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 distance d
Weight of ruler = (W*x)/d. (equ 2)
Diagram
Method for experiment a
1. Set up the arrangement shown in figure 1, check that the point p is in equilibrium.
2. Note the value of masses A, B, and C and measure the angles LPO θ and MPO φ.
3. Keep masses A and B constant and note the new value of angles θ and φ for
different values of mass C
4. Record results in tabular from.
Method for experiment b
- Set up apparatus as in fig 2.
- Find 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 where 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 say to me that the error need not have been so large, and that I read the angle quite well.
For exp B
Conclusion
In conclusion I have found out that equ 1 stand 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 were 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. This is some of the anomalies 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 form 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 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 to 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.
