Solving for Muzzle Velocity: Understanding the Heat Problem at a Crime Scene

[Physic_Scholar]

At a crime scene, the forensic investigator notes that the 8.2 g lead bullet that was stopped in a doorframe apparaently melted completely on impact. Assuming the bullet was fired at room temperature (20 degrees celsius), What is the minimum muzzle velocity of the gun that fired the bullet?

Anyone have idea on how to get muzzle velocity and what they mean by that?

so I figured this to be a latent heat of fusion with the Latent heat constant=25kJ/kg or 5.9kcal. So u apply Q=mcdelt T going from 20 celsius to 0 and then add the heat of fusion Q=mL and you can solve for total heat. How do you go from there to get the muzzle velocity? Could anyone help?

 

[siddharth]

Since the bullet completely melted on impact, I think you have to assume that the entire Kinetic Energy of the bullet before collision was converted to heat energy which melted the bullet. Then, from the conservation of Energy, you can get the velocity of the bullet before collision

 

[Physic_Scholar]

So from conservation of energy, you only have kinetic energy of bullet 1/2mv^2 whic is set to equal the latent heat of Q=mL. The units of mass cancels and so you just have v= to the value of the latent heat constant in kcal/kg? How do I convert to speed?

Can someone help me? I don't know how I can equate using cons of energy to units of velocity.

 

[siddharth]

When you are using the conservation of energy, you are equating in units of energy.
That is, in SI, $$\frac{mv^2}{2}$$ represents the Kinetic Energy in Joules. Similarly, $$Q=ml$$ is also in Joules(in SI).
So, when you find the velocity from this, the units will match.
If you use SI units for all your calculations, the value you get for velocity will have the units of m/s.