# Splitting/Exploding object & Momentum

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1. May 19, 2017

Hi,
1. The problem statement, all variables and given/known data
A free falling object of mass "m" falling from some height, collides the floor in speed of 20 m/s (perfectly elastic collision). In his 1/2 height back up he splits into 2 pieces- ¼m which going downward and ¾m keeping upward. The ¼m reaching the floor after ½ second.
1) What is the object velocity right before the split?
2) What is the velocity of the small object (¼m) right after the split?
3) What is the velocity of the big object (¾m) right after the split?

2. Relevant equations

3. The attempt at a solution
So I used conservation of energy to solve the first question. the initial height is 20.4m. it means the splitting point happened at 10.2m.
mgh = ½mv2 , v= 14.14 m/s

Now I'm looking on the second question, because I know the falling time I can use kinematic equation.
0 = 10.2 +v0t +½at2
-10.2 = 0.5v0 + ½⋅(-9.8) ⋅0.52
-7.55 = 0.5v0
v0 = -17.95

To figure out the big object velocity I used the coservation of momentum and here is where I got stuck

if a already have a negative velocity which determine the direction should I add a minus sign to the conservation of momentun equation too?
-¼mv0 + ¾mV0 = m⋅14.14
here when I put into the equation the negative velocity of v I get V0 = 12.87

in the other hand , with positive momentum :
+¼mv0 + ¾mV0 = m⋅14.14

I get V0 = 24.83

For some reason I think the first equation answer is more logical , It doesn't make sense that the ¾m accelarated too much after the split.
But it feels wrong when I get negative velocity and in the momentum equation I need to add negative sign as well .The negative velocity will do it anyway, won't it?

Thanks a lot!

Last edited by a moderator: May 19, 2017
2. May 19, 2017

### haruspex

But it makes even less sense that it moves more slowly after the split.
Certainly not. The conservation equation does not care whether the values to be plugged in are positive or negative, the equation remains the same.

3. May 19, 2017

Thanks. If it doesn't care about the values inside why it gives me different answers ?

4. May 19, 2017

### haruspex

Because you changed the sign in the algebraic equation. The equation, as an algebraic statement, is the same whether the values are positive or negative.
If you have an equation x+y=z, and you are told x=-1, that does not change the equation to be -x+y=z.

5. May 19, 2017

Thanks a lot.
Is it logical that after the explosion/splitting the bigger mass has more kinetic energy than the smaller mass? this is what I got here and it also doesn't make sense to me.

Last edited: May 19, 2017
6. May 19, 2017

### haruspex

Yes, that can happen. Consider e.g. if the explosion had been exactly enough to halt the smaller mass. It would have lost all its KE as a result, while the larger mass would have gained KE.