(a)The "lead" in pencils is a graphite composition with Young's modulus of about 1 x10^9 N/m^2. Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.

Question

(a)The "lead" in pencils is a graphite composition with Young's modulus of about 1 x10^9 N/m^2. Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force  of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.

johnweldon1993 · Answer

Well remember how everything is connected

$$\large \delta = E\epsilon $$
And we know
$$\large \delta = \frac{F}{A}$$
and
$$\large \epsilon = \frac{\Delta L}{L}$$
So

$$\large \frac{F}{A} = E\frac{\Delta L}{L}$$

Just solve that for $\large \Delta L$

$$\large \Delta L = \frac{FL}{AE}$$

*You'll see later this is actually the deflection