# To investigate whether the amount of paper cup cake holders affects the time taken to fall a certain distance

When I do this experiment to find the terminal velocity I will drop 1 cake cup from a certain height ( which will be kept constant throughout the experiment.) When the cake cup is dropped a stop watch will start, then will be stopped when the cake cup hits the ground. I will then repeat this experiment using 2 cake cups, then three and so on. Altogether I will take 10 different weight readings, each weight reading done 3 times, so I can have a wide range of accurate results a total of 30 giving me a spread to plot on a graph.

When doing the experiment, to make sure it is fair I will do the following things: Make sure the cake cup is dropped from the same height each time, if it wasn’t then the results would be inaccurate.I will make sure the same person times the cake cup falling, this is because different people have different reactions. We will keep the same sized cake cups, as a different surface areas would lead to wrong results ( I will presume that the cake cups I use will weigh the same). When doing the experiment I will make sure there is nothing that could affect my results E.G wind or obstacles in the way, this would effect the falling time of the cake cup, therefore giving inaccurate results. The variable I will be changing will be the amount of cup cake holders, however there are many more variables I could change in order to make a comparison with other sets of results.

During the experiment it is essential to ensure the cup cakes reach ‘terminal velocity’ in order to find this I took some preliminary results in the form of a pre-test.Pre-TestThis was completed before the main experiment by taking 10 cup cake holders ( the maximum amount of cups I will use in the experiment), and timing how long they took to reach the ground from different heights. (In these preliminary results I changed the height so I could get several readings and plot them onto a distance time graph. From this graph I could then see when the cake cups had reached their terminal velocity.Height1.0 metre2.03.

04.05.02.563.

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183.183.293.30It was clear from the results of the pre-test that the cup cakes had reached terminal velocity between 4 metres and 5 metres because the speed from this height would not increase anymore so we decided for the main experiment to use a constant height of 4.

6 metres.Prediction:I predict that the terminal velocity will increase as I increase the weight of paper cups therefore the times will decrease when more paper cups are dropped and terminal velocity is reached.Justification for prediction:I think that the weight affects terminal velocity because I know that heavier objects fall faster than lighter ones. (E.G a brick falls faster than a feather). Bigger objects push air molecules out of the way faster than small objects when they fall to the ground.

As air resistance affects the terminal velocity, terminal velocity occurs when gravity and air resistance are balanced causing the increase in acceleration to stop. At the instant of release there is no friction because the object is not moving. The weight of the object makes it accelerate downwards, because gravity is acting on it, the heavier the object the faster it will accelerate, because gravity is a constant force, it always stays the same; the velocity and the air resistance have to increase to balance it. So unless the weight of the paper case changes there is always the same force of gravity acting on it.

So I expect that there will be a straight line of best fit on the graph. This is the reasoning behind my prediction.Equipment:I will use the following equipment throughout the experiment -* Metre Rulers (x5) (maximum height 4.6)* Paper Cups (x10)* Stop ClockDiagrams:Fair test:To ensure my results are accurate and fair I will:* Drop all of the cup cakes from the same height of 4.6 metres at the same angle.* Dropping each one 3 times and then finding the average.* Use the same size and type of cake case each time.* Make sure the same conditions are kept constant throughout.

Variables:If I needed to complete the experiment again and compare my results with another then I could change one variable. These however must be changed one at a time or the tests wouldn’t be fair and the results would be inaccurate because the results would be vague due to the uncertainty of how they differ from before due to having more than one variable.The range of variables for this experiment are :Number of cup cake holders- I chose this one because it is probably the most simple and easy to set up yet has the best outcomes and most accurate results as patterns and graphs can be made with ease.Conditions- This change would mean testing just one cup cake holder in various conditions and making valid observations and reasoning to why and which conditions affect the rate of terminal velocity.The way it which it is dropped- If this variable was used then the cup cake holder could be dropped sideways therefore decreasing the surface area meaning the air resistance will be less and as a consequence the terminal velocity changingResults:Table 1-Results 30 drops 10 different weights.Figure 1Amount/Attempt1st2nd3rd13.313.

