The lead ball flies at a speed of 20 m / s and hits the steel plate. How much will the temperature of the ball

The lead ball flies at a speed of 20 m / s and hits the steel plate. How much will the temperature of the ball change after impact if 50% of the mechanical energy is transferred to the internal one?

Data: V (speed of flight of the lead ball) = 20 m / s; η (percentage of the mechanical energy of the ball, converted into internal energy) = 50% (0.5).

Reference values: Cc (specific heat of lead) = 140 J / (kg * K).

We express the change in temperature of the lead ball under consideration from the equality: Cc * m * Δt = η * m * V ^ 2/2, whence Δt = η * m * V ^ 2 / (2 * Cc * m) = η * V2 / (2 * Cc).

Let’s calculate: Δt = 0.5 * 20 ^ 2 / (2 * 140) = 0.714 ºС.

Answer: The temperature of the lead ball will increase by 0.714 ºС.