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Thanks very much for everyones contribution! I think I got it now.

Yes, you're right.

Thanks very much for your input. I will try this problem again, this time with a better understanding! The reason geometry is not allowed for this problem, is because this is not actually from a geometry class. This problem is from one of my modules on inequalities, sets and logic (to summarise).

This is the solution: Unfortunately I was not able to make sense of it, but perhaps it makes more sense now that I saw all the replies here. The values of the linear functions which determine the sides of the triangle ##a(x,y) = 2x+y-2##, ##b(x,y)=2x-3y-6##, ##c(x,y)=x-y-1## opposite to...

"Let's take the two points we are given, P and Q, and add the origin O as well to give us more data. Now, taking the lines in the order given, we plug in the x value of our point and say whether the y value is greater than or less than the expression in x on the RHS:" I am not sure what to...

What does that information about whether the retuned y-value from the functions is greater or lower than the one from the point?

Yes, I believe this would work, although perhaps more complicated. The solution refers to a method like the one stated by several threads above, however it is written in a way that does not really make sense on its own. The only thing I can tell is the use of some inequalities. That's why I...

Okay so I have tried to work this out like you said, although a bit confused. Please correct me if I did any mistakes in here. First rearranged the equations in the form ##y=mx+c##: ## \left.\begin{matrix} y= -2x+2\\ y=-\frac{2}{3}x+2\\ y=x-1 \end{matrix}\right\}triangle ## Then, finding the...

I tried doing this problem, but couldn't find a solution that wouldn't involve a sketch... Finding the vertices was all I've got. Thanks in advance.

True, that makes sense.

Alright, I guess this will remain a mystery. Thanks for the contribution.

Hmmm... This is the website, in case you want to have a look: https://www.ukessays.com/essays/mathematics/how-can-integral-calculus-be-derived-and-applied-to-find-the-volumes-and-surface-area-of-complex-three-dimensional-objects.php I can't figure out what kind of geometry could have been used...

I've never actually done this, so I was wondering if someone could show me how this is done. One way I tried was by simply using ##cos^{-1}## in order to cancel the cosine, but that gave me a different value, so I assume this is not how you are supposed to do this. --> I know I am supposed to...

Yes, I understand what you wrote. However, I feel like this mainly applies to wheels that deform on the surface, such as a deflated tire for example (correct me if I'm wrong), so how can you apply any equation to find the Frictional Force for basically a hard wheel on another surface? (besides...

Thank you! On the website you have linked in your comment above I have found the following equation: $$F=\frac{Nb}{r}$$ Would this then give me the force due to the rolling resistance directly? That means I wouldn't need to use the equation above? Because essentially I am trying to find out the...

I was looking for a way to calculate the friction arising from the axle and wheel of a standard lab cart. I came across this research paper: https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/PhysEd4.pdf That derived the following equation for the coefficient of rolling...

Nevermind, I believe I phrased this wrong. I meant why you cannot substitute y to estimate x. Because I remember the prof saying that you can substitute x to estimate y, but not the other way around. And I forgot the reason and didn't find anything on this on the internet, so I thought maybe...

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Got it, thanks!

So you are saying that it is implied due to the dot product, but just not shown in the equation. I am not sure I fully understand what is going on, but I get what you are saying.

Yes, it is ##\phi =\iint_{S}B\cdot dS##

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Yes, I think the same thing. Although I don't believe they would accept me taking the exact model he has done and use that, but maybe getting a little help perhaps is ok...

The problem is this is a graded project and I am not sure if I would be allowed to share this with other people who could help with that. Also, I think that if I post my results on here, it would appear as plagiarism if an originality check is made (even though they are mine), so I just want to...

Yes, thank you :) The results were good and pretty accurate I believe, so that turned out well. The voltage probe did the job, it was possible to set it to record data at higher speeds, so this was no problem. Thanks to everyone who contributed as well. I have learned a lot, which is always...

I didn't use an oscilloscope, because that was too complicated to use, but instead I went for a voltage probe, which displays the voltage on the computer like an oscilloscope would. The formula you have derived were helpful for understanding, however I wanted to do this project on my own...

I finished my experiment (using insulated wire), this time I had very little fluctuations so overall some good results. Although the best fit curve turned out to not be fully linear, but slightly curved. Ill have to have a look into that. If anyone is interested in seeing these results, you...

