Question

Part A A rod cf length L is clamped rigidly at both ends. Its temperature increases by an amount AT, and in the ensuing expansion it cracka to form two atraight pieces, s shown in the figure (Figure 1). coefficient of linour expansion a Find an expression for the distarioo d shown in the fiqure, in terrns of L0. AT. and AXh Reouest Answen Submit Provide Feedback Figure 1 of 1

Answer 1

change in length = original length *coefficient of linear expansion *change in temperature

$\Delta$L = L_o*$\alpha$*$\Delta$T

The new length of the rod = Lo +Lo$\alpha$*$\Delta$T

= Lo(1 + $\alpha$*$\Delta$T)

now it clamps at the midpoint so half of the length = Lo/2 ( 1 + $\alpha$*$\Delta$T)

Using Pythagoras Theorem we have

(Lo/2 ( 1+$\alpha$*$\Delta$T))^2 = Lo^2 + d^2

d = sqrt( (Lo/2 ( 1+$\alpha$*$\Delta$T))^2 - Lo^2)

= Lo *sqrt( ( 1+$\alpha$*$\Delta$T)^2 /4 - 1)