In this paper the energy dissipated through friction is analysed for a type of friction dampers used to reduce squeal noise from railway wheels. A one degree-of-freedom system is analytically studied. First the existence and stability of a periodic solution are demonstrated and then the energy dissipated per cycle is determined as a function of the system parameters. In this way the influence of the mass, natural frequency and internal damping of the friction damper on the energy dissipation is established. It is shown that increasing the mass and reducing the natural frequency and internal damping of the friction damper maximizes the dissipated energy.