A forensic investigator notes a 7.2g lead bullet stopped in a door frame melted completely on impact. Assuming the bullet was shot at RT (20C) what would the investigator calculate as the minimum nozzle velocity of the gun to be? (C_lead = 130J/kg*C), (L_lead = 2.5*10^4J/kg) Lead melts at 327C
Q = mc(delta)T
K = 1/2*m*v^2 (?)
The Attempt at a Solution
I know that the objective of this problem is to use the energy to determine the velocity. I found that Q = 287.4J. I'm not sure what to do from here, however. If I multiply 2.5*10^4J/kg by 0.0072kg, I get 180J. Do I subtract this from 287.4J, and use the result to calculate velocity? Is the difference kinetic energy? I'm not sure if I'm on the right track here. Any help is appreciated!