Fill in the blank: The potential energy of a particle of mass 𝑚 moving on the greatest slope line of a smooth inclined plane when it is at height ℎ above the ground surface equals blank.
Here is our particle moving on the greatest slope line of the inclined plane. It is at height ℎ length units above the ground at this point. Now, the potential energy represents the potential that the object has to do work as a result of being in this location. Then, the downward force of this particle due to gravity is given by 𝑚𝑔, where 𝑔 is the acceleration due to gravity, usually 9.8 meters per square second.
We know that the work done is the force multiplied by the distance traveled. The force required to move the particle up the plane is parallel to the force acting downwards, so it’s equal to 𝑚𝑔. This means the work done and, hence, the gravitational potential energy is equal to the product of 𝐹 sub 𝑔 and its height.
We can therefore say that the gravitational potential energy is given by 𝑚𝑔ℎ, assuming that gravitation acceleration is constant over this height. So the potential energy of this particle then is 𝑚𝑔ℎ.