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La physique de Angry Birds

mardi 24 mai 2011

Voir en ligne : Wired

I was going to finish my analysis of the Green angry bird, but I was distracted when Angry Birds for the Chrome browser came out. Now, I have to work my way back up the level to get back to the green bird. Alas.

The new Chrome-based angry birds does do something new. It gives me a new method for capturing the motions that I need to analyze. Previously, I was stuck with either using YouTube videos that others created or using a camera to record my own iPod. Neither of these worked too well.

Now that I am running the game on a computer, I can use screen capture software. After trying both Quicktime’s video capture and Snap Pro X, I wasn’t too happy. First, Quicktime only captures the whole screen and the frame rate wasn’t too hot. Snap Pro X also didn’t have too great of a frame rate. I found screencast-o-matic.com, a free Java-based screen capture tool. This seemed to work much better. Also, a video camera to the screen seems to work better with a computer screen than it does with the iPod.

But what can I do with these new tools ? Let me go back and answer a question that I have always considered.

Does the Bird’s Launch Speed Depend on the Angle ?
If the bird is indeed shot from an elastic cord, then technically the bird should go faster when shot horizontally than when it is shot straight up. Why ? Physics. Let me draw a diagram for a bird that is shot straight up. Also, let me assume that this sling shot is just a spring.

JPEG - 17.3 ko

Let me assume a spring with a spring constant k and a bird mass of m. How do I find an expression for how fast it will be when it leaves the sling shot ? Yes, use the work-energy principle. Why ? Because I know the starting and ending positions, but I don’t know the time. Since work-energy doesn’t use time, it is a perfect fit.

I will let the Earth + bird + slingshot be my system and it will start at y1 = 0 meters and end at y2 = s. Since I have the Earth and the slingshot both in my system, I can have both gravitational potential energy and spring potential energy. Oh, let me point out that the bird starts from rest and there is no work done on the system. The work-energy principle would say :

JPEG - 20.4 ko

Maybe it wasn’t clear, but the spring potential energy is (1/2)ks2 and the gravitational potential energy is mgy. Now, I can solve for the final velocity :

JPEG - 10.3 ko

But what if I shoot at an angle ? What will change ? Really, just the starting and ending height. Here is a diagram :

JPEG - 14.7 ko


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