# IB Extended Essay research project on relativity

• Juan2g19
In summary: There are many potential problems with this approach, including the fact that the membrane is not a good model of space-time, that the mathematics is complex, and that one needs a fair bit of mathematics to even begin to approach understanding the concepts.
Juan2g19
Homework Statement
I am trying to pick an investigation for my physics EE (research project)
Relevant Equations
No
Hi guys, I am a first year IB student who has to pick his EE topic. The Extended Essay is an independent, in-depth study of a chosen topic within one of the IB subject areas. I chose to do mine on physics. I have to write 3500 - 4000 words for my EE. I've chosen a set up for an investigation / experiment except now I dont exactly know what investigation I should do. The research question should be in the format: How does changing cx affect y.

The experiment set up is stretching an elastic material over a circular frame, just like a trampoline. With this set up I can investigate many parts of physics, namely gravitation, relativity and maybe something related to the propagation of waves.

Do you guys have any suggestions about what I could do my experiment on?

Thanks a lot for any help, I appreciate it.

If your research question should be in the format "How does changing x (the independent variable) affect y (the dependent variable)" and you are already sold on the idea of stretching some elastic material over a circular frame, then you need to ask yourself first and foremost, "What should my independent and dependent variables be given this setup in front of me?" Then take it from there.

Ok thanks. I'll think about it this way and I'll try and come up with some ideas.

Hi @Juan2g19. I used to supervise IB EE's some years ago.

I guess you are thinking that using a stretched elastic sheet (as a model of 4D space-time) will allow you to do some sort of gravity/relativity-related investigation. This seems problematical: a ‘stretched elastic sheet’ is not a good model of space-time, it is only used as simple visual aid when explaining gravity. And the underlying theory is very complex.

It’s well worth looking at the following IB site. It provides examples of marked Physics (and other) EEs and briefly explains the reasoning behind the marks awarded: https://ibpublishing.ibo.org/extend...l?doc=d_0_eeyyy_gui_1602_1_e&part=1&chapter=1

If you haven't already done so, a quick Internet search should produce plenty of alternative ideas.

vanhees71, berkeman and Grelbr42
As @Steve4Physics said, a rubber membrane isn't great for a relativity model.

What level of mathematics do you have? Is this high school or university? I am trying to guess whether you could reasonably be doing solutions to a wave equation, boundary conditions, and such. And whether it is reasonable to ask you to calculate things such as the normal vibration modes of such an object.

There are lots and lots and lots of things you can do with a membrane that are fun and possibly look good also. Just a couple Youtube vids. Headphone warning! They have loud tones playing.

Calculating those vibration modes is a really interesting bit of mathematics. I would guess you would want to have at least a year of calculus first.

Such membranes get you into just bunches of possible physics. All of the following as a function of frequency. Standing waves, normal modes, resonance, speed of a wave in such a membrane as a function of thickness and tension, efficiency as a loudspeaker or a microphone membrane, how size, shape, and weight of the membrane effects that efficiency, what happens if there is water on one side and air on the other, or just air on each side but at slightly different pressure. What if the material is not uniform? What if you warm or cool this part relative to that part? How can you measure the temperature without interfering with the movement of the membrane? How about a square vs a circle vs a rectangle vs other shapes? Where is the best spot for a loudspeaker magnet to hook on to the membrane? Or a microphone pickup? Can you find a way to have a non-fixed edge for part of the membrane, and how will that affect the normal modes? And that's just the barest possible start.

Careful! If you do too good a job you might get scouted by a stereo maker. Or a scientific instrument company.

PeroK and berkeman
Calculating normal modes is a mathematical exercise which does not appear to be the scope of this assignment.
Juan2g19 said:
The research question should be in the format: How does changing cx affect y.
To me this means something like
1. Change some independent variable x and measure a dependent variable y.
2. Get an idea of how y might depend on x by plotting the results.
3. Develop a mathematical model that can reproduce the experimental results reasonably well.
4. If applicable, investigate if the mathematical model can be used to make testable predictions.
If the setup must involve a stretched membrane, then one can look at the stretching of the membrane (y) under load (x) and determine whether it obeys Hooke's law, whether it depends on past history (hysteresis) or on temperature, etc.

