The bacterium, Thiovulum majus, a species that metabolizes sulfur, is about \(18 \mu \mathrm{m}\) in diameter and can swim, if provoked, at speeds of up to \(600 \mu \mathrm{m} / \mathrm{s}\). We would like to look at some of the consequences of that behavior. We assume that T. majus moves through a solution that is very much like water at \(40^{\circ} \mathrm{C}\) but with a specific gravity of 1.1 and a viscosity 1.5 times that of water [28].

a. Given the speed and size of T. majus, what is the Reynolds number associated with its motion?

b. What is the drag force experienced by the cell?

c. How much power would the cell have to generate to move at its top speed?

d. How much work does the cell do to travel \(1 \mathrm{~cm}\) at top speed?

e. If a single molecule of glucose yields 30 molecules of ATP to power the cell and metabolism of a molecule of ATP generates roughly \(20 k_{b} T\) of energy, how much glucose is used to perform the work required in part (d). Assume the temperature is \(40^{\circ} \mathrm{C}\).