In this paper, the dynamic model for planar continuum manipulators that was presented in our previous work is extended to include new terms reflecting the effects of potential energy. First the gravitational potential energy of the manipulator is derived. Then, the elastic potential energy of the manipulator is derived for both bending and extension. Finally, the effects of the total potential energy are included in the dynamic model. Numerical simulation results are presented for a planar 3-section extensible continuum robot manipulator. The results show a much stronger match to physical continuum robots than with previously available models.