Variables
Independent Variable: Mass on ruler
Dependent Variable: Depression of ruler
I have kept the distance that the ruler is from the edge of the table constant, (95cm is over the edge of the table.) I have not altered the set up of the apparatus throughout the experiment for measuring either the depression for the known masses or the unknown mass. I have kept the way that I have measured the depression the same throughout and to ensure that this is as accurate as possible I have used a protractor to take the measurements, (see ‘method'.)
Diagram
Method
The apparatus was set up as shown above. I measured the ‘depression’ of the beam when it was not loaded. Then I loaded the beam with the masses, increasing in 100g intervals each time. I allowed the ruler to bend and stay in position (ie: not moving) before taking the measurement. To ensure that my measurements were as accurate as possible I used a meter ruler which was clamped upright at the end of the ruler with the weights on and then used a protractor flat against the edge of the upright ruler to measure how far the other ruler bent.
Whether I measured from the top or bottom of the ruler would make a difference of nearly ½ cm to the measurements. However as long as I measured form either the top or the bottom (and did not alter this throughout the experimeny) it would not make any difference to the graph (I measured from the top.) After I had put on all 8 masses (800g) I took them all off and checked the ruler went back to the same point as before (which was 14.2mm.) I then repeated the experiment again so that in all I did the experiment a total of 3 times, I would then out the averages.
Results
Depression of unknown mass = 20.2 + 0.05
Analysis
I thought that my graph/results would show a proportional increase between the load of the ruler and the depression, this is shown to be the case. (See graph.)
Gradient of graph: ∆d /∆m 26.5/500 = 0.053
Unknown mass: 20.2mm depression = 370g mass
Modifications
I did not have to make any changes to the original plan for the know masses. I was told how to set up the apparatus and how to carry out the experiment so there were no problems. However when I went to measure the unknown mass I did not know how to attach this to the ruler. There was a loop of string at the end of the ruler which I had hung the weight hanger on. But the unknown mass also had string loop so I could not just hang this on the ruler. I did think of putting a hanger on the ruler and then in turn putting the unknown mass onto this and then subtracting the depression for the hanger from the overall depression but I decided against this as it would increase the error in my experiment. So instead I just looped the string loops together which held long enough for measurements to be taken.
Evaluation
My uncertainty is + 1mm because I was using a meter ruler and therefore this was the smallest measurement on it. I could probably improve this uncertainty by using a more precise instrument for measuring it, (probably a vernier scale.) Finding the averages of my results will have helped to ‘improve’ any anomalous results. I do not appear to have any anomalies and my graph has a good line of best fit with a positive correlation, therefore my results must have all been quite accurate.
To improve my experiment I could test my results further by using more unknown masses and then calculating the mass using my graph this would mean that I would be able to weigh the mass and then check that with my graph to see how accurate my results are. I could also improve the uncertainty by using a smaller scale as I have already mentioned.
Conclusion
My results have shown that my hypothesis was right and that my experiment has shown that the cantilever does obey Hooke’s Law. (That “stress is directly proportional to strain”.) In other words the mass that I put onto the ruler (cantilever) had a direct and proportional affect on the depression of the ruler.
The values which I got for my experiment were what I expected and gave a positively correlation graph which I thought it would.
Part of my aim was that I would be able to work out an unknown mass by using the graph which I have drawn form my results. I have done this sand found that unknown mass gave a depression of 20.2 mm and therefore the mass was 370g.