How the Angle of a Ramp Affects the Speed of a Cylinder Moving Down It
Length: 2267 words (6.5 doublespaced pages) Rating: Red (FREE)                                  
How the Angle of a Ramp Affects the Speed of a Cylinder Moving Down It
Ã˜ Aim: To see how the angle of a ramp affects the speed of a cylinder moving down it. Ã˜ Preliminary Work I carried out some preliminary tests to see any problems, which could occur and anything, which could be improved. I first tried timing the cylinder with a stop watch timer, although this may be slightly inaccurate because of the result being reliant on the timers reactions, we felt this to be most efficient. By setting at 5Â° we got a result of 1.39s. The results of the experiment with the stopwatch are shown below. The weight of the cylinder in the set of results below is 198.18g. Here, we are testing how long the cylinder takes to reach the end of the ramp  i.e. not the time it takes to completely stop Preliminary Experiment Angle (Â°) Time 1 (s) Time 2 (s) Time 3 (s) Average (s) 5 1.59 1.42 1.69 1.50 10 0.98 0.91 1.02 0.97 15 0.77 0.78 0.73 0.76 20 0.53 0.61 0.64 0.59 [IMAGE] Ã˜ After the 20Â° angle we found it was becoming difficult to time the cylinder and also to support the ramp. So we decided to change the range from 5Â° 45Â° to a more suitable range of 3Â°  30Â° and also to carry out the experiment 5 times instead of the 3 allowing us to get a better average. We had previously decided that all the cylinders should be rolled from a height of 30cm to begin with, although this could be used as a variable later on. Ã˜ One can clearly see from this set of results that a trend develops in the average time in seconds. That is to say that apparently the steeper the angle of the ramp, the less time the cylinder takes to leave the ramp. This means that, in my preliminary and most simple results there is no direct proportion between x and y as the line on the graph a) is a curve, and b) does not pass through the origin as demonstrated on the next page. However, what it does show is satisfactory enough to make a calculated prediction for the experiment. Ã˜ Hypothesis: my prediction in its most simple form is that in the experiment, the general trend of the results is that when y is big, x is smaller, and when y is small, x is bigger. This trend should stay intact through the experiment even if we change the variables quite considerably. For example, if we change the weight of the cylinder then the trend will still be as mentioned. Later, I will work out the potential energy of the cylinders using the formula E = m.g.h, where m is the mass of the cylinder, g is gravity, and h is the heightof the ramp. We can work out the height of the ramp by using trigonometry. In the diagram below we know that the hypotenuse of the triangle is 30cm long, and that the angle is defined. [IMAGE] The equation for x is: Sin (whatever the angle is, example 10Â°) x hypotenuse (0.3m) = Sin10Â° x 0.3 = 0.05cm (3 s.f.). Ã˜ Using this information we can now work out the PE of the cylinder. E = m.g.h ========= = 0.19818 x 9.8 x 0.05 = 0.10J Factors Ã˜ Angle of ramp: The experiment could be affected by the angle of the ramp for example a 10Â° angle could have a higher amount of potential energy than a 3Â° angle. Ã˜ Surface type of ramp: The surface of the ramp may affect the outcome of the results because any type of grip on the surface could slow it down and also such things as lubricants on the ramp could make the ramp slippery in effect speeding up the ramp. Ã˜ Weight/mass of cylinder: The mass of the cylinder affects the results because the weight could either slow it down or even speed the cylinder up, as there will be a greater amount of potential energy pulling on the cylinder. Ã˜ Surface of cylinder: The surface of the cylinder could affect it because just like the 'surface type of the ramp' the cylinder's surface could slow it down. All these factors contribute to the overall performance of the cylinder and indeed the result takings. It is imperative therefore that fair testing is incorporated into the method. For example, variables like the weight of the cylinder need to be kept constant where necessary: picking up a different cylinder that looks similar is no good. Fair test The experiment will be a fair test as there will only be one variable factor: the angle. All the other factors will stay the same such as the material used and the cylinder used: this means that there will not be any bias issues in this experiment. Later on to broaden the variety of results we could change the weight of the cylinder to compare speeds, times and angles. List of apparatus required for experiment beginning 24/1/02  ïƒ¼ Metal/wooden cylinder  ïƒ¼ Ramp ïƒ¼ Metre stick ïƒ¼ Angle measurer ïƒ¼ Stopwatch The stopwatch must be reliable and have a clear screen to prevent confusion, which could seriously jeopardise the results of the experiment. As well as