Question

17.19 Q

A machinist bores a hole of diameter 1.31 cm in a steel plate at a temperature of 25.5 ∘C.

1-

What is the cross-sectional area of the hole at 25.5 ∘C .

Express your answer using four significant figures.

2-

What is the cross-sectional area of the hole when the temperature of the plate is increased to 150 ∘C ? Assume that the coefficient of linear expansion remains constant over this temperature range.

Express your answer using four significant figures.

Answer 1

1) A°= π * d ^2 / 4
A°= 3.14 * (1.31)^2 / 4 = 1.347 cm2 =1.347 * 10^-4 m²

2) A = A° ( 1 + 2 α Δ t )
α steel = 13 * 10^-6 / °C
A = 1.347*10^-4 ( 1 + 2 * 13 *10^-6 * 150 )
A = 1.347*10^-4 ( 1 + 3.9 10^-3 )
A = 1.35225 *10^-4 m²