# Does Every Stationary Body Possess Potential Energy?

#### 26 SEP 2017

#### CLASS

Conservation of energy is one of the defining fundamental principles of physics, yet the early scientists were faced with a dilemma. A brick dropped from the second story of a building had energy, and if you were standing under it, you'd have a very concrete demonstration of that fact. But when it's just sitting on a window ledge it doesn't look as if it has energy. So scientists came up with the concept of potential energy -- the idea that a stationary object can "store" energy. The only thing that matters is the difference in potential energy between a starting location and an ending location, and that's the same if the object is moving from 500 to 400 feet, or from 100 to 0 feet. So you can pick whatever value you want to define potential energy, as long as the difference is right.

## 1 Energy and Work

You can imagine that the brick on the ground has no energy -- it's just sitting there. Then you carry it upstairs. When you carry it upstairs you are doing work on the brick. You can think of your carrying it as you transferring energy from yourself into the work it takes to get the brick upstairs. Well, if you take energy from yourself and put it into the brick, then it must still be there -- that's what the conservation of energy means. When you put the brick on the windowsill, it is not moving, so it has no kinetic energy -- which is the energy of motion. But you have stored energy in the brick. That stored energy is what's called potential energy.

## 2 Conservation of Energy

By calculating the work it takes to move the brick up the stairs and the energy of the brick when it falls, physicists have come up with a definition of potential energy. It gets a little complicated under different conditions, but for the potential energy of the brick it's pretty easy: the potential energy is equal to its acceleration due to gravity, multiplied by the height from its expected landing point. When the brick is on the windowsill it has no kinetic energy, but it's full of potential energy. In the instant before the brick hits the ground it has lots of kinetic energy, but it has used up all its potential energy.

## 3 Changing Potential Energy

Now imagine you dig a hole in the ground right beneath where the brick will fall. When you drop the brick, and in the instant before it reaches ground level, it will have exactly the same kinetic energy as it had before there was a hole. But this time, the brick doesn't stop there, it keeps speeding up until it reaches the bottom of the hole. That is, in the moment before it hits the bottom of the hole it will have more kinetic energy than it did before. But it can't end up with more kinetic energy than the potential energy it started with. So somehow, by digging a hole underneath the brick on the windowsill, you added more potential energy to the brick -- without ever touching the brick itself. This could be a problem for the whole idea of potential energy -- and the whole principle of the conservation of energy.

## 4 Zero Potential Energy

The situation is rescued, however, because the only thing you can measure is the difference in potential energy between one spot and another. For example, you could say a brick has 20 joules of potential energy on the second-story windowsill and 0 joules on the ground. But you could also say the brick on the second story had 100 joules of potential energy and 80 joules on the ground. The difference between the starting and ending position is 20 joules in each case. It's only the difference in potential energy that counts, so it doesn't matter where you decide the brick has a potential energy equal to zero -- you can decide the potential energy is equal to zero at the ground, at the second story, at the roof, or anywhere else, so long as the difference between the starting and ending points is the same.

## 5 Potential Energy Everywhere

The universe is full of forces, not only gravity, but electromagnetic force, and other forces called "weak" and "strong" forces. Although all of those forces get weaker the further away two objects are from each other, they are always present, all throughout the universe. Any object within any of these fields of force has potential energy, so it's reasonable to say that every stationary body in the universe has potential energy.