Question

The two diagrams below represent a metalrod with an initial leangth $L_{1}$ which is then stretched (elongated) to a length $L_{2}$

The strain measure $(\epsilon)$ is defined as a ratio of elongation with respect to the original length and is given by the formula:

$$ \epsilon = \dfrac{L_{2}-L_{1}}{L_{1}}$$

1. Express $L_{1}$ as the subject of the formula.
2. Hence, or otherwise, calculate the value of $L_{1}$ if $\epsilon=0.8$ and $L_{2}=18$ cm
3. Convert the value obtained in 2 to a binary number.

Answer 1

1. eL1 = L2 - L1

    eL1 + L1 = L2

         L1(e + 1) = L2

          L1 = L2/(e + 1)

2. L1 = 18/(0.8 + 1)

        = 10 cm

3. 10 = 8 + 2 = 2^3 + 2

        = 1010