What is the potential energy of a block on the floor if the zero level is at 2h/3 above the floor?

To understand the potential energy of the block on the floor, we first need to consider the reference point for potential energy, which is defined at the zero level specified at a height of ( \frac{2h}{3} ) above the floor.

The formula for gravitational potential energy (PE) is given by:

[ 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.

Since the zero level is at ( \frac{2h}{3} ), when the block is on the floor, it is at a height of ( 0 ) relative to the floor but at ( -\frac{2h}{3} ) relative to the zero level. To find the potential energy of the block when it is at this height, we can substitute ( h ) in our potential energy formula:

[ PE = mg \left(-\frac{2h}{3}\right) ]

This simplifies to:

[ PE = -\frac{2mgh}{3} ]

Thus, the potential energy of the block on the floor is