Physics Project Ideas

Off-topic
1

Hey all,

For my last session in college, I have to do a project integrating matter from all of my physics classes, plus some mathematics. To give you an idea, what we saw are the basics of physics and maths : mechanical (mainly Newton’s Laws of motion), strenght of materials, electricity and magnetism (Coulomb, Ampère, Faraday, Biot, Savart and mainly Maxwell’s laws and equations), waves, optic, modern physics (special and general relativities, string theory), differential and integral calculus (in two, three and four dimensions), linear algebra, vector geometry, statistics and probabilities.

The project can be to build something or to study theorically something (with calculations or computer simulations). The point is to compare theoretical and experimental data. Here is a list of ideas my team came up with, or previous projects :

  • Building an E-uni (not for transportation purposes, only self-balancing) : way too complicated, programming-wise.
  • Building a sort of Segway (again, only self-balancing) : still too complicated and expensive.
  • Measuring and calculating the Earth’s attraction with various techniques (pendulum, launch of an object, etc) : too simple physics and mathematics.
  • Building a Foucault pendulum to calculate our latitude : too big because of the rotation implied in the concept itself. Also, most of Foucault pendulums previously made needed a push from time to time (using precise motors or something similar).
  • Studying the flight of a boomerang/football/golf ball : too hard to recreate the same flight every times.
  • Calculating the mass of an electron using a cathode ray tube (J.J. Thomson’s experiment).
  • Calculating the speed of light using a Michelson interferometer.
  • Studying the motion of a double pendulum.
  • Finding the resonance frequency of a certain system.

As you can notice, we are really going in many different directions. What I would like is the get some of your ideas, no matter how silly or hard they may seem. Just keep in mind that we do not have access to a particule accelerator or similar devices (that’s why we cannot really choose a subject concerning modern physics). :roll_eyes:

Thank you,
Hugo

2

For my final I analysed the effect of adding more water to a crystal glass to change its resonant frequency,used a mic and some free audio software. Ended up being a really good one because you can then talk about stuctures that have been brought down by resonating.

If you end up doing it, Id be happy to send you my notes if i can find them

Or the feasibility of magnet powered cars

trollcar.jpg

3

You do have a particle accelerator!

4

Too simple? Hardly! Cavendish’s experiment requires quite a lot of math. It was an advanced experiment in my undergraduate curriculum.

Sounds like someone’s never made a potato cannon before. This one’s a snap with just a few parts from the hardware store.

Millikan’s experiment is much simpler and provides the same result.

The mathematics involved here aren’t suitable unless you’ve studied at the graduate level. Building a double pendulum, however, is quite simple… and they’re beautiful to watch!

This sounds like a winner to me. Find a simple system and calculate / estimate a theoretical frequency.

Then get a tone generator or keyboard, an amplified speaker, and induce resonance. See if the driving frequency is close to your estimate.

For bonus points, break something using sound energy.

Go for it! Let us know what happens.

5

Yes, you’re right, thanks for bringing that up. We had thought of a torsion balance before, but not for that use. At the moment and from what we had read, we thought for some reasons that we needed some sort of anti-friction gel. But I now I see that the assembly is more simple than I thought…

Ahahah ! No, I’ve never made a potato cannon. However, tell me if I am wrong, I don’t think such a cannon prevents balls to have a spinning effect. Plus, unless we find a way to mount a camera to another ball which has a parallel trajectory to the first one we want to study, it would be hard to understand the movement/forces involved. Also, we are limited by space. We could have access to a gym, but even then, I would think that the range of this cannon is greater than the length of the gym.

Another very interesting idea ! The problem with the cathode ray tube experiment is that the manipulations, while enough complicated, were quite short compared to the amount of work supposed to be involved in the project.

Really ? I thought some differencial equations along with Laplace transform and the Lagrangian (not sure how to call that in English…) would have been sufficient. Note that I was not talking about chaotic motion here. And yes, that are really fun !

By simple system, you mean something like a glass filled with various amounts of water, like dan de man mentionned ? It’s an idea, but I find the maths quite basic to my taste and there are already other groups working on something similar.

Yet, thank you both of you, you brought some really interesting ideas. For now, I am considering Cavendish’s experiment, Millikian’s experiment, the double-pendulum and another one I forgot to talk about : the physics behind the flight of a helicopter (and probably building a very simple one).

We wanted to calculate the lift force that could be deployed by the helicopter (and compare the efficiency of different types of blade) by suspending it to a force detector and calculating the difference when it’s turned on. We then wanted to compare this result to a theoritical result, and then comes the problem : we cannot find an equation describing the lift constant.

Anyways, I know I am being picky, but I would really like to do something interesting and challenging for this final project. Thanks again every one !

