Physic Homework

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 2.5 N. The lead is 0.35 mm in diameter and 53 mm long.



Round your answer to 5 decimal places.

Answer 1

Young's modulus, E, is given by the equation E = σ/ε, where σ = F/A, and ε = ΔL/L₀, giving E = (F/A)/(ΔL/L₀) = L₀F/(AΔL). F is force, A is cross sectional area, L₀ is the original length, and ΔL is the change in length. We need to rearrange for ΔL to get ΔL = L₀F/(EA) = (53mm*2.5N)/(1.0x10⁹ N/m² * π * (.35/2mm)^2) = .00138m or 1.38mm.