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.

A Strange Ocular Observation

I don’t know if it’s just my eyes. I observed something strange while sitting at the bus window last week. But I confirmed it a few days back. I looked at an object illuminated by the setting Sun. To my left eye it seemed to be illuminated by a bluer source while to my right eye the source seemed redder. I think the following images will explain better.

This is an edited photo. As of now I don’t have any explanation. I don’t even know if it has to do with optics or physiology. I would like you to try it out and do comment if you also observe it. But I won’t be able to tell you the exact conditions. It is not always visible to me and the difference is very small.

The Digital Multimeter

Sometime in the third week of April, 2010 I bought a Digital Multimeter(DMM). It cost me Rs. 150. But the experiments I did with it were very interesting. Apart from the usual find the voltage, find the resistance experiments I did a lot of interesting things.

Measuring the resistance of the Human body.

Well I just turned the knob to the 2000kΩ and held the two terminals in my two hands and pressed hard. I got a reading of about 500kΩ. Then I held the two terminals at two points on the same finger and I got a reading of about 400kΩ. Such a small change in resistance. The resistance is clearly not proportional to the length here. Can you guess the reason? Well here’s another point. I made my hands wet and got a reading of about 80kΩ.

Brain waves or what

Now I did the same thing with the millivoltmeter. And to my surprise I got a reading of 10-20mV. So there was a potential difference between my hands. And between two points on my head it was about hundred mV.

Handshake detector

I went back to the megaohmmeter. My brother and I held a terminal each in the left hand and then shook hands. As we shook hands the multimeter showed a reading i.e. it had detected our handshake.

Now the reason I think why I got a strange reading in the first experiment. Our body is a somewhat good conductor on the inside(Don’t ask me why, but I think it is due to all ions in the blood). But the skin is a bad one. In both the cases, viz. the one in which I held the terminals across the length of my hands and the one in which I held them between two points on the same finger, the current had to pass through two layers skin and I think that explains everything.

Electrolysis and Galvanic cell

Well then I and my brother made a galvanic cell. We took a table salt solution in a small cup made of I don’t know what but something insulating. And then measured the voltage across the terminals, it was something small and soon fell to zero. Then we used a different electrode: an aluminium foil and generated about 500mV. Then we started testing everything that was there in house. Later we even added some vinegar and aluminium sulphate(which had no visible effect). Finally after experimenting so much the maximum voltage we got was about 900mV with aluminium foil as the anode and the pencil as cathode.

Now we started doing electrolysis. We started with a pencil cell. And a gas started evolving at the cathode lost metal at anode. And now to quicken things up we used the voltage across the mobile phone charger with pencil anode and Al cathode. I don’t remember the value of the current measured but I think it was more than 1A. And the surface was swarming with bubbles. Then I did the test about which I had only read so far; I took a lighted matchstick and brought near the bubbles. And it did explode with a pop sound. This time there was some gas at the anode also. And it smelled bad. The only gas which I could think of was Chlorine. It must have come from NaCl. But I don’t know any method of testing it.