Kinetic Energy Lost in Bullet Penetrating Can

[Mivz18]

Problem:

A bullet of mass 0.018 kg and initial speed 300 m/s penetrates an initially stationary pop can of mass 0.055 kg and emerges with a speed 200 m/s.

A) What is the initial momentum of the bullet and pop can system?
I found this answer by 0.018 * 300 = 5.6

B) What is the final momentum of the bullet?
I found this answer by 0.018 * 200 = 3.6

C) How fast is the can moving after the bullet emerges?
I found this answer by 0.018(300-200) and then took that quantity and divided it by 0.055 = 32.73 m/s

D) How much kinetic energy was lost (to heat, sound, deformation of can and bullet,...) in the process? Give your answer as a positive number.

Here is my problem. I don't know how to obtain this. I thought that maybe I could calculate it by KE1 + KE2 = KE1 + KE2 where the left side of the equation is before the collision and the right side is after. Then when I add the right side, it is a little off from the left, so I thought that was the KE lost. However, the online program I'm using says it isn't. What am I doing wrong or how can I go about achieving this?

 

[NateTG]

I think you have the right idea. Perhaps you missed something setting up your equation - can you show it with numerical values filled in?

 

[Mivz18]

This is what I got:

(1/2)m1v1 + (1/2)m2v2 = (1/2)m1v1 + (1/2)m2v2
(1/2)(0.018)(300^2) + (1/2)(0.055)(0^2) = (1/2)(0.018)(200^2) + (1/2)(0.055)(32.73^2)

From this I get 810 = 389.46
where 810 - 389.46 = 420.54 Lost ??

 

[Mivz18]

nevermind, answered my own question, lol. Thanks!

 

[NateTG]

Yeah, you might want to set up the equation like this:
$$KE_f=KE_0+\Delta E$$
So that you end up solving for an unknown rather than setting up a broken equality.