Question

It is claimed that if a lead bullet goes fast enough, it can melt completely when it comes to a halt suddenly, and all its kinetic energy is converted into heat via friction. Find the minimum speed of a lead bullet (initial temperature = 27.4 °C) for such an event to happen.

Answer 1

354.72 m/s

Step-by-step explanation:

`m` = mass of lead bullet

`c` = specific heat of lead = 128 J/(kg °C)

`L` = Latent heat of fusion of lead = 24500 J/kg

`T_(i)` = initial temperature = 27.4 °C

`T_(f)` = final temperature = melting point of lead = 327.5 °C

`v` = Speed of lead bullet

Using conservation of energy

Kinetic energy of bullet = Heat required for change of temperature + Heat of melting

`(0.5) m v^(2) = m c (T_(f) - T_(i)) + m L\\(0.5) v^(2) = c (T_(f) - T_(i)) + L\\(0.5) v^(2) = (128) (327.5 - 27.4) + 24500\\(0.5) v^(2) = 62912.8\\v = 354.72 ms^(-1)`