If the potential energy of a block at the table is mgh/3, what does this indicate about its height?

When considering the potential energy (PE) of an object in a gravitational field, the formula for gravitational potential energy 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 of the object above a reference level (usually the ground or floor).

In this scenario, the potential energy of the block is expressed as mgh/3. This indicates that the potential energy is one-third of what it would be if the block were at a height of h.

To find the height corresponding to this potential energy, we can set up the equation:

mgh/3 = mgh’.

Here, h' represents the height we want to find. By rearranging this equation, we can isolate h':

h’ = h/3.

This means that the height of the block is one-third of the maximum height (h) indicated in the problem. Thus, if we consider the whole height being h, then at h', which corresponds to the potential energy being mgh/3, the block would be at the height of 2h/3 above the floor.

This conclusion aligns with the understanding of potential energy in relation to height, demonstrating that the block