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# Making Sense of Data

Extracts from this document...

Introduction

UNIT 2862 – (c) Making Sense of Data

Ben Crundwell - 2021

26th April 2002

DETAILS OF THE EXPERIMENT:

DATA TAKEN FROM THE EXPERIMENT:

ORIGINAL CALCULATIONS:

TROLLEY ACCELERATION:

THE ANGLE OF THE SLOPE:

VERTICAL HEIGHT ABOVE THE LIGHT GATE:

PROBLEMS WITH THE RESULTS:

## Details of the Experiment:

The data which was provided was taken from the following experiment: An air track was set up at a slight angle and a small trolley was placed on it. The trolley had a 10cm long flag attached to the top of it, so that a light gate could time how long it took the trolley to pass a given point. There were two light gates set up exactly 10.0cm apart which gave 2 separate time readings for different starting positions up the sloping air track.

## Data taken from the Experiment:

The experiment was completed and some data was extracted from it and given for analysis and calculation. The data which was taken from the experiment is given below:

 Ta/s Tb/s y/cm 0.268 0.206 10.0 0.205 0.173 20.0 0.173 0.152 30.0 0.174 0.154 40.0 0.153 0.139 50.0 0.139 0.128 60.0 0.130 0.120 70.0 0.119 0.113 80.0 0.112 0.106 90.0
 Constant Value Length of flag on trolley 10.0 cm Mass of the Trolley 179 g Distance between gates 10.0 cm Acceleration of free fall 9.81 m.s-2

## Original Calculations:

The first few calculations to be

Middle

In order to see what this data is representing it can all be plotted onto a graph showing the calculated velocities of the trolley at the different heights up the slope (y) given in the original data. This Graph has been plotted and included on the next page.

By looking at the data on the graph a simple line of best fit was plotted on the Velocity at A data, this line shows how close the results are together and how well correlated they are. As can be seen, the data is all related very closely together as the line fits very well into the data.

## Trolley Acceleration:

Another graph of the Velocity at A against the Velocity at B was plotted to check the data. This shows how the speed changed along the trolley’s journey and due to the almost perfect straight line fit it seams obvious that the speed of the trolley is increasing at a steady, constant rate. This suggests that the acceleration of the trolley is constant as physics suggests it should be through Newton’s Laws stating that F=ma therefore in order for the trolley the change its acceleration it would have to change either the force acting on it which is gravity and wont change or it has to change mass, which it also cant. Therefore Acceleration must stay constant. One of the general equations of motion can be used here:

The formula above can be used to calculate the velocity on an individual trolley experiment. This will give the acceleration of the trolley because we know that v is the velocity at point B, u is the velocity at point A and s is the distance between A and B which is 10cm. From this information the following accelerations were calculated from the data:

 Ta/s Tb/s y/cm Acc/ms-2 0.268 0.206 10.0 0.482 0.205 0.173 20.0 0.481 0.173 0.152 30.0 0.494 0.174 0.154 40.0 0.457 0.153 0.139 50.0 0.452 0.139 0.128 60.0 0.464 0.130 0.120 70.0 0.514 0.119 0.113 80.0 0.385 0.112 0.106 90.0 0.464

Conclusion

10, 20, 30, 40, 50, 60, 70, 80, 90

they should be:

10, 20, 30, 30, 40, 50, 60, 70, 80

This shows how the data has become out of line and therefore needs further investigation. In order to see whether the height readings are correct a formula can be constructed to use the acceleration and velocities between points A and B and the angle of slope, regardless of the actual distance up the slope to calculate what y was for that test. This equation comes from the Kinetic Energy equation: K.E. = 0.5 x m x v2 and the Gravitational potential energy equation used in the previous problem to form:

This formula was then used on the data from the experiment to calculate what the actual distance y was:

 V A (ms-1) y MEASURED y CALCULATED 0.373 0.1000 0.140 0.488 0.2000 0.240 0.578 0.3000 0.337 0.575 0.4000 0.333 0.654 0.5000 0.431 0.719 0.6000 0.522 0.769 0.7000 0.597 0.840 0.8000 0.712 0.893 0.9000 0.804

The data in the table does help to highlight that the data does come out of line but it also highlights that the early results are approximately 5cm out. This could be because the velocity is measured over a 10.0cm flag which would average the velocity to the middle of the flag thus making the actual distance y 5.0 cm further than expected.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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