However, I would agree that using a stretched membrane to investigate relativity is like using an arrow to investigate the properties of vectors and vector spaces.

Thanks for all the responses.

After taking your advice on the fact that an elastic sheet wouldn't be appropriate to investigate relativity I would now be investigating something a bit simpler. My research question could now be related to gravity and orbiting bodies and would be something like: Modelling gravity. Seeing how the mass of the central object affects the radius / orbit velocity (or other variable) of the smaller object. Inititally this would only have two bodies, but I could further complicate it by introducing another smaller mass orbiting the mass thats orbiting the big mass although I'm not yet sure how exactly I'd be investigating that. The website looks like it's going to be very helpful for writing my EE and in my EE I'll develop a mathematical model for the experiment to see if the results match, although I might to this with a simulator instead.

@Grelbr42, I do Maths AA HL so I'm finishing calculus right now (I'm doing differential equations) and I feel pretty comfortable with calculus although that could change very quickly knowing how complicated maths can get. The YouTube videos about creating 2D standing waves with salt is very interesting and impressive although I have already decided and bought the materials for creating my previously stated set up. I will still talk to my supervisor about the salt experiment though because it's quite interesting.

My experiment set up is very similar to this .

If you have any more suggestions / advice for my research question or different dependent variables, or any advice in general then I'd appreciate it a lot. Thanks again.

That is not a science model, it is a visualization / pop sci model.

vanhees71
Thanks @malawi_glenn you're right. It's not a scientific model but isn't it still useful? It provides me with a visual representation of gravity which could maybe let me investigate some of its properties like how the central mass affects the orbit of smaller masses. Can I still use this visualisation as the basis for my measurements?

Juan2g19 said:
Thanks @malawi_glenn you're right. It's not a scientific model but isn't it still useful?
Not as a model of gravity, but don't let that put you off doing this as a project - you can investigate why it is not a useful model!

Juan2g19 said:
It provides me with a visual representation of gravity which could maybe let me investigate some of its properties like how the central mass affects the orbit of smaller masses. Can I still use this visualisation as the basis for my measurements?
The key thing to measure is the relationship between orbital period ## T ## and orbital radius ## r ## for circular orbits around a given central mass. We know from theory and observation of "real" gravity (e.g. in the Solar System) that this relationship is that ## T^2 ## is proportional to ## r^3 ## or ## T = k r^{\frac{3}{2}} ##. Compare plots of your collected data for ## T ## vs ## r ## with that for "real" gravity.

TeethWhitener and Steve4Physics
Juan2g19 said:
Thanks @malawi_glenn you're right. It's not a scientific model but isn't it still useful? It provides me with a visual representation of gravity which could maybe let me investigate some of its properties like how the central mass affects the orbit of smaller masses. Can I still use this visualisation as the basis for my measurements?
How are you going to make the small body to actually orbit the large one rather than just falling along some sort of spiral?

Steve4Physics
@Juan2g19, take heed of @nasu's question in Post #11!

There are various practical problems you will have to address. Imagine exactly how you will perform all steps of the experiment, e.g. how will will you release the ball (assuming you plan to use a ball)?

Don't be tempted to omit this preparatory detailed thinking or you may hit major problems when you actually do the experiment.

Minor edit.

Thanks @pbuk I like the suggestion of measuring the relationship with orbital period and orbital radius. I'll most likely use that idea for my actual investigation if I get the model to work. But I tested the set up today and I found that as @nasu said and @Steve4Physics valdiated, the friction acting on the smaller mass is too big causing the orbital radius to decrease very quickly and fall into a spiral making it hard to measure the orbital radius although I might still be able to measure the orbital period. A solution to this could be to carry the investigation out on a trampoline which I have in my summer house. The trampoline's surface has a lower coefficient of friction so maybe it could work better there and although the orbital radius would still drop, it would be much less significant and I would just have to accept this as a source of unreliability in the investigation. This unreliability would give me something to talk about which is good and it would make it easier to compare the model I am using with a simulation of real gravity which is also an advantage.

