Parasitic nematodes are nasty little critters that borrow through the soft tissue of their hosts with undulatory swimming that looks like an eel.

Parasitic nematodes are nasty little critters that borrow through the soft tissue of their hosts with undulatory swimming that looks like an eel. Like an eel, the nematode generates bending with superficial muscles that are oriented parallel to the length of the body. Unlike an eel, there is no endoskeleton in a nematode, so it is not obvious how contraction on one side of the body creates a bend, instead of shortening the body. When the muscles relax, the body passive springs back to a straight posture. This paradox is resolved by considering the fiber winding of stiff fibers in the cuticle that covers the surface of the body. Use a graph of the relationship between the fiber angle and the volume enclosed by a helix to (1) predict the approximate fiber angle in the cuticle, (2) explain how the cuticle resists compression by the body when the longitudinal muscles contract, and thereby straightens when the muscles cease to contract. Please label the curve(s) on your graph and define any symbols. Be sure to indicate how contraction by the muscles relates to fiber angle. State your assumptions.