The light gate will measure how long the piece of cardboard on top of the trolley cuts the beam of light for, allowing me to calculate the speed using the formula:
Speed = Distance
time
I will then work out the amount of kinetic energy that has been transferred from the spring to the trolley, using the formula:
Kinetic energy = ½ m v 2
I will carry out the experiment three times for each compression of the spring and then take an average. This will ensure that my results are as accurate and reliable as possible. This will also minimise the effects of any anomalies
I will record my results in a table, firstly only taking measurements of how long it takes the card to pass through the light gate and the length of compression. This will make it easier to calculate the speed and kinetic energy after obtaining what I need from the experiment.
Variables affecting the outcome
To ensure that my experiment is fair, there are certain variables that I plan to keep constant. These include:
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Mass of the trolley – I will control this by using the same trolley for each individual experiment. I will also makes sure that I use the same piece of cardboard on top of the trolley ensuring that the weight cannot be varied in any way.
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Surface – Different surfaces could cause different resistances (friction), this would affect the speed at which the trolley travelled, in turn, affecting the amount of kinetic energy transferred. To ensure that the speed does not vary because of the surface, I shall be using the same surface throughout the investigation. I will also try to keep the surface clean, as small pieces of grit or other contamination could well affect the course of the trolley.
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Temperature – This variable is very hard to control, as I will be conducting the experiment in the science lab, which will be at room temperature (this can increase and decrease at anytime). The fairest way that I can carry out the experiment is to run it all on the same day or aim to do it at the same time each day. This will minimise variation in temperature as much as possible.
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Distance of the card from breaking the light gate – This variable is very important as it will affect the outcome directly. I will be placing the card on top of the trolley so that it lines up to be less than 2cm away from breaking the laser on the light gate. This will ensure that the light gate measures the trolley’s speed when it is almost at it’s fastest and when the most energy has been released. The reasoning behind not placing the card closer to the light gate is that there is a chance that the card would break the laser before the spring has been compressed.
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Spring used – Different springs will have different constants, therefore the same spring must be used throughout an experiment. As we are not finding percentage changes, only averages, the spring must not only be kept the same throughout each individual experiment, but the whole investigation. The only problem that I foresee in doing this is that the spring might have a tendency to change shape, however this should not affect the investigation dramatically.
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Length of Card – It is important that this variable stays the same because if the card passes through the light gate for a longer time due to it’s length (when it is actually travelling at the same speed), the light gate will measure it as having a lower velocity. To reduce the risk of this happening I will use the same piece of card throughout the experiment.
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The angle at which the card passes through the light gate – If the card passes through the light gate at a very abnormal angle the reading will not be accurate. To eliminate this counteracting variable I will ensure that the card always passes through the light gate at a right angle, by taking great care to measure and line it up each time
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The surface that the spring is compressed against – The surface that the spring is compressed against must be substantial enough not to move and absorb any of the energy that the spring gives. Therefore a hard surface such as a wall shall be used throughout the experiment.
The variable that I am going to change is the compression of the spring. I will be compressing the spring at 1cm intervals, which will give me a range of at least six results, as the spring is over 7cm long. This range is substantial enough to allow me to put my results into a graph and identify whether or not there is a definite correlation.
Prediction
I predict that the shorter the spring is (the more it is compressed), the further and faster the trolley will travel. I believe this because the more compressed the spring is, the more elastic energy it will have, meaning that more energy overall can be transferred into kinetic energy which will make the trolley move. In theory, the compression of the spring will be directly proportional to the kinetic energy transferred. This would produce a linear progression in any graph drawn up from the results, where y = kx. However, I anticipate that the results generated will not enforce this prediction due to the counteracting variables stated above.
I therefore predict that as we increase the compression of the spring, the rate at which the transfer of energy increases will decrease. This is because the faster the trolley is moving, the larger the resistance of forces such as air resistance or friction.
Results
To work out the speed that the trolley was travelling at I shall be using the formula:
Speed = Distance
Time
Distance is equal to the length of the card = 5cm = 0.5m
To work out the kinetic energy I used the formula:
EK = ½ m v2
The mass being the mass of the trolley which was 459.58g
I will now draw several graphs that will represent this data and indicate whether there is a definite correlation
Analysis
My results show that the further the spring is compressed, the faster the speed of the trolley and larger the amount of kinetic energy transferred thus supporting my prediction.
