# Classroom physics: free body diagram of Ariane 5

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I’ve been recently teaching Physics to 8th graders. We have finished the chapters on motion, forces, and friction, and just covered gravity. As part of this chapter, though not included in the curriculum or book, I introduced the concept of the free body diagram [1]. In the first session introducing this concept, most students didn’t really grab what it is or why it is important.

For the last session before the vacation, I started the class by playing a video of the Ariane 5 [2] launch that occurred on 29 August 2013 of the French Guiana:

I paused it at several positions to explain the forces acting on the rocket before and after ignition and after liftoff. I made it clear that the force of thrust must be greater than the weight of the rocket for it to liftoff. Moreover, I drew the free body diagram of the rocket both before liftoff and when it was airborne.

Free body diagram of Ariane 5 the moment of liftoff. Copyright ESA [3]

Free body diagram of an airborne Ariane 5. Copyright ESA / CNES / Arianespace / Photo Optique vidéo du CSG – S. Martin [4]

Of course they had lots of questions beyond the chapter objectives like why doesn’t the rocket fall when the handles leave it, where does the smaller rockets fall to, why is the rocket [appearing to be] going down [along with the boosters]?

I did not mention the weight of the rocket nor the thrust force required to lift it off. According to WolframAlpha, the Ariane 5 G has a mass of 777 tons (ie; 777000 kg) [5] which amounts to $777\times10^{3}\times9.81 N \approx 7.62\times10^{6} N = 7.62 MN$. According to the launch video above (1:36)  the two solid rocket boosters account to 90% of the thrust amounting to 14 MN ( 7000 kN each) [6], that is 12.6 MN, over a total combustion time of 130 seconds (~2 min 20 sec). The solid boosters and the 130 second combustion time is enough to liftoff the rocket and propel it, with ever-increasing speed, to get out of Earth’s atmosphere before which they get separated.

#### Footnotes

[1] Ariane 5 http://www.arianespace.com/launch-services-ariane5/ariane-5-intro.asp
[2] “Force Diagrams (Free-body Diagrams)” . Western Kentucky University. http://physics.wku.edu/phys201/Information/ProblemSolving/ForceDiagrams.html
[3] Ariane 5 at liftoff source: http://spaceinimages.esa.int/Images/2011/06/Ariane_5_ES_flight_V200_ATV-2
[4] Airborne Ariane 5 source: http://spaceinimages.esa.int/Images/2011/05/Ariane_5_flight_VA2023
[5] WolframAlpha: Ariane 5 https://www.wolframalpha.com/input/?i=ariane+5
[6] Ariane 5 User’s Manual http://www.arianespace.com/launch-services-ariane5/Ariane-5-User’s-Manual.asp