4.1.2.P3

In the picture at the right is shown a frame from a video in which a group of amoebas are spread at random on a glass slide. A small needle introduces a bit of a chemical that attracts the amoebas. As the chemical spreads through the water in which the system is immersed, the amoebas begin to move towards the source of the chemical and are soon moving at an (on the average) constant velocity. We will build a model about what forces are responsible for the amoebas’ horizontal motion. (Ignore gravity.)

Our simplest biological model is that the amoebas respond to a difference in the density of the chemical (more on the side near to the needle, less on the side farther away) and do something in response. What? Here are two hypotheses:

• H1. The amoebas crawl along the glass slide, pushing along.
• H2. The amoebas move off the glass and swim in the fluid in which they are imbedded.

A. In order to decide which hypothesis makes sense, start by drawing a system schema  that would allow either hypothesis. In addition to your usual labels, mark interactions that would only be present in hypothesis 1 with an “H1” label and interactions that would only be present in hypothesis 2 with an “H2”.

B. Now draw two free-body diagrams for a moving amoeba; one assuming hypothesis H1 and another assuming hypothesis H2. Be sure to label each force in your diagram identifying the type of force, who is causing the force, and who is feeling the force. Under each diagram indicate if any pairs of forces are equal and give a reason why you think they are equal.

C. The experiment is repeated with a glass slide that is essentially frictionless. In this case the amoebas do not move towards the needle. Tell which hypothesis you think this supports (if either) and explain why you think so.

Wolfgang Losert and Joe Redish 1/15/13