Theory: Radar guns are, in their most simple form, radio transmitters and receivers. They send out a radio signal, and then receive the same signal back as it bounces off the objects. However, the radar beam is different when it comes back, and from that difference the radar gun can calculate vehicle speed. The gun uses the Doppler Effect to calculate the speed of the object in the beam’s path. Using a comparison of frequency shift between received images instead of the frequency shift between sent and received frequencies creates what is known as moving radar, the radar must be stationary to measure speed.
By utilizing a number of different equations, it is thought that the accuracy of a Hot Wheels Radar Gun will be found. The equations that will be used are as follows:
1. A distance of 10m was measured out and marked with chalk. 2. Three markers were used to mark out the distances of 0m, 5m, and 10m. 3. The radar guns settings were changed to 1:1 and km/h. 4. The apparatus was set up as shown in the above diagram (with the exception of the car).
5. The car was positioned parallel to the 10m line, and given a run way that was long enough to reach the required velocity by the 0m marker. 6. The video camera was positioned and turned on, in order to record the event. 7. The car passed through the markers at a constant velocity of 20km/h. 8. An instantaneous velocity of the car was measured with the radar gun as soon as it passed through the 0m marker while step 6 was still occurring. 9. This process was repeated another 2 times, 10. Results were recorded. 11. Steps 6-9 were continued, instead replacing the 20km/h with 30km/h then again with 40km/h.
12. The recorded video was then transferred into the programme “virtual dub” to find the time it took for the car to travel 5m. A distance of 5m was used opposed to the initial procedure of 10msimply because it looked as though the car may have been slowing down at approx. the 8-9m mark on some of the recordings. 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.
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 ï¿½ 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.
The data that was accumulated shows that the radar gun has an average accuracy of 93.473% 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.