For this investigation I have been asked to find out how different masses on a spring effect the extension when the springs are in parallel, series and on a single spring.

Preliminary work

                                           

For my preliminary work I carried out my planned procedure to see if there had to be any alterations made to the method. I carried out the test and I decided to use a sprit level to make sure that the ruler is level and so I could take a reading at exactly 90°.

These were the results that I got from the preliminary test using just the two springs on their own.

I have decided to extend the amount of masses that I put on to the springs to 1kg because I will get a wider range of results.

Diagram

                

                

        

Method

• Set up your equipment as shown above
• Measure the springs to make sure that they are nearly the same length
• Hang the spring on the clap stand and add the first mass to the spring making sure you measure the mass so make sure that they are nearly the same mass
• Add on the masses at 100g intervals measuring the extension each time and recording.
• When you get to 1kg to exactly the reverse and see if the spring has reached it elastic limit
• Do this for both springs separately
• Then repeat for the springs in parallel and series
• Now repeat the experiment another 2 times

Things to remember when carrying out the practical

• Wait until the spring has stopped bouncing then take the reading
• Make sure you look directly at the ruler when taking readings; it also may be useful if you had a piece of string to measure the extension then measure it against the ruler.
• Make sure spring hasn’t deformed each time new masses are added by taking the masses off and measuring it and referring to the original length of the spring recorded in the table

Results

The extension of one spring

The extension by two springs in series

The extension of two springs in parallel

Calculating the spring constant:

Single spring

Spring constant, k=            =              =        =         =23.310Nm-1

Two springs in series

Spring constant, k=            =        =                =              =12.285Nm-1

Two springs in Parallel

Spring constant, k=            =                     =               =                =48.780Nm-1  

Analysis

Accuracy

Two systematic errors were introduced into this experiment; because a ruler was used to measure the extension of the spring, there is ±0.001m error introduced. Another error, called parallax error, was also introduced and I estimate this error to be ±0.004m. This gives a combined systematic error of: ±0.005m. The extension of the spring was given by: extension = final length -original length, but the ruler was positioned very accurately so that with no load the original length was zero, the extension was just taken as the final length.

Conclusion

I was correct in my prediction that two springs in series would have a spring constant half that of a single spring: this experiment shows that the spring constant of two springs in series was 0.5 (to one decimal place) of the spring constant of the single spring. I was also correct when I predicted that the spring constant of two springs in parallel would be twice that of a single spring: this experiment shows that the spring constant of two springs in parallel was 2.0 (to one decimal place) of the spring constant of the single spring. The results also show that the extension is proportional to the load: "An object obeys Hooke's law if the extension produced in it is proportional to the load”.

This can also be shown by varying the load on different arrangements of springs to achieve the same extension, a spring with load m, two identical springs in. parallel with load 2m, and two identical springs in series with load m/2 have the same extension.

By using the spring constant of a single spring (k) it is possible to determine the spring constant for any number of springs in series or parallel:

Spring constant of springs in parallel= number of springs x k

Spring constant of springs =  

The strain potential energy (energy stored while under load) can be calculated using:

Elastic potential energy= ½ x stretching force x extension

Spring constant compared to the elastic potential energy

This shows that there is an opposite link between elastic potential energy and the spring constant depending on the arrangements of springs that is shown in Table 4. This shows that there is more potential energy stored in the springs in series that has the lowest spring constant and the smallest amount of energy is stored in the springs in parallel that has the highest spring constant. The relationship is the exact opposite of the spring constant, where the spring constant halves the energy doubles and vice versa.

Evaluation

I obtained very accurate results from this experiment and there was only one anomalous result' this was for the single spring at a mass of O.9kg (see graph); this must have been due to a random error. All other average results were within O.OO5m of the line of best fit that is shown on the x-axis error bars on the graphs. An average of three readings was taken to decrease the chance of random errors in the results.

The method used in this experiment has many limitations that cannot be overcome easily. For example, the metre rule is very inaccurate however since large distances are being measured a device such as a vernier scale cannot be used. The parallax error is also a very large error in this experiment and this could be overcome by using a mirror behind the spring when it is being measured and this can be used to line up the pointers, this would greatly decrease the amount of parallax error but would not eliminate it completely.

I also recorded the compressive force; it was exactly the same as the extension so I didn’t put it in my results table.

The limitations of the accuracy in this experiment were discussed in the section called Accuracy above.