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# AS OCR B Advancing Physics Coursework - Making Sense of Data

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Introduction

AS Physics Coursework – Making Sense of Data

An experiment was carried out in which the velocity of a falling mass was measured using a light gate:

The results are shown in the table below:

 Height Above Light Gate(mm) Velocity#1(m/s) Velocity#2(m/s) Velocity#3(m/s) 20 0.61 0.62 0.51 70 1.12 1.11 1.10 120 1.52 1.62 1.50 170 1.76 1.72 1.79 220 1.93 2.03 1.99 270 2.26 2.28 2.30 320 2.45 2.50 2.46 370 2.62 2.67 2.63 420 2.84 2.80 2.89 470 2.96 2.97 2.99 520 3.18 3.13 3.20 570 3.30 3.44 3.34 620 3.53 3.53 3.40 670 3.62 3.64 3.67 720 3.84 3.62 3.83 770 3.86 3.84 3.83 820 4.03 3.97 3.99 870 4.18 4.12 4.14 920 4.36 4.41 4.20

Provided with these results I have initially decided to look at any relationship between the actual figures collected, with the plan of calculating and exploring further data later.

I am therefore looking at the relationship between the distance the object fell, and its velocity as it passed through the light gate. An average of the velocities measured in each experiment has been calculated and the height at which the weight was dropped has been multiplied by 1000 to convert it to metres. I have created a graph of these values.

 Distance fallen /m Average Velocity/ ms-1 0.02 0.58 0.07 1.11 0.12 1.55 0.17 1.76 0.22 1.98 0.27 2.28 0.32 2.47 0.37 2.64 0.42 2.84 0.47 2.97 0.52 3.17 0.57 3.36 0.62 3.49 0.67 3.64 0.72 3.76 0.77 3.84 0.82 4.00 0.87 4.15 0.92 4.32

I added a curved line of best fit to the graph, showing positive correlation between the distance fallen and the velocity of the object as it passed through the light gate.  The line is curved until about 0.3 metres but then becomes more linear, which would be expected if acceleration due to gravity is constant – as a straight line shows constant acceleration. The velocity values from smaller distances appear to be anomalous, suggesting some error involved in the experiment. This could be because any errors in height make up a larger proportion of the overall distance the mass had fallen when dropped from lower heights.

Middle

1.88

0.38

3.84

1.92

0.40

4.00

2.00

0.41

4.15

2.07

0.42

4.32

2.16

0.43

The kinematic equation: s = ut+½at2 can also be used to calculate acceleration. Again, u=0 due to the fact that the object starts from rest, this simplifies the equation to:

 Distance fallen /m Time/s Time2 /s2 0.02 0.07 0.0048 0.07 0.13 0.0159 0.12 0.16 0.0241 0.17 0.19 0.0375 0.22 0.22 0.0492 0.27 0.24 0.0561 0.32 0.26 0.0671 0.37 0.28 0.0786 0.42 0.30 0.0873 0.47 0.32 0.0999 0.52 0.33 0.1076 0.57 0.34 0.1151 0.62 0.36 0.1265 0.67 0.37 0.1353 0.72 0.38 0.1464 0.77 0.40 0.1606 0.82 0.41 0.1684 0.87 0.42 0.1761 0.92 0.43 0.1811

These results comply with the AS Advancing Physics book, which suggests that the acceleration of an object in freefall is about 10m/s-2, however the actual figure for acceleration of all freefalling objects on Earth is 9.81m/s-2 so there is a small amount of error within the data, also indicated by the slight difference in the two calculated acceleration values.

I have decided to look a little more closely at the error involved in my calculations. I believe the main source of error in the actual experiment is likely to be caused by the metal strip used to break the beam of the light gate. Due to the extra 16g on one side of the block, its centre of mass has changed, possibly making it fall at a slight angle. It is likely that this effect would be exaggerated the higher the distance fallen meaning, as the metal strip is pointing increasingly further down, effectively an object of greater and greater width is breaking the beam as it goes diagonally through the strip of metal. This would result in the beam being broken for relatively longer and the measured velocity being slightly less. Also the beam is being broken when the total mass has not travelled as far, which, in relation to the very first graph would also mean the velocity could be less.