023.2422.392.052.3831.951.951.

9941.661.71.

7351.591.491.

5361.381.431.4971.381.431.3881.341.

381.3391.271.511.21101.201.261.17The results above show all 3 attempts in order to gain an accurate average to be able to plot a graph to simplify the results collectively.

The graph shows a steady decrease in the time take for the cups to drop as more weight is added. If we were to increase the amount further then the graph would continue to form a steady slight curve until it made an end with a drop closer to 0.5 m/s. (marked with a star) There were however some anomalous results during the experiment and these have been highlighted in the results table(figure 1.)with an underline. Also another observation was that there were also some results that stood out according to there row, this means that they do not follow a pattern and seem out of place where they stand.

These can be seen marked with a star. These results can be put down to either human error or a slight change in a variable such as the conditions, to correct this another retest should have been done to clarify any anomalous results.Average:Amount of cup cakesAverage (2.dp)Average (1.dp)13.193.

222.272.331.962.041.701.751.

541.561.431.471.401.481.351.491.

331.3101.211.

2The table rounds up all the data from the previous graph and gives an average to allow me to plot it onto a graph with a reading closest to either1dp or 2dp.The equation:Speed = Distance ? TimeI used this to find the speed within my terminal velocity experiment, if you substitute the worded equation with the data all of the speeds can be found in m/s. I have used the average reading closest to 2.dp/Table:Amount of cup cakesSpeed m/s11.4422.0332.3542.

7152.9963.2273.2983.4193.46103.80Analysis:The results gained from the experiment show that my prediction was correct, as the amount of paper cups increase the terminal velocity is faster, the shorter time it takes for it to hit the ground. So then the more paper cake cases that were dropped the faster its terminal velocity.

At the instant of release there is no friction because the object is not moving. The weight of the object makes it accelerate downwards, because gravity is acting on it, the heavier the object the faster it will accelerate.The results show that the terminal velocity increases steadily each time. 3.15m/s is the average increase in the terminal velocity each time another paper cake case is added. This shows that adding extra weight increases the terminal velocity. This is because terminal velocity is when the air resistance becomes equal to the gravitational force acting on the object and so the acceleration stops.

The heavier the object the shorter time it takes for it to reach its terminal velocity.Evaluation:I think the experiment worked quite well, a lot of reliable results were obtained which could be analysed easily and this meant we were able to complete the aim. Most of the results are quite reliable; we did 3 experiments at each weight (3 drops with a total of 10 cup cakes) and took an average, which meant they were quite reliable. But because of human error they may not have been as reliable as they could have been, these human errors are responsible for the anomalous results on the graph. We could have improved the experiment by using electronic sensors, to drop the paper cases, this would have eliminated human error.The main error I think was delayed reaction times. When the cup/s were dropped, it would have taken the timer some time to start the stopwatch after it had passed the beginning of the timing point. Also if different people were timing they would obviously have different reaction times therefore affecting the results.

If I did this experiment again I would have the same person each timing, also I have the person timing standing at a point where they could clearly see when the cake cup passed. Also the stopwatch could only be measured to an accuracy of a 10th of a second.Another problem that occurred was that when the cake cup fall though the air there was some movement. The cup tended to sway from side to side which meant there would not be a constant area,(meaning the surface are constantly changing) which would obviously effect our results as there would be extra movement from side to side. If I were to do the experiment again, it would be hard to eliminate this error. The only way this could be slightly improved would be to ensure the best conditions possible to do the experiment in (a wind and draft free place.

)After I had plotted my graph I found that there were one or two anomalous results, and this could have been because of any of the errors above. I re-tested this result and my new result fitted in better than the original result. I can conclude that the terminal velocity does depend on the weight, and this can be clearly seen when looking at my graph which follows a steady decline in the time take for the cups to drop. If I had decided to use the way it was dropped as variable then my results would have differed slightly, this is because the surface area would change if for example they were dropped at an angle then the times maybe would have had a slower decrease. The graph would have looked more or less the same but the time taken for the cups to fall would be longer.

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