Conservation of Energy

Conserved quantities are useful in mechanics: they allow us to make short-cuts in calculations. For example we have already encountered conservation of momentum. The principle of conservation of momentum states that the momentum of a collection of particles is a conserved quantity, provided the particles do not interact with any force fields. In collisions the momentum of particles before and after the collisions are the . This allows us calculate the velocities of the particles after the collision without knowing any of the details of the forces acting between them (which are unbelievably complicated and still the subject of research). Consevation of energy is similarly useful. Here we will look at conservation of energy in a uniform gravitational field. We will see that, if we are interested only in positions and velocities, conservation of energy offers a simpler way to solve problems.