Gravitational Potential Energy

Gravitational Potential Energy (GPE)

The following diagram gives the formula for gravitational potential energy. Scroll down the page for more examples and solutions on how to use the formula.

Gravitational potential energy is the energy stored in an object due to its position above the Earth’s surface.

This is due to the force of gravity acting on an object. Gravitational potential energy is calculated as follows:
E_p = m × g × h

Where:
E_p is the Gravitational Potential Energy, measured in Joules (J).
m is the mass of the object, measured in kilograms (kg).
g is the acceleration due to gravity. On earth, g ≈ 9.8 m/s²
h is the height of the object above a chosen reference point, measured in meters (m).

Key Concepts about Gravitational Potential Energy (GPE)

• GPE increases as height increases.
  
• At ground level, (h = 0), GPE is typically defined as zero.
  
• Lifting an object converts work into GPE.
  
• When the object falls, GPE converts to kinetic energy (ignoring air resistance):
  

\(GPE_{top} = KE_{bottom} \Rightarrow mgh = \frac{1}{2}mv^2\)

Videos

Examples:

1. A crane lifts a 75kg mass a height of 8 m. Calculate the gravitational potential energy gained by the mass (g = 9.8 N/kg).
   
2. A ball with a mass of 500g is lifted onto a shelf which is 1.5m above the ground. Calculate the gravitational potential energy gained by the ball (g = 9.8 N/kg).

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Gravitational Potential Energy - IGCSE Physics

Examples:

1. How much G.P.E. does a 5kg rock that is 10m above the ground has?.
   
2. A helicopter is flying at a height of 1.5km. If it has 50MJ of G.P.E., what is the mass of the helicopter?
   
3. A boy throws a 0.2kg rock up with a speed of 5m/s. If all the kinetic energy becomes gravitational potential energy, how high will the stone go?

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