Question

Estimate the speed that a lead bullet must have in order that it melts completely when it strikes a target. Assume that all the bullet’s kinetic energy goes into heat and that the bullet is initially at 20oC. The specific heat capacity of lead is 130 J / (kg oC), its melting point is at 327oC its latent heat of fusion is 24.5 kJ/kg.

Answer 1

Step 1: Find energy required to melt 'm' kg bullet:

Q = Q1 + Q2

Q1 = energy required to raise temperature of bullet from 20 C to 327 C = m*C*dT

Q2 = energy required to melt the bullet = m*Lf

Q = m*C*dT + m*Lf

Using given values:

Q = m*130*(327 - 20) + m*24.5*10^3 = m*(130*307 + 24.5*10^3)

Q = m*64410

Step 2: Now to generate same amount of energy, initial kinetic energy of bullet should be equal to required energy, So

KE = Q

(1/2)*m*V^2 = Q

V = sqrt (2*Q/m)

V = sqrt (2*64410*m/m) = sqrt (2*64410)

V = required speed of bullet = 358.915 m/s

V = 359 m/s

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