A steel splinter falls from a height of 1000m, how much the splinter will heat up

A steel splinter falls from a height of 1000m, how much the splinter will heat up, if we assume that only 40% of the potential energy is converted into heat.

To calculate the change in temperature of a steel fragment, we will use the formula: η = Q / Ep = Cc * m * Δt / (m * g * h) = Cc * Δt / (g * h), from where we express: Δt = η * g * h / Cc.

Constants and variables: η – process efficiency (η = 40% = 0.4); g – acceleration due to gravity (g ≈ 10 m / s2); h is the height of the fall of the fragment (h = 1000 m); Сс – specific heat capacity of steel (Сс = 500 J / (kg * K)).

Let’s calculate: Δt = η * g * h / Сс = 0.4 * 10 * 1000/500 = 8 ºС.

Answer: The steel splinter should have heated up to 8 ºС.