A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, calculate the initial speed of the bullet. The initial temperature of the bullet is 27∘C and its melting point is 327∘C. Latent heat of fusion of lead = 2.5 × 104 J kg−1 and specific heat capacity of lead = 125 J kg−1 K−1.
Let the mass of the bullet = m.
Heat required to take the bullet from 27∘C to 327∘C.
= m × (125 Jkg−1K−1)(300K)
= m × (3.75 × 104 J kg−1).
Heat required to melt the bullet
= m × (2.5 × 104Jkg−1)
If the initial speed by v, the kinetic energy is 12mv2 and hence the heat developed is
12(12mv2) = 14mv2. Thus, 14mv2 = m(3.75+2.5) × 104Jkg−1
or, v = 480 m s−1.