Video: Gravitational Potential Energy

An object with a mass of 10 kg is positioned 15 m above the surface of an unknown planet. The object has 1800 J of gravitational potential energy. What is the acceleration due to gravity at the surface of the planet?

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Video Transcript

An object with a mass of 10 kilograms is positioned 15 metres above the surface of an unknown planet. The object has 1800 joules of gravitational potential energy. What is the acceleration due to gravity at the surface of the planet?

Okay, so we have an object with a mass of 10 kilograms at certain distance above the surface of an unknown planet. Let’s draw that surface this way. And as the problem statement explained, this is indeed an unknown planet.

Let’s say further that this is our mass. And we’re told that that mass exist at height of 15 metres above the surface of this planet. And in addition to all that, the mass of this object, we’ll call it 𝑚, is 10 kilograms. We want to solve for the acceleration due to gravity at the surface of our unknown planet.

To start working in this direction, let’s write up a mathematical equation for the gravitational potential energy of a mass of object. We typically write that as capital GPE. And this is equal to the object’s mass multiplied by its height above some reference point multiplied by the acceleration due to gravity of the gravitational field that’s in. Now often, we shorthand this as lowercase 𝑔, indicating that we’re on the surface of the Earth. That’s often a safe assumption to make. But in this case of course, it’s not a good one. After all, we’re not on Earth. We’re on some other planet.

So let’s write our expression for the gravitational potential energy of this mass, this way. We’ll write it as 𝑚, the mass of our object, multiplied by its height above some reference point multiplied by 𝑔 sub p, where we understand that 𝑔 sub p is the acceleration due to gravity of this particular planet.

Okay, knowing that, let’s refer to another bit of information revealed to us. We’re told that this object has 1800 joules of gravitational potential energy. Remember that that’s what 𝑚 times ℎ times 𝑔 is equal to, gravitational potential energy, which means that we can take our expression, 𝑚 times ℎ times 𝑔 sub p, and set it equal to 1800 joules.

And then, since we’re interested in solving for 𝑔 sub p, the acceleration due to gravity on the surface of this planet, let’s divide both sides of this equation by 𝑚 times ℎ. When we do that, these factors cancel out on the left-hand side of our equation. And now, it’s a matter of substituting in the values for 𝑚 and ℎ. Recall that 𝑚 is 10 kilograms. And ℎ is 15 metres.

So the acceleration due to gravity on planet unknown is equal to 1800 joules divided by 10 kilograms multiplied by 15 metres. This comes out to 12 metres per second squared. So the acceleration due to gravity on this planet is about 20 percent greater than that on planet Earth.

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