One of the most valuable tools that physicists use to understand the universe is to analyze what is happening to the energy of an object. Let’s start by looking at an example.
If you set a coffee mug down your desk, you don’t expect it to spontaneously move. In fact, if you see it begin to move, your first assumption probably be that something is causing the desk to move: perhaps there is an earthquake (in which case you would notice other objects begin to move as well); or someone is hiding under the desk and lifting one side to tilt it. We know from experience* that an object at rest will not start moving all by itself. We also know from experience that in order to make something move, you need to directly interact with it. For small objects like a mug of coffee this is not a problem, but if you want to move a heavy object, you will become tired and your muscles will feel weak—you will have lost some energy.
We could say that a moving coffee mug has some amount of energy, but a stationary one in the same location does not. (The location is important in ways we’ll see when we discuss the different kinds of energy.) Another way of saying that an object will not start moving all by itself would be to say that an object does not spontaneously gain energy. And we can say that for one object to gain energy, another one will lose energy.
At the most fundamental level, we can define energy as follows:
Energy is a property of an object which can be transferred to other objects or converted into different forms, but cannot be created or destroyed.
The SI unit for energy is the joule (J). It is named after James Prescott Joule, a Scottish brewer and scientist who extensively studied heat and energy in the 1800s. One joule is roughly the energy required to lift a small apple up by a distance of a meter.
6.1 Conservation
In colloquial, everyday language, when we say we are “conserving” something, we mean that we are minimizing how much of it we use. This is not the same as the scientific meaning of conservation. In physics, a quantity that is conserved is one that does not change: a conserved quantity can neither be created nor destroyed.
For example, mass is a conserved quantity. You can take a block of wood, and break it up into many little pieces, and scatter them around, but the total amount of mass has not changed. Or, you could burn the block; you would end up with some ash and many gasses released as vapor (for example, any water in the cells of the wood would boil and be released into the air), but the total amount of matter would not change. There is the same amount of mass in the universe today as there was fourteen billion years ago. It may change forms, but the total amount is constant.
The same is true of energy—there is the same amount of energy in the universe now as there was at the big bang, and as there will be far into the future. Everything we do involves the energy changing forms, but the total amount is constant. The fact that energy is conserved is precisely why it is such a useful tool for doing physics.
6.1.1 Budgeting
Below is an interactive that will help you see how energy is conserved. We have bars for the kinetic energy (energy related to motion) and potential energy (energy related to position) as well as the total energy. You can imagine this like a person skiing down a mountain. At the very top, they at a high elevation but not moving very quickly (large potential energy, small kinetic energy). As they go down the mountainside, they gain speed, increasing their kinetic energy, as the potential energy decreases. However, the total energy remains constant.
6.1.2 Mass-energy equivalence
Example
This example is adapted from a problem in Conceptual Physics by Benjamin Crowell, licensed under CC-BY-SA 3.0. The book can be found at http://www. lightandmatter.com/cp; the license can be found at http://creativecommons.org/ licenses/by-sa/3.0.
*This is actually a risky train of thought. Relying on simple everyday experience can often lead us to the wrong conclusions. In this case, everyday experience is in agreement with rigorous controlled experiments.