Question

A 9.00-g lead bullet leaves the rifle at a temperature of 80.0 ˚C and hits a steel plate. If the bullet melts on impact, what is the minimum speed it must have? a) 221 m/s b) 251 m/s c) 335 m/s d) 350 m/s

Answer 1

Solution:

Here, kinetic energy of the bullet will gets converted into heat energy required to melt the bullet after impact.

=> 1/2 mv² = mc ?T + mL

where, m = mass of the bullet,  ?T is the temperature difference = 600-(273+80) = 247K. { Mellting temperaure of lead bullet = 600K}

c = specific heat = 125 Jkg^-1K^-1 and L = latent heat of fusion = 2.5*10^4 Jkg^-1

=> 1/2 v^2 = c ?T + L

=> v^2 = 125*247*2 + 2.5*2*10^4

=> v = 335 m/s.

Hence, option (c) is correct.