Method:
I am going to put a stool on a desk and attach an elastic band to two legs of the stool. This will act as a catapult. I will then push a 100g margarine tub back into the elastic band a certain distance and let it go. I will then measure how far it travels using a ruler (1m) and a set square. I will repeat this, moving the margarine tub back into the elastic band different distances and measure how far it goes each time. I will attach the weights to the back of the tub as I do not want the tub to use rotational kinetic energy as it would affect my results. To minimise rotation, I must apply the force closest to the centre of mass (the weight).
Prediction:
I predict that how much you pull back the elastic band is directly proportional to how far the margarine tub will go. I think that the more you pull back the elastic band, the further the tub will go. If you pull back the elastic band so that it is exerting a force of 5N, the margarine tub will go Xcm. If you pull back the elastic band so that it is exerting a force of 10N, I believe the margarine tub will go 2Xcm.
So: Force applied by elastic band ∝ Distance travelled by margarine tub
This is the graph I expect to see:
I will now further my investigation and use an equation to predict my results. This is based on the conservation of energy. The energy stored in the elastic band is equal to the energy used to move the margarine tub.
I have done a preliminary test and I have found out how far you have to pull back the elastic band for it to exert a force of 2, 3, 4, 5 and 6N.
2N = 7cm
3N = 11cm
4N = 15cm
5N = 18cm
6N = 21.3cm
The equation I will use is: work (J) = force (N) x distance (m)
Work = energy used by tub
Force = the force of the elastic band or the weight of the tub
Distance = the distance elastic band is pulled back or the distance the tub travels
For example:
Elastic band: Work = force x distance
Work = 2N x 7cm
Work = 2N x 0.07m
Work = 0.14J
Margarine tub: 0.14J = 1N (100g) x d (distance)
d = 0.14J / 1N (100g)
d = 0.14m
d = 14cm
Here is my table of predictions:
Here is a graph of my table of predictions:
This graph contradicts the one I drew earlier as this one obviously curves. If my prediction of Force ∝ Distance is correct, this graph should be a straight line. However, looking at my prediction table I have noticed that the distance travelled by the margarine tub is proportional to the product of the force applied to the elastic band and the distance elastic band is pulled back. I know that the product of the force applied to the elastic band and the distance the elastic band is pulled back is the amount of energy stored in the elastic band.
So my new prediction is:
Energy stored in the elastic band ∝ Distance travelled by the tub
Results:
I have not included the results in red in my averages as they appear to be anomalous.
From my averages I have drawn up a graph on the following page.
Analysis:
My results reflect my prediction extremely well as my results graph is just like my predicted graph. In my results graph, I have excluded the two anomalous results (which I believe to be measurement errors) as they would affect my graph and give me a biased graph. The first result on my graph is also anomalous; I think this is due to human error. Making an error in the small measurements would be more common than in the large. For example: making a mistake when measuring 2N, would be more common than making a mistake when measuring 6N with the equipment I am using. This is because when you read the Newton meter you the needle might be 3mm off of the number you are trying to get. If this were to happen while measuring 6N this might only be 5% off what it should be, but if this were to happen while measuring 2N this might be 15% off what it should be.
I have discovered from my graph that my prediction of:
Energy stored in the elastic band ∝ Distance travelled by the tub
was correct.
However, this equation does not involve friction, but this must be present to slow and stop the tub. So the equation must be:
Energy stored in the elastic band ∝ (Distance travelled by the tub + some frictional term)
It is out of the scope of this investigation to find out what the frictional term is.
The second half of my prediction is correct and I successfully managed to explain what would happen using my knowledge of forces and some formulas.
Evaluation:
I think my experiment went extremely well as everything went to plan and I believe that my results were fairly reliable and quite accurate. I managed to notice that I had two anomalous results
The method worked well because the experiment was completed quickly and smoothly. It produced reliable and accurate results all round apart from two which I believe to be down to be human error.
I have circled the anomalous results on my graphs. As all my other results seem to be so close to my line I can only put this down to human error.
Here are some ways in which I could have improved the experiment:
- Instead of using a mechanical Newton meter I could have used a more reliable electronic one.
- Instead of using a meter ruler by the side of the stool, I could have had the measurements drawn or printed on the tabled or on a long sheet of paper laid underneath the stool and where the tub is going to go. This would have improved my measurements as I would not have lost accuracy using the ruler and the set square.
If I was to do this experiment again I would take more measurements to put further backing behind my prediction. I would take measurements from 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5 and 6N. I would also involve the two improvements stated above.