Everyone stand up. In your group, one person controls the left side, a different person controls the right side, and someone is the observer/director.

Starting from about 100 g on each side, and without using the weights, change the state of the system from its initial state so that $x_L$ is increased by 4 cm and $x_R$ is increased by 3 cm. (Note that students might try to change both things at the same time. You can ask them to be more systematic and to describe precisely how they are changing from the initial to the final state.)

• Make a sketch of the processes you used to go from the initial to the final state. What axes make sense for your sketch?

• What language would you use to communicate how you changed the state of the system?

• Is it possible to find a different “path” from the initial to the final state?

• Is $W_L$ the same along the different paths?

• Is $W_R$ the same?

• Is $\Delta U$ the same?

Wrap-up note: the graph you make here is filled up with states. The paths represent things you do to the system that change the state of the system, from an initial state, through a bunch of intermediate states, and eventually to a final state.