Question

A lead bullet of unknown mass leaves a rifle at a temperature of 87 C and hits a steel plate. Upon impact exactly half of the bullet's mass melts. Assume that only 40% of the bullet's initial kinetic energy goes into increasing its temperature and then partially melting it. What was the initial speed of the bullet? melting temperature of LEAd: 327 C specific heat of Lead: 0.13E3 J/(Kg.K) Latent heat of fusion: 22.9E3 J/kg

Answer 1

Total Energy is conserved during the phase changes.

As Energy required to change the temperature of lead bullet is m*S*T = m*0.13*10³ J ..................(1)

Energy required to melt the lead bullet on hitting with steel plate is (m')L = (m/2)*22.9*10³ J...............(2)

Both the energies are used by 40% initial kinetic energy of bullet

Total Energy is conserved during the phase changes.

As Energy required to change the temperature of lead bullet is mS = m*0.13*10³ J..................1`

Energy required to melt the lead bullet on hitting with steel plate is (m')L = (m/2)*22.9*10³ J...............2

Both the energies are used by 40% initial kinetic energy of bullet

m*0.13*10³ + (m/2)*22.9*10³ = 0.40*(K.E_i)

m*0.13*10³ + (m/2)*22.9*10³ = 0.40*1/2*mv²

v² = 57900

v = 240.62 m/s

= 0.40*(K.E_i) = 0.40*1/2*mv²

v² = 57900

v = 240.62 m/s