Question

3) A lead bullet initially at 30 C just melts upon striking a target. Assuming that all of the initial kinetic energy of the bullet goes into the internal energy of the bullet to raise its temperature and melt it, calculate the speed of the bullet upon impact. (Specific heat of lead is 0.128 kJ/kg K and lead latent heat of fusion is 24.7 kJ/Kg and melting point of lead is 600 K).

Answer 1

The speed of bullet is 354.2 m/s

Step-by-step explanation:

initial temperature, T = 30 degree C

specific heat, c = 128 J/kg K

Latent heat, L = 24.7 x 1000 J/kg

melting point = 600 K = 327 degree C

Let the mass is m and the speed is v.

Kinetic energy = heat used to increase the temperature + Heat used to melt

`(1)/(2) mv^2 = m c (T' - T) + m L\\\\0.5 v^2 = 128 * (327 - 30) + 24.7* 1000\\\\0.5 v^2 = 38016 + 24700 \\\\0.5 v^2 = 62716\\\\v = 354.2 m/s`