# Equilibrium Experiments

Aim:
To investigate the theory of equilibrium via the completion of two experiments that rely on the use of equations TPLcos +TPMcos, which can be rewritten as (Mass Ag) cos+(Mass Bg) cos For the second part of the investigation, I will try to prove the equation
(W*x)/d +weight of a ruler.

Introduction
In this investigation, I will carry out two experiments, which in each case will prove a different aspect of the theory of equilibrium. There are two theories’ I wish to prove. The first is ” tension (Tpl) in the string Pl is equal to the weight of A and tension in the string pm (Tpm) is equal to the weight of B. For equilibrium the sum of the vertical components of these two tensions must be equal to the weight of c. Which means that:
Tpl cos + Tpmcos = MassCg
which can be written as
(MassAg) cos  +(MassBg) cos = MassCg (equ 1)
Also: the moment of a force about a point is equal to the magnitude of the force x its perpendicular distance from the pivot. For equilibrium, the moment of the weight about the pivot will be equal to the moment in the opposite direction due to the weight of the ruler.
Therefore (W*x)= weight of the ruler times distanced
Weight of ruler = (W*x)/d. (equ 2)
Method for experiment A:

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Set up the arrangement shown in figure 1, check that the point p is in equilibrium.
Note the value of masses A, B, and C and measure the angles LPO and MPO.
Keep masses A and B constant and note the new value of angles and  for different values of mass C
Record results in tabular form.

Method for experiment B:

Set up apparatus as in fig 2.
Find a point of equilibrium.
Note value for the mass used and the distances x and d.
Repeat last two stages for several sets of masses and record results in tabular form

Calculation
These were done on paper by hand for ease of presentation
Error Analysis
I have generated my errors on the fact that I thought that I could only read the I choose the error of. The way in which I got the final answer out was to run through the calculation twice, once with the answer I got – the error and then again this time with the answer I got + the error. I think that in the first experiment I was a little over the top with the error. I said that I could read the angle to about 5. But when I did the calculation again with the new values. I found that the gap was quite large. And that I was quite close to the true value and that although the value did fall in the gap, the gap could have been a lot smaller. This says to me that the error need not have been so large and that I read the angle quite well.
Conclusion
In conclusion, I have found out that equ 1 stands true. In the aim, I set out to see if I could prove it I have put in all the results. The answers I get out are generally good. They are the same as the mass or in the cases where they are not, they are close and fall well in the range of the errors. Problems with this experiment: the main problem I had with this experiment is the way I was told to find the angle. This way was not that accurate. It left a large margin for error. These are some of the anomalies that may have crept in. For the second of the two experiments, I found that the mass of the ruler was 0.128g. This was obtained by weighting the ruler on a set of scales. After putting the numbers through the formula for weight of ruler, and then dividing the output by g, which was 10, I managed to get a value for the mass of the ruler.
On average this value was 0.119g, which is only about 7% away from the real mass of 0.128g.on farther analysis and after calculating the upper and lower bounds by changing the results by adding or subtracting the errors I found that the outcome from adding the errors to the results and the outcome from subtracting the errors was the same, 0.119g. This meant that the error was not a large enough value to affect the results in a significant way. Therefore finally I found that the mass on the ruler to 0.119g this is 7% out for the value, which I recorded as the mass for the ruler. The reason for this is unknown. I can only guess the reason. One possibility is the mass I recorded for the ruler was out. And as my results are so consistent this is a large possibility.

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