Physics IA: Distance B/w Pendulum & Alum. Block, Finding Damping Coefficient

[qumbo19]

TL;DR Summary: I am doing an experiment for my Physics IA and don't know the theory behind it

I am working on a Physics experiment for my school where I vary the distance between a simple pendulum and an aluminium block, and get the damping coefficient for each distance. Below are the images of the setup and the data I collected:

Image of setup:

Image of data:

As you can see from the setup, I use some glass to raise the height of the aluminium block in increments. I know the theory is that the eddy currents somehow oppose the motion of the pendulum and thus causes the damping, but I can't find any equations that connect the two. What graph can I do to obtain some values related to the setup? I can't find much theory on this experiment and would really appreciate some help on this! I have tried finding the relationship between the two: by b = k d^n. Where k and n are constants to be found, b is damping coefficient and d is distance, and then I log both sides and find them from the gradient and intercept. But I don't even know if this is a valid approach.

 

[Baluncore]

Welcome to PF.

1. Plot the field of the magnetic pendulum. Is it symmetrical? As the pendulum swings, the magnetic field will induce eddy currents proportional to the number of lines, and the rate that those lines cut the aluminium over one pendulum swing.

2. Plot the data curves you measured. What mathematical function do they look like? Maybe it is 1/d²?

 

[berkeman]

TL;DR Summary: I am doing an experiment for my Physics IA and don't know the theory behind it

I am working on a Physics experiment for my school where I vary the distance between a simple pendulum and an aluminium block, and get the damping coefficient for each distance. Below are the images of the setup and the data I collected:

Image of setup: https://ibb.co/F8Jx1Sp
Image of data: https://ibb.co/4fLPKTH

As you can see from the setup, I use some glass to raise the height of the aluminium block in increments. I know the theory is that the eddy currents somehow oppose the motion of the pendulum and thus causes the damping, but I can't find any equations that connect the two. What graph can I do to obtain some values related to the setup? I can't find much theory on this experiment and would really appreciate some help on this! I have tried finding the relationship between the two: by b = k d^n. Where k and n are constants to be found, b is damping coefficient and d is distance, and then I log both sides and find them from the gradient and intercept. But I don't even know if this is a valid approach.

Please do not post transitory links to your images and data. Instead, use the "Attach files" link below the Edit window to attach your images to your post. That way when the original source images go away in a few years, future visitors will still be able to see what you are asking about. Thanks.

 

[TSny]

I have tried finding the relationship between the two: by b = k d^n. Where k and n are constants to be found, b is damping coefficient and d is distance, and then I log both sides and find them from the gradient and intercept. But I don't even know if this is a valid approach.

I think that's worth trying.

 

[qumbo19]

I think that's worth trying.

How could I validate if thats the correct relationship if there is no literature on the actual?

 

[TSny]

How could I validate if thats the correct relationship if there is no literature on the actual?

I don't know. But I think it would be worthwhile to see if you can discover a relationship between $b$ and $d$ that fits your data fairly well.

I think the eddy currents might be complicated. So, I don't know if it would be easy to derive a theoretical relationship between $b$ and $d$.

I guess the strength of the eddy currents (and therefore of the damping) would be roughly proportional to the average magnitude of the $B$ field at the surface of the block for a given distance $d$. If the magnet can be approximated as a magnetic dipole, then the strength of the magnetic field would vary with distance $d$ from the magnet as $\approx 1/d^3$. So, if the damping is proportional to the strength of $B$ at the block, then you might expect $b$ to vary inversely as the cube of $d$. But that's handwaving at best. It could be more complicated.

 

[qumbo19]

Ok, thanks. I'll find n and k from the log log graph and see what values I find. But do you think there any equations that could connect the variables or not?

 

[qumbo19]

I don't know. But I think it would be worthwhile to see if you can discover a relationship between $b$ and $d$ that fits your data fairly well.

I think the eddy currents might be complicated. So, I don't know if it would be easy to derive a theoretical relationship between $b$ and $d$.

I guess the strength of the eddy currents (and therefore of the damping) would be roughly proportional to the average magnitude of the $B$ field at the surface of the block for a given distance $d$. If the magnet can be approximated as a magnetic dipole, then the strength of the magnetic field would vary with distance $d$ from the magnet as $\approx 1/d^3$. So, if the damping is proportional to the strength of $B$ at the block, then you might expect $b$ to vary inversely as the cube of $d$. But that's handwaving at best. It could be more complicated.

Well I just checked and the value of n I got was 3.244, and so I think you were right with your theory, so thanks a lot. Do you know any good resources I can look at to learn about magnetic dipoles and just magnetism in general to describe this in my experiment.

 

[TSny]

Well I just checked and the value of n I got was 3.244, and so I think you were right with your theory, so thanks a lot.

A wrong theory can give a right prediction (by chance). However, a right theory should not give a wrong prediction. So, if you had gotten something much different from 3, then it would imply that my argument for $1/d^3$ is wrong or incomplete.

There are other factors besides the strength of B at the surface of the block. According to Faraday's law of induction, the induced currents in a portion of the surface of the block should be proportional to the rate of change of the magnetic flux through that portion. That means that the speed of the magnet as it swings over the surface is an important factor. The average speed during a swing depends on the length of the pendulum as well as the amplitude of the swing. If you were keeping the length and amplitude constant as you changed $d$, then the average speed might not have varied much between measurements. Otherwise, this is something that would influence the damping in addition to the variation of B with distance $d$.

There could be other factors that I haven't thought of. It is interesting that you got an exponent of approximately 3 for $1/d^n$ in the damping.

Do you know any good resources I can look at to learn about magnetic dipoles and just magnetism in general to describe this in my experiment.

I don't know of a good resource. It would depend on your educational background and level of understanding so far. You could try browsing the web for relevant material. Search for topics such as "magnetism", "magnetic dipoles, "Faraday's law of induction", "induced current", "eddy currents", and "magnetic braking".

For example, see this link which was one of my first hits with "magnetic braking".

 

[qumbo19]

A wrong theory can give a right prediction (by chance). However, a right theory should not give a wrong prediction. So, if you had gotten something much different from 3, then it would imply that my argument for $1/d^3$ is wrong or incomplete.

There are other factors besides the strength of B at the surface of the block. According to Faraday's law of induction, the induced currents in a portion of the surface of the block should be proportional to the rate of change of the magnetic flux through that portion. That means that the speed of the magnet as it swings over the surface is an important factor. The average speed during a swing depends on the length of the pendulum as well as the amplitude of the swing. If you were keeping the length and amplitude constant as you changed $d$, then the average speed might not have varied much between measurements. Otherwise, this is something that would influence the damping in addition to the variation of B with distance $d$.

There could be other factors that I haven't thought of. It is interesting that you got an exponent of approximately 3 for $1/d^n$ in the damping.I don't know of a good resource. It would depend on your educational background and level of understanding so far. You could try browsing the web for relevant material. Search for topics such as "magnetism", "magnetic dipoles, "Faraday's law of induction", "induced current", "eddy currents", and "magnetic braking".

For example, see this link which was one of my first hits with "magnetic braking".

Ok great, I will look into those resources. This is for a highschool experiment.