An object held at a point above the ground has 2352 joules of gravitational potential energy. The object’s mass is 20 kilograms. How far above the ground is the object?
Okay, let’s make a quick sketch of this scenario. Let’s say this is our object. And here’s the ground. We’re told that our object has a mass of 20 kilograms and also that it has a particular given amount of gravitational potential energy. Based on this information, we want to solve for how far above the ground, we can call this distance ℎ, the object is.
To start figuring this out, let’s recall a mathematical relationship for gravitational potential energy. We can abbreviate this as capital GPE. And it’s equal to the mass of an object multiplied by the acceleration due to gravity on the gravitational field that’s in multiplied by its height ℎ above some reference level. In this equation, the values of 𝑚 and ℎ are situation dependent. 𝑔, on the other hand, so long as we’re at or near the surface for the Earth, is a constant value. We’ll treat it as exactly 9.8 metres per second squared.
Now, if we write out this equation for our scenario, we can say that we know GPE that’s given to us in the problem statement. We know 𝑚 that’s also given. And it’s ℎ, the height above ground, that we want to solve for. We can algebraically rearrange this equation so that it reads ℎ is equal to the gravitational potential energy of our object divided by its mass times gravity. And it’s at this point that we can start substituting in for these terms.
For GPE, we’ll substitute in 2352 joules. And then, for 𝑚, the object’s mass, we’ll substitute 20 kilograms and for 𝑔, the acceleration due to gravity, 9.8 metres per second squared.
When we enter this expression on our calculator, to two significant figures, we find a result of 12 metres. This then is the height of the object above ground.