Method
Aim:
In the experiment I wish to discover the effect that height and weight have on terminal velocity.
Method:
The equipment will be set up as shown in the diagram. At first one cake case shall be dropped from varying heights, and the time it takes for the case to hit the ground shall be measured. To be sure that the time recorded is only for when the cake case is falling at terminal velocity, we will drop the cases from 20 cm above the height we are measuring, so by the time it passes that point it is travelling at a constant speed. The height from which we drop the cake case will then change, to determine if height affects terminal velocity.
To discover if weight holds an affect on terminal velocity, the number of cake case dropped will increase to four. And each time the experiment above will be repeated. To make sure that the results are safe and there are no abnormalities, each drop will be repeated three times, and an average time will be taken.
To make sure the experiment is fair; only one variable will be varied at a time. For instance if we are changing the weight and measuring that we must make sure we time it from the right height or we will be getting a bias set of results. We must also guarantee that the drag of each object stays the same, as increased drag, leads to decreased terminal velocity, and we don’t want to measure drag in this experiment.
Terminal velocity will then be calculated by using the equation,
Speed = Distance/Time. As all terminal velocity is, is a maximum speed. This will be measured in cm/s.
Apparatus:
Retort stand
Clamp
Boss
Stopwatch
2 x 100 cm rulers
5 cake cases (same size)
Goggles
Safety: As this experiment uses pointy metal objects, which due to the very nature of the project will be at our eye level, I have decided that it will be an appropriate precaution to wear goggles to prevent the risk of injury to our eyes.
Diagram:
Preliminary work:
In my preliminary work, the factors which affected the motion of a falling ball bearings of different weight in gelatine solution, and water. I discovered that the factors that affect the speed of a falling object are:
The drag of an object, (Its shape and size).
Its weight.
The resistance of the substance of which it is moving through.
This is also partly the reason why I believe that, I believe all factors must be controlled very carefully, and the drag, and the air resistance must not change, so no windows must be open. My results also gave me the trend that as mass increased so did the time in which it took to travel between two given points. I expect this to be the same in my SC1, as I believe all falling objects are affected by the same fundamental factors.
Prediction:
I predict that the weight of the cake cases will affect terminal velocity. I think that the more cases stacked on one another, the faster terminal velocity will be. This is for the following reasons.
If we say that terminal velocity is,
Force of gravity (weight) = Force of air resistance
Downwards Upwards
Then the heavier the falling object, the faster it will be going before, the air resistance equals its self out.
I think this will be in direct proportion, and show it self as a straight line on a graph. This is because if the weight of a falling object is doubled, then the force that stops it accelerating will have to double and so, the speed that it reaches terminal velocity at will double as well.
However I do not think that changing the height will affect the terminal velocity at all, unless we are timing the falling object before it has reached its terminal velocity, and is still accelerating. I don’t think height will change terminal velocity, because once an object has reached terminal velocity and the weight acting downwards, has equalled with the air resistance, this wont change, no matter what the height is. If we drop it from further up and time it for longer, the same results should be apparent as to when you drop it from lower down with the same weight and drag.
For example, if I time a cake case from 20 cm that takes 4 seconds to hit the ground, and then from 100cm which takes 20 seconds to hit the ground, by using the equation
Speed =Distance/Time the results will be the same, 5cm/s.
Obtaining Evidence
1 Cake Case 0.51g
2 Cake Cases 1.06g
3 Cake Cases 1.76g
4 Cake Cases 1.92g
5 Cake Cases 2.24g
Calculations To Explain the results Table
The average time of fall was calculated by adding together the times for each of the three falls, for that specific weight and height and dividing by three.
Time Of Fall 1 + Time Of Fall 2 + Time Of Fall 3
3
The Answer is given in seconds
On the results table the average time of fall was used to calculate the terminal velocity.
To Calculate the Average Terminal velocity for each weight, all terminal velocities for each weight were added together and divided by five.