I'm going to have to wait a month to be able to see if the trampoline model works because I don't have a trampoline available right now so in the meantime I should try and think about other possible investigations. One other investigation which caught my interest was using the technique of photoelasticity to investigate stress strains in objects with different materials, shapes, volumes and properties in general. However, the theory behind photoelasticity seemed quite difficult so it pushed me off of it. If anyone has any suggestions for either investigation or wants to say anything I'd greatly appreciate it. I've already recieved a lot of help so thanks everyone for it.

Steve4Physics said:
There are various practical problems you will have to address. Imagine exactly how you will perform all steps of the experiment, e.g. how will will you release the ball (assuming you plan to use a ball)?

Don't be tempted to omit this preparatory detailed thinking or you may hit major problems when you actually do the experiment.
This is good advice up to a point, however it is common in science projects to find that you DO hit problems with your first set-up and have to refine it as you go along. If you spend all your time thinking you won't have enough time left for doing, so I'd encourage you to start as soon as you can - which is what you have done, so that is great.

Juan2g19 said:
I tested the set up today and I found that as @nasu said and @Steve4Physics valdiated, the friction acting on the smaller mass is too big causing the orbital radius to decrease very quickly and fall into a spiral making it hard to measure the orbital radius although I might still be able to measure the orbital period.
Yes, the motion is a spiral not a true orbit, however you can measure the average radius for each rotation. This way you should get three or four different measurements at different radii for each trial! What you need is some way of accurately recording position and time so you can take measurements. Can you think of a piece of equipment that will help you do this?

Juan2g19 said:
A solution to this could be to carry the investigation out on a trampoline which I have in my summer house. The trampoline's surface has a lower coefficient of friction so maybe it could work better there
A trampoline works very differently to an elastane sheet: the surface hardly stretches at all with most of the movement being in the springs around the edge. I'm not sure it will work very well for this experiment, and
Juan2g19 said:
I'm going to have to wait a month to be able to see if the trampoline model works
would be a bad idea as you risk it not working and you running out of time. It will also probably be easier to rig measuring equipment in the lab at school (which is where I assume you are doing this) than your summer house at home.

## What is the IB Extended Essay and how does it relate to a research project on relativity?

The IB Extended Essay (EE) is a core component of the International Baccalaureate (IB) Diploma Programme, requiring students to conduct independent research and write a 4,000-word paper. A research project on relativity within this framework would involve exploring a topic related to Einstein's theories of Special or General Relativity, formulating a research question, and conducting in-depth analysis to address this question.

## How do I choose a suitable research question for my Extended Essay on relativity?

Choosing a suitable research question involves identifying a specific aspect of relativity that interests you and is feasible to explore within the scope of the Extended Essay. Consider focusing on topics such as time dilation, the equivalence principle, or gravitational waves. Ensure that your question is clear, focused, and allows for thorough investigation and analysis.

## What resources are essential for conducting research on relativity for my Extended Essay?

Essential resources include academic books and journals on relativity, reputable online databases like JSTOR or Google Scholar, and educational websites such as NASA or the Einstein Online portal. Additionally, consulting physics textbooks and seeking guidance from your EE supervisor or a physics teacher can provide valuable insights and direction.

## How can I effectively structure my Extended Essay on relativity?

Effectively structuring your Extended Essay involves organizing it into clear sections: an introduction outlining your research question and objectives, a literature review summarizing relevant theories and studies, a methodology section detailing your research approach, an analysis and discussion section presenting your findings, and a conclusion summarizing your results and their implications. Ensure each section logically flows into the next and supports your overall argument.

## What are common challenges in researching relativity for an Extended Essay, and how can I overcome them?

Common challenges include understanding complex theoretical concepts, finding reliable sources, and effectively analyzing mathematical data. To overcome these, break down complex ideas into simpler components, use multiple sources to verify information, and seek help from teachers or online forums when needed. Time management and regular progress reviews with your supervisor can also help keep your research on track.

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