Acceleration of a Trolley
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Plan An unbalanced force causes an object to accelerate. The acceleration happens in the same direction as the resultant (or unbalanced) force. The size of this depends on the mass of the object and the size of the force. The force on a small object is bigger than the same force acting on a bigger object. If the mass stays the same but the force gets bigger, the acceleration also increases. The equation to find acceleration is: [IMAGE][IMAGE] when [IMAGE]= acceleration, [IMAGE]= velocity at the end, [IMAGE]= velocity at the start, and [IMAGE]= time The variables which could affect the acceleration of a trolley down a ramp are: The mass of the trolley,  (the size of the trolley), if the same force acts on a bigger object it will accelerate less than that force on a smaller object. The continuous force,  (how much the object is pushed), the bigger the push or force, the bigger the acceleration. The gradient of the slope,  (the height of the slope that the object moves down), the bigger the gradient, the bigger the acceleration will be as the object travels down it, because less friction acts against an object which travels down a steeper slope and friction reduces the acceleration of an object. The variable which I have chosen to investigate is the gradient of the slope. I think that out of all the variables, this is the one which is easiest to measure and to change accurately, ensuring a wide variety of reliable data. I predict that the as I increase the height of the slope (or the angle between the floor and the ramp), the acceleration will increase, due to a more direct force from gravity caused by less friction on a steeper slope. [IMAGE] Light gate Light gate Trolley Angle between floor and ramp Ramp I will measure the acceleration of the trolley by running it down a How to Cite this Page
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ramp, through a light gate. The light gate is connected to a computer
which monitors the acceleration by measuring the speed of the interrupt cards on the trolley as they pass through the light gate. I will need to measure the height of the ramp for each experiment; the computer will measure the acceleration. The heights I will be measuring are: 10cm,15cm, 20cm, 25cm, 30cm, 35cm, 40cm I will do each experiment three times and take the average result for each height to ensure an accurate result. To make sure that it is a fair test, I will make sure that the back wheels of the trolley are always 60cm from the light gate at the beginning of each experiment. The height will always be measured accurately with a cm ruler. The computer program which measures the acceleration of the trolley down the slope is accurate to 0.01 m/s/s. This will ensure that my results are accurate. I will measure the acceleration of the trolley at each height three times, and then take the most sensible result or average, excluding anomalies and therefore ensuring reliable results. Obtaining Evidence Results of acceleration of a trolley experiment Height (cm) Acceleration (m/s/s) Average Acceleration Angle between floor and ramp 10 0.27 10 0.24 0.26 3 10 0.26 15 0.75 15 0.70 0.75 4.7 15 0.75 20 1.38 20 1.06 1.36 6.2 20 1.34 25 1.94 25 1.57 1.76 7.8 25 1.78 30 2.45 30 2.42 2.44 9.3 30 3.10 35 3.21 35 2.70 2.79 10.9 35 2.88 40 2.93 40 2.67 2.80 12.5 40 3.01 There were 5 (highlighted in red) anomalous results in the 21 experiments carried out. I used my judgement to decide on a representational average which excluded these. Averaging all the results would mean that they would not be as accurate; the anomalies would throw off the balance and create an inaccurate average. Analysing Evidence [IMAGE] This graph shows how the acceleration increases as the slope gets steeper but by less each time. I predict that if I had continued to increase the slope past 40cm, there would be more of a curve as the acceleration would begin to converge, and not increase by so much each time. I thought a more accurate way of measuring the increase in acceleration would be to look at the angle between the floor and the ramp. To work this out I used the mathematical formula:[IMAGE][IMAGE] [IMAGE] This graph shows the correlation between the angle and the height. I was expecting more of a curve and I think that if I had again gone further than 40cms I would have been able to draw more from this graph. Next I compared the angle to the acceleration to see if it was a more accurate way of measuring the increase in acceleration as predicted. [IMAGE] It is clear from this graph that the points roughly follow a straight line although unfortunately I don't think that this is any more accurate than the graph comparing height to acceleration. Although my results weren't exactly as I predicted, (I expected more of a curve on the graph involving height and the angle), it is still clear that as the height of the ramp increased, so did the acceleration of the trolley. This is due to the decreasing amount of frictional force acting on the trolley as the gradient increases leading to a greater resultant force and faster acceleration. Evaluating Evidence There were a number of anomalous results in my experiments. Although I listed them in my table of results, I was careful not to include them when taking an average acceleration for each height. I could see that doing this would make the average inaccurate and used my judgement to take a reliable average. The computer which measures the acceleration is very accurate and therefore I think that the anomalies must have been caused by the method. The trolley could have started too far back or forwards or maybe could have hit the light gate on its way through. The height of the ramp, although kept at the same for each set of 3 experiments could be measured more precisely for more accurate results. The fact that each of my experiments was done three times increases the reliability of my results. I think that it is important to do each experiment three times. That way, if you have very conflicting results, it is easier to see which the anomaly is and which the two reliable results are. If I was going to redo my experiments I would change a number of things. I would do more heights, increasing it to 60 or 70cms. That way, it is easier to see patterns on and draw conclusions from your graphs. I would be careful to keep all other variables, apart from the height, the same at all times. I would also try and be more precise about measuring the height of the ramp. These would make the experiment generally more accurate. Another idea I had on how to perhaps make the experiment more accurate would be to use set angles rather than set heights. E.g. 5 degrees, 10 degrees, 15 degrees, and work out the height using trigonometry accordingly. 
