Question

Two wires of metals A and B have unloaded lengths l_A and l_B and equal  cross sectional area α. They are loaded as in the figure with weights W₁ and W₂ . 

If the Young’s moduli are Y_A for A and Y_B for B, calculate elongations in A and B due to loading.

Answer 1

The free body diagrams are shown for wire A, loads W₁ and W₂ , and wire B. We see that

T_B = W₂ ...(i)

T_A = W₁ + T_B ...(ii)

The stress in wire A is

The stress in wire B is