Background theory
To explain what happens, we must use scientific evidence to prove this. First we must know about Newton’s third law:
Resultant force = Mass x Acceleration (f = m.a)
In this experiment, mass is kept constant so it cannot affect the resultant force. This means the only variable to change the resultant force is acceleration. Therefore for the resultant force to increase, the acceleration of the cup cakes must increase. When the cup cake starts to fall at the very start, its resistance is 0.00N. The smaller cup cake will have a higher acceleration because due to its smaller surface area, it will have less friction in the air and higher resultant force. The air particles in the air collide with the cup cake as it falls down and if fewer particles are colliding with the cup cake, then it will have a higher acceleration, faster velocity and higher resultant force. As the air resistance increases, it will eventually equal the resultant force of the cup cake and will fall at a constant velocity. This is because air resistance increases with increase of velocity. This is known as terminal velocity. The small cup cake with a smaller surface area will fall at a faster terminal velocity because its air resistance (friction) is less great and therefore its acceleration is faster and so resultant force will be greater.
Terminal velocity is achieved by Newton’s 1st law: Balanced forces do not affect the movement of an object: it remains stationary. But in this case Newton also says if the object is already moving it continues to move at the same speed and in the same direction.
Apparatus
- Two 100.00cm rulers
- 2.00g of plasticene
- A large cup cake
- A small cup cake
- A stop watch
- A Balance (to measure mass of cup cakes for fair test to 2 d.p.)
- Sellotape
- Right angled set square
Method
- Get all apparatus as listed above
-
Using a right angled triangle to make sure the ruler is 900 to the ground, place one 100cm ruler up against the wall and attach it to the wall firmly using sellotape.
- Using the right angled triangle again, firmly attach the other 100cm ruler on top of the other 100cm to the wall using sellotape. The right angled triangle is used to keep the rulers at right angles to the ground so no anomalous results appear due to the rulers not being straight.
- Place the large cup cake on the balance. It will be lighter then 0.33g. To make it to 0.33g which I am going to use for both cup cakes, add a little bit of plasticene at a time until it reaches 0.33g
- Do the same as above but with the smaller cup cake to make it a fair test with both cup cakes being the same mass at 0.33g.
- Remember to find the mass of the cup cakes each time before it is dropped to make sure it is a fair test.
- Starting from 50.00cm, drop each cup cake 3 times so an average time can be recorded. Use the stopwatch to time how long it takes the cup cake to reach the ground. When dropping the cup cake, make sure it is dropped at exactly 50.0cm each turn by using the right angled set square level to the height. Measure from the bottom of the cup cake. Start the timer when it starts dropping immediately and stop the timer as soon as the bottom of the cup cake reaches the bottom. Each cup cake must be dropped in the same way, with its bottom facing the floor. Make sure the cup cakes are dropped straight and that no winds are affecting the results or any obstacles i.e. the wall and windows open. Record all observations.
- Repeat the above up to 240.00cm going up 10.00cm each time and recording all observations. Put all results into a results table.
- Make sure it is a fair test.
Results
Mass used = 0.33g for both cup cakes
Heights = 50.00cm going up 10.00cm to 240.00cm
3 results were taken at each height for each cup cake to make an average result.
It appears that no anomalous results appeared in my table
Analysis
From looking at the graph, it shows that the higher the cup cake is dropped at, the longer the time it takes for it to reach the floor. It seems that from my figures and graph, if height doubles then time does not halve. There is no connection of doubling/halving at all. The large cup cake has taken longer to fall to the ground than the smaller cup as I predicted at given heights. This is because the larger surface area causes more friction with the air particles in the air giving it a larger air resistance. This means that the acceleration would be slower than the smaller cup cake as shown by the less steep curve at the start of the graph. Also the larger air resistance meant that its terminal velocity would be less great and therefore it will reach the ground through a longer period of time. The resultant force of the cup cake is due to this formula:
Resultant force = Mass x Acceleration
As the mass is equal for both cup cakes, the only variable will be acceleration. Because of the larger air resistance, its acceleration is not as high and therefore its resultant force will not be high, hence the slower terminal velocity and then its longer period of time to reach the floor.
The terminal velocity is shown by the roughly drawn straight line as shown on graph for both cup cakes. My prediction is correct about this terminal velocity being reached because Newton says: if the object is already moving it continues to move at the same speed and in the same direction. This is made by the air resistance equalling the resultant force of the cup cake. The gradient of the two cup cakes are different. The large cup cake shows its terminal velocity was not as great as the smaller cup cake with its less steep gradient. My prediction proves correct that the larger cup cake was going to fall at a smaller terminal velocity due to its smaller acceleration and there smaller resultant force using the formula F = m.a.
The graph also shows at the start the acceleration of the cup cakes were being made by the little curves drawn on the graph. The gradient of the smaller cup cake is steeper which indicates that it had a higher acceleration than that of the larger cup cake, scientifically proven above by its smaller surface area.
Evaluation
It seems from my results and the graphs well fitted line that the experiment went very well. The method used does seem to be quite accurate but may be altered to improve the experiment so further investigation can occur. The accuracy of my results do seem pretty good as shown by the good fit of the line on the graph and no anomalous results appearing in graph or table. I do not think more accurate results will alter much of my results but if I wanted to make this experiment even better, I can use apparatus that will measure my results more accurately as I will further explain later.
My method does seem to perform the experiment with many precautions as I always checked the constant qualities all the time. Each set of reading was done in the same way, with a right angled triangle to make sure that the bottom of the cup cake was level with the height given, the mass was constantly checked, that the cup cake was dropped bottom first and that no interference of wind etc. affected the results.
One method that might have altered some results is the reaction time of stopping the timer when the cup cakes hit the floor and also the reaction time to start the clock when it first drops. This may alter some results dramatically but it seems it has not in this investigation but to make it more accurate; we could use sensors to know when it starts dropping and know when it reaches the ground. Starting and stopping the stopwatch with your reaction time of yourself can make the results very inaccurate.
Some repeated values were a little bit off than the others but were not that dramatic. This is probably due to the reaction time of starting and stopping the stopwatch as stated above and could be improved. The range of readings may have also been improved by making more readings at the start when the cup cake is first released. This could give more detail and information how much more the smaller cup cake accelerates than the larger cup cake. There is no point in making range of readings more than 240.0.cm because from using scientific evidence, we know that terminal velocity will carry on until it reaches a halt on the ground. To improve data, more readings may have been taken. Instead of taking readings every 10.00cm, we could have taken readings every 5.00cm to produce more data so we could reinforce our conclusion.
