Answer to Question #174029 in Classical Mechanics for Vyncen

Question

Young's modulus for steel is 2×10^11N/m^2. A weight of 100N hangs from a steel wire of length 3m and cross-sectional area 1.5×10^-6m^2. If the extension is 0.25mm, calculate the extension produced

Answer 1

The extension is 0.25 mm as stated in the condition of the problem. Check whether this is a correct value.

The stress is

$$\sigma=\frac{F}{A}=66.67·10^6\text{ N/m}^2.$$

The strain is

$$\epsilon=\frac{\sigma}{E}=\frac{\Delta l}{l},\\\space\\ \Delta l=l\frac{\sigma}{E}=1·10^{-3}\text{ m}.$$

Thus, the actual extension should be 1 mm