When Lucy lifts an object from the floor to above her head, the potential energy of the object increases. This is because gravitational potential energy is dependent on the height of the object above a reference point (in this case, the floor). The formula for gravitational potential energy (PE) is:
\[ PE = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity, and
- \( h \) is the height above the reference point.
As Lucy lifts the object, the height \( h \) increases, leading to an increase in potential energy.
Thus, the correct answer is D: the object's potential energy will increase.