How is potential energy related to mass and height?

Potential energy is directly proportional to both the mass of an object and the height it is raised to.

Potential energy is a form of energy that an object possesses due to its position relative to other objects. It is stored energy that has the potential to do work. In the context of mass and height, we are specifically talking about gravitational potential energy. This is the energy an object has due to its position above the Earth's surface.

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 above the ground. This formula shows that the potential energy is directly proportional to both the mass and the height. This means that if you double the mass or the height, you will also double the potential energy.

For example, if you lift a 1 kg object 1 metre off the ground, it will have a potential energy of about 9.8 joules. If you lift a 2 kg object to the same height, it will have a potential energy of about 19.6 joules. Similarly, if you lift the 1 kg object to a height of 2 metres, it will also have a potential energy of about 19.6 joules.

So, the more mass an object has, and the higher it is lifted, the more potential energy it will have. This is why heavy objects and high places can be dangerous - they have a lot of potential energy that can be converted into kinetic energy (the energy of motion), causing damage or injury.