is expressed in pascals (Pa), so we can multiply the stress by the value of Young's modulus to get our final answer:
Stress = (1.44*10^-3 N/m^2) * (1.9*10^11 Pa)
Stress = 2.736 N/m^2
So, the stress needed to produce a strain of 1.44*10^-3 for a metal with a Young's modulus of 1.9*10^11 is 2.736 N/m^2. I hope this helps to clarify the process for you. Let us know if you have any further questions. Happy learning!
