Unicellular organisms such as bacteria and protists are small objects that live

Question

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| = 6Rv. We will lump 6 into a new quantity called where = 6. What are the units of in terms of mass M, length L, and time T?

The paramecium in the problem is swimming through a fluid while moving at approximately a constant velocity as a result of wiggling its cilia. What can you say about the net force that is being exerted on it while it is doing this?

Let Fapp be the force applied by the paramecium and let's model the viscous force as we did in the videos as |Fvis| = Rv. In terms of Fapp, , and R, what is the constant speed at which the paramecium is traveling?

Hint: Start with F = ma. What are the sum of the forces? What is a if the paramecium is traveling at constant speed?

Explanation / Answer

|Fvis| = 6Rv

now = 6

then dimensions of   = F/Rv= (Kg-m/s^2)/(m)(m/s) = kg/m-s

= M1L-1T-1

part B

For constant velocity acceleration is zero so net force = 0

Part C

Fapp - Fvis = ma

for constant velocity a = 0

Fapp = Fvis

Fapp = Rv

v = Fapp/R

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