How Fast Must a Bullet Travel to Melt on Impact?

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    Thermodynamics
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SUMMARY

The discussion centers on calculating the minimum nozzle velocity required for a 7.2g lead bullet to melt upon impact with a door frame. The forensic investigator utilizes the specific heat capacity of lead (C_lead = 130 J/kg°C) and the latent heat of fusion (L_lead = 2.5 x 10^4 J/kg) to determine the energy needed to raise the bullet's temperature to its melting point (327°C) and subsequently melt it. The total energy required is calculated as Q = mc(ΔT) + mL, leading to a conclusion that the kinetic energy must equal this total energy to find the necessary velocity.

PREREQUISITES
  • Understanding of thermodynamics, specifically heat transfer and phase changes.
  • Familiarity with the concepts of specific heat capacity and latent heat.
  • Knowledge of kinetic energy calculations (K = 1/2 * m * v^2).
  • Basic algebra skills for manipulating equations and solving for unknowns.
NEXT STEPS
  • Calculate the total energy required to heat and melt the lead bullet using the formula Q = mc(ΔT) + mL.
  • Learn how to derive the minimum velocity from kinetic energy equations.
  • Explore the implications of bullet velocity on forensic investigations and material science.
  • Study the effects of different materials and their melting points in impact scenarios.
USEFUL FOR

This discussion is beneficial for forensic investigators, physics students, and anyone interested in the mechanics of projectiles and material properties under impact conditions.

riverjib
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Homework Statement


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


Homework Equations


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!
 
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What is the total energy needed to melt the bullet? Remember, it has to be first heated up to the melting point, and the total energy is equal to energy needed to heat it and then melt it. This energy has to come from the kinetic energy.
 

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