Observations of the Pipe Nebula have led to the discovery of dense starless cores. The mass of most cores is too small for their self-gravity to hold them together. Instead, they are thought to be pressure confined. The observed dense cores' mass function (CMF) matches well with the initial mass function of stars in young clusters. Similar CMFs are observed in other star forming regions such as the Aquila Nebula, albeit with some dispersion. The shape of these CMF provides important clues to the competing physical processes which lead to star formation and its feedback on the interstellar media. In this paper, we investigate the dynamical origin of the mass function of starless cores which are confined by a warm, less dense medium. In order to follow the evolution of the CMF, we construct a numerical method to consider the coagulation between the cold cores and their ablation due to Kelvin-Helmholtz instability induced by their relative motion through the warm medium. We are able to reproduce the observed CMF among the starless cores in the Pipe Nebula. Our results indicate that in environment similar to the Pipe Nebula: (1) before the onset of their gravitational collapse, the mass distribution of the progenitor cores is similar to that of the young stars, (2) the observed CMF is a robust consequence of dynamical equilibrium between the coagulation and ablation of cores, and (3) a break in the slope of the CMF is due to the enhancement of collisional cross section and suppression of ablation for cores with masses larger than the cores' Bonnor-Ebert mass.