It is one other yr and one other Star Wars Day—Might the 4th be with you. Following my custom, I’ll take some ingredient from Star Wars and do some cool physics. For this yr’s put up, I am going to take a look at the tip of The Empire Strikes Again. The wonderful thing about utilizing this film is that it is so previous—greater than 40 years—that I haven’t got to fret about spoilers. I imply, if you have not seen it by now, are you actually going to look at it?
So, right here is the scene: Leia, Lando, and Chewbacca use the Millennium Falcon to flee from the Imperial forces on Bespin. On their method out, they seize Luke (he was actually simply hanging round). As soon as they get off the planet, in fact, Darth Vader is there to intercept them along with his Star Destroyer. Lando says, “Oh, no biggie. We are going to simply make the leap to lightspeed and skip out of this technique.” Nicely, that doesn’t work. The Imperials have disabled the hyperdrive.
R2-D2 is the actual hero right here. He’s onboard the Falcon speaking to the Bespin central laptop—, simply sharing lubrication strategies and dropping some gossip on the foolish issues C-3PO says. The central laptop comes again with a rumor: The hyperdrive has been turned off. So now R2 is aware of what to do. He rolls over, and with the flick of a change—growth. There goes the Falcon, proper off into hyperspace. Hopefully they’re wanting the place they’re going and gained’t hit a planet or one thing.
Now for the cool physics. When the starship makes the leap to hyperspace, R2 goes flying backwards contained in the Falcon. It is as if he was on a turbocharged bus when the driving force hit the fuel, and he isn’t seatbelted in. If we take the within of the bus because the reference body, then we might want to add a faux power to account for the acceleration. I imply, it is not essentially a faux power. Based on Einstein’s equivalence precept, there is no distinction between an accelerating reference body and a gravitational power.
So, within the reference body of the accelerating Falcon, there seems to be a gravitational-like power that pushes in the other way because the acceleration. The magnitude of this power on R2 can be equal to his mass multiplied by the acceleration of the spaceship. If R2 has fully frictionless wheels (or no less than very low friction), then because the Falcon accelerates ahead he would speed up backwards with respect to the ship’s body. That is a very good factor—as a result of I simply must measure R2’s acceleration as seen from contained in the spacecraft.
This implies we get to do some video evaluation. If I do know the dimensions of stuff contained in the Falcon, then I can decide the place of R2 in every video body. Additionally, with a recognized body price I can get the time for every of those positions. For the gap scale, I’ll use the peak of R2-D2 and the body price that’s embedded within the video (in order that it performs again on the right velocity). My favourite instrument for getting this knowledge is Tracker Video Evaluation. (It is free.) After all, there are some small points with this evaluation. The digicam pans and zooms—however I can compensate for that movement by how R2 strikes with respect to the wall. With that, I get the next plot of place vs. time: