Potential energy is a property of position. If a body is in such a position that, if released, it would begin to move, it possesses PE.
Consider, as an example, a body that is held at a height h above a fixed level. If that body is released it will begin to fall, i.e. it will begin to possess KE. So before it is released it has the potential to move, hence the name for energy due to position.
The value of the PE is equal to the work needed to raise the body through a vertical distance h.
The work done in raising a body of mass m is the work done against gravity, i.e. mgh.
PE = mgh
If the body falls from rest and reaches a speed v at the bottom then, using gives , i.e.
Therefore confirming that potential energy is converted into kinetic energy.
There is no absolute value for the PE of an object, as the height h is measured from some particular fixed level. If a different level is chosen the PE is changed without the body itself moving. It follows therefore that in every problem the level from which height is measured must be clearly specified. As the PE of an object that is on the chosen level is zero, in this book we identify this datum by m
arking it 'PE = 0'.
Negative Potential Energy
If an object is below the datum, the value of h is negative (h is the height above the datum), so the object has negative potential energy.
Note that there is another type of potential energy. It is called elastic potential energy (EPE ) and it is a property of an object attached to a stretched elastic string.
Question
A window cleaner of mass 72kg climbs up a ladder to a second-floor window, 5m above ground level Assuming that the window cleaner can be treated as a particle find his potential energy relative to the ground. He then descends 3m to clean a first-floor window. Find how much potential energy he has lost. Use g. = 9.8. ) Is the assumption reasonable?
