Data Collection and Processing:
Tables
Table 1:
Table 2:
Table 3:
Calculating and finding uncertainties:
To find the uncertainty of a measurement one must simply find the limit of reading for the instrument being used and half it. The limit of reading is equal to the smallest graduation of the scale of an instrument. E.g. it can be seen above that the “time taken according to V.D.” table has an uncertainty of 0.005 seconds. This is because the smallest graduation in time shown on virtual dub is 0.01 seconds, hence 0.01/2 = 0.005.
Converting into percentage uncertainties:
When viewing the results of percentage accuracy the uncertainty must also be in percentage form. The following formula can be utilized to find this, percentage uncertainty = (uncertainty/value) × 100.
After finding the percentage uncertainty, one is able to find a more accurate uncertainty for the “I.V. km/h"
Finding velocity and Accuracy
To be able to compare the R.G. velocity to the instantaneous velocity one must first know the following components, time and distance. The formula, V= s/t gives you the velocity in m/s; however it then needs to be converted into km/h. This is done by multiplying the value by 60², then dividing by 1000, like so: value in km/h = m/s value × 60² ÷1000.
The accuracy of the radar gun was found by dividing the small velocity by the greater velocity, multiplied by 100. For example, if ones results showed that the radar gun gave a reading of 21km/h where in actual fact the car was travelling at 19km/h. They would use, accuracy (%) = 19/21 ×100, which equals 90.48%.
The uncertainty for the “I.V. km/h” section of the table was found by multiplying the value by the percentage error. E.g. 20.224 has a percentage uncertainty of 2.5%, therefore 20.224 × 0.025 = an uncertainty of 0.5056, which is presented as one significant figure.
Analysis of Results
After observing and analysing the tables, a number of things were learned about the accuracy of more than just the radar gun. For example the velocity of the speedometer (expected value) proved to be very inaccurate due to the fact that the limit of reading is 10km/h. This extremely high uncertainty lead to the I.V. (actual velocity) not once matching the expected value (as seen in tables 1-3.) Therefore, one cannot simply assume that the car is travelling at a constant velocity because that’s what shows on the speedometer, but must use a more accurate device/tool such as virtual dub.
Table 4 shows the accuracy of the radar gun decreasing as the velocity increases, in other words accuracy is inversely proportional to velocity. The inaccuracy of a higher velocity is also shown in the “Difference between R.G. velocities to I.V.” column of table 4, where as the velocity increases so does the difference, which is also known as the difference being proportional to the velocity.
An average accuracy of the radar gun can be calculated by taking the sum of the percentages and dividing it by the number of percentages. The same method applies for the uncertainty.
Average accuracy of radar gun = sum of percentages/ number of percentages
= (97.111+98.888+............+91.185) / 9
= 93.473%
Uncertainty = sum of uncertainties/ number of uncertainties
= 12/9
= 1.33
= 1
The average accuracy of the radar gun is 93.473% ±1. However this accuracy has only be taken from a small range of velocities (19km/h – 42km/h.) Due to the inverse proportionality of accuracy and velocity, if there was to be more velocities added to the results it would change the overall accuracy.
Graphs
Graph 1:
Graph 2:
Analysis of Graphs:
Graph 1contrasts the R.G. velocity to the actual velocity, (I.V.) with the blue line representing the R.G. velocity and the red representing the I.V. It can be seen that most of the R.G. readings are higher than that of the actual velocity and the difference between two points are generally the same from starting from trial no. 4. However, if looking at only the first 3 trials, both the R.G. velocity and the I.V. are almost identical. This is due to the fact that the accuracy is inversely proportional to the velocity. To compensate for any uncertainties, error bars have been added according to the data shown in the R.G. velocity column in tables 1-3 and the I.V. km/h column in table 4.
Graph 2 displays the accuracy of the radar gun as a percentage. Again, if a linear line of best fit is added to the scatter graph, it is shown that the accuracy is generally, inversely proportional to the velocity. The accuracies have also tended to condense as the velocity increases, which may mean that as the velocity increases the gradient decreases. Hence, the velocity is inversely proportional to the gradient of an “accuracy vs percentage” graph.
Conclusions and Evaluations:
A large number of individual errors may have been present in the experiment such as: misreading, error when recording, breakdown in communication, poor use of arithmetic when calculating components of the experiment, using wrong theory and equations, etc. The driver of the car may not have reached the desired velocity by the time he reached the 0m mark and, to further add to the possible error, may have slowed down before the 10m mark in order not to hit the velocity recorder. This is why a distance of 5m was used instead of 10m. As a result of not travelling a constant velocity through the 10 metres, the person recording the velocity may have pressed the trigger of the radar gun when the car was either still speeding up or slowing down. This would lead to an error in the data. The recorder of the results may also have written R.G. velocity down incorrectly due to a breakdown in communication, carelessness, etc.
Systematic uncertainty was also present in this prac, due to the fact that some of the instruments that were used were not as accurate as desired. For example, the hot wheels radar gun could only measure whole numbers, and the rounding system it uses is unknown.
Random Errors such as the uncertainties gained from rounding off data may also have affected the accuracy of the results. The experiment took place outside; therefore the environment could have affected the result such as wind, air resistance, change in temperature, etc. Not collecting enough data would have definitely affected the results, there were only nine trials conducted which is certainly not enough.
The formula, Percentage Deviation = (Exp Value – Accepted Value) / Accepted Value × 100% can be used to determine the preciseness of the overall accuracy.
Percentage deviation = (100 - 93.473) / 100 ×100
= 6.527%
The percentage deviation at 6.527% is quite large; this is possibly due to the fact that there are so many possible errors that could have occurred.
Conclusion
The data that was accumulated shows that the radar gun has an average accuracy of 93.473% ± 1 for velocities that range approx. 20km/h-40km/h. After observing the tables and graphs it can be seen that velocity is inversely proportional to the accuracy of the radar gun, hence the accuracy decreases as the velocity increases. It was also gathered that the gradient of an “accuracy vs I.V.” decreases as the velocity increases, again another inverse relationship. The average accuracy was found to be 6.527% off 100% accuracy, which is a reasonable outcome, depending on the way one looks at it. In summation, this experiment was an overall success as the aim to find the accuracy of a Hot Wheels Radar Gun was met, and much was learned about the components that make up aspects of physics such as constant velocity, instantaneous velocity, etc.
Recommendations
In relation to the possible errors that may have occurred, if this experiment were to be repeated, the following modifications would be made.
- Measure the velocity of the car with a more accurate device. This would in turn cause the final uncertainty to be smaller and the accuracy higher.
- A larger space to conduct the experiment. An area such as an airport run way would be ideal for this experiment as it would give ample time for the driver to reach and maintain a constant velocity.
- More care should be taken in both the recording and calculating process of data to reduce error.
- Prac should take place in doors, to avoid environmental factors that may contribute to a higher error.
- Rounding should be kept to a bare minimum in order to accumulate the most accurate data.