Hugo

6

So we chose the double pendulum, despite the advanced math involved. We will study the motion of a simple pendulum first to find the amount of time we can “safely” study the motion of a double pendulum without too much loss.

I started to play with equations from what we have gathered of informations and I understood and re-proved the path leading to the final equations. But then, that’s where I am stock. I have the (probably differencial) equations for the angular acceleration of both angles, but I don’t know how to resolve them to find the angles in function of the time and the initial angles. Here they are, along with a diagram :



According to some websites, it could be possible to solve these with the “Runge-Kutta Methods”, but I am very not familiar with these and I don’t understand how they could apply here. Anyone has an idea ?

Thanks !

Hugo

7

That looks pretty sweet, I learned the Runge-Kutta method two years ago but I can’t remember much about it. This page gives a bit of an overview and one of it’s references is this paper which may or may not be of use.

8

sorry for dp
you might be able to find more info, worked examples etc in a text book like mathematics for engineers/physicists

9

Yes.

Take classes in numerical, and possibly computational, methods for solving D.E.s and the method should be clear to you.

This isn’t a subject in which one can simply read a Wikipedia article and become proficient. This takes time, study and practice.

I’d recommend you choose a simpler project.

10

Unfortunatly, it is too late to choose another subject. And I stand by my decision.

Maybe I am misinterpreting your last post, but if I am not, I can understand your reaction. I might have sounded arrogant or like a know-it-all, and I am sorry for this. However, I still think you might be underestimating the tools that are to our disposition.

We will see what happens. Chances are that you will be right, but atleast we will have had fun trying different techniques. Chances are also that we will learn a bunch more with this project than with something easier like a roller coaster or a catapult, where all equations are known and familiar to us.

Thanks though for your help !

EDIT : Oh and, if that was what you were refering to, I did not consult Wikipedia for this project (even if it can often be a great source of references).

11

I think what maestro8 is pointing out is the Runge-Kutta methods (fourth order is common and adequate, sixth order is generally overkill) are numerical methods. You won’t get a closed-form solution to that set of equations which are coupled, non-linear differential equations. You can, however, approximate the system with difference equations and code a repetitive integration program and get cool plots of how the displacements of the pendula change with time given specific initial conditions. The problem will require four initial conditions for each “solution” or better, for each model. Because the equations are non-linear, getting a model for one set of initial conditions won’t necessarily give you any insight into a model using a different set of initial conditions. In order to gain some understanding of the behavior of the system, many models have to be simulated.

Maybe there are packages available now that allow you to use a graphical interface to input your system. Back in the day, the equations had to be coded in FORTRAN or C, C++, etc.

The much simpler and less accurate integration routines used Newton’s rule (first order, simple slope fit) the trapezoid rule (second order) and Simpson’s rule (third order). The order refers to how many preceding calculated points are used in estimating the next solution point. These numerical methods crawl along one point at a time plotting the motion.

12

Such is the plight of a young physics student. Having learned a few equations (F=ma), he thinks that’s all there is to know about mechanics.

As you continue to study physics, you will realize there are many subtleties that aren’t explained with the approximations you’ve been taught in your first and second years of studies.

There are a lot of details hiding in what you might consider “error”. Things like drag and friction. Assumptions about initial conditions. Approximations of geometry.

Sure you can predict the results of a roller coaster going down a track to 10% or maybe 5% but can you get your predictions to 1% or 0.1%?

Even the simplest experiments can yield great challenges. You just have to look for them.

13

What more can I say ? You both just shut me up for a while. I guess learning to be humble is part of the deal too. :slight_smile:

Maestro, this integration class is actually going to be my last physics class, fortunatly (for you) or unfortunatly (for me). After this session in college, I will go to university in a completly different discipline and my knowledge of physics will thus remain at the F=ma level.

I will now go back to the decryption of Harper’s post, which is in itself a whole new challenge for me !

14

I’d recommend you go back to studying the double pendulum. :slight_smile:

15

You know, I always considered your comments to be displaced or insignificant. And then, I found JC. I now know that’s where all the smart thoughts can be found. :slight_smile:

16

Little update :

We changed a bit the purpose of our project, which was at first to study the motion of a double pendulum. It is now to study different types of pendulums (not worded like that in French, but you get the idea), including a hypothetical simple harmonic oscillator (probably just a simulation of a simple pendulum with no friction), damped harmonic oscillator (simple pendulum) and double pendulum.

We will not be according a lot of time to the first two ones, as we studied the first one in class and the second one seems, from what I have seen and read about it, quite complicated. We will probably just mention the fact that the damped oscillator does not follow exactly the same curve as the simple oscillator, that the peaks are determined by a certain function.