For ease of understanding all calculations have been made to one decimal place.
In my graphs, terminal velocity will be calculated by working out the gradient and not via the table.
Conclusion
In this experiment I have learnt that as the weight of a falling object increases so does the terminal velocity, but the height of a falling object does not affect the terminal velocity at all.
Graph 1-5 each plot the drop height against the time of fall for each of the 5 different drop weights. The fact that a straight line can be drawn in each graph proves that height does not affect terminal velocity but is directly related to the time of fall and the speed. By working out the gradient of the graph this gives us the terminal velocity. We can see that this is extremely close to my calculated velocity in my table and so gives me a good idea that this method works.
Graph 4 plots the average terminal velocity against the number of cake cases. There is an exponential curve on my graph. This curve suggests that terminal velocity does increase with weight, at a big rate at first, and then the rate at which it increases becomes less.
I think that the height did not affect the terminal velocity for this reason. Once an object has reached terminal velocity and the weight acting downwards, has equalled with the air resistance, this wont change, no matter what the height is. If we drop it from further up and time it for longer, the same results should be apparent as to when you drop it from lower down with the same weight and drag.
For example, if I time a cake case from 20 cm that takes 4 seconds to hit the ground, and then from 100 CM which takes 20 seconds to hit the ground, by using the equation
Speed =Distance/Time the results will be the same, 5 CM/S.
However weight did affect terminal velocity, the more cake cases, the faster and the terminal velocity was. I think this is because
If we say that terminal velocity is,
Force of gravity (weight) = Force of air resistance
Downwards Upwards
Then the heavier the falling object, the faster it was going before, the air resistance equalled its self out.
However this was not directly proportional, as it was represented as a curve in the graph. I do not understand this as I think as the weight of a falling object is doubled, then the force the force that stops it accelerating (air resistance) will have to double also and so, the speed that it reaches terminal velocity at will double as well.
In general I think my conclusion supported my prediction. As I predicted the height did not affect terminal velocity but the weight does. Also I said as weight increased so would terminal velocity, which is what happened. However I predicted that this would be in direct proportion, which it turned out not to be. As previously stated I can not understand this, as I believe the factors which this depends on are more complicated than I have covered.
Evaluation
I thought that my method was considerably accurate for how basic it was. Only basic scientific equipment was used, and the experiment was very dependant on my self instead of scientific equipment such as a QED Light Gate ………… The results I gained show pretty much the pattern I had expected despite the curve in my graph. I was very pleased with the ease of the experiment and the results I obtained, as it was easy to establish both the effect of both height and weight on the cake cases. I think my results were pretty accurate, and were good enough to support a firm conclusion, as I did each drop three times, and all the results support each other how I expected them to. However I believe they could have been more accurate by using equipment such as a QED Light Gate ……….
Human error may account for the unexpected indirect proportion shown in my results, however seeing as all the graphs show the same thing I do not believe this to be the case. When the average terminal velocity was plotted against the number of cake cases, 3 cake cases did not seem to fit into the curve. I think this is merely down to human error and not due to any scientific reasoning, however the result is not far off what was expected and so it doesn’t bother me in a major way.
To improve this experiment I could have used more scientific equipment, such as a QED Light Gate, so human error would not play such a big a risk as it did using my experiment. By using a QED Light Gate at either end of a selected distance, and dropping the cases through the LED, this would have provided me with extremely accurate results.
If I were to extend my experiment I would use a greater range of cake cases to determine whether the curve continues in the terminal velocity or whether this was just a fluke result. I would also do a smaller change in weight between each case, by doing something like putting a ball of plastascene inside.
If I was to do an additional experiment I would change that drag of the object and the weight as I know that these both affect terminal velocity. I can predict that the drag will affect terminal velocity as the greater the drag the greater the air resistance and so the slower the terminal velocity will be. However I do not know if this is directly proportional, or how it acts with weight so it would be interesting to find out.
