When doing this experiment it is important to make sure that cake cup has reached it’s terminal velocity. In order to find this out I took some preliminary results.
I did this by taking 6 cake cups ( 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.
After I had plotted my distance time graph I could see when the six cake cups had reached their terminal velocity (marked with a dotted line on the graph .) It had reached it’s terminal velocity by 2.5 metres. So this means that we will drop the cake cups from a height of 4 metres and start the timing after 2.5 metres. By doing this we will know for sure that our cake cup/s have reached their terminal velocity.
Prediction : I predict that the terminal velocity will increase as I increase the weight of paper cups,(double the weight would mean double the terminal velocity.)
Justification for prediction :
I think that the weight affects terminal velocity because i know that heavier objects fall faster than lighter ones. (eg 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 effects the terminal velocity, terminal velocity occurs when gravity and air resistance are balanced. I think that if we double the weight then the terminal velocity will double because, weight will effect the terminal velocity.
Larger paper cups have more energy than smaller paper cups when they fall, so larger cups can push air molecules out of the way more easily.
When a cake cup falls there will be friction with the air molecule. If the cake cup slides though the air then the weight will be directly proportional to the velocity so therefore my prediction will be correct.
Preliminary Results
Analysis
From looking at my graph, I can see that there is a linear relationship. This graph does not pass through the co-ordinates (0,0) as I predicted it would.
I predicted that if you double the weight then the terminal velocity would double, but this prediction was wrong. When there was 1 cup the terminal velocity was 0.7m/s, but when I doubled the weight ( 2 cups ) the terminal velocity was 1m/s, so clearly this was not double.
My graph tells me there is a relationship between the weight and the terminal velocity. My graph was not directly proportional as it did not pass through the points (0,0).
As my graph is a straight line I can use the equation :
y = mx+c.
I can use this equation to modify my prediction.
I would the use this equation to try and find the terminal velocity of 8 cake cups.
y= mx+c. (m=gradient, c= y intercept)
y= 8 x 0.24 + 0.44
Terminal velocity = 2.3m/s
I then tested this by doing the experiment like before and the terminal velocity = 2m/s. Allowing for reaction times and other errors this shows me that my modified prediction is almost correct.
Evaluation
After doing this experiment I can say that it was successful, although not very accurate. There were several errors that may have effected the terminal velocity.
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 effecting the results. If I did this experiment again I would have the same person each time timing, also I have the person timing standing at a point where they could clearly see when the cake cup passed. Also the stopwatch’s, realistically could only be measured to an accuracy of a 10th of a second.
This part of the experiment was as accurate as it could be, if it was to be improved, specialised equipment would have to be used.
Another problem that occurred was that when the cake cup fall though the air there was some turbulence. The cup tended to sway from side to side which meant there would not be a constant area, which would obviously effect our results as there would be extra movement from side to side. If I was 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.)
Besides these errors the experiment was successful.
After I had plotted my graph I found that there was one anomalous result, and this could have been because of any of the errors above. I re-tested this result and my new result fitted in alot better than the original result. ( The anomalous result occurred with 4 cups, and the is circled on my graph.)
From my results table and graph I can say that the terminal velocity did increase as the amount of cake cups increased, but it did not double. 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 straight line.