A body of mass four kilograms had a gravitational potential energy of 2136.4 joules relative to the ground. Determine its height. Consider the acceleration due to gravity to be 9.8 metres per second squared.
We’re told in this statement that the body we’re considering has a mass of four kilograms. We’ll call that value 𝑚. We’re also told it has a gravitational potential energy of 2136.4 joules. We’ll call that value PE. We want to figure out the height of the body above ground. We’ll call that value capital 𝐻. And we’re told to treat the acceleration due to gravity to be 9.8 metres per second squared.
To start on our solution, let’s recall that the gravitational potential energy of an object is equal to that object’s mass times the acceleration due to gravity multiplied by its height above some baseline, usually ground level. In our case, we’re told the potential energy due to gravity, the mass, the acceleration 𝑔 and want to solve for capital 𝐻, the height.
Rearranging our expression, we find that 𝐻 is equal to PE over 𝑚𝑔. Plugging in for these values, when we calculate 𝐻, we find it’s 54.5 metres. That’s the height above ground of this object.