Determine the lowest height from which a hammer weighing 19 N should fall so that the temperature of a copper

Determine the lowest height from which a hammer weighing 19 N should fall so that the temperature of a copper plate weighing 0.01 kg increases by 10 * C from its impact. The specific heat capacity of copper is -380 J / (kg * C)

Pm = 19 N.

g = 9.8 m / s ^ 2.

mp = 0.01 kg.

Cm = 380 J / kg * ° С.

Δt = 10 ° C.

h -?

When the hammer falls, all of its potential energy En is converted into kinetic Ek, and then into the internal energy of the plate U.

En = ΔU.

Due to the increase in internal energy, the temperature of the copper plate increases, it heats up.

Ep = m * g * h = Rm * h.

We find the change in the internal energy of the plate by the formula: ΔU = Cm * mp * Δt.

Rm * h = Cm * mp * Δt.

h = Cm * mp * Δt / Rm.

h = 380 J / kg * ° C * 0.01 kg * 10 ° C / 19 N = 2 m.

Answer: The smallest drop height of the hammer is h = 2 m.