How Do You Calculate the Masses of Fragments from a Decaying Particle?

[Pengwuino]

So the problem is

An unstable particle with a mass of 3.34 x 10^-27kg is initially at rest. The particle decays into two fragments that fly off along the x-axis with velocity components 0.987c and -0.868c. Find the amsses of the fragmments. (Suggestion: Conserve both energy and momentum).

So i setup ymv = ymv (for the second)
I figured out both y's
I then used E=mc^2 to find the rest energy and got like, 3.0x10^-10
I divided that in half and then used (y-1)mc^2 (At this point in the post i realized what i did wrong i hope lol)
to figure out what mass would give 1.5x10^-10

That would give me each mass... am i correct?
Im re-doing my steps as we spoke so i hope I am right :D

*Edit*

Ok so i did still do it wrong... i still need help :)

 

[joshuaw]

I am a little confused by your description of the set up.
You would be good to follow the following method:
1) convert 3.34X10^-27 kg to eV/c^2
2) use you energy relation to solve for one of the two masses(since they must be different to conserve momentum for linear trajectories to one another)
3) solve for your momentum. gamma1*m1*v1=(-1)*gamma2*m2*v2(since one velocity is along the neg x and the other along the positive x)
4) now you should have two equations with two unknowns, so it is ready to be solved.

By my calc(with some round off) you should get m1(v=.987c) approx.=140 MeV/c^2
and m2 approx. = 500 MeV/c^2

Like I said these are not exact but close. You can always check if iyour solution is right with the energy or momentum conservation.

 

[thepatientmental]

Hi there,

Based on the information provided, it seems like you are on the right track! However, there are a few things that need to be corrected in your approach.

Firstly, when setting up the conservation of momentum equation, it should be written as:

m1v1 = m2v2

Where m1 and v1 represent the mass and velocity of one fragment, and m2 and v2 represent the mass and velocity of the other fragment.

Secondly, when using the conservation of energy equation, it should be written as:

E1 + E2 = (m1c^2) + (m2c^2)

Where E1 and E2 represent the initial energy of the unstable particle and (m1c^2) and (m2c^2) represent the rest energies of the two fragments.

Thirdly, when solving for the masses, you will need to set up a system of equations using the two equations above and solve for m1 and m2.

So, to answer your question, your approach is correct but there are some minor errors that need to be corrected. Keep up the good work and don't hesitate to ask for help if you need it!