What is the minimum muzzle velocity required to melt a lead bullet on impact?

[terry2112]

1. Homework Statement

hey guys, i am new in this forums and would love help with a question i have encountered with an assignment that i am doing.The question is :

At a crime scene, the forensic investigator notes that a 8.2g lead bullet that was stopped in a door frame apparently melted completely on impact. Assuming the bullet was fired at room temperature(20 degree celcius), what does the investigator calculate as the minimum muzzle velocity of the gun?

cheers

2. Homework Equations


equation i tried is 0.5mv^2=3/2 k T

k=boltzman constant

3. The Attempt at a Solution

i got a really really small answer for it so i doubt that is the correct solution to it. I read through that part in my textbook and don't seem to find any similar questions. Hope that someone is able to clarify and make me understand what i am suppose to do.I have a test coming up as well,so solutions and an explanation to this question would be very much appreciated.

Cheers

 

[Doc Al]

equation i tried is 0.5mv^2=3/2 k T

The bullet is not an ideal monoatomic gas!

Instead, consider the specific heat of the bullet.

 

[terry2112]

i'm still a bit confused,sorry,not really that good at this part in physics!

specific heat is energy required to increase the temperature by 1 degree.

not really sure how this applies to this question.

cheers

 

[Doc Al]

You have the amount of energy that was used to increase the temperature of the bullet: that's the bullet's initial kinetic energy. Using the specific heat of lead you can calculate the initial speed in terms of the change in temperature.

Read this: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html"

[edit: You are given the temperature change and need to calculate the speed. I had it reversed.]

 

[terry2112]

i have found the specific heat of lead to b 0.0305.
I have the mass of lead 130 J/kg.degree celcius

By using that, how am i able to find the amount energy used to increase the temperature of the bullet? i need the change in temperature?would that be the melting point of lead? then q=0.5mv^2?

 

[terry2112]

Sorry,melting point of lead - the initial temperature?

cheers

 

[Doc Al]

i have found the specific heat of lead to b 0.0305.
I have the mass of lead 130 J/kg.degree celcius

You want the specific heat of lead in J/gm degree celcius. The mass of the lead is given.

By using that, how am i able to find the amount energy used to increase the temperature of the bullet? i need the change in temperature?would that be the melting point of lead? then q=0.5mv^2?

Since you're told that the lead melts, you know the final temperature is the melting point of lead. The energy is the kinetic energy of the bullet (which depends on speed). Set up an equation and solve for the speed which just melts the lead.

Just to be clear (I had left this out earlier ): The initial KE of the bullet ends up doing two things: (a) raising the temperature of the bullet to the melting point; this involves the specific heat of lead; (b) melting the bullet; this involves the heat of fusion (phase change) of lead. When you set up your equation, be sure to use the total energy of (a) + (b).