Whoops part 2

If you remember from last time, I calculated the amount of work being exerted by an aerial faith plate, then used my answer to calculate the distance a projectile would fly. I asserted that if I could predict where the projectile would land using the amount of work being done, then work is a measurement that is actually conserved by an aerial faith plate. The only problem is that in calculating the initial velocity of a projectile off an aerial faith plate, equal masses cancel out. Equating work to kinetic energy and solving for velocity, we find that:

v = √(2*W/m)

and given that

W = m*a*d,

we actually have

v = √(2*m*a*d/m)               [bolded for emphasis]

And if the two masses are the same, they cancel out. So last time when I correctly predicted the distance my projectile would travel, I erroneously claimed that I was able to do so because that work done by aerial faith plates was conserved. It was actually because my calculations cancelled out mass, so being able to calculate the distance my projectile traveled had nothing to do with work.

So, I reran the experiment, this time with a weighted sphere, which, according to the game, has a larger mass of 75 kg. Plugging in to the equations above and running the same experiment as last time, we find that the weighted sphere should travel about 5 panels if the aerial faith plate enacts the same amount of work on any object it launches. As you can see in the video below, that clearly doesn’t happen.

Work done by the aerial faith plates isn’t conserved. It appears as if they ignore the mass of an object and so subsequently calculating the amount of work an aerial faith plate exerts isn’t useful. It appears they use a different factor to determine the path a projectile will take, which will be investigated soon.

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the ideal gas law

Portal 2 can help students study more than just mechanics.

Thanks again to Yasser Malaika from Valve for sharing this awesome demonstration of the ideal gas law made using the Puzzle Maker. If you watched the Games for Change presentation last week, this should look pretty familiar (see 22:30).

There’s a lot more to explore with this concept. Expect to see more of it in the future.

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terminal velocity part 1

Portals slow you down! Go figure.

A more in depth analysis:

Portals automatically drop your velocity to about 7.8 u/s (or 1000 game units/s) as you go through them, which is why your terminal velocity drops when you go through portals more often. Every time you hit a portal, your speed drops to 7.8 u/s. If you have less distance to fall after your speed drops, your speed has less time to increase. In the longer drops, you have more time to pick up speed, meaning your terminal velocity, as measured in this experiment, will be higher.

This video is meant to describe a way to quickly and easily run experiments in a classroom. Without knowing that portals affect your velocity ahead of time, this experiment would give students a strong indication that something weird is going on and the relationship between portals and velocity is worth investigating.

Console Commands:

sv_cheats 1 (must be done first but only has to be done once)
host_timescale 0.001 (slows time to 1/1000 speed)
host_timescale 1 (brings time back to normal)

Timing and Momentum Flings

In one of my lesson plans, I challenge students to build a level in which they have to use perfect timing to catch a cube that’s launched with a momentum fling. The simpler the setup, the better. Here’s an example of such a level.

Of course, the math behind a momentum fling is pretty easy. Making the catch is all about putting the moving platform in the right place at the right time.

I’ll be reusing this level for an upcoming video on the effects of friction in Portal 2.

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