 So far we've talked about the motion of objects by analysing the forces acting on them Now sometimes we won't be able to measure or even know about all the forces acting on an object But we'd still like to say something quantitative and predictive and this is where the much more general concept of energy can be useful No doubt you've already heard about different kinds of energy, chemical energy, electrical energy or nuclear energy for example But what is energy really? Well, it's actually just a kind of accounting system that lets us keep track of interactions between objects and physical systems A little bit like money lets us keep track of the exchange of goods and services in a social and economic system But a really big difference between energy and money is that energy is conserved The total amount of energy in the universe stays the same and it can only be transferred from one attribute of a system to another attribute or from one system to another So for example an accelerating car transfers chemical energy into heat by burning petrol And then some of this heat energy is transferred into making the car go faster or increasing its kinetic energy If the car drives up a hill Then some of the chemical energy is used to move the car and everything in it further away from the center of the earth This means the chemical energy of the petrol has been converted into what's called gravitational potential energy If the driver now stops and gets out of the car and drops a ball It will fall and change this potential energy into kinetic energy Now this idea of energy and keeping track of its different forms and how it changes from one form to another is Already a very powerful conceptual framework But as physicists we need to make it quantitative We need numbers and equations that tell us how to determine those numbers from things we can measure One thing that is fairly easy to measure is temperature an increase in the temperature of something means its thermal energy is increased So within the SI system the unit of energy is called the joule and one joule is the amount of energy required to heat 0.24 grams of water by one degree centigrade Now this definition probably seems a little bit arbitrary, but it makes the equations for other types of energy look neater For example that kinetic energy of an object is one half MV squared When mass is measured in kilograms and velocity is measured in meters per second with energy in joules If the joule was defined differently then the factor of one half would be different But with this definition we see that the joule is a derived quantity that in terms of basic units is kilograms times meters squared divided by second squared Now when we talk about energy and use it to analyze a physical system We are almost always studying a change in state So when we say the kinetic energy is one half MV squared We really mean that it took that much energy to change the object from being still to moving with velocity V This reference to a change in state is particularly important when talking about potential energy It is meaningless to say that an object has x joules of potential energy Potential energy must always be given relative to some reference state For objects near the surface of the earth changing the height of an object corresponds to a change in gravitational potential energy proportional to the object's weight as follows Remember little g here is acceleration due to gravity at the earth's surface Another common type of potential energy related to motion is the elastic energy in a spring The reference state here is the spring in its relaxed state with no forces being exerted on it Then if delta x is the change in length from this rest length The corresponding increase in potential energy is delta ES equals one half K delta x squared K is called the spring constant and it quantifies how stiff the spring is So now you've heard about a variety of different types of energy and how these are quantified