Albert Einstein is pondering how to write his (soonto-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? E = mc4?). Pretend that Albert knows nothing about dimensional analysis, but since you are taking a fluid mechanics class, 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, showing all of your work. Compare this to Einstein's famous equation—does dimensional analysis give you the correct form of the equation?

To study Brownian motion, Bob, a student at the University of Ottawa, used his camera to capture the positions (i.e. displacements) of 50 microscopic dust particles floating on the surface of the water of his aquarium. By setting his camera to record 10 frames per second and noting down each particle's 2D displacement for each recorded frame, he managed to obtain the following mean-displacement vs time graph: 1600 1400 1200 2 1000 V 800 600 400 200 20 40 60 80 100 120 140 Time (s) a. Use the above mean-displacement graph to roughly approximate the diffusion coefficient D of the dust particles with units of um? /s. b. From the diffusion coefficient estimate in a), calculate the root mean- square displacement expected between each consecutive frame? c. Are the diffusion coefficient D and mean-square displacement calculated reasonable for a microscopic particle, or did Bob make a mistake in his calculations? Mean-square disp. (cm²)

Please please please answer everything as fast as possible please NOTE: This is not a graded question, this is not a graded question

When measuring with a muline, it was measured as n=10 when the speed was 1.1 m/s, and as n=32 when the speed was 1.5 m/s. What is the velocity formula?

been having some trouble with this problem: Michelson used rotating mirrors, similar to those shown below, to calculate the speed of light. Light is emitted from the light source, reflects from mirror surface X to the plane mirror, and then to the position of surface Z. By the time the light moves from the X to Z position, mirror surface X will have moved to the position of mirror surface Z. The light then continues to the observer. The distances from the light source and the observer to the rotating mirrors are negligible. The distance from the rotating mirrors to the plane mirror is 35.0 km.If the mirrors are rotating at 480 rev/s, the speed of light calculated from the given information is

A galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.

1. Consider two time interval measurements: t1 = 0.84±0.8 sec and t2 = 0.96 ± 0.8 sec. Considering their uncertainties, can you conclude that the two measurements are the same? Explain.