# Day 131: Discovering Momentum Conservation

College-Prep Physics: This year, I taught energy before momentum for two reasons…

- In my opinion, the conservation of a scalar quantity (like energy) is simpler than conservation of a vector quantity (like momentum).
- Collisions are an easy way to “break” the energy model, i.e., it’s not useful for analyzing collisions. There are several collisions which all start with the same amount of kinetic energy, but have different outcomes.

So yesterday we analyzed the energy transfers in various collisions:

- Red & Blue Pasco carts and tracks
- Logger Pro with Motion Detector
- Air Track Simulation from Tony Wayne

Elastic collision: 1 kg @ 4 m/s collides with 1 kg @ rest

8 J of E_{k }–> 8 J of E_{k}

Inelastic collision: 1 kg @ 4 m/s collides with 1 kg @ rest

8 J of E_{k} –> 4 J of E_{k }+ 4 J of ΔE_{th}

Inelastic head-on collision: 1 kg @ 4 m/s collides with 1 kg @ -4 m/s

16 J of E_{k} –> 16 J of ΔE_{th}

Kinetic energy not always constant before/after. Outcomes ranged from all kinetic transferred to none transferred.

YET — there seems to be a pattern. In the inelastic collision, the speed drops by half. In the inelastic head on collision, the speeds “cancel out.”

Students naturally asked what happens if we change the mass of the carts. So we demoed a few examples in the remaining time:

- What happens in head on inelastic collision between a light cart and a heavy cart going the same speed? (Goes slower in direction of heavy cart.)
- How might we get them to stop after collision? (Make the lighter cart travel faster.)

TODAY

Explored a careful sequence of collisions where students had to draw before/after pictures, bar charts, and look for what remained the same (based on a similar progression from Etkina). Again, we used the Red and Blue Pasco carts and tracks to see the collision and used the Air Track Simulation to collect quantitative data. To get a feel for how the conversation flowed, it’ll be helpful if you read a post from 2 years ago called Inventing Momentum.

What’s new this year is that I’ve created a worksheet to help students keep organized notes for the discussion (snapshots below).

Here’s the progression of collisions:

*A 1-kg red cart moving right at 4 m/s collides elastically with a 1-kg blue cart at rest. *We draw speed bar charts and we see that speed is constant before and after.

*A 1-kg red cart moving right at 4 m/s collides inelastically with a 1-kg blue cart at rest.* We draw speed bar charts, but see that **total speed** is constant before and after. Does this new pattern still work with the previous scenario?

*A 1-kg red cart moving right at 4 m/s collides inelastically with a 1-kg blue cart moving left at 4 m/s*. Total speed is NOT constant, but **total velocity** is constant. So now our bar charts become velocity bar charts. We draw the negative velocity bars downward. Does this new pattern still work with the two previous scenarios?

*A 2-kg red cart moving right at 2 m/s collides inelastically with a 1-kg blue cart moving left at 4 m/s.* Total velocity is NOT constant. But the total “mass-velocity blocks” are constant before and after (see Inventing Momentum). So now our bar charts become mass-velocity bar charts. Does this new pattern still work with the all the previous scenarios?

*A 2-kg red cart moving right at 3 m/s collides inelastically with a 1-kg blue cart moving left at 3 m/s.* Total “mass-velocity blocks” are constant before and after.

*A 2-kg red cart moving right at 3 m/s collides elastically with a 1-kg blue cart moving left at 3 m/s. *Total “mass-velocity blocks” are constant before and after.

You can download a Word version of the worksheet: MomentumFindAPattern 2014

##MTPM

Yes! Energy naturally precedes momentum.

For many collisions in the momentum unit, my student also make energy bar charts to examine if it is an elastic collision (Ek “conserved”) or inelastic (Ek transferring to/from some other storage mode). Do you make a distinction between inelastic and perfectly inelastic (sticky) with your college prep class?

I’ve always placed my momentum bar charts on their side to help distinguish them from the energy bar charts. The +/- momentum signs naturally sync with the cart moving right and left. What I haven’t done is emphasize the 2-D blocks of momentum. I love that idea, and I really like your lesson progression. I think I’ll call them momentum block diagrams (or charts?) instead of momentum bar charts.

Since I think your really motivates the idea of examining the “mass*velocity” quantity and is a natural way to start the momentum unit. Perhaps, at this point, the plunger cart / explosion lab fits into the progression?