My text book (Fundamentals of Physics by Halliday, Resnick, and Walker) mentions the following about the work done in internal energy transfers:
An initially stationary ice-skater pushes away from a railing and then slides over the ice. Her kinetic energy increases because of an external force F on her from the rail. However, that force does not transfer energy from the rail to her. Thus, the force does no work on her. Rather, her kinetic energy increases as a result of internal transfers from the biochemical energy in her muscles.
This is confusing me a lot. The energy transfer is clearly internal but work must be done by the force as work done is defined as the (dot) product of force and displacement and the definition makes no reference to any transfer of energy.
I thought work done by a force just means that the force is causing a transfer of energy to (or from) an object, and gives no information about whether the energy is coming from the object exerting the force.
My confusion is not over whether work is being done or not but which force is doing the work which ends up causing the change in kinetic energy.