Question

In figure the upper wire is made of steel and the lower of copper. The wires have equal cross section. Find the ratio of the longitudinal strains developed in the two wires.
Figure

Answer 1

The Required Ratio is 20:13

Explanation:

Given,

1. Both wires have equal Lengths & Cross Sectional Area, so block applies equal tensions on both.

So, $L_s_t_e_e_l = L_C_u$

$A_s_t_e_e_l = A_C_u$

$F_C_u = F_s_t_e_e_l$

$\frac {Strain\ of\ Cu}{Strain\ of\ steel}$ = $\frac {\frac {\Delta L_s_t_e_e_l}{L_s_t_e_e_l}}{\frac {\Delta L_C_u}{L_C_u}}$ = $\frac {F_s_t_e_e_l\ L_s_t_e_e_l\ A_c_u\ Y_c_u}{A_s_t_e_e_l\ Y_s_t_e_e_l\ F_c_u\ L_c_u}$

Using $\frac {\Delta L}{L} = \frac {F}{AY}$

⇒$\frac {Strain of Cu}{Strain of steel} = [tex]\frac {Y_c_u}{Y_s_t_e_e_l} = \frac {1.3\times 10^1^1}{2\times 10^1^1}$

⇒$\frac {Strain\ of\ steel}{Strain\ of\ Cu} = \frac {20}{3} = 1.54$

The required ratio for, the longitudinal strains is 20 : 13.