For this investigation I will explore and examine the behaviour of springs when applied a weight and a force to them. I am aiming to achieve a direct relationship between the period it take to complete 30 oscillations and the weight applied to the spring.
Planning:
Prediction:
Similar to my aim I predict a directly relationship between the period it takes to complete a number of oscillations and the weight or mass applied to the spring. This means that as I increase the amount of weight or mass the period should also increase.
If there is a direct relationship between the period and the weight the graph should have a straight line because as the x value increases the y value should increase proportionally. This prediction is based on Hooke’s law which states that the extension of a spring is directly proportional to the weight or mass applied to it.
I will find out the correct equation after I get my results and convert them into a graph.
Fair testing:
Controlled variables:
My controlled variables are the variables which I control/ have to control in each and every experiment that I carry out to make sure that all of them are extremely accurate and the results they produce are reliable.
My first controlled variable is the amount of extension I put on the spring before letting it go and timing it. I had decided on a fixed extension I would use on all experiments but after my preliminary experiments were carried out I found out that the amount of extension put on the spring did not affect the time it took for completing 30 oscillations.
I controlled the amount of extension because I thought that it would affect the time it takes for a number of oscillations.
The next controlled variable is the number of oscillation for timing because if this variable wasn’t kept constant/ same during all the experiments then my results would be inaccurate and investigation unreliable. This would be because I would be carrying out different experiment each time if I change the number of oscillations.
I will also use the same spring each time because I believe that different springs have different elastic limits and therefore will affect my results.
Precision/ accuracy:
These are some things that I will have to do so that my experiments will remain precise and accurate:
* Fix the retort stand so spring will not wobble
* Attach a G-clamp to the retort stand so that it is stable
* Adjust a ruler to measure extension, I will attach it to the side of the retort stand so that measurements are accurate
* I will count the oscillation in the middle as the top could vary
Method:
These are a list of apparatus needed to carry out this experiment:
* Retort stand
* G-clamp
* Spring
* Weights(100 g each)
* Ruler
* Stop watch
* Hook for holding the weights
The following is a step by step procedure that I followed to carry out my experiments:
* Attach your spring to the retort stand and fix it so that spring won’t wobble.
* Adjust a G-clamp to stabilize the retort stand.
* Adjust a ruler to measure extension.
* Fix the spring on the retort stand.
* Attach the desired amount of weights onto the spring and get ready for the experiment.
* Measure and extend the spring 3 cm down.
* Let go of the spring and start timing 30 oscillations.
* Stop the timer after 30 oscillations are complete and record the time.
Repeat the same procedure for all experiments.
This is a diagram of the set up:
Preliminary experiments:
Before performing my actual experiments I carried out some preliminary experiments to get comfortable with the experiments so that I can do them with ease actually. While doing my preliminary I found out a few interesting facts. I first found out that changing the amount of extension of a spring will not change the period. I also found out that the spring was wobbly so I adjusted the retort stand and attached a G-clamp. I said that my extension was going to be 3 cm for each experiment and that my minimum weight was 200g and maximum was 800g. This is because less than 200g is very difficult to measure and thus make inaccuracy more and I believe that the elastic limit for my spring was 800g. I decided to take 5 readings for each mass as I thought that this number was enough to produce a complete graph.
Obtaining Evidence
Final experiment result:
Weight or mass
Period 1
Period 2
Period 3
Period 4
Period 5
(g)
(s)
(s)
(s)
(s)
(s)
200
10.3
10.2
10.3
10.2
10.2
300
13.2
13.2
13.2
13.2
13.2
400
14.5
14.5
14.4
14.5
14.5
500
16.0
15.9
16.0
16.0
16.0
600
17.5
17.5
17.5
17.5
17.5
700
18.7
18.7
18.8
18.6
18.7
800
20.4
20.4
20.3
20.5
20.4
Processed data:
After looking at the data I realised that the weight is directly proportional to time2. So I decide to take an average of the periods and square them.
Weight or mass
Period 2
(g)
(s 2)
200
104.0
300
174.2
400
210.3
500
256.0
600
306.3
700
349.7
800
416.2
Conclusion
Graph based on the final experiment results:
Graph based on the processed data:
Calculations:
After looking at my results of the preliminary experiments I found out that the possible equations are:
* Mass is directly proportional to time
* Mass2 is directly proportional to time
* Mass is directly proportional to Time2
I then found my relationship which was mass and time was m=t2; I came to this conclusion by trying out all the possible equations until I reached the correct one. This would make the relationship would be directly proportional.
Explanation:
Basically I got what I had predicted which was that there should be a direct relationship between the mass or weight and the period of the spring to oscillate 30 times; a direct relationship is when the y axis is increased when the x axis is increased. This is because as the mass on the spring is increase the time for completing 30 oscillations should be slower therefore increases.
Conclusion:
At first I got a graph looking like the first one, I wasn’t sure whether it was a straight line or a curve so I decided not to add any line at all. I then used the function (m=t2) which is mentioned in the calculations part. I used this function to square all the period values so that my graph would be directly proportional and would pass through the origin. I did so and produced the second graph.
Looking at the second graph onto which I have added a line of best fit we can see the good correlation coefficient which was produced. This is proof of both accurate and reliable results. The points are either on the line of best fit or they are extremely close to the line which shows that I did not have any anomalies.
My conclusion supports my prediction as it proved my theory of there being a directly proportional relationship which is shown on my second graph.
Evaluation
Accuracy of method/suitability of evidence:
I think that the method which I used to complete this investigation was a reliable one to produce good results which it has done as I used the standard method described by our teacher. The method was also precise and reliable because all the experiments I completed for each mass were extremely close if not exact. However, I believe that I could have experimented two more mass, 900g and 1kg which would have increased the reliable area of the graph which is between the minimum and maximum value. It also would have clearly shown either a straight line or a curve.
Quality of evidence:
You can see from looking at my graphs that my results were accurate and produced a good graph because the second graph show a straight line going through the origin which relates to a directly proportional relationship. The correlation coefficient I got for the graph was 0.997 which is extremely good and you can see that all the point are either on the line or very close which suggests that there are no anomalies.
Anomalies:
Fortunately, I didn’t find any anomalies in my experiments and my graphs which prove the accuracy of my method and the reliability of my results.
Improvements:
At the moment I can only thing of one improvement. The reason for a few points a little away from the best fit straight line is probably the result of an error while counting the number of oscillations which relates to a fault in human reaction time which of course cannot be corrected. I had been provided with sufficient amount of time and should have preformed my experiments with a little more precision.
Sufficiency of data:
I think that my data was sufficient enough but it could have been better. I should have done experiments on two other masses, 900g and 1kg so that my graph would be more complete. However, this does not mean that my results were not reliable as I mentioned that the correlation coefficient was 0.997 which means that all points were extremely close to the line if not on the line. As you have seen from the graph and results box that my results make my investigation successful.
Further work:
First of all I would experiment on different types of springs with different coils and different elastic limits to find the out how it affects the period. I would also use more variety of masses. Finally I would use either a motion detector or a light sensor which would automatically measure the time and would reduce the errors carried out because of human reaction time.
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