Thermodynamics, bullet fired into ice

Question

I'm beginning to study basic thermodynamics and I want to solve this exercise:

It fires a lead bullet from $3g$ to $30^oC$ with a speed of $240\frac{m}{s}$ to a block of ice at $0^0C$. How much ice melts? (the bullet remains embedded in the ice).

I think that the energy becomes kinetic friction: $$Q=K=\frac{1}{2}mv^2=86,4J$$ Then, I can find the mass of ice from the ecuation of latent heat: $$Q=mL_{f}$$ $$\implies m= 0,26 g$$

Is this correct? Do not influence the temperature of the bullet?

Thanks for your help.

Answer 1

You've made an excellent start on the problem, and you've identified most of the relevant equations. However, you do need to take the temperature of the bullet into account. Since you know what the bullet is made of (lead) and how much mass it has, you can figure out how much heat it will lose coming down to the temperature of the ice. That heat will also contribute to melting some ice.

As a side note, in this case, there's infinite ice, so you don't have to worry about running out of ice to melt. In other problems, you need to watch out for situations where you have a finite mass of ice and it all might melt, so that you have to calculate how much heat goes into melting the ice, then account for the rest of the heat warming up the ice + bullet system.