@bob012345 @Charles Link I have a question about the experiment, when I am using bare copper, the coils are not allowed to touch am I correct? Because I have seen this being done on YouTube with the coils touching, but I am unsure if this is correct. If this is not allowed, would insulated wire...

Why are you not using an integral? And where does the ##2\pi## come from since the area of the circle is ##\pi r^{2}##

Perfect, that answers my question. And you did use the equation for B from post #25 am I correct

What exactly do you mean by over a spherical section? what exactly was manipulated?

So does the derivation come from substituting ##B_{z}(z)## into ##\phi = \int \vec{B}\cdot \vec{dA}##

What exactly did you do to get this equation? No need to show your working, I am just wondering what you did. Perhaps I can derive this myself for fun. ##q_{m}=B_{z}(z)## right?

That makes sense. That wouldn't be too bad to be honest. I am going to see how much effort that will require, but I might actually do this. Also in combination with using an oscilloscope perhaps.

Yes, that actually makes much more sense. I am going to see if I have one in the lab, or else I will simply get one. That way it would be much more easy to see what the actual voltage induced is at any point in time, e.g. in the middle of the coil. (which was one of the issues I had with the...

Yes, the method with the tubes is something I already did to make the results more reliable, as of course the angle would vary the flux. I used paper instead, since it is hard to make plastic tubes for the right dimensions. I will take your advice and get back with some results. Note: I am...

Ok, thank you for your contribution. I will start off by doing the experiment and perhaps mention the theoretical way that this could be calculated (analytically). Since you're saying experimental is best and you seem to have done similar stuff, do you have any suggestions as to how I could make...

The experimental data that I collected was pretty inconsistent, since I think the magnets are moving through the coil too fast, leaving not enough time for the voltmeter to read it properly or something. I am still trying to find ways to improve this methodology, so unit I will have done so, I...

How exactly did you determine this equation? I couldn't find this anywhere so I assume you derived this one yourself ?

I don't see the point in using the Simpsons rule to be honest... I just looked it up and it seems to me as if its simply a way to get around having to work out the integral (which is no problem for me)... I also think that this is perhaps too simple to include in this project. And if I...

Yes, this is the kind of shape of the bottle. What I thought for the bottom was to model one hole and then kind of subtract that by the number of holes there are... I don't know if doing approximations would really be appropriate here. I am not familiar with Simpsons rule, but I will have a...

I am just finding the volume without counting for wall thickness, which is something I will mention in the evaluation part if there should be small errors. For the method: This is basically a topic I chose on my own and decided to do it using integration, since the math behind it is...

I actually have the bottle, however I do not want to post the concrete bottle or I am going to get a plagiarism strike for posting my own stuff on here. So here is a brief sketch of the contour of the bottle, if this is any help to you. For the forms of data: I basically took an image and...

So would I have to create a special function for the induced emf depending on height? Does the time factor in the equation not solve this problem? I would rather like to solve this the proper mathematical way instead of making assumptions, since that would be too easy and not very accurate.

Alright I will see what I can do and get back to you when I am done. This will take a while though.

Indeed I think the method from post #25 is good, anything else would be clearly out of my capabilities I must admit. In this particular instance I am struggling to understand how to express ##R## and ##\phi## properly in the equation.

Solving the double integral itself should not be a problem, my issue is still that I don't know how exactly to express all of this into the formula in the correct manner. This is something I mentioned in post #79... perhaps someone can help a bit with that... I have the same problem for the long...

So if I understand this correctly ##R## is going from the centre of the enface to ##a##, which is the radius of the magnet... Wait no that doesn't make sense. By this logic it would simply be the radius. Is perhaps point 0 in the very middle of the magnet? For ##\phi## I understand you have to...

Yes, I know quite a bit about integral calculus. I have taken a course althoughI have taught myself a lot of it already since I did some math projects on integral calculus and used it quite a bit for several physics problems. I mean this is not a necessity, but I thought it would be a nice...

That was explained very well, but now my question is how can I possibly integrate ##R## and ##\phi## if there is no value for them? Like my question now is how can I proceed to solving this integral with these two unknowns? I also understand it is not solvable by hand and requires a special...