As a first step in the study of the toxicity of nanoparticles, we investigate here the energy behaviour of three distinct carbon nanoparticles interacting with a lipid bilayer; namely fullerenes, nanotubes and nanocones, using the Lennard-Jones potential together with the continuous approximation. For an assumed circular hole in the lipid bilayer, a relation for the molecular interaction energy is determined, involving the circular hole radius and the perpendicular distance of the nanoparticle from the hole. For each nanoparticle, the relation between the minimum energy location and the hole radius b is found, and for example, for a fullerene of radius 15 Å, for b > 19.03 Å, the nanoparticle relocates from the surface of the bilayer to the interior, and as the hole radius increases further it moves to the centre of the bilayer, remaining there for increasing hole radii. When the system has no external forces, the nanoparticle will not penetrate through the lipid bilayer but rather remains enclosed between the two layers.