Short answers, pulled from the story.
William Rankine, a Scottish engineer and physicist, coined the term potential energy in 1853. This introduction marked a pivotal moment in the history of science by distinguishing energy of configuration from energy of activity.
Conservative forces ensure that the work done on an object depends only on its initial and final positions rather than the path taken. The work done by a conservative force equals the negative change in potential energy, allowing scientists to assign a single scalar value to every point in space.
Gravitational potential energy near the Earth's surface is calculated using the formula U equals mgh, where m is mass in kilograms, g is the local gravitational field, and h is the height above a reference level in metres. The acceleration due to gravity is approximately constant at 9.8 metres per second squared in this context.
The work of a horizontal spring on a body is calculated using the function U equals one-half kx squared, where k is the spring constant and x is the displacement from the equilibrium position. This energy arises from the electromagnetic force between atoms and molecules that constitute the object.
Nuclear potential energy powers the Sun through hydrogen fusion, where 600 million tonnes of hydrogen nuclei fuse into helium nuclei each second. This process releases about 4 million tonnes of mass as heat and radiation, keeping the solar core hot.