this, the metre stick used for measuring must be very accurate and with clear incisions as to where the markings are. The angle measurer (or protractor) must be used with great diligence and readings should be double checked at all times. Each time the ramp is used in a practical lesson, the same ramp must be used next time in order to maintain consistency throughout. Lastly, the metal cylinder must be used each time, also to endorse fair testing and continuity. Diagram In the diagram shown on the next page, I have shown exactly how I planned this experiment to work. It was a success in my opinion, as it was fair, safe and reliable in equal measure. [IMAGE] SECTION O: OBTAINING EVIDENCE Method Ã˜ Collect the apparatus Ã˜ Setup as shown in the diagram Ã˜ Set the angle of the ramp at 3Â° Ã˜ Place the cylinder at the top of the ramp and let go Ã˜ Get partner to start timer at this point Ã˜ Stop the timer when cylinder reaches end of ramp Ã˜ Put the result into the result table and repeat experiment 5 times Ã˜ Add 3Â° to the angle and repeat the experiment Ã˜ The mass of the cylinder here was 0.19818kg Ã˜ The distance from the bottom here is 30cm, or 0.3m (i.e. the distance it rolls). Results Final tests Angle (Â°) Time 1 (s) Time 2 (s) Time 3 (s) Time 4 (s) Time 5 (s) Average (s) 3 1.95 2.10 2.18 2.32 1.96 2.10 6 1.40 1.51 1.48 1.35 1.30 1.41 9 1.02 1.01 0.94 0.98 1.01 0.99 12 0.98 0.99 0.89 0.94 0.98 0.96 15 0.80 0.77 0.76 0.79 0.82 0.78 18 0.65 0.67 0.63 0.64 0.59 0.64 21 0.62 0.54 0.61 0.60 0.50 0.57 24 0.44 0.48 0.46 0.46 0.51 0.47 27 0.42 0.38 0.41 0.37 0.45 0.41 30 0.34 0.41 0.38 0.33 0.35 0.36 From this set of data, using the formula Speed (m/s) = Distance (m) / Time (s), we can ascertain the speed of the cylinder on its way down the ramp. Using the average time for each angle (shown above in red) we can put these results in a table (remembering the distance is always 30cm) Angle (Â°) Time (s) Speed (m/s) 3 2.10 0.14 6 1.41 0.21 9 0.99 0.30 12 0.96 0.31 15 0.78 0.38 18 0.64 0.47 21 0.57 0.53 24 0.47 0.64 27 0.41 0.73 30 0.36 0.83 From this, we can successfully conclude that the steeper the angle becomes, the speedier the cylinder becomes, in a graph looking like this: [IMAGE] SPEED IS PROPORTIONAL TO ANGLE SIZE AS THE LINE OF BEST FIT PASSES THROUGH THE ORIGIN We can also now work out the potential energy of the ramp by using the formula. PE=m.g.hFor example, if we take the formula: h = sin Î¸ x hypotenuse and use it row one of the above table then we can work out the height. In this case it is Sin3Ëš x 0.3m =0.02m. Taking this figure into account, and knowing what the weight of the cylinder is and also knowing gravity is 9.8, then we can work out the PE of the cylinder for all angle sizes. Example: PE = m.g.h 0.19818 x 9.8 x 0.02= 0.03J Therefore I will predict that the PE of the cylinder grows as the angle gets steeper. This is because I believe that as the height is the only changing variable then it is obvious that when this figure increases it will also increase the product of the three figures that are multiplied. It is also noteworthy that by using this rule when keeping height constant and varying the mass of the cylinder, then the heavier the cylinder the more PE it has. Angle sizeËš Mass of cylinder kg Gravity Equation for height Height (m) Potential energy (J) 3 0.19818 9.8 Sin aËš x 0.3 0.02 0.03 6 0.19818 9.8 Sin aËš x 0.3 0.03 0.06 9 0.19818 9.8 Sin aËš x 0.3 0.05 0.1 12 0.19818 9.8 Sin aËš x 0.3 0.06 0.12 15 0.19818 9.8 Sin aËš x 0.3 0.08 0.16 18 0.19818 9.8 Sin aËš x 0.3 0.09 0.17 21 0.19818 9.8 Sin aËš x 0.3 0.11 0.21 24 0.19818 9.8 Sin aËš x 0.3 0.12 0.23 27 0.19818 9.8 Sin aËš x 0.3 0.14 0.27 30 0.19818 9.8 Sin aËš x 0.3 0.15 0.29 My previous theory was correct. As the angle size increases on the ramp, the potential energy of the cylinder also increases in a graph looking like this: [IMAGE] PE IS PROPORTIONAL TO ANGLE SIZE AS THE LINE OF BEST FIT PASSES THROUGH THE ORIGIN Now we can experiment by using different masses for cylinders and also by measuring the distance the cylinders take to stop 1) Change mass of cylinder to 0.055kg as opposed to 0.19818kg before, with the length from which it is released remaining at 0.3m Angle size Mass of cylinder (kg) Time 1 Time 2 Time 3 Average time (s) Average speed (m/s) 3 0.055 2.18 2.12 2.22 2.17 0.14 6 0.055 2.01 2.05 2.02 2.03 0.15 9 0.055 1.96 1.99 1.95 1.97 0.15 12 0.055 1.77 1.85 1.8 1.81 0.17 15 0.055 1.69 1.72 1.69 1.72 0.17 18 0.055 1.23 1.4 1.29 1.31 0.23 21 0.055 1.02 0.97 1.01 1 0.3 24 0.055 0.89 0.86 0.92 0.89 0.34 27 0.055 0.75 0.75 0.76 0.75 0.4 30 0.055 0.58 0.54 0.52 0.55 0.55 [IMAGE] Here is a graph demonstrating the relationship between speed + angle size for where the mass is 0.055kg: We can therefore work out the potential energy of the lighter cylinder. I predict using both knowledge from previous work and by using logic that the lighter cylinder will have less potential