We use the effects of mass segregation on the radial distribution ofdifferent stellar populations in the core of 47 Tucanae to findestimates for the masses of stars at different post-main-sequenceevolutionary stages. We take samples of main-sequence (MS) stars fromthe core of 47 Tucanae, at different magnitudes (i.e., differentmasses), and use the effects of this dynamical process to develop arelation between the radial distance (RD) at which the cumulativedistribution reaches the 20th and 50th percentile and stellar mass. Fromthese relations we estimate the masses of different post-MS populations.We find that mass remains constant for stars going through theevolutionary stages from the upper MS up to the horizontal branch (HB).By comparing RDs of the HB stars with stars of lower masses, we canexclude a mass loss greater than 0.09 {M}<SUB>⊙ </SUB> during thered giant branch (RGB) stage at nearly the 3σ level. The slightlyhigher mass estimates for the asymptotic giant branch (AGB) areconsistent with the AGB having evolved from somewhat more massive stars.The AGB also exhibits evidence of contamination by more massive stars,possibly blue straggler stars (BSSs), going through the RGB phase. We donot include the BSSs in this paper due to the complexity of theseobjects; instead, the complete analysis of this population is left for acompanion paper. The process to estimate the masses described in thispaper is exclusive to the core of 47 Tuc.