An increase in the weight of an object or the height to which it is raised will result in an increase in the potential energy the object possesses. In our experiment this means that there will be greater potential energy if the elastic band is pulled back further. The elastic potential energy is energy stored when something is stretched or compressed. This is present in the pulled rubber band.
Newton’s second law of motion states that:
II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
From this we know that the external force exerted by the elastic band will be directly proportional to the acceleration of the object, in this case the margarine tub. From this it seems reasonable with the fact that the acceleration, being directly proportional to the force, is inversely proportional to the mass. I can show this mathematically by assigning each variable a random number. If, for example we had to find out the acceleration of an object of mass 2 g.
Which was by an external force of 10 Newton's, by using the equation above we would figure out the answer is 5.
a= 10/2
a= 5
If we used an object with a bigger mass e.g. 5, keeping constant the external force exerted we would notice the acceleration has diminished to 2.
a2= 10/5
a2= 2
This proves that acceleration is inversely proportional to mass. Now I will also prove that the acceleration is directly proportional to the external force exerted. I'll change the external force exerted to 20 N, keeping the mass constant.
a= 10/2 a2= 20/2
a= 5 a2= 10
This proves that with the increase of the external force, keeping the mass constant, the acceleration increases as well. Therefore if the acceleration increases the space covered will be bigger. Therefore if, keeping the external force constant, and increasing the mass, the margarine tub will travel less.
From this research I have produced a predicted graph as shown below of stopping distance v mass.
Equipment
- Electronic balance (accuracy of 0.01 grams)
- Margarine Tub
- Meter ruler
- Sand (& a spoon to measure it out).
- Chalk
- Elastic Bands
- Stool
- Newton Meter
- Marker pen – to indicate where the elastic band and margarine tub should be placed/ pulled back to each time.
Diagram
Method
- Set up the equipment as shown in the diagram above.
- Measure out and mark with chalk, accurately the distance for the elastic band to be pulled back from the stool to give the correct amount of force using the Newton meter. Decide on a suitable launch point, which will have no obstructions or varying surfaces.
- Measure the correct amount of sand to be used and attach lid securely. I will use the range of 30-300g of sand with 10 intervals starting at 30g and increasing by another 30g each time. I will also be then repeating the experiment twice giving a total of 3 trials. It is difficult to get the measurement of mass of sand exact each time and so I will allow it to be within 0.5g difference lower or higher.
- Weigh down the stool to ensure that it does not move backwards with the force of the elastic band.
- Stretch back the elastic band from the stool legs and place the margarine tub central and on the marked line.
- Let go of the band and let the tub slide to a halt before measuring the distance travelled and recording the results.
I will measure the distance from the start point to the nearest point of the tub and use the Newton meter to find the correct amount of force.
Safety
To ensure that the experiment is carried out safely I will do the following:
- Be careful not to stretch the elastic band too far back and that it is secure as it can hit and hurt people with force if it flicks off the stool.
- Ensure that the lid is fixed down securely as sand can be a safety hazard if it gets into eyes or people can slip up.
- As we will be doing the experiment in the corridor we must be aware of the space and watch out for people walking past.
Fair Test
To obtain accurate and reliable results the experiment must be a fair test. When launching the margarine tub I will place it next to the elastic band and pull it back to the same place each time to keep this factor constant. As well as this, all other variables must be kept constant including:
- The Surface used – if this changes or has bumps/dips it could adjust the amount of friction, energy transfer etc.
- Use the same elastic bands to ensure the same elasticity and force.
- Leave the stool at a fixed point and use the same area to work in throughout the experiment as well as making sure that it travels in a straight line.
- Repeat the experiment 3 times for each mass and use the same tub and exact weight (repeat immediately one after the other to ensure mass is exactly the same).
- Always use all of the same equipment and measure from the same point and to the same part of the margarine tub. Also fix the measuring tape down as it can move easily, affecting results.
- The force and change in weight each time (30g to 300g with 30g progressions) must be constant to produce good results of a suitable range.
