The potential energy of an object is defined by the formula:
\[ PE = mgh \]
where:
- \( PE \) is the potential energy,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) near the Earth's surface),
- \( h \) is the height of the object above a reference point (in this case, the floor).
When an object is lifted from the floor to a position above someone's head, its height \( h \) increases. As a result, the potential energy of the object also increases. Specifically, the change in potential energy can be calculated by finding the difference in height between the starting position (the floor) and the final position (above the head).
If we denote the height of the person's head as \( h_1 \), and the height of the floor as \( h_0 = 0 \), then the height relative to the ground increases from \( h_0 \) to \( h_1 \). Thus, the increase in potential energy, \( \Delta PE \), as the object is lifted is given by:
\[ \Delta PE = PE_{final} - PE_{initial} = mg(h_1 - h_0) = mgh_1 \]
Therefore, as the object is lifted to a height above a person's head, its potential energy increases in proportion to its mass, the acceleration due to gravity, and the height to which it is raised.