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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.

Respuesta :

Answer:

354.72 m/s

Explanation:

[tex]m[/tex] = mass of lead bullet

[tex]c[/tex] = specific heat of lead = 128 J/(kg °C)

[tex]L[/tex] = Latent heat of fusion of lead = 24500 J/kg

[tex]T_{i}[/tex] = initial temperature = 27.4 °C

[tex]T_{f}[/tex] = final temperature = melting point of lead =  327.5 °C

[tex]v[/tex] = Speed of lead bullet

Using conservation of energy

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

[tex](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}[/tex]

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