mind when I saw this was: is each of the new birds 1/3 the mass or are all the new birds the same mass as the original. Was mass created?

To explore this question, I had to set up some tests. My previous analysis used existing Angry Birds, but in this case I wanted certain things to happen. I know this isn’t the perfect set up, but there was no choice. I used my video camera to record some shots in Angry Birds for analysis. Oh, you want to see the video? I don’t think you really do, but here it is.

Before I look at the blue bird (I will just call it Blue), let me look at the red bird again. In the above video, Red is shot towards a rock and collides. I don’t know the mass of the rock, but I can still get some info. First, a quick check. If I look at the vertical motion of Red both before and after the collision with the rock, it has a vertical acceleration near -9.8 m/s². Ok, that is good. This video agrees with my previous analysis.

What about the horizontal motion of Red?

There are some good things here. First, the horizontal velocity is constant before the collision (23.2 m/s). It is also constant after the collision (-2.2 m/s). Finally, what about the rock?

This gives a horizontal velocity of 7.8 m/s. The vertical motion has a similar acceleration compared to Red (as it should). Now for some physics. What happens when Red collides with the rock? Here is a diagram.

This shows Red and the rock before, during and after the collision. The red arrows represent the momentums of the objects. Notice that the only forces on the objects are during the collision. The force the rock exerts on Red is the same magnitude as the force Red exerts on the rock. Odd? No, it is not odd that these have the same magnitude because they are the same force. This is the whole point of Newton’s third law – that forces are an interaction between two objects.

Before going further, let me go over the momentum principle. It says that forces change the momentum of an object (change is the key word here). In particular:

Since the magnitude of the force on Red and the rock are the same AND the time these forces are applied is the same, the change in momentum should be the same magnitude.

Note, I am using “rb” subscript for Red and “ro” for the rock – just in case that wasn’t clear. From the data above, I know the velocities of Red and the rock before and after the collisions. Also, the rock is initially at rest and the forces are only in the x-direction. I can write:

I can’t get the mass of Red, but I can get the ratio of the mass of Red to the rock. This gives:

So, the rock is almost three times more massive than Red (hmmm….I wonder if this is the same ratio of their areas). Enough about Red, but I needed to get some standard mass. In this case, I will create the new unit – mr. 1 mr equals the mass of Red. So, the mass of the rock is 3.1 mr.

Blue Bird (Blue)

Now, I am just going to do the same stuff for the blue bird (Blue). In this first collision, I am not going to make him multiply into 3 birds. He is just the one. Maybe you are bored with my graphs and maybe you are not. Well, here they are and you can look at them in more detail if you are interested (click the image to enlarge).

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If you look at the functions that I fit to the data, you can see:

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Using the exact same calculation as for Red, I get (oh, bb subscript is for Blue):

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If the mass of Blue is 0.006 times the mass of the rock and the mass of Red is 0.35 times the mass of the rock, then the mass of Blue must be:

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So Red has a mass that is almost 60 times larger than Blue. Little Blue Bird.

Multiplying Blue Bird

What about in the case where Blue multiplies? Does each new bird just have 1/3 the mass of the original? Back to Tracker Video – AGAIN. For this case, I made Blue turn into three birds right before hitting the rock. Here is the x-data for Blue before the collision and for the rock after the collision:

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From this, I get the velocity of Blue before as 23 m/s (just like before) and the final x-velocity of the rock as 5.5 m/s. What about after the collision? Then I need to keep track of 4 things after the collision: the three blue birds and the rock. Here are some graphs.

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My notion for the velocities, I will call them v_bba-x v_bbb-x and so on for the Blues after the collision. So, here are the velocities (the x-velocities – I am going to drop the x-notation, technically it should be there though).

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I know the mass of Blue (in terms of the mass of Red). I also know the mass of the rock. From this, I can look at the momentum of the stuff before the collision and the momentum of the stuff after the collision (in the x-direction). Initial momentum:

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And what about the total momentum after the collision? How about I assume that each of the three new Blues has the same mass as the one before. This would give a final momentum of:

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This is not good. This final momentum is more than 30 times the initial momentum of the one blue bird. This is with the assumption that the mass of the blue birds magically increased. Wow. Ok, let me assume that all three of these birds hit the rock (which I am pretty sure is not true).  If that is the case, what would the mass of each Blue have to be to get that momentum (assuming that they all have a horizontal velocity of 23 m/s – which probably isn’t true).  Using this before and after momentum, the mass of each of the 3 new blues would be:

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That means that each of the new blue birds has a mass over 10 times the original blue bird.  Here are some options for this discrepancy:

• Momentum is not conserved in Angry Birds.  No one says it has to use the same models as real life, right?
• The velocity of the 3 birds (at least in the x-direction) is not the same as the one bird it came from.  Maybe they got a little speed-boost.  I don’t know.  The way I ran this experiment, I couldn’t really measure the speed after they multiplied.  But, I could measure this – save it for another post.
• The mass changes.  Not just 3 times as much, but around 30 times as much.

Conclusion

So, what does this all mean? Is this analysis useful? Well, yes it should be useful. The final momentum of the stuff (birds and rocks) is much more than the one angry bird.  Therefore, you will have more of an effect if you expand the blue bird before it hits something. There is unlikely to be a situation where you would be better off not expanding them.

See what physics gives you? Angry Birds strategery.

Authors: Rhett Allain

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