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# This experiment is designed to approximate &amp;igrave;, the coefficient of friction, for two surfaces. We used a piece of rubber on the bottom of a wooden block on a wooden table.

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Introduction

Mechanics Coursework

This is experiment is designed to approximate μ, the coefficient of friction, for two surfaces. We used a piece of rubber on the bottom of a wooden block on a wooden table.

## Assumptions

To undertake this experiment, first I developed an equation allowing a straight line to be plotted from our results. This will test if Coulomb’s law is correct. The main assumptions made in this experiment are:

1. Acceleration is constant

2. The strings are light and inextensible, and the pulley is light and smooth

3. g, gravity is 9.8

4. Coulomb’s law is correct

5. There is no air resistance

6. F=ma

These assumptions have different weights in affecting our results. Some are more likely to affect our results, whilst others will only have a small effect.

 Assumption How strong the effect is on results Acceleration is constant This will have a moderate effect on the results. We can see that the acceleration is not constant. This is because friction does change slightly with velocity, and we are ignoring air resistance Light, inextensible strings In fact the strings do stretch slightly, and do have a small weight. This will affect the results as forces will not be constant during the experiment, and therefore produce irregular acceleration. Light, smooth pulley This will affect the results in the same way as above. We attempted to use the smoothest pulley available, but obviously it can never be perfectly smooth. That the pulley has mass does not affect our results, as we are not dependent on the pulleys mass for our results. Gravity is 9.8 This will introduce a systematic error into our calculations, but as we will use this assumption for both the results and the model, it will not make a difference for our experiment. Coulomb’s law is correct This will make a big difference to our results. By assuming that , our calculations are fairly simple. However, this linear model is incorrect. This will affect our results considerably, and may results in a curve being plotted from our results instead of a straight line. No air resistance This will have a mild effect on the results. Because the block of wood and the weights are fairly small, the effects of air resistance are negligible. However there will be a small effect, which again may force the results into a curve rather than a straight line. This assumption will not impact our results very much at all. For macroscopic objects, such as we are dealing with, this law is a very good model. However if we were to repeat the experiment using single atoms for the objects, this would be a bad model.

Middle

(2)

(3)

Using (Coulomb’s Law)

(4)

Substituting equation 4 into equation 1

Substituting into equation 3

(5)

Assuming constant acceleration (see note above)

As

Substituting into equation 5

The two variables will be m1 and t. By putting , we can cancel m2 from the equation.

Setting

Conclusion

Revision of the process

To improve the experiment, it would be better to use light gates to improve accuracy for timing. On the results that we collected, the higher speeds resulted in wider error bounds and thus less accuracy. This is because it was a lot harder to accurately measure these fast times. Measuring the distances we were moving over more accurately would also increase accuracy, as would more accurate measurement of mass. However, accuracy is not the main issue in this experiment. For this experiment, it seems that our model is incorrect, rather than the results.

To improve this experiment, our assumptions need to be changed. Most assumptions are fine, but the assumption of Coulombs law is very inaccurate. This assumption of a linear relationship forced our results into a curve. To achieve a more meaningful analysis of these results, we need a better model on which to compare them. However, more accurate models for friction are much more complex and far less simple to use.

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