# What affects the Motion of a Trolley on a Runway

Variables:> Mass of trolley> Surface the trolley is running on> Height of the runway> Distance the trolley travelsThe variable I have decided to change is height of the runway in relation to velocity.Prediction:Predicted results:Height (m)Velocity (m/s)0.051.00.101.40.151.70.202.00.252.20.302.4I predict that as the height increases, the velocity also increases. This is because the formula for velocity is:v = ((2gh)(where v = velocity, g = gravity, h = height)So if the height increases, v must also increase. Gravity on earth is always 10m/s2, therefore the formula for velocity can be simplified to:v = ((20h)A predicted sketch graph of the results would probably be as below:The law of conservation of energy says that potential energy (PE) at the top = kinetic energy (KE) at the bottom, therefore all the energy in potential energy at the top must be transferred into two things at the bottom, movement and heat. Any energy at the bottom which is ‘missing’ must have been transferred into heat energy, by friction. We know that if there was no friction, all the energy would be turned into velocity, and the predicted results reflect this ‘perfect’ result. However, there will be an amount of friction in the actual experiment, so the differences in results of predicted and experimental should be able to be explained by friction, and how this causes heat energy to be lost.Trial experiments:For my trials I was going to do experiments with the height ranging from 10cm up to 50cm in 10cm intervals. However, I discovered that this was impractical to go above 30cm, because the clamp we used to hold the runway up could not hold the runway above 30cm. The runway is also quite heavy, so it would not really be possible for someone to hold it for that reason. Also, the height of the runway may not be constant because it would be almost impossible for someone to constantly hold the runway at a constant height during the experiments. This would mean that the results would not be reliable. Therefore from the trial experiments I worked out that to get at least 5 results I would have to have my range as from 10cm up to 30cm, in 5cm intervals.I only got 3 results from the trial experiments as I was planning to have an interval of 10cm, but as this was impractical I only went up to 30cm, therefore only getting 3 results for the trials:Height (m)Velocity (m/s)0.100.950.201.340.302.11Method:We set up the experiment as above with the data logger connected to the light gate so it could record the results by itself reliably and accurately. The data logger then relays this information to the computer, and the software we used was able to work out the actual velocity by itself, so there was no chance of human error. This also meant we could easily take 2 or 3 repeats of each measurement from which to take an average.We started the measurements at 5cm, measuring from the top of the table to the top of the runway at where the trolley was starting, and we took 3 results from that point. We repeated this for the other measurements, up to 30cm and took an average.We kept the test fair by using the same trolley each time, repeating the experiments for each height straight after each other to make sure the height could not change even slightly and used the same runway each time to ensure that there was the same amount of friction.Results:Height (m)Velocity (m/s)Result #1 Result #2 Result #3Average Velocity (m/s) (to 2dp)0.050.380.370.100.280.100.950.960.960.960.151.321.331.341.330.201.611.621.611.610.251.821.851.821.830.302.062.102.072.08Analysis:The graph shows that there is positive correlation in relation to the height of the runway and the velocity of the trolley. The line of best fit is a convex curve, which indicates that the gradient of the line/curve decreases as the height increases.In my original prediction, I expected the two sets of results to be different, and I was correct in predicting this because on the graph, the experimental results were significantly lower than the predicted results. This is due to the amount of friction on the runway which the trolley must overcome and so the friction turns some of the PE at the top of the runway into heat energy at the bottom, so some energy which is calculated as velocity is lost at the bottom.The two curves seem to be getting closer to each other as the height increases, and this may be because that although the friction is increasing, the velocity is also increasing, and as momentum is directly proportional to velocity in the equation:momentum = mass x velocityit will increase at approximately the same speed as velocity, so when friction tries to slow the trolley down, the momentum is one of the opposing forces, and so friction can make less of an effect.Evaluation:I think that this experiment was very successful but if I had been able, I could have changed a few things to make the results better and more reliable. If I had wanted to have a larger range of results, I would have had to extend the runway because I could only go up to a certain height with the runway the length it was – if it had been too high, the trolley would have been free-falling! However, this would mean that another variable was being changed – the distance the trolley travelled – so I could not have done this because then I would not be able to say that a certain thing happened because of ONE variable, it would be both. If I had wanted to go any higher, I could have used how far the runway was in terms of degrees, and although I would only be able to go up to 90ï¿½ before the trolley was in free-fall, it would have been a more reliable way of measuring how high the trolley was.Another way I could have changed the experiment would have been to use an air-track instead of a runway for the trolley to travel along. An air-track reduces friction down to almost zero by making sure the trolley does not even touch the track, it is suspended by the air blown up from the track, and so any movement will send the trolley straight off the other end. This would have improved the results dramatically, because they would have looked much more like the results of the prediction.Most of the results are near enough to the line to not be counted as anomalous results, but there is one anomalous result, which is indicated on the graph. This was caused by the trolley getting caught halfway through the light gate on the last reading of the first measurement, so the velocity was vastly reduced, and in turn, brought down the average.If I had the time I would redo this experiment, using an air-track, and I would focus especially on the height between 0 and 0.1m to see what happens there – whether there is a straight line, or if there is a curve. I would also like to increase the height, but use a protractor instead to measure the degrees so I can go higher. This would show if and where the curve of the line of best fit comes almost horizontal, because the trend at the moment shows that it might become almost horizontal, at approximately 0.6m on the experimental curve, and probably fairly near that for the predicted results. 