- I must also use the same stool because the distance between the two front legs may differ from stool to stool, affecting my results
Preliminary/Pilot Experiment
I have done a preliminary experiment to test my method and find a suitable range of masses and force to use and to decide on values of variables to keep the same. The results showed that it would be suitable to use 20N (Newton) of force each time and use mass values from 30 grams to 300 grams so that results provide both a good range and enough to draw an accurate graph as well as leaving enough time to repeat the experiment for accuracy. I will not use 0 grams of sand, as found in previous trials that this will enable the margarine tub to flick up, which will affect the results and so will be ruled out. To begin with I tested both 10 and 20 Newton force and used masses ranging from 30 grams to 210 grams with regular divisions of 60 grams. The 10N results showed that it would be a good idea to increase the force as the masses did not travel very far. It showed that with we could quite easily use higher masses (up to 300 grams) and smaller divisions to get a better range of results as the distance travelled measurements are quite far apart/differential. The results are measured to 1cm with the distance travelled as this is the highest accuracy available on a metre ruler and mass of sand to 2 decimal places as this is the most accurate on the electronic balance although the measurements are not exact each time (maximum of 0.5 grams out) as it is difficult to find the exact amount of sand. We also found that it is easier to use two elastic bands rather than the one, as it does not need to be stretched as far and is more stable. Each time the margarine tub is launched we found that the elastic band is pulled back to 13 centimetres for a 10N force and 23cm for 20N I have decided to mark these measurements on the floor with chalk so that it is equal each time. I will also be doing this experiment in the corridor rather than the classroom as there is more working space which could help to improve the method.
Preliminary results:
Unfortunately an anomalous result has already occurred as highlighted in red on the second table of results (20 Newton experiment). This shows that the method may need improving and we will take more care when measuring. To do this I will use a tape measure rather than meter ruler.
From these graphs I can see that the 10 Newton graph gives the predicted curve but as I will be doing 10 different weights the 20 Newton graph shows me that this is a more suitable force as weights that are between and above those tested in the preliminary work are needed to complete the graph. The last result on the second (20N) graph is obviously an anomalous result as it does not fit into the predicted pattern, which is shown in the first (10N) graph.
Final Experiment Results:
Conclusion
Enough results were obtained from the method to produce a good graph. The results show that like predicted in my hypothesis that as the mass of sand increases the distance travelled (stopping distance) decreases when using the same projecting force. This is shown by the negative correlation on the graph. This is because as the mass is increased more friction occurs. The more friction there is, the less time and less distance it takes for the kinetic energy to transfer into heat energy. I have used averages of the results so that I can see the overall trends more clearly. As you can see the curve shows the trend-line where y is inversely proportional to x (exponential). This is because as the mass increases so does the amount of friction produced which means that it takes less time and distance for the kinetic energy to transfer into heat energy.
The last anomalous result highlighted in red in the table (210g) may have affected the graph and so I will take this into account as well as the other two anomalous results which seem to have affected the results as the three average results which are slightly out from the trend-line on the graph are the ones which could have been affected by these.
In the first stage of the experiment the distance travelled did not half when the mass was doubled e.g. 30g compared to 60g. However when looking at later experiments the 120g - 240g average distance travelled decreased from 218.3 to 120.6 and 150g - 300g decreased from 181.6 to 87.3. Both were very close to the prediction.
Evaluation
There are only 3 results, which are not exactly fitting to the trend-line. Although these seem to be anomalous they are still very close to what was expected. These results could be explained in that although I was very as careful and precise as possible with keeping variables constant and the measuring, the margarine tub does not always travel in a straight line and the elastic band does not pull back to a central position each time. Another factor that could have caused a problem with the results is the elastic band for two reasons. As I used two elastic bands in the same position on the stool it is possible that one has more elasticity than the other, which means that the force may vary slightly. Also the elastic band can become denatured during the course of the experiments as it is being constantly exposed to strong forces. To resolve this I would use only one stronger elastic band, which I would replace after each different mass experiment.
I feel that overall my experiment was accurate and produced good results as each repeat did not vary much from the others. If I repeated the experiment again I think I would again get similar reliable results and if I took into account the above mentioned improvements it is likely that the experiment would be even more accurate and so there would be an even smaller range and less variety in each experiment and so more accurate averages could be found. To improve my current results I have missed out anomalous results when plotting the graph to improve accuracy, if I had the time I would have repeated these to increase the accuracy of the averages.
My aim was to investigate how far a margarine tub can travel when a force is applied. Within this I could also investigate the other option of changing force rather than mass. However, within the experiment changing mass I could also do the same experiment but experiment with a wider range of masses to get a better overview of what would happen and also use more regular intervals to increase the accuracy.