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To calculate the potential energy gained, we can use the formula PE = mgh, where m is the mass of the object (14 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (40 cm or 0.4 m).
PE = (14 kg)(9.8 m/s^2)(0.4 m) = 54.88 J
Therefore, the potential energy gained when Nan lifts the suitcase onto the bench is 54.88 J.