Gravitational Potential Energy:
Gravitational potential energy is the energy stored in an object due to its position in a gravitational field.The higher an object is positioned relative to a reference point, the more gravitational potential energy it has.
Explanation:
Potential energy at some height depends on the object’s mass (m), the strength of the gravitational field g (typically near the Earth’s surface), and its height h above a reference point.
Formula: U=mgh
where U is the gravitational potential energy,
m is the mass of the object,
g is the acceleration due to gravity (approximately 9.8 m/s2 on Earth),
and h is the height above the reference point.
Influence of Mass (m) on GPE
Directly Proportional: The gravitational potential energy is directly proportional to the mass of the object. This means that if the mass doubles, the gravitational potential energy also doubles, assuming the height remains constant.
Example
This example demonstrates that doubling the mass from 2 kg to 4 kg doubles the gravitational potential energy from 196 joules to 392 joules.
Influence of Height (h) on GPE
Directly Proportional: The gravitational potential energy is directly proportional to the height of the object. This means that if the height doubles, the gravitational potential energy also doubles, assuming the mass remains constant.
Example
This example demonstrates that doubling the height from 5 meters to 10 meters doubles the gravitational potential energy from 98 joules to 196 joules.
Summary
When the mass of the object doubles, the gravitational potential energy doubles.
When the height of the object doubles, the gravitational potential energy doubles.
