A 40 kg gymnast dismounts from the uneven bars, flips into the air, and lands on her feet. Just before hitting the mat, her body was moving downward at 8.2 m/s, and between the give of the mat and her bending her knees, her body's center of mass travels downward 40 cm (before she quickly straightens up and poses for the judges). What was the average force of the floor on her legs as she came to a stop?