Momentum of Block A and B Colliding

[Tim Wellens]

Homework Statement

The whole problem is in variables, which tends to confuse me a little.

We have two blocks that collide, Ma and Mb. Initially Ma experiences a positive velocity. Mb experiences a 0 velocity. Finally, Ma experiences a negative velocity, while we do not yet know Mb's final velocity. Mb=3Ma

Find which one of the blocks (if either) has a larger change in the magnitude of the momentum. Explain.
If the initial speed of block A is 20 m/s and the final speed is 5 m/s. What is the final velocity of block b?
In which case, if either, does block a exert a larger impulse on block b?

Homework Equations

p=mv
m1v1=m2v2

The Attempt at a Solution

1)[/B] I'm not sure how I would calculate variables with a change in magnitude any further than this
ΔPa= -MaVaf-MaVai= -2
ΔPb= MbVb-0=MbVb
So, block A has the larger change in the magnitude of the momentum since it would change by 2MaVa, while block B changes by 1MbVb.

2) Pai+Pbi=Paf+Pbf
Ma(20m/s) +0=Ma(-5m/s)+ 3MaVbf
divide Ma out of the left side, and the rest of the Ma's cancel.
20m/s= -5m/s+3Vbf
25m/s=3Vbf
Vbf=8.3m/s

3)I'm not sure how to calculate this. I know Impulse= J= Δp, and I know that block A overall exerts the greater magnitude of momentum. I guess for "which case" it must mean initial or final. I think in the final case block A would be exerting a greater impulse on block b because that's when block B actually has a velocity and moves from the impact of block a. But I am not sure how that relates to Δp, if we aren't dealing with both the initial and final, rather just one "case".

 

[haruspex]

ΔPa= -MaVaf-MaVai= -2

How can you say it equals -2? You don't even have any specified units, let alone any numeric values yet.
Think about signs. What should the signs look like when you take the difference between two values?

To answer this part of the question you will need to think about energy. What do you know about the total kinetic energy before and after?

 

[Tim Wellens]

I was just kind of thinking about it in terms of -1 - 1. The sign of MaVaf is negative, the sign of MaVai is positive.
In terms of kinetic energy, both -MaVaf and MaVai would have positive kinetic energy due to the block being in motion. Block B would initially have zero kinetic energy, but finally would have positive kinetic energy. So, in total there would be more kinetic energy in the final case due to both block A and B being in motion.

 

[haruspex]

I was just kind of thinking about it in terms of -1 - 1. The sign of MaVaf is negative, the sign of MaVai is positive.
In terms of kinetic energy, both -MaVaf and MaVai would have positive kinetic energy due to the block being in motion. Block B would initially have zero kinetic energy, but finally would have positive kinetic energy. So, in total there would be more kinetic energy in the final case due to both block A and B being in motion.

The change in momentum is final momentum - initial momentum, i.e. mass x (final velocity - initial velocity). Yes, the velocity values will have opposite signs, but that doesn't change the algebraic equation.

Kinetic energy is always non-negative, but the total cannot increase. You need to use that fact to answer this question.