An exercise machine for performing barbell type free weight lifting exercises has a power cage or Smith press type frame, an elongated bar held on the frame in a substantially horizontal resting position, and an adjustable exercise mass assembly that allows a user to select an exercise weight from among a plurality of choices of different exercise weights provided by the exercise mass assembly. The exercise mass assembly is separate from the bar and any auxiliary weight plates carried on the bar. A cable and pulley system operatively connects the bar to a movable portion of the exercise mass assembly that provides the selected exercise weight. A powered actuator sets up the bar for performing a weight lifting exercise by lifting the movable portion of the exercise mass assembly up above a second portion of the exercise mass assembly that remains stationary during the particular weight lifting exercise.