Pendulum Investigation

Energy transfers

It is easy enough to write down the energy equations.

At the top of the swing the potential energy is a maximum and the kinetic energy is zero. At the bottom of the swing the potential energy is zero and the kinetic energy is a maximum. So, all the potential energy is transferred to kinetic energy by the time the bob has reached the bottom of the swing. This follows from the Law of Conservation of Energy which states that energy can not be created or destroyed, only transferred from one type to another.

h₀ = maximum height
v₀ = maximum speed

KE at bottom = GPE at top:
½mv₀² = mgh₀

The maximum speed v₀ is the only unknown quantity and can be calculated from this equation. Note that the mass m can be cancelled from both sides of the equation before it is rearranged.

½v₀² = gh₀
v₀² = 2gh₀
v₀ = √(2gh₀)

We can calculate the maximum speed for any pendulum bob given its initial starting height, but is this any use to us? Is it possible to calculate the time of swing from this data and relate it to the length of the pendulum? It is not obvious how this could be done.

For these reasons the calculations have not been included in the theory of the write up, although these are the sorts of thing you might think about when trying to work out a prediction. You could, perhaps, just briefly mention the equations to show that you know them. They would not need to be explained in detail because they are 'standard' equations.