How to Determine the Final Velocity of an Iron Block?

[volcore]

Homework Statement

A mysterious crate has shown up at your place of work, Firecracker Company, and you are told to measure its inertia. It is too heavy to lift, but it rolls smoothly on casters. Getting an inspiration, you lightly tape a 0.60-kg iron block to the side of the crate, slide a firecracker between the crate and the block, and light the fuse. When the firecracker explodes, the block goes one way and the crate rolls the other way. You measure the crate's speed to be 0.058 m/s by timing how long it takes to cross floor tiles. You look up the specifications of the firecracker and find that it releases 9 J of energy. That's all you need, and you quickly calculate the inertia of the crate.

Relevant Equations

This interaction appears to be an explosive separation one, my text book gave an equation of
ΔK + ΔE int = 1/2 m1* v1f^2 + 1/2 m2 * v2f^2 + ΔE int = 0

Since the problem gave me the kinetic energy and inertia of the iron block, I could plug it into the equation K = 1/2 mv^2 to get the final velocity, I got sqrt(30) for the block's final velocity. From there, I don't really know where to go, I could plug it into the equation above, but ΔE int is unknown, and my professor never mentioned how to find it.

 

[volcore]

Never mind, I was able to solve the problem by plugging the numbers into a different equation, 0 = m1v1f + m2v2f.

 

[Cutter Ketch]

First a caveat: I don’t like this problem. You have to assume all of the firecracker’s energy goes into kinetic energy. That would never happen. Ok, fine, I’m over it.

Second, under that assumption your energy equation is correct.

Third, as the problem is written your equation has two unknowns, the mass of the crate, and the final velocity of the block. One equation can’t be solved for two unknowns. Do you know anything else?

 

[Cutter Ketch]

Ah, yes. You got to it before I could reply. You need conservation of energy and momentum.