(a) The “lead” in pencils is a graphite composition with a Young’s modulus of about 1×109 N / m2 . 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. (b) Is the answer reasonable? That is, does it seem to be consistent with what you have observed when using pencils?

Solution to 31PE

Step 1 of 3</p>

We need to find the change in length of the lead if we apply a force of while pushing it into the pencil.

We have to use the concept of elasticity and linear strain to compute the change in length.

Given data:

Young’s modulus of elasticity,

Force on the lead

Original length of the lead,

Radius of the lead,

Cross-sectional area of lead,

Step 2 of 3</p>

(a)

We will use the concept of elasticity:

is the change in length due to application of tensile force.

is the Young’s modulus of elasticity

is the cross -sectional area

is the initial length.

is the tensile force.

Thus, the change in length is,