As for the double pendulum, we “built” it (not too hard :roll_eyes: ) using fishing line and two different masses. We plan to vary the lenght of the line and the initial angles, but not the masses.

We did two tests for the double pendulum, one with the first angle approximatly equals to 30º and the second angle equals to 0º, and the other test with both angles set at about 35º. Using Tracker and Excel to collect the data and Maple and Excel to approximate the motion of both masses in the two systems (we used RK4 and a step of 0,06), we came up with these graphics :

First test, mass 1 :
http://img10.imageshack.us/f/cimg0617m1.jpg/
First test, mass 2 :
http://img151.imageshack.us/f/cimg0617m2.jpg/
Second test, mass 1 :
http://img195.imageshack.us/f/cimg0644m1.jpg/
Second test, mass 2 :
http://img833.imageshack.us/f/cimg0644m2.jpg/

The curves do not fit perfectly, but there are many explanations, the best one being the fact that we used fishing line and not some kind of rigid rod. Also, I did not show more of the graphics, because after these 8 or so seconds, both the experimental and the theoretical systems get too crazy to study something interesting. However, I am still pleased with these results. Now, all there is to do is a lot more tests with different initial angles and length !

Am I mistaking, or if we do a 3D graphic of the angle of one of the masses in function of the time and the initial value, we will not notice any kind of interesting surface ?

Thanks to whoever made it to the end of this post !

Hugo

17

By “theoretical” I take it you mean the prediction of the RK4 model?

The initial conditions for the first model one would expect to produce more interesting results as the two characteristic frequencies (though a non-linear system does not really have “characteristic” frequencies) immediately manifest themselves.

The second case, as you describe it, has the fishlines in a straight line at 35º. It that right? One would expect this system to exhibit something like a single sinusoidal frequency for quite a while if the masses are not substantially different. Especially if the mass closer to the pivot is the smaller one or if the masses are close together. Even more so (and approaching linear) if the initial angle were smaller.

Cool simulations and measurements. How does the logging system make measurements? Did you have to code the RK4 model or was there a GUI you could use?

I’m having trouble trying to figure out what you mean by this. A language mismatch, perhaps?

18

Yes, I meant to say the prediction of RK4, sorry.

And again yes, the second case has the fishline completly at ~35º and does act quite like a simple pendulum, especially since the smaller mass is in the middle.

Not really sure about what you mean by logging system, but if you meant how we collected and analyzed the data, we filmed the double pendulum using a high-speed camera. Then, with “Tracker”, a very simple and handy software, we tracked each mass and converted these cartesians coordinates into angles.

We coded the RK4 using Maple. We could have used a function in the “NumericalAnalysis” package called RungeKutta in which you can just plug your values, but I think it would have been harder in our case, since it was not really an ODE.

Thank you for your interest !

Hugo

EDIT : Just saw your edit, probably my mistake. What I meant to say was this : will we see something interesting in the graphic of θ(θ0,t), or not at all since it is a choatic system ?

19

Which θ0? As long as one is incremented slowly and the other one is consistent (always vertical or always co-linear for instance) you will see a smooth surface in which features of the system evolve. For example, if the θ0 of both masses are the same (co-linear) during the initial oscillations the period will increase smoothly as the initial angle increases. As you mentioned earlier, having something rigid rather than fishline would help so you could go to initial angles of greater than 90º. As you go to initial angles approaching 180º the waveform approaches a square wave and the period becomes very long. So much for characteristic frequencies. Your fishlines won’t let you invert the pendula, though.

In the case where one initial angle remains vertical and the other slowly increases, two distinct periods should emerge. They should both elongate with increasing initial angle and the dominate amplitude will shift from one to the other. Your surface will probably look like two hills decreasing in amplitude into two valleys and the valley between them erupting into a hill.

Or, because it’s non-linear, it won’t look anything like I described. This is the most likely scenario.

It sounds like you’re going to go blind watching this thing for hours on end. Go out and ride to give your eyes a break.

20

Don’t worry, we were not planning on doing this graphic using experimental data, only with the predictions of RK. :stuck_out_tongue: I think that would be rather simple, probably long though to calculate all these values at all these initial angles.

Also, we need to take into account the uncertainty. I have already determined the experimental one (I am saying “one”, but obviously it is not a constant) for the simple and the double pendulum, the theoretical one for the simple pendulum, but when it comes to the double pendulum, we cannot calculate it using traditionnal differencial methods, since there is no function representing the position of each mass. The only other way we have learnt is to calculate the difference between the maximum and the minimum and divide that by 2. However, would this be really appropriate here ? Usually, we use this method for experimental uncertainty…

I don’t want to seem like I am asking you to do all the work (even if it’s not a big part of the project), so feel free to tell me to think harder about it by myself if you think you should.