If the potential energy (PE) of an object is lowered to half its original height while it remains in a uniform gravitational field (near the surface of the Earth), the new potential energy will also be halved compared to its original potential energy. This relationship is described by the formula for gravitational potential energy:
PE=m∗g∗h
Where:
PE is the potential energy.
m is the mass of the object.
g is the acceleration due to gravity.
h is the height above a reference point (e.g., the ground).
If the height (h) is halved, the potential energy (PE) will also be halved, assuming the mass (m) and the acceleration due to gravity (g) remain constant. This demonstrates the direct proportionality between potential energy and height in a gravitational field.