Energy
Energy and Thermal Physics

# Galileo's pendulum

Teaching Guidance for 14-16

Galileo was interested in predicting how bodies move. He allowed an object to roll down and up a curved track, and showed that it rose to roughly the height from which it was released, regardless of the shape of the track.

Galileo recognized that, unfortunately, the experiment was marred by the effects of friction.

## Experiment: Demonstrate Galileo's rolling ball

Scientists seek to demonstrate phenomena clearly. They try to eliminate any undesired external influences (in this case, friction), in order to show an underlying principle.

Galileo's rolling ball

Why is a ball a good object to use here? Why might a toy car be worse? Or a block of wood?
A ball is a good choice because it is likely to roll with very little friction, provided it does not slip on the track. Toy cars and blocks of wood suffer more from the effects of friction. In the demonstration, the observer would have to accept that they would reach their original height if there were no friction.

Galileo went on to use a pendulum to demonstrate the same phenomenon. He believed that this would be even less affected by friction.

## Experiment: Set up a simple pendulum

Demonstrate how it swings.

What effect would friction have on a pendulum like this? How can you tell that friction is having little effect?
Air resistance and friction at the point of attachment might slow down the pendulum. The amplitude of the pendulum changes only slowly
• the effect is probably not noticeable from one swing to the next.
• ## Experiment: Demonstrate Galileo's pin and pendulum

Galileo's pin and pendulum

What is the principal observation of this experiment?
The bob (mass) always returns to its original height, regardless of the original height of release or the presence of the interrupting rod.
How would scientists explain this today, using the idea of energy?
The bob has GPE at its highest point; this is transferred to KE as it moves downwards and back to GPE as it rises again. Since energy is conserved and none is lost from the system (in the absence of friction), it can return to its original height.

In fact, the idea of the conservation of energy was far in the future when Galileo described and explained his experiment. Instead, he talked in terms of momento and impeto. These terms correspond (more or less) to what is now called momentum.

Later, Newton also used the idea of momentum, which he regarded as the fundamental property of a moving object. The idea of kinetic energy was not established until the mid-19th century, 200 years after Galileo's death.

Ideas like that of energy, which scientists today take for granted, are not self-evident. Both momentum and kinetic energy were identified when people realized that they were conserved quantities in certain situations.

## Acknowledgement

We are grateful to David Sang, author of this Case Study.

###### Energy
appears in the relation ΔEΔt>ℏ/2 ΔQ=mcΔθ E=hf E ∝ A^2
has the special case Photon Energy
is used in analyses relating to Emission/Absorption Spectra Phase Change