Physics Help Forum Initial velocity of lead bullet at 27 degrees Celsius

 Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum

 May 1st 2011, 06:52 PM #1 Junior Member   Join Date: Mar 2011 Posts: 25 Initial velocity of lead bullet at 27 degrees Celsius I really do not know where to begin with this one. What i have written down is: T = 27 degrees Celsius final velocity = 350 m/s Latent heat of fusion for lead = 24,500 J/kg c (of lead) = 130 J/kg*K Somehow, I need to calculate the mass of the bullet. Once i find the mass, i can plug that into: K = 1/2 m v ^2 for when the bullet is at rest and when it is shot out of the rifle and then solve for "v (initial)"? Am i on the right track? Thanks
May 1st 2011, 07:00 PM   #2

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 Originally Posted by pre pt marc I really do not know where to begin with this one. What i have written down is: T = 27 degrees Celsius final velocity = 350 m/s Latent heat of fusion for lead = 24,500 J/kg c (of lead) = 130 J/kg*K Somehow, I need to calculate the mass of the bullet. Once i find the mass, i can plug that into: K = 1/2 m v ^2 for when the bullet is at rest and when it is shot out of the rifle and then solve for "v (initial)"? Am i on the right track? Thanks
There is, of course, a relationship between the final speed of the bullet, the initial speed of the bullet and the work done on it. In this case the work would be due to air resistance and (I'm assuming) is going to manifest itself as heat ie temperature. So
W = -Q = K(final) - K(initial)

If you can find Q you can find the difference in the kinetic energies. But you need a final temperature to get Q. (Notice that since Q = mC(Delta)T so the m's cancel in the work equation. You don't need the mass of the bullet.) And is the question providing the heat of fusion or did you give that? That doesn't help unless the bullet is melting...

-Dan
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 May 1st 2011, 07:37 PM #3 Junior Member   Join Date: Mar 2011 Posts: 25 The original problem was: What must the initial speed of a lead bullet be at a temperature of 27.0^\circ C so that the heat developed when it is brought to rest will be just sufficient to melt it? Assume that all the initial mechanical energy of the bullet is converted to heat and that no heat flows from the bullet to its surroundings. (Typical rifles have muzzle speeds around 350 {\rm m/s}.) For the latent heat of fusion, i referenced that from a table in our physics textbook.
May 1st 2011, 10:07 PM   #4

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 Originally Posted by pre pt marc The original problem was: What must the initial speed of a lead bullet be at a temperature of 27.0^\circ C so that the heat developed when it is brought to rest will be just sufficient to melt it? Assume that all the initial mechanical energy of the bullet is converted to heat and that no heat flows from the bullet to its surroundings. (Typical rifles have muzzle speeds around 350 {\rm m/s}.) For the latent heat of fusion, i referenced that from a table in our physics textbook.
Okay, so Q = mL + mC(Delta)T. The final temperature you need is teh melting point of lead.

-Dan
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 May 12th 2011, 11:24 AM #5 Senior Member   Join Date: Jun 2010 Location: NC Posts: 408 Hello, pre pt marc, There is a similar solution here. It should give you some undestanding of method. Springfield Rifle Musket (D325) Good Luck! Jim
 May 13th 2011, 08:41 AM #6 Senior Member   Join Date: Jun 2010 Location: NC Posts: 408 Hello pre pt marc, I thought I left a reference before. I don't see it? Maybe it got lost. There s a proper solution to your problem at this URL: Springfield Rifle Musket (D325) By the way, this event does not involve heat. 1) Heat transfer requires time; the impact is immediate. 2) The temperature of the bullet goes up. Hence, were there heat, the direction would be "to the surroundings," which would forestall melting. It is best to use an energy equation. Good Luck, Jim

 Tags bullet, celsius, degrees, initial, lead, velocity