yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Calculating gravitational potential energy | Modeling energy | High school physics | Khan Academy


3m read
·Nov 10, 2024

In previous videos, we have introduced the idea of energy as the capacity to do work, and we have talked about multiple types of energies. We've talked about kinetic energy, energy due to motion. We've talked about potential energy, which is energy by virtue of position.

When we're talking about potential energy, we're talking about it relative to some other position. In particular, in this video, we're going to talk about gravitational potential energy, which is potential energy due to position in a gravitational field.

So let's say that this is the surface of the Earth. Let's say that I have a 5-kilogram mass right over here, and let's say that it is 10 meters above the surface of the Earth. My question to you is: how much more potential energy does it have in this position than when it is in this position, when it is sitting on the surface of the Earth, 10 meters lower? Pause the video and try to think about that.

All right, now let's work on this together. So our gravitational potential energy is going to be equal to our mass times lowercase g, which you can view as the constant for Earth's gravitational field near the surface of Earth. The reason why I say near the surface of Earth is, as you get further and further from Earth, this thing could actually change. But near the surface of the Earth, we assume that it is roughly constant.

Then you multiply that times your height. So calculating this is pretty straightforward as long as you know what g is. We can approximate g as 9.8 meters per second squared. So when you multiply all of this out, this is going to be equal to your mass, which is 5 kilograms, times the gravitational field constant, so times 9.8 meters per second squared, times your height, which in this situation is 10 meters.

So times 10 meters, and so this is going to be equal to 5 times 9.8, which is 49, times 10, which is 490. We have kilograms, and then we have meters times meters, so times meter squared per second squared. These might seem like strange units, but you might recognize this as also the units of force times distance, which we could also express in terms of joules.

So this is 490 joules, which is our unit for both energy and our unit for work. Now let's make sure that this makes intuitive sense. Well, one way to think about it is: how much work would it take to go from here to here? Well, you're going to be lifting it a distance of 10 meters.

As you're lifting it a distance of 10 meters, what is the force you're going to have to apply? Well, the force you're going to have to apply is going to be the weight of the object. The weight is its mass times the gravitational field. So in order to put it in that position from the ground, you're going to have to do its weight times the height, or 490 joules of work.

You can do 490 joules of work to get it there, and then you can think about it as that energy being stored this way, and now it can then do that work. How could it do that work? Well, there's a bunch of ways you could do it. You could have this attached to maybe a pulley of some kind, and if then if it had another weight right over here, and let's just for simplicity assume it has the same mass.

Well, if you let this first purple mass go, it's going to go down, and if you assume that this pulley is completely frictionless, this mass is going to be lifted by 10 meters. So if you have a 5-kilogram mass that is lifted by 10 meters in Earth's gravitational field, near the surface of the Earth, you would have just done 490 joules of work.

So hopefully this makes sense why you're just really taking the weight of the object times its height, and hopefully it also makes sense that it then has the capacity to do that amount of work. In this case, we said relative to sitting on the ground.

More Articles

View All
15 Expensive Things That Are NOT Worth the Money
You dream about becoming rich so you can afford everything you ever wanted, only to find out that you hate having to take care of so many things. Most expensive things are just a clever way to separate rich people from their money. If last Sunday, we look…
The Strangest Secret By Earl Nightingale
I’d like to tell you about The Strangest Secret in the world. Not long ago, Albert Schweitzer, the great doctor and Nobel Prize winner, was being interviewed in London. A reporter asked him, “Doctor, what’s wrong with men today?” The great doctor was sile…
Principles for Success: "Everything is a Machine" | Episode 5
Principles for success: an ultra mini-series adventure in 30 minutes and in eight episodes. Episode five: everything is a machine. Sometimes things happen that are hard to understand. Life often feels so difficult and complicated. It’s too much to take …
Electron configurations with the periodic table | Chemistry | Khan Academy
Let’s explore electronic configurations. It’s basically arranging electrons of different elements in various shells and subshells. Let me quickly show you some examples. Yes, this will look overwhelming, but for now, focus on these numbers: 1, 2, 3, 4, 5,…
Beginning of the Greco Persian Wars | World History | Khan Academy
This right here is a map of the Persian Empire in 490 BCE before the Common Era, and you see that it is an extensive empire. It was established by Cyrus the Great and then his successors. We talked about it in previous videos, how they were able to conque…
Buddhism: Life is Suffering
Birth is suffering; aging is suffering; sickness is suffering; death is suffering; sorrow and lament, pain, grief, and despair are suffering. Association with the unpleasant is suffering; dissociation from the pleasant is suffering; not to get what one wa…