Conservation of Energy
What is the principle of conservation of energy?
In physics, the term conservation refers to something which doesn’t change. This means that the variable in an equation which represents a conserved quantity is constant over time. It has the same value both before and after an event.
There are many conserved quantities in physics. They are often remarkably useful for making predictions in what would otherwise be very complicated situations. In mechanics, there are three fundamental quantities which are conserved. These are energy, momentum and angular momentum.
If you have looked at examples in other articles—for example, the kinetic energy of charging elephants—then it may surprise you that energy is a conserved quantity. After all, energy often changes in collisions. It turns out that there are a couple of key qualifying statements we need to add:
-
Energy, as we’ll be discussing it in this article, refers to the total energy of a system. As objects move around over time, the energy associated with them—e.g., kinetic, gravitational potential, heat—might change forms, but if energy is conserved, then the total will remain the same.
-
Conservation of energy applies only to isolated systems. A ball rolling across a rough floor will not obey the law of conservation of energy because it is not isolated from the floor. The floor is, in fact, doing work on the ball through friction. However, if we consider the ball and floor together, then conservation of energy will apply. We would normally call this combination the ball-floor system.
What do we mean by system here?
In physics, system is the suffix we give to a collection of objects that we choose to model with our equations. If we are to describe the motion of an object using conservation of energy, then the system should include the object of interest and all other objects that it interacts with.
In practice, we always have to choose to ignore some interactions. When defining a system, we are drawing a line around things we care about and things we don’t. The things we don’t include are usually collectively termed the environment. Ignoring some of the environment will inevitably make our calculations less accurate. There is no indignity in doing this however. In fact, being a good physicist is often as much about understanding the effects you need to describe as it is about knowing which effects can be safely ignored.
Consider the problem of a person making a bungee jump from a bridge. At a minimum, the system should include the jumper, bungee, and the Earth. A more accurate calculation might include the air, which does work on the jumper via drag, or air resistance. We could go further and include the bridge and its foundation, but since we know that the bridge is much heavier than the jumper, we can safely ignore this. We wouldn’t expect the force of a decelerating bungee jumper to have any significant effect on the bridge, especially if the bridge is designed to bear the load of heavy vehicles.
Responses