The first graph showing the compression of the spring against the speed of the trolley shows a line of best fit that is almost in a straight line, showing that as the spring is compressed the speed increases. Notice however, that the gradient at the top of the line is shallower compared to that at the bottom. This shows that the rate at which the speed is increasing, is decreasing.
The second graph showing the compression of the spring against the kinetic energy that it produces shows a line of best fit that is curved, shows us that as the spring is compressed the amount of kinetic energy transferred to the trolley increases. This line should be straight and can be proved.
Elastic energy (that stored in the spring) = ½ k x2
Elastic energy = constant x
Elastic energy = Kinetic energy
½ k x2 = ½ m v2
Constant 1 = x k2 Constant 2 = x v2
x2 = Constant 2 x v2
Constant 1
x2 = Constant 3 x v2
Therefore, for both speed and kinetic energy a straight line graph should be produced, but as nothing is perfect and the complete amount of elastic energy will not be transferred to kinetic energy, some will be lost during the transfer, the graph does not show a linear progression. This entirely supports my prediction apart from one element. I stated in my prediction that the rate at which kinetic energy was transferred would decrease. It would seem that the second graph shows a shallower gradient at the bottom than at the top. This indicates that the rate at which kinetic energy is being transferred increases as the spring compressions get larger.
There are a few anomalous results in this investigation. The most obvious is that in the second graph produced showing how the compression of the spring affects the amount of kinetic energy transferred. You will notice that the compression of 5/6cm are the same. Both are of equal distance from the line of best fit suggesting that neither one of them is correct. If either of them was lying on or near the line of best fit, then it would easier to suggest possible causes for this anomaly.
The trolley is at its fastest speed exactly after the spring is released. This means that the trolley will have been affected by resisting forces such as friction, slowing it down, before reaching and passing through the light gate. Therefore we will have been measuring the trolleys speed when it is not at its fastest. If the amount of friction or air resistance was more on one experiment than others, this could possibly explain anomalies.
Evaluation
The procedure used to investigate how the compression of a spring affected how much kinetic energy was transferred was safe and fairly secure. The results obtained were not as accurate as they could have been, various anomalous results were found showing lack of accuracy and precision.
Results in this experiment are very hard to make accurate due to frictional forces which cannot be controlled. During this investigation anomalous results were found. The first which is a repeated result was most likely a transcription error (data was copied wrong) as it seems highly unlikely that the exact same result to two decimal places would occur.
Other problems could have derived from uneven flooring which would have absorbed energy due to the shock, causing less to be transferred to the trolley, miscalculations and drag on the trolley.
The results that I have acquired are not particularly reliable. This is down to the fact that they have not produced a straight line graph of any kind. The results show curves and almost straight lines. This could be due to many factors, but the two most likely are that of:
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Friction – not only between the wheels and the surface they are running on, but also on the bearings inside etc
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Air resistance – building up more as the velocity increase, a factor that is impossible to control.
Changes that could be made to the investigation that may improve the reliability and accuracy of my results include:
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Air table – the use of this would surely cancel out the large majority of friction, increasing the chances of it not affecting the experiment, increasing the chances of precise results.
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Repeat anomalous readings – by doing this we could maybe neutralise any anomalies, showing that our results are once again more reliable.
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Repeating the investigation with ticker tape – Even though ticker tape is not very accurate as there is a lot more calculations involved leading to far more transcription errors, it would be enough to support the results we currently have, and tell us how correct they are.
To further or back up the evidence we currently have there are other investigations that could be carried out. These include:
- Using a different spring with a different spring constant would allow us to see if the graphs produces gave the same as the current ones. The experiment would be carried out in the exact same way as this one was, changing nothing except the spring on the back of the trolley. We would have to do the same number of compressions, use the same card on top the trolley, use the same trolley, just change the spring.
- To further the experiment we could investigate how the weight of the trolley affected how much kinetic energy was transferred. This time however we would only compress the spring to one measurement, maybe 4cms. Then we would vary the mass of the trolley by adding weights to the top of it. I would have to have at least 6 different weights to produce enough results to show whether or not there is a correlation.
These further investigations may help to support my current results or explain anomalies.
