Via Physics Today's Facebook: On this day in 1859 (and on the day before) one of the largest geomagnetic solar storms ever recorded struck Earth. The Aurora Borealis was seen as far south as the Caribbean. Telegraph systems all over Europe and North America failed. In the Pacific Northwest, the aurora was so bright that people could read a newspaper at night by its light. According to calculations by insurers Lloyd's of London and risk assessor AER, if a storm of the same magnitude struck the US now, it would cause up to $2.6 trillion worth of damage. The storm is known as the Carrington event after the British astronomer, Richard Carrington, who recorded the storm's genesis as a sunspot on 28 August.
And...on with the show.
Example: You pull a box of rocks in a wagon across your yard. You grab the handle at a 45 degree angle, and muscle your box of rocks across the yard at a sold 100N of force, constantly, for a distance of 10 meters. What is the total work done on your journey?
We can calculate the work with the following formula:
In Episode 064, we learned the 5 steps for doing any dot product.
1) Identify two vectors- in this step you will need to simply locate the two vectors you’ll be “dotting”.
So far, so good. We know that we need the Force and the displacement, which are given in the problem: F = 100N, and d = 10m.
2) Identify number of dimensions- i.e. [2,0] and [4,3] are both two dimensional, because there are two numbers, or components, inside the brackets, [2,0,5] and [4,3,-9] are 3-dimensional vectors.
.... uh oh. Our force vector and displacement vectors are not given in terms of coordinates, we're simply given their magnitudes. If you recall from the end of Episode 064, I had mentioned that there is a "quick" way to perform the dot product, which was
where F and d are not bold, representing the magnitudes of the vectors, and theta being the angle between them.
So, we simply multiply 100N*10m*cos(45) = 1000*sqrt(2)/2 = 707.10 J!
