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

Answer:

354.72 m/s

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

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