How does potential energy relate to height and mass?

Potential energy is directly proportional to both the height of an object above the ground and its mass.

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. The most common type of potential energy you'll encounter in physics is gravitational potential energy. This is the energy an object possesses due to its position in a gravitational field, typically related to its height above the ground.

The formula for gravitational potential energy is PE = mgh, where PE is the 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 of the object above the ground. This formula shows that potential energy is directly proportional to both the mass of the object and its height above the ground. This means that if you double the mass or the height of the object, you will also double its potential energy.

For example, if you lift a 1 kg object 1 metre off the ground, it will have a potential energy of 9.8 joules (since 1 kg x 9.8 m/s² x 1 m = 9.8 joules). If you lift the same object 2 metres off the ground, its potential energy will double to 19.6 joules. Similarly, if you lift a 2 kg object 1 metre off the ground, its potential energy will also be 19.6 joules.

It's important to note that potential energy is a form of stored energy. It represents the work done to lift the object to that height against the force of gravity. If the object is dropped, this stored energy will be converted into kinetic energy as the object accelerates towards the ground. This is a demonstration of the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed from one form to another.