Some of the most difficult (and most important) experiments in the history of physics had to do with making connections between different concepts. What about the connection between objects moving around (kinematics) and objects changing temperature (thermodynamics)? That was a tough one. It’s called the mechanical equivalent of heat and it was explored in 1868 by James Joule.
The basic idea was to have a mass that moves down due to the gravitational force. This mass is attached to a string that connects to a spinning paddle in a container of water. As the mass moves down it spins the water and adds energy to it—hopefully increasing the temperature. The change in gravitational energy of the mass should be equal to the change in thermal energy of the water.
OK, we actually already know this relationship. But it’s still fun to reproduce it. To do that, first we need to know about the different forms of energy. First there is the gravitational [...]