Elastic Collisions (Kinetic energy)

[Magma828]

Homework Statement

A nuclear fusion reaction occurs when a deuterium nucleus, mass 2m, and a tritium nucleus, mass 3m, combine (each with velocity v in opposite directions). Most of the energy released in the fusion is carried away in the kinetic energy of the product neutron, mass m, and velocity 5v. The other product is a helium nucleus, mass 4m, and velocity v.

(a) Show in terms of m and v that momentum is conserved in the process.
I've done this part, I don't need help with it. I'm just posting it incase it's a sub-step for the next part. The answer is -mv=-mv

(b) Calculate the kinetic energy released in the fusion in terms of m and v.

I'm stuck with part b. For part a I had to use all the data in the question, I'm guessing that for part b I only have to use the masses and velocities before the collision.

Homework Equations

E_k = 0.5mv²

The Attempt at a Solution

This is what I've done so far:
E_k = 0.5mv²

v₁ = 1v
m₁ = 2m
v₂ = 1v
m₂ = 3m

E_k1 = 0.5m₁v₁²
E_k1 = 0.5x2m1v²
E_k1 = mv²

E_k2 = 0.5m₂v₂²
E_k1 = 0.5x3m1v²
E_k1 = 1.5mv²

E_kT = E_k1+E_k2
E_kT = (mv²)+(1.5mv²)

But the answer in the book is E_kT = 12mv²...

I think I may have messed up in the algebra, or maybe I need to use the data after the collision too.

 

[tiny-tim]

Welcome to PF!

Hi Magma828! Welcome to PF!

I'm stuck with part b. For part a I had to use all the data in the question, I'm guessing that for part b I only have to use the masses and velocities before the collision.

No, the total KE after is greater than the total KE before …

the difference in energy must have come from somewhere, and it comes from the "nuclear energy" released.

Try again. ​

 

[Magma828]

Hi Magma828! Welcome to PF!


No, the total KE after is greater than the total KE before …

the difference in energy must have come from somewhere, and it comes from the "nuclear energy" released.

Try again. ​

Ahh of course. I'd just spent the previous hour doing part a using the principle of conservation of momentum and decided to invent the principle of conservation of kinetic energy

So it's the exact same method but just with the after-collision velocities?

 

[tiny-tim]

It's the exact same method with all the velocities.