A machinist bores a hole of diameter 1.360 cm in a steel plate that is at 24.2 ∘C. What is the cross-sectional area of the hole when the temperature of the plate is increased to 156∘C? Give an answer in cm2 with 3 significant figures. Assume that the coefficient of linear expansion remains constant over this temperature range.

Respuesta :

Answer:

[tex]A=1.4598 cm^2[/tex]

Explanation:

The cross sectional area of the hole can be find using

Δ[tex]A=2*\alpha *A_0*T'[/tex]

[tex]A-A_0=2*\alpha*A_0*T'[/tex]

[tex]A=A_0*(2*\alpha*T'+1)[/tex]

[tex]T'=156-24.2=131.8C[/tex]

[tex]A_0=\pi *r^2[/tex]

[tex]A_0=\pi *0.68cm^2=1.452 cm^2[/tex]

Steel coefficient [tex]\alpha=1.2x10^{-5}C^{-1}[/tex]

replacing to find A

[tex]A=1.4552cm^2*(2*1.2x10^{-5}C^{-1}*131.8C+1)[/tex]

[tex]A=1.4598 cm^2[/tex]