Prediction – I think that the compression of the spring will follow Hooke’s law for extension and compression. This states that the force is directly proportional to the extension/compression induced up until it reaches its elastic limit. When plotted on a graph, the results will produce a straight line. I believe that compression will follow this law as the spring will not reach its elastic limit. When a quantity is directly proportional to another, it could also be seen as equalling the other quantity multiplied by a constant. For the force-extension graph,
F α E .˙. F α C
F=kE .˙. F=kC
Analysing
Results table
C1,2,3 represent the 3 original readings that were taken. As you can see, it was found that one set of results (C2) appeared erratic. A significant reduction in compression took place here, and it was believed that this was the set of results that were wrong. A graph was plotted with the averages including this set was plotted, it avoided the origin. It was assumed it was because of this set of results so another line was plotted on the same graph to see what effect C2 had on the graph. This line was plotted from the averages of C1 and C3 only. The line moved further away from the origin. This meant that these results couldn’t possibly be right, and meant that C2 was in fact correct. The cause of the two anomalies was investigated. The first thing that was looked at was the plunger, and the problem stared us in the face. If the plunger wasn’t on the tip of the spring, it would give us an extra few millimetres on the first reading. This tied in with the extreme difference we were getting on the first reading (double the other compressions). This also explained why the graph did not pass through the origin. The point at which it cut the y-axis was the compression when the force applied was 0N. On the original readings, the line of best fit cut the y-axis at 2.7mm. This meant that an extra 2.7 mm were being gained on the first reading when the plunger was not on top of the spring. Two more sets of results, C4 and C5, were taken as repeat readings making sure that the plunger was on top of the spring.
These results were more consistent with C2 and are shown in the table opposite. A graph using the average of these results was plotted and the line of best fit passed through the origin. The gradient of this best fit line was found by dividing the increase in y values, by the increase in x values. The gradient of the graph is equal to the constant of the spring. So, 12.5/0.024 = 527 N/m (3.s.f)
Evaluating
The most significant measurement was the first one. As you saw, if that measurement was wrong, the rest of the measurements would be out. This would push the best fit line away from the origin. Possible sources of error in this experiment could only have come from the marking and subsequent measuring of the spring compression. The error that occurred in the measuring of the compression for C1 and C3 was a systematic error as the plunger was incorrectly calibrated. Errors in the measuring of the compression with the ruler were random, as the last figure had to be estimated to the nearest 0.5 mm. To calculate the potential error, I will redraw the graph and draw 2 lines of ‘worst fit’. These will be either side of the best-fit line and the difference in gradients will illustrate the error in the spring constant. The difference in the gradients is 25. This means that the spring constant in the trolley is 527 N/m ± 25 N/m (3.s.f). With the low margin of error, my results are thought to be quite reliable and accurate. If the equipment and time were available, it would have been a good idea to take measurements with the trolley not only pointing up, but down, left and right as well. The average of the average of the repeat readings would minimise any effect of gravity on the spring. This may give a different, and more accurate, representation of the spring constant.
Energy stored in a spring
Major investigation
Investigation the conservation of energy
Planning
Aim – to see what percentage of potential energy in the spring is converted to kinetic energy in the trolley.
Apparatus
Wooden board
Rubber wedges
Light gates
Trolley 1
Trolley 2
G-clamp
Foam block
Wooden blocks
10 cm interrupt card
Sticky tape
Timer
Diagram
Plan – I am going to investigate the amount of energy converted from potential energy stored in the spring when compressed, to kinetic energy in the trolley when released. To do this, the apparatus will be set up as shown above. The board must be angled to limit and reduce the effect of friction on the trolley. This would indicate a higher energy loss than is actually true. The variable that will be changed is the compression of the spring. This will give different values for energy transfer and will lend itself to a more accurate value for the percentage of energy transferred. The variable to be kept constant is the mass of the trolley. With the variance in the compression, it would be too much work to vary the mass of the trolley.
There are many safety aspects in this test. Care is needed when compressing the spring as a lot of energy is stored, and if it is let go can break a finger, the trolley needs to be stopped before it reaches the end of the board as it can fall on and injure feet. To combat this, the board is placed against a wall and a foam block is placed at the end to prevent damage to the wall. Care is needed when looking at the light gate as it emits a strong light that can cause arc eye.
Four readings for each compression 0.5cm – 6cm will be taken and an average taken. To measure the compression, each compression will be marked on a label, and the label placed onto the plunger. This will take out any error of perspective in the viewing of the scale. After each set of readings, the compression will be increased by 0.5cm and four readings taken. This process will be repeated until the four readings for the 6cm compression have been taken.
The timer can measure velocity to 0.001 ms-1, the scale on the plunger will measure to 0.5cm and the width of the interrupt card is correct to ±0.5mm.
Prediction - I think that energy will be lost and the energy stored in the spring will, mostly, be transferred to the trolley as kinetic energy. Some energy will be lost as heat and sound for the transfer to obey the law of conservation. The formulas for the calculations of potential and kinetic energies are:
Potential Energy = ½ x spring constant x compression2
Kinetic Energy = ½ x mass of trolley x velocity2
Analysing
Results table – See additional paper.
From the results table, it is easy to see that most of the energy stored in the spring is transferred to kinetic energy in the trolley. There is, however, a deficit as predicted. The average percentage of energy lost during the transfer is 32%. This means for every Joule of energy transferred, 0.32 Joules will be lost. This energy is transferred into small amounts of heat energy, but most of the lost energy ill be transferred into sound energy. Most of the energy stored however, as predicted, was converted to kinetic energy in the trolley.
Evaluation
Possible sources of error in the measurements are in the time values from either a mis-calibration or a wrong cutting size of the interrupt card, and errors in the compressing of the spring. Each time the spring was compressed, it was nearly impossible to compress it to exactly the same length as the time before. This would lead to discrepancies in the results. The smaller the discrepancies, the more accurate the compression was. Also, the release of the trolley was important. It could be a significant source of error because the longer the trolley was held for, the more it would be slowed down and the less accurate the results are. This means the results obtained are most probably less than the actual readings. The higher percentage energy loss for the 1 cm compression could be due to this reason along with the lesser percentage losses of the 2.5 cm and 4.5 cm compressions. The expected results were achieved with one exception. The 1 cm compression lost, on average, half of the energy stored in the spring was wasted. This could have been due to the aforementioned reasons, or it could be due to the friction of the label against the plunger housing.
The most significant measurements are that of the compression. This is because in the calculation of the potential energy, these values are squared, and if the wrong units are use, (e.g. mm and not m) the difference in calculated values and actual values will be much greater.
The techniques applied were, I felt, the most suitable ones. The label on the plunger, although may cause a little friction, was a better way of measuring the compression as it took out the viewing perspective of looking at the label from different angles each time. With the label on the plunger, you could only look at it from one angle behind the trolley. The tilting of the board was appropriate as it effectively eliminated the effect of friction on the trolley. This would have resulted in a much higher loss of energy than was actually possible. The way in which the trolley was released was the best which I could think of. By using hands to pull it back, and then letting go and releasing the grip on the trolley as fast as possible, I was able to control it myself and take every measurement using the same method of release.
The reliability of my data may be called into question by third parties because of my method of measuring the compression with the label on the plunger. I believe these doubts to be false. I believe that my results are the most accurate that I could achieve with the equipment and time available. To improve the accuracy of my results, if the time and equipment were available, I would like to take many more readings, the wooden board replaced with ice and the wheels replaced with blade tracks. This will reduce the friction to almost zero, and this will give a lot more accurate reading that by even tilting the board.
