Imagine a snapshot of a ball sitting on an incline. If it was being held there by some imaginary force, it would stay motionless. Realistically, the ball will roll down the incline. The ball has some form of energy due to its height and unless an outside force interferes with the balls natural inclination to roll down the incline, that energy will transform form gravitational potential energy into kinetic energy.
Gravitational potential energy (GPE) is the energy an object has that depends on how far from the surface of the Earth it is. In other words, it is the energy that it has due to its vertical position. The higher the object is from the surface of the Earth, the more GPE it has. It is directly proportional to the weight (mg) of the object and its height (h).
Gravitational Potential Energy (GPE)
\(\large\mathsf{ GPE = mgh }\)
...where m is mass, g is the acceleration of gravity, and h is height. GPE is measured in Joules.
GPE is not a vector quantity, so you can use magnitudes only for these values in problem solving. Also, h can be referenced from some reference surface, so it doesn't always have to be the surface of the Earth. It could be the height of a table or top of a building. It is important to define your reference point so if you are comparing two objects, you refer to the same reference surface.
Question
Consider three different scenarios where an object changes height from 0 m to 2 m above the surface of the Earth: in one case it is lifted straight up, in another it is pushed it up an incline, and in a third case it is carried it up stairs. What can you say about that object's change in gravitational potential energy?
Remember that the gravitational potential energy depends on the weight of the object and the object's height. The amount of work done vertically to change that object's potential energy is the same, no matter the path taken to get there. Keep in mind that you cannot change an object's gravitational potential energy by strictly moving horizontally, so we only take into consideration the vertical direction when working with GPE.
Question
What is the gravitational potential energy of a 5.00 kg object that is 4.00 meters off of the ground?
Use the equation for GPE to solve:
\(\mathsf{ GPE = mgh }\)
\(\mathsf{ GPE = (5.00 \text{ kg})(9.81 \text{ m/s}^2)(4.00 \text{ m}) }\)
\(\mathsf{ GPE = 196 \text{ J} }\)