Uncertainty

This blog post is just a poke at the uncertainty theory learnt in school, so...

Student A is a studious physics student, and thinks about physics even after school (shock!). In fact, the very moment he noticed that there was a newly installed solar panel installed at the side of the hill near his home, he decided that it would be great to calculate its power output, and put his knowledge of uncertainties to the test as well!

Via a protractor-bob improvisation, he manages to guess the slope of the solar panel via triangulation. However, as he is lazy to climb the hill, the way he derives the length of the solar panel is via subtracting the height of the lower edge of the panel from the height of the top (using a map to measure the distance from his house to the panel). As a result, the uncertainties are not exactly small, and he estimates the length of the (square) solar panel at 12 meters plus or minus 5 meters.

Using that value, he calculates the area of the solar panel.

Following that, he realises that the amount of sunlight received is somewhat unknown to him, due to poor geographic knowledge of his own surroundings. As such, he decides that the intensity of sunlight would nominally be pegged at 1000W/m^2, give or take 100W/m^2.

Lastly, he realises that he does not know the efficiency of the solar panel. Through internet research, he pegs it at 15% plus or minus 3% (i.e. 12% to 18%).

Finally, he computes his answer, and is feeling extremely satisfied with himself... until he calculates the uncertainty. He then concludes that he made a mistake somewhere in his calculations and goes back to clearing his usual piles of homework.