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What is the spring constant?

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Introduction

Jon Adderley

Energy stored in a spring

Preliminary investigation

What is the spring constant?

Planning

Aim – to gain an average compression rate of the spring in the trolley in order to find the spring constant.

Apparatus

Clamp stand

2 clamps

2 bosses,

24 0.98N weights

2 weight holders

3 labels

Pencil

Sprit level

Trolley

Ruler (measures to nearest 5 x 10-4m)

Diagram

Plan – I am going to investigate the spring constant of the spring in the trolley to enable me to calculate the energy stored in the spring in the major investigation. To calculate the spring constant, I need to plot my results onto a graph and draw a line of best fit. The spring constant is equal to the gradient of this straight line. To obtain my results, the above apparatus will be collected and set up as shown above. The spirit level will be used to check that the trolley is perpendicular to the ground. The trolley needs to be perpendicular to the ground for 2 reasons. 1). So that all of the weight of the weights act on the spring and not a component, 2). So that there is no friction between the plunger and it’s housing. The variable that is being changed is the force applied to the spring; 0.98N will be added in each of the 12 increments.

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Middle

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)image01.png

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.

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Conclusion

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.

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