Physics Question

Question

The “lead” in pencils is a graphite composition with Young’s modulus of approximately 1.0×10⁹ 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 5.6 N. The lead is 0.51 mm in diameter and 53 mm long.

Round your answer to 5 decimal places

Answer 1

The equation to use here is F / A = Y ΔL / L₀ where F is the force in newtons, A is the cross- sectional area, Y is Young's modulus, ΔL the change is length, L₀ the original length.

Changing the length and diameter to meters

A = pi x (0.51 mm x 1 m / 1000 mm)² = 8.16714 x 10^-7 m²

L₀ = 53 mm x 1m/1000 mm = 5.3 x 10^-2 m

Solve for ΔL, ΔL = F x L₀ / Y x A = 3.63408 x 10^-4 m

Check math.