Question

1. (15 pts) Albert Einstein is pondering how to write his (soon-to-be-famous) equation. He knows that energy E is a function of mass m and the speed of light c,

but he doesn't know the functional relationship (E = m²c ? or E = mc^4 ?).Pretend that Albert knows nothing about dimensional analysis, but since you are taking AE208, you help Albert come up with his equation. Use the step-by-step method of repeating variables to generate a dimensionless relationship between these parameters. Show all your work for full credit. Note: For consistency, use the mass-length-time-temperature (m-L-t-T) system of dimensions, not the force-length-time-temperature (F-L-t-T) system that some of you may have learned in another class. Compare to Einstein's famous equation – does dimensional analysis give you the correct form of the equation?

Fig: 1