Momentum: Collisions; Unable to get correct answer, using wrong formula?

Apollinaria

Hello again everyone!

I've been plowing through yet another worksheet and thought I'd been okay until my solutions and formulas stopped working :( I was wondering if someone could tell me what I'm doing wrong. Thanks for reading!

1. The problem statement, all variables and given/known data
- A 225g ball moves right with a velocity of 30cm/s. (.225kg and .3m/s)

- This ball collides with a 125g ball also moving to the right with a velocity of 10cm/s.
(9.125kg and .1m/s)

- After they collide the velocity of the 125g ball is 24cm/s(.24m/s) to the right. What is the velocity of the 225g ball after the collision?


2. Relevant equations & 3. The attempt at a solution
I showed all of my work (information and relevant equations) in the attached document. What I don't understand is why it's all wrong and why the direction I got is negative (it's positive in the answer key).

Any help would be really appreciated. I have a whole page of these to do but this one is stopping me as I am obviously doing something wrong.

Attached Thumbnails

 

TSny

Hi Apollinaria. Why did you set the final total momentum equal to zero?

Apollinaria

Hi again TSny, I based it on notes; "If an explosion is occuring in an isolated system, the momentum is conserved but the momentum before the explosion is zero."
We were given a formula:

P₁' + P₂' = 0

Is there something else I should be using that I'm not aware of?...

TSny

Well, in the case of the explosion, the bomb was just sitting there. So, it had no momentum. Thus, the final total momentum must be zero.

But, you have a different problem. What is the total momentum of the two masses before the collision?

Apollinaria

So I can only use that formula for when one of the objects is stationary?

p=mv

p₁= .225kg x .3m/s = 0.0675
p₂= .125kg x .1m/s = 0.0125

p₁ + p₂ = 0.08

azizlwl

There should be 2 P₁ and 2 P₂.

Apollinaria

So I should be using this.......

p₁ + p₂ = p₁' + p₂'

instead of......
P1' + P2' = 0

?

azizlwl

Using symbols P₁₁, P₂₁, P₁₂ and P₂₂
or P_1i, P_2i,P_1f,P_2f make them clear of their states

Apollinaria

I know. However, my confusion isn't with the symbols or states but with which formula to use for that particular problem.

TSny

Yes, that's how to set it up. As azizlwl points out, it might be clearer if you use appropriate subscripts to denote initial and final values. But, if you are used to using primes for final values, ok.

azizlwl

You find the TOTAL initial momentum and final TOTAL momentum.
For conservation of momentum, the total initial momentum must be equal to total final momentum.

Apollinaria

You are amazing :) I use primes because having an obscene amount of subscripts get really confusing. Thanks for the nudge in the right direction

Apollinaria

Thank you very much for both of your suggestions. I realize in some cases its easier to label initial and final values with "correct" subscripts but it gets messy and long to write out every single time. I finally got this figured out :)