Question

The "lead" in pencils is a graphite composition with a Young’s modulus of approximately 1.0×10^9 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.

a) 0.048 mm
b) 0.096 mm
c) 0.144 mm
d) 0.192 mm

Answer 1

The change in length of the lead in an automatic pencil is approximately 0.048 mm.

Step-by-step explanation:

To calculate the change in length of the lead in an automatic pencil, you can use Hooke's law, which states that the change in length is directly proportional to the force applied and inversely proportional to the Young's modulus. In this case, the force applied is 4.0 N and the Young's modulus is 1.0 x 10^9 N/m^2. The lead is 0.50 mm in diameter and 60 mm long. We can calculate the change in length using the formula:

Change in length = (Force * Length) / (π * (Radius^2) * Young's modulus)

Plugging in the values:

Change in length = (4.0 N * 60 mm) / (π * (0.25 mm)^2 * (1.0 x 10^9 N/m^2))

After performing the calculations, the change in length of the lead is approximately 0.048 mm.