Conservation of Momentum and KE (bullet through a pop can)

[CaptainSFS]

Homework Statement

A bullet of mass 0.008 kg and initial speed 300 m/s penetrates an initially stationary pop can of mass 0.042 kg and emerges with a speed 210 m/s.

What is the initial momentum of the bullet and pop can system?
=2.4 kgm/s

What is the final momentum of the bullet?
=1.68 kgm/s

How fast is the can moving after the bullet emerges?
=17.143 m/s

How much kinetic energy was lost (to heat, sound, deformation of can and bullet,...) in the process? Give your answer as a positive number.
=(i don't know)

Homework Equations

p=mv

KE=.5*m*v²

The Attempt at a Solution

I tried finding different values for the initial and final velocity of the system many different ways, and then plugging into the KE equation to get the difference in KE. Every value I find seems to be incorrect.

I took the inital momentum (2.4) and divided it by the total mass of the system (.05) to find the initial v (48). I'm not sure if this is correct or not. I've tried other values, but this is the one I've been most comfortable with, it may very well likely be incorrect.

As for the final velocity, I've found different values, none I'm too confident with.

Any help is much appreciated. Thx. :)

 

[Rake-MC]

Ignore the momentum for this part of the question.

You know by conservation of energy, the initial energy in the system must equal final energy (although some will be 'lost' to heat and sound in this question so it will not equal final for the measured amounts).

$$\frac{1}{2}m_{b}v_1^2 + \frac{1}{2}m_cv_2^2 = \frac{1}{2}m_bv_3^2 + \frac{1}{2}m_cv_4^2$$

Solve for the initial value and then the final value. Subtract final from initial and you will get the amount that dissipiated to heat sound etc.

 

[CaptainSFS]

Hey, thanks. That makes sense, I should have been thinking that simple. It worked out, thanks again. :)