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Academic Studies
Mathematics

 

 

Modelling Comparisons

These graphical comparisons between experimental and theoretical results are shown in different colours on the same axis for each value of q . Only the median experimental value of d is used to plot the graphs as this is representative of all the experimental values of d. Centimetres are used as units for d and l are in metres.

A graph for q = 35 can be found on the next page.

 

Analysis

Throughout values of q it is easy to observe that the theoretical results for d are substantially larger than experimental results. Error bounds for experimental data may account for a small part of the different between values of d, but not as much as almost 20cm (q = 24, l = 1). Differences between experimental and theoretical are less for q = 30 and q = 35, this perhaps suggests less resistive forces acting upon the ratchet socket. If the resistive force was friction is would explain why, as q increases the difference between theoretical and experimental results is reduced. For small values of l the difference between experimental and theoretical values is comparably small, there are less resistive forces present when there is a small distance travelled by the ratchet socket over the slide.

Measuring of q is prone to errors Using a ruler to measure two lengths of the slide, values could be out by only a small distance. Yet when these values are used to calculate q they are divided. This multiplies any small errors that occur through measuring and could have a large effect if there is a negative error in the divisor and a positive error on the top:

As q becomes larger, the difference in d between the two modelling methods, diminishes. The experimental and theoretical results never meet, showing that the theoretical is not considering a vital variable that effected the experimental.

 

Evaluation

There are forces other than present which were not taken into consideration when the theoretical model was made. Wind and air resistance are negligible in a room with windows and doors closed whilst the experiment took place. Moreover if there was a draft it would have a very small effect on a heavy object like a ratchet socket. The main resistive force is clearly the friction between the ratchet socket and the slide. When the socket slid down it made a noise, when there is a sound present there is energy being lost. The sound was the result of friction between the two metal surfaces. After consideration, there are no other possible reasons for such a difference between the two models. As three sets of data have been obtained, further corrections to the theoretical model will be more comprehensive. The theoretical model must be adapted to allow for friction and other negative forces on the object.

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