energy because it is the only variable that changes. In this way, when the mass increases this will cause the product of the three variables (mass, gravity and height) to increase and vice versa. Angle sizeËš Mass of cylinder kg Gravity Equation for height Height (m) Potential energy (J) 3 0.055 9.8 Sin aËš x 0.3 0.02 0.01 6 0.055 9.8 Sin aËš x 0.3 0.03 0.02 9 0.055 9.8 Sin aËš x 0.3 0.05 0.03 12 0.055 9.8 Sin aËš x 0.3 0.06 0.03 15 0.055 9.8 Sin aËš x 0.3 0.08 0.04 18 0.055 9.8 Sin aËš x 0.3 0.09 0.05 21 0.055 9.8 Sin aËš x 0.3 0.11 0.06 24 0.055 9.8 Sin aËš x 0.3 0.12 0.06 27 0.055 9.8 Sin aËš x 0.3 0.14 0.08 30 0.055 9.8 Sin aËš x 0.3 0.15 0.08 Again, as predicted, the potential energy of the cylinder increases as the angle of the ramp grows steeper. It shows clearly in comparison with the graph for when the mass of the cylinder is 0.19818kg that there is a considerably less amount of PE when the mass is less. This is due to the fact that the equation for PE (PE = m.g.h, where h is a changing variable and the m & g are constant) is dependant on both the angle size (translated using trigonometry into height) and the weight of the cylinder because as one cannot change gravity in a physics room easily then the totals of the other variables determine the result. For the next stage of my experiment, I have decided to change one of the variables, namely the hypotenuse length from which the cylinder is dropped. Beforehand, it was 0.3m and has remained so throughout the recent tests. Now however I will change it to 0.6m to investigate whether this will affect the PE attained by the cylinder. This is the table of my results. Angle sizeËš Mass of cylinder kg Gravity Length of hypotenuse Height (m) Av. Time (s) Speed (m/s) 3 0.19818 9.8 0.6m 0.02 2.11 0.28 6 0.19818 9.8 0.6m 0.03 1.87 0.32 9 0.19818 9.8 0.6m 0.05 1.45 0.41 12 0.19818 9.8 0.6m 0.06 1.25 0.48 15 0.19818 9.8 0.6m 0.08 1.14 0.52 18 0.19818 9.8 0.6m 0.09 0.99 0.61 21 0.19818 9.8 0.6m 0.11 0.76 0.79 24 0.19818 9.8 0.6m 0.12 0.63 0.95 27 0.19818 9.8 0.6m 0.14 0.51 1.18 30 0.19818 9.8 0.6m 0.15 0.45 1.33 We can see clearly once again that the speed increases steadily as the angle gets steeper and the length of the hypotenuse grows. If we put these results in comparison with when the length of the hypotenuse was 0.3m then these results emerge: [IMAGE] It seems that the speed of the cylinder changes quite a bit when the angle of the ramp is quite low, but then the two sets of results become more equal as the angle size increases. SECTION E: EVALUATION From looking at the results it is clear that both my aim and predictions were achieved and that the prediction was correct. I also found that the speed was increased and that the potential energy increased with the angle. Looking at the graphs shows that the results were mainly affected by the angles between 3Â°  15Â°. The second graph shows a positive correlation between the angle and the speed. I felt that the experiment was done to the best of my ability and went well overall. I did all that I could to ensure that the investigation was fair except for the fact that we used a stopwatch instead of a ticker timer. Although another negative side being that the table that we used to hold up the ramp could have one of two effects. One that they could alter the angle slightly, which affects the results. Two it may allow the wood to slip or even tilt to one side, which may affect the results too. Using the table and the stopwatch were both not scientific which meant that the results could be possibly bias. To improve the investigation I would redo the experiment in the same fashion but use the ticker timer and a better material to hold the ramp in place. Although I still feel that my results were accurate enough to draw a firm conclusion as I had repeated the experiment 5 times and found an average which gave the desired result. In most cases my predictions were 100% correct, as I related them to the results of my preliminary work and used scientific knowledge and logic to make a calculated hypothesis. I also feel that my results were as accurate as possible in a situation where one is under considerable time pressure and in a busy environment. If I had been given more time I would have probably tested the distance a cylinder rolled after it left the ramp, although these results are circumstantial once one has worked out the speed and PE of a cylinder. I did not include these results into my analysis as I felt investigating time made for a more interesting investigation where it would be easier to plot graphs that aided my showing of results. Also, I may have measured the diameter of the cylinders, although this might not have proven anything. This concludes my investigation. How to Cite this Page
MLA Citation:
"How the Angle of a Ramp Affects the Speed of a Cylinder Moving Down It." 123HelpMe.com. 24 Apr 2014 <http://www.123HelpMe.com/view.asp?id=148985>. 
