11) Add a Newton weight on to the mass hanger.
12) Record the extension of the spring against the ruler.
13) Repeat this procedure until 6 Newtons have been placed on the mass hanger.
Series springs.
1.Set the apparatus as shown in the diagram.
2) Check that the pointer, pencil, is at 90o from the springs to the ruler.
3) Hang the mass hanger on to the springs
4) Record the extension of the springs against the ruler.
5) Add a Newton weight on to the mass hanger.
6) Record the extension of the springs against the ruler.
7) Repeat this procedure until 6 Newtons have been placed on the mass hanger.
8) Remove a Newton weight.
9) Record the extension of the springs against the ruler.
10) Repeat this procedure, removing all the Newton weights until only the mass hanger is left.
11) Add a Newton weight on to the mass hanger.
12) Record the extension of the springs against the ruler.
13) Repeat this procedure until 6 Newtons have been placed on the mass hanger.
Parallel Springs.
1.Set the apparatus as shown in the diagram.
2) Check that the pointer, pencil, is at 90o from the springs to the ruler.
3) Hang the mass hanger on to the springs. N.B. Make sure that the mass hanger is always balanced.
4) Record the extension of the springs against the ruler.
5) Add a Newton weight on to the mass hanger.
6) Record the extension of the springs against the ruler.
7) Repeat this procedure until 6 Newtons have been placed on the mass hanger.
8) Remove a Newton weight.
9) Record the extension of the springs against the ruler.
10) Repeat this procedure, removing all the Newton weights until only the mass hanger is left.
11) Add a Newton weight on to the mass hanger.
12) Record the extension of the springs against the ruler.
13) Repeat this procedure until 6 Newtons have been placed on the mass hanger.
Fairness.
Rulers should be vertical at all times, not diagonal or horizontal.
The springs should be vertical at all times.
The same springs should be used in each experiment.
The readings of the stretch of the spring should be read at eye level each time, at 90o
The pointer should be kept at 90o at all times.
For fairness and to improve accuracy repeats will be carried out.
Variables.
The load should increase steadily by 100 grams each time.
The extension should be measured in the same way each time, preferably centimetres.
The extension or stretch should be measured with a ruler each time.
Pilot Study.
I began by setting the apparatus up correctly. I proceeded to do the single spring first. I measured the length of the spring, to work out the extension when I added weight to it. Then I added 1 Newton to the spring and recorded the extension, and proceeded to do this until I reached 6 Newtons. Then I removed 1 Newton one-by-one and recorded the reduction. This made my results more accurate. The experiment had no obvious problems.
I then proceeded to do the experiment with the springs in series. I connected the springs together and started to add the weight, as before. I discovered that I needed to hang the springs off the table, as they would touch the tabletop with the full weight on them. So I have decided to hang the springs off the table when I do my actual experiment.
Lastly I did the experiment with the springs in parallel. I did the same as the single spring, but I used a pencil to balance the mass hanger between the two. This was very complicated as the mass hanger was difficult to balance. So I have decided to try and cut a groove for the mass hanger in my actual experiment.
I also attempted using heavy amounts of weights in each set of springs; this is a table of my results for a single spring.
After 20 Newtons had been added the load became too great for the spring to hold and the elastic limit of the spring was exceeded. Furthermore the clamp stand became unbalanced and the extension became too long to be measured by the meter ruler. After testing these amounts of Newtons I decided to try smaller amounts of Newtons and I gained these results.
After using these amounts of Newtons I concluded that these amounts would be far more suitable for this experiment that the larger amounts of Newtons. The smaller amounts of Newtons gave more accurate results, the clamp stand was steady, the extensions could be measured on the meter ruler and none of the spring didn’t reach its elastic limit.
Comparing gradients (from graph).
I have worked out the ratios of the gradients and I have then cancelled them down to the simplest form to make it easier to compare them.
Decimals.
Series spring Single spring Parallel spring
8.3 : 3.6 : 1.8
4 : 2 : 1
Hooke’s law.
Series spring Single spring Parallel spring
K = ¼ : K= ½ : K= 1
= 0.25 : =0.5 : =1
Conclusion.
I have plotted my results, graphs and gradients and I can say that my hypothesis was correct, as my results are reasonably accurate. My hypothesis stated:
1) I think that the stretch of the two springs in series will be double the stretch of a single spring.
2) I think that the stretch of the two springs in parallel will be half the stretch of a single spring.
Therefore if x were to be the single spring:
1) The springs in parallel would be ½ x
2) The springs in series would be 2x
My results reflect my hypothesis, for example on average when one Newton was added to the single spring it extended 3cm, the springs in parallel extended 1cm and the springs in series extended 7cm. Furthermore, on average when six Newtons were added to the single spring it extended 22cm, the springs in parallel extended 12cm and the springs in series extended 51cm. This shows a positive pattern, demonstrating Hooke’s law.
My results can be explained by the formula: F = kx, the deformation of a material is proportional to the force applied to it provided the elastic limit is not exceeded.
My graph is a straight-line graph because the extension is directly proportional to the extension so the graph will reflect this by rising gradually, although if the spring had yielded the graph would have shown a curve.
Evaluation.
My experiment was fairly accurate and there were no major problems due to the pilot study. I had three anomalies in my results, circled in red on my graph. Two of the anomalies occurred early on in the experiment, firstly when 1 Newton was added to the springs in series and secondly when 2 Newtons were added to the single spring. The other anomaly occurred when 6 Newtons were added to the springs in parallel. The two anomalies at the beginning of the experiment could have occurred due to human error, the reading may not have been read at 90o. The other anomaly could have occurred due to the spring yielding or again it could be due to human error and the extension could have been read incorrectly.
The errors mentioned above could have been caused by the following error:
The pointer (pencil) was not always at 90o,as it would not stay at an accurate 90o due to the spring’s movement.
The pencil, which held the mass hanger with the parallel springs, would not hold the mass hanger in one fixed position, so it was not always balanced.
The clamp stand was slipping due to the weight of the mass hanger.
The extension of the springs was not always read at eye level, due to human error.
The ruler cannot be completely accurate; the ruler is only accurate to +/- 0.1 centimetres.
These points can be improved by:
Design a new pointer, for example a fixed piece of metal to the spring and use a spirit level to make sure it is at 90o.
Design and make a piece of plastic with measured and cut grooves for the mass hanger and the springs to be securely placed on.
Fix the clamp stand to the work area.
Use a spirit level to make sure that the extension is always read at 90o.
Further experiments could be done to follow on from this experiment. Two experiments, which could be carried out, are firstly using three or four springs in series and parallel formations to see whether a relationship can be found. Secondly, springs of different materials could be used (for example copper, aluminium and plastic) to test how different materials affect the extension of springs.
Test one.
Test two.
Hooke’s Law states that:
Due to the molecular make-up of different metals it may be possible that r (the distance between the molecules in the metal) maybe different. In a further experiment we could investigate the elasticity point in different metals. This could give us indication to their usefulness in building materials, i.e. in suspension bridges. In a suspension bridge the cable needs to be strong, yet, elastic. This enables the bridge to move in the wind without snapping.