Another source of error could potentially come from the way the metal strip is attached. It is not impossible that, being attached with blu-tack, it could have moved from its perpendicular position relative to the block. If it pointed down, this could compound the above problem and decrease measured velocity. If it was pointing up, the reverse effect could be true. Of course, due to human inconsistency, the mass may not be dropped in the same way each time which could contribute further error to the data.

The initial error in measured values can be seen in the results with differing repeat values of velocity. It is these values which have been used in every calculations and errors would therefore be compounded. I have therefore added range bars to the velocity-time graph using the table below to show the maximum and minimum values for velocity recorded around the average.

 Average velocity – minimum recorded velocity(m/s) Maximum velocity –average recorded velocity(m/s) 0.07 0.04 0.01 0.01 0.05 0.07 0.04 0.03 0.05 0.05 0.02 0.02 0.02 0.03 0.02 0.03 0.04 0.05 0.01 0.02 0.04 0.03 0.06 0.08 0.09 0.04 0.02 0.03 0.14 0.08 0.01 0.02 0.03 0.03 0.03 0.03 0.12 0.09

Conclusion

 mass/g gravity/ms-2 0.516 9.81 Distance fallen (m) Potential Energy/ J Kinetic Energy/J 0.02 0.1012392 0.0867912 0.07 0.3543372 0.3178818 0.12 0.6074352 0.617181867 0.17 0.8605332 0.796156467 0.22 1.1136312 1.014871667 0.27 1.3667292 1.3411872 0.32 1.6198272 1.5740322 0.37 1.8729252 1.7981568 0.42 2.1260232 2.085812467 0.47 2.3791212 2.280903467 0.52 2.6322192 2.5926162 0.57 2.8853172 2.9127168 0.62 3.1384152 3.136465867 0.67 3.3915132 3.424660467 0.72 3.6446112 3.653970867 0.77 3.8977092 3.810972467 0.82 4.1508072 4.121122867 0.87 4.4039052 4.436269867 0.92 4.6570032 4.822332467

The graph shows that both energy forms increase in direct proportion to the distance fallen. The gradients are almost exactly equal (equations of lines shown in corresponding colour) proving the conservation of energy. However there is a 0.1007 difference in gradient and the lines can just be seen to be unequal - particularly towards the lower end of the graph. I am therefore going to investigate whether there is any relationship between the distance fallen and the difference between energy forms, to see where the kinetic energy was lost – most likely as heat from friction.

 Distance fallen (m) Difference between kinetic energy and potential energy/ J 0.02 0.0144 0.07 0.0365 0.12 0.00975 0.17 0.0644 0.22 0.0988 0.27 0.0255 0.32 0.0458 0.37 0.0748 0.42 0.0402 0.47 0.0982 0.52 0.0396 0.57 0.0274 0.62 0.00195 0.67 0.0331 0.72 0.00936 0.77 0.0867 0.82 0.02969 0.87 0.0324 0.92 0.165

There seems to be little correlation between the difference in potential and kinetic energy and the distance the object fell from. I would have perhaps expected there to be greater difference as the height increased, due to the fact that the speed of a falling object has been proved to increase with the height it has dropped from – increasing the effect of air resistance and therefore friction, creating heat. Although due to the scale of this experiment, it would be probable that any effect of this nature is very difficult to see.

In summary, I have calculated the acceleration due to gravity of a falling object and consequently recognised the error involved, before going on to prove the conservation of energy by calculating the potential and kinetic energy of the falling mass.

This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.

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4 star(s)

Overall, this is a very good investigation. There has been some thought to the reasons behind the uncertainty of results and some good use of data. 4 stars.

Marked by teacher Pete Golton 06/06/2013

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