Experiment to determine gravity from a spring using digital techniques

Sample graph from datastudio:

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Part 2

• The equilibrium position of the spring is recorded when there was no mass on it, and this was taken as the 0 position.
• 50g of mass is put on the spring and the extension of the spring is recorded. The mass holder and pointer do not need to be weighed, because they were already on the spring when the equilibrium position was recorded. The mass of the mass was also weighed, to keep the results as accurate as possible.
• This process was repeated with other masses, in 50g increments, with the total mass on the spring being weighed each time.
• From this, a graph of mass against extension can be plotted, and a value for gravitational field strength calculated.

Results

Part 1

The graph of mass against period squared is shown below:

The spring constant of the spring can now be calculated in the same way as in experiment 1.

Uncertainties

Calculating Uncertainty in k

The LINEST function in excel is used to calculate the uncertainty in the gradient and therefore in k.

Using LINEST, the uncertainty in the gradient is:.

Therefore the value for k obtained is:

Uncertainty in Each Point

The uncertainty in the mass can be seen as ±0.001kg, as it is a digital balance so the reading error is ± half a scale division. This uncertainty is very small, and the error bars for this are too small to be seen on the graph.

The uncertainty in period squared is comprised of two components, the calibration uncertainty and the reading uncertainty. The calibration uncertainty is calculated by calculating 0.5% of the value, then adding the smallest digit of this to it, because it is a digital instrument measuring the time. The reading uncertainty is ±one scale division, because it is a digital timer, and this is ±0.0001, a very small uncertainty. Because this uncertainty is so small, it has no effect on the total uncertainty of each value for period squared, and is considered negligible. For this reason, just the calibration uncertainty will be taken as the uncertainty for the period. The percentage uncertainty for period is calculated, and this is doubled, because uncertainty doubles when the period is squared. When this is calculated, it is found that the uncertainty in each value is 1%, due to the precise methods used in the experiment, and the errors bars are too small to be seen on this graph.

Part 2

The graph of mass against extension is shown below:

A value for gravitational field strength can now be calculated in the same way as in experiment 1.

Uncertainties

Calculating Uncertainty in g

This is done in the same way as for experiment 1.

LINEST is used to calculate the uncertainty in the gradient of the mass aginst extension graph. The gradient is .

The uncertainty in g is calculated by combining this uncertainty value with the uncertainty for k.

So the value for g calculated in this experiment is:

Uncertainty in Each Point

The uncertainties in the mass are once again ±0.001kg, which is very small, and again the error bars on this graph are too small to see.

For the uncertainty in the extension, ±half a scale division can be taken as the uncertainty for the extension. This is ±0.0005m, which is once again too small to be seen on the graph.

Discussion

Conclusion

This experiment has confirmed that period squared is directly proportional to mass. It also confirms Hooke’s law, that F=kΔx for a spring experiencing a force F and extension Δx.

This experiment also calculated a value for gravitational field strength as being

.

Evaluation

Overall, this experiment can be seen as a success, with the value calculated for gravitational field strength being very close to the generally accepted value of

9.81Nk-1. The value obtained is only 0.05Nkg-1 out, within experimental error.

In part 2 of the experiment, the pointer supplied to read the extension was inaccurate, as it would point down when there was little mass on it, and further upwards when a heavier mass was applied. To try to counteract this, the pointer was held perpendicular to the spring when reading the extension. This should ensure that all readings for extension are taken at the same level; ensuring consistency in the results is maintained. If the experiment were to be repeated, a more accurate pointer would be found.

When measuring the period of the oscillations of the SHM in part one of the experiment, the spring would often swing back and forth, often leaving the path of the motion sensor, which caused the result to be ruined and the attempt for the mass had to be repeated. In order to overcome this, the spring was pulled down as straight as possible, to prevent this happening.

A CD was attached to the bottom of the spring, in order to increase the area that the motion sensor “sees”. This increased the accuracy of the motion sensor, as it is more likely to see a larger area, thus improving results. The mass of the CD was taken into account when weighing the masses.

It was found that the motion sensor worked best when closer to the spring. In order to facilitate this, a labjack was placed on top of a stool, to get the motion sensor as close to the spring as possible. The labjack also provided a level surface for the motion sensor, instead of the curved surface of the stool.

Overall, the experiment can be seen as a success with measurements being precise and accurate, giving a small error. This shone through in the results, where the value obtained for gravitational field strength was very close to the generally accepted value.