How do engineering mechanics relates to electrical engineering?

It really depends on what sub-discipline you choose to go into. For certain topics in EE, like microelectronics, or communications, there won't be a whole lot of correlation. For something like Power Systems, or Controls, you might see a little more.

For example, in controls, you may need to make an electronic control system for a mechanical device. In power systems, a good working background in mechanics may help if you get into the generation side.