Gravitational Potential Energy (GPE)

Gravitational potential energy is the stored energy an object possesses due to its position in a gravitational field. It depends on the object’s mass, the gravitational field strength, and its height above a chosen reference point.

 The work done to move an object of mass \( m \) from a reference level to a height \( h \) against the gravitational field.

Formula:

\( E_p = m g h \)

where:

• • \( E_p \) = gravitational potential energy (J)
  • \( m \) = mass of the object (kg)
  • \( g \) = gravitational field strength (\( 9.8 \, \text{m/s}^2 \) on Earth)
  • \( h \) = vertical height above the reference point (m)

Key points:

• • The reference level can be any convenient position, often the ground.
  • GPE increases as height increases and decreases as the object moves down.
  • It is a form of mechanical energy that can convert to kinetic energy during motion.

Relation to Work Done:

Work done in lifting an object = increase in its gravitational potential energy.

Energy Conservation Connection:

When an object falls freely (neglecting air resistance):

Loss of GPE = Gain in kinetic energy

\( m g h = \dfrac{1}{2} m v^2 \)