A way of finding the coefficient of friction

It feels really nice when you propose a theory and later find out that it is right. This is what happened with me. Here’s a page from Journal de Brouillons.

“

Another method of finding co-efficient of friction μ

Date: 1/3/2009

I’ve found a new method to find the co-efficient of friction of bodies cylindrical in shape. It requires a thread and something which can measure force like a spring balance and some weights.

The things are arranged as in the diagram.

The weight of the weight when it is free is found. Let it be T₁.

Now the maximum and minimum tensions(for which the system is in equilibrium) of the string connected to the spring balance is found. Let them be T_2max and T_2min.

ΔT = T_2max – T₁ = T₁ – T_2min
Consider a small section of the string wrapped around the object. Let it subtend an angle dθ.

Then the normal force due to this segment

= T sin(dθ/2) + (T+dT) sin(dθ/2)

≈ Tdθ

Under limiting conditions;

f= f_max =μ_sN = μ_sTdθ

For the string to be equilibrium

T + dT = T + f

dt= f = μ_sTdθ

_T2∫^T₁ dT/T = ₀∫^θμ_sdθ
ln(1+ΔT/T) = μ_sθ
μ_s=ln(1+ΔT/T)/θ

if ΔT/T is small enough (if ΔT/T =1/50 the following approximation gives 1% error.)

μ_s=ΔT/Tθ

However the spring balance may have some friction and it will change the values. So it should be taken into consideration.

I would also like to ….

…

”

The remaining text has some other methods of finding the coefficient friction. And now these are the results I got

T1	T2
50	25
100	58
150	85
200	117
250	141
300	175
350	209
400	246
450	284
500	293

And this is the table of values which tell about the relationship between T2 and θ. It is exponentially decreasing.

Angle of Wrapping	T2
π	175
3π	80
5π	30
7π	13
9π	5
11π	3

And ΔT/T was never small enough.

LPS and the 3D image

I did this on 15, January, 2010. I was flashing a torchlight at a light bulb. If I kept the torch and the bulb at some place and moved myself about in the room, the position of the image of the torchlight on the bulb changed.Now if I was standing at A, I would see the reflection of the torch at P and if I were at B it would be at Q.

(of course the bulb wasn’t switched on)

Voila!

Well here’s the LPS. The Local Positioning System. All I have to do is look at the position of the image of the torchlight in the bulb and I can know my position in the room. ( Can I? )

That’s the theory. Then I tried to make it work. I took a bulb and painted red, blue and green stripes on it hoping that the colour image would tell me the position of the image. But the image was still white. So my brother darkened the colours. Now the reflection was not there.

But I noticed one more thing. If you get close to the bulb and flash a light on it, you can see the image formed by the interior curved surface of the bulb, the image of the filament. A great 3D image. Yes 3D! Try it if you don’t believe. Hold the bulb in your left hand and the torch on the right as shown and look from an angle similar to the one shown in the figure.

Here is a photo of the image which I took.

The first post

In this blog you will mainly find the various experiments done by me and the strange results that I have seen. There might be something else also. Do try them out if you can and comment what you found.