Unicellular organisms such as bacteria and protists are small objects that live in dense fluids. As a result, the resistive force they feel is large and viscous. Since their masses are small their motion looks very different from motion in a medium with little resistance. In this problem we'll model the motion of a paramecium on a spreadsheet and explore how these situations differ. Paramecia move by pushing their cilia (little hairs on their surface) through the fluid. The fluid (of course) pushes back on them by Newton's third law. We will call this force of the fluid on the cilia of the paramecium "the applied force", Fapp(since it wouldn't happen if the paramecium didn't try to move its cilia). This is the force that moves the paramecium forward. Since in this problem we are exploring how the motion of the paramecium depends on the parameters of applied force, mass, and resistance, we wont worry about how the cilia move to produce a consistent forward force.

For the paramecium problem, we know that we will be dealing with the viscous force on the paramecium. From your reading, you should know that the viscous force can be modeled as having magnitude |Fvis| = 6ÏμRv. We will lump 6Ïμ into a new quantity called β where β = 6Ïμ.

Required:
What are the units of β in terms of mass M, length L, and time T? â