Question

The “lead” in Ballpen is a graphite composition with Young’s modulus of approximately 1.2×10⁹ N/m². Calculate the change in length of the lead in an automatic ballpen if you tap it straight into the ballpen with a force of 7.8 N. The lead is 0.55 mm in diameter and 80 mm long

Answer 1

The change in length is

$$\Delta l=\epsilon l.$$

The stress:

$$\sigma=\frac FA=\frac{4F}{\pi d^2}.$$

On the other hand, this stress can be expressed as

$$\epsilon=\frac \sigma E=\frac{4F}{\pi d^2E}.$$

Finally, the change in length is

$$\Delta l=\epsilon l=\frac{4Fl}{\pi d^2E}=2.19\text{